The last advanced financial derivative we're going to talk about are options. And again, I've given you pretty extensive notes and some good examples of what options are and how they're utilized and how they're valued. So these slides just represent pretty much an overview of the notes from the lesson content. We'll actually, we'll talk about the definition, the types of options, some of the terminology, the benefits and risks of using options, what happens when options expire, how options are valued, and then we'll just have a summary of the key learning points. Options are another type of financial instrument used to manage risk and or to speculate. An option contract gives the holder the right but not the obligation to buy or sell futures contracts at a specified price at any time in the future prior to the expiration of the option contract. Now, keep this in mind, this is an important point. If you're buying an option, in other words, you're the holder of the option, you have the right but not the obligation to either buy underlying contracts or sell them. You do not have to. Types of options contracts, there's two types, the call and the put. A call is an option to buy. In other words, within the option, you have a designated commodity and the number of contracts and a specified price. Your option position is long. Once you buy a call option, since you have the right to buy the contracts, your option position is considered long. Many times, the holder is short the underlying commodity. In other words, let's say a crude oil refiner would want to buy a call option for crude oil contracts, thus having the right to buy the crude oil contracts at a certain price. Again, not the obligation. So while their physical position is short, their options position is long. On the flip side, we have the put option. This is an option to sell the underlying contracts. Again, the option position here is short. Why? Because they have the right to sell. Many times, the holder is long the underlying commodity. For example, a crude oil producer may want the right to sell their crude or to sell contracts in the financial marketplace at a predetermined price, which is stated in their option. Again, to the extent that they exercise, they have the right to sell. We consider their option position to be short because their physical commodity position is in fact long. The most popular type of option is the futures option or the commodity option. It is exchange traded option calling for the delivery of a futures contracts. However, options can be traded in the over-the-counter market and at times can call for physical delivery. And then note, my footnote, having the options contract means you have the right. You have contracts or can sell contracts. The premium, this is the price of the option. The premium value reflects the risk of the underlying commodity and its value is made up of two components. In other words, this is the price you'll have to pay. Just as in the lesson notes, I talked about car insurance and you have a premium. The premium is what will cost you to have this type of risk insurance. There are two pieces, the intrinsic and the extrinsic. When you think of the intrinsic, think of the embedded value. As soon as you execute the option, you're going to have a strike price and there's going to be a market price or what we call the asset price. So it's the positive difference between the strike price and the price of the underlying commodity. So for example, if in your contract you set a strike price of $52 and the current market is $50, the intrinsic value of that is $2. So we know that the premium would be at least $2. The writer or seller of the option you're dealing with isn't going to make any money. Part two of the premium then is what we call extrinsic, which is the time value of money. So think about it this way, you enter into an options contract on a particular day but that particular underlying contract won't expire until some point in time in the future. Well, every single day with market changes in price, volatility and those types of things as well as the time that gets closer and closer to expiration, the value of that option changes. So in other words, the premium that the writer of that option would then charge you is going to change every day and this is reflected in what we know as the Greeks, the theoretical models that calculate the various differences in the extrinsic value. So when you have the premium and you know what the intrinsic is, all remaining value other than the intrinsic is the extrinsic and it consists of the components that we talk about as the Greek values. So for the example above, if the premium for this particular option of $52 was $2.50, we know based on the fact that the intrinsic is $2 that the extrinsic part of the premium or the time value of that premium is $0.50. Okay, the strike price, that's the buyer-sell price as detailed in the options contract also known as the exercise price. Expiration, which again, it's the date by which the outcome of the options contract, whether it's sold, exercised or just abandoned, has to be determined. Now the options expire typically one to three days prior to the expiration of the underlying futures contract. So for natural gas options as an example, it's one day prior to the expiration of the underlying contract and we know that the underlying contract for natural gas on NIMEX expires three working days prior to the first of the month. Therefore, natural gas options expire for working days prior. So they have to be executed or they just go ahead and settle. And the Greeks, these are the theoretic values projected from mathematical models that are used to measure the sensitivity of an option's price to quantifiable factors. When we refer to the Greeks, we're talking about delta, gamma, theta, vega and rho. And again, I'm not going to hold you responsible for these, but these are the definitions of the Greeks themselves. Benefits of an option, the option premium is a fraction of the cost of the underlying commodity.  You could buy the contracts outright or you could buy a call option where you have the right to purchase those at a certain price level if in fact you need to exercise it. But it's only costing you the premium upfront. You're not buying the contracts unless the price exceeds your option price and then you want to enter into those contracts. And because of that, you can potentially control a large number of futures contracts for relatively small cost. So you could hold several contracts of crude oil and rather buy them outright, you're paying the premium on a call option. This gives you considerable amount of leverage in the marketplace. Now, the option buyer's risk is known and limited to the amount paid for the option premium. So again, your exposure as someone who buys the option is strictly what you paid. You can't lose any more than the premium. Now, the risk is that these are time-sensitive investments. They basically, the value of the options can tend to deteriorate from the time in which they're exercised until the actual expiration date. Now, the option seller is the writer of the option. That's the other term we use for them. And they are at risk to unlimited potential losses. If you're buying a call option, you're buying a ceiling price. You will never pay more than the price, the strike price in your agreement. Well, the seller of that option or the writer of that option has that exposure if the price runs right through that. When options expire, they can expire worthless. In other words, you've never executed the option. They can be sold for the intrinsic value if one is in an option buyer position, or the option is purchased for its intrinsic value if one is an option seller position. So in other words, as we talked about the intrinsic value, as the options come up anytime between the time they're executed and the time that expires, if there's value in that, someone trading options could in fact cash that in or settle it and make some money on it. Or the option gets exercised sometime before expiration or it automatically is exercised on expiration.


Today's episode is sponsored by Squarespace. Well, the prophecy foretold that this might happen. What prophecy, when? Don't ask questions. 2023 was a year that brought quite a bit of change to my photography and it wasn't all bad. I had some incredible opportunities to shoot some semi-wonderful if you squint work, but it was never really the kind of work that was slower, more intentional, and thought out. After some introspection, I realized I hadn't shot any 8x10 last year. It's been over a year actually, since I've hurt myself in that way. Let me explain. Two years ago, my buddy Cale and I packed a ball of our large format gear, which for me was only 8x10 at the time. When we hit the road up into the mountains, limited only by the format. Though some okay work was produced, it was certainly backbreaking. It was tiring and ultimately, yeah, it was really expensive. I only just last week financially recovered from it. But just like having a baby, the humans really only remember the good parts, I guess. So now I'm starting to think, I was just a wiener back then. I was like Steve before he was Captain America. And now, well, I guess I'm still like Captain America, just, you know, current day. 8x10 is a beautiful format. If you can get it right, the resolution is just absolutely insane. And the depth of field you can achieve with it is something else entirely. Though this all comes at quite a cost, you know, literally and figuratively. For starters, the film is pretty expensive because it's basically the size of a printer paper. The gear is expensive because it has to be precisely made and you have to be on sticks at all times. You even have to slowly load the sheets in film holders one at a time. It's like you're getting ready to fire a musket that takes like five minutes to reload. Meanwhile, Genghis Khan and his army is charging at you or whatever. I don't know, time periods that well. But at the end of the day, it's super rewarding and totally worth it, right? Right, guys? Anyone? Oh my God. There's film in here. What was the last 8x10 I shot? It's gotta be ectochrome, right? This baffles me.  After parking really f***ing far away and loading up the same amount of gear you'd bring on a deep sea expedition, I hiked in to our first location. This location was interesting but just like a Las Vegas hooker. It was riddled with signs that many people had been there. I didn't really love how much graffiti was all over the place, so I was kind of at a loss trying to find the right composition. A lot of detail to be captured here for sure. Perfect. Luckily a lot of the graffiti there was less of the penile variety which is just oh so common in places like these. On the toilets, kind of trying this new thing where I scout the location before I set up for a photo, you know? We'll see how well it works. I'm not gonna shoot a picture of the toilet if that's what you're wondering. So on that topic, my new strategy for large format these days, especially 8x10, is to leave my comrades, I mean all my gear, and do a quick clean sweep of the perimeter, kind of like an army rat deep in the jungles of NAMM as night begins to fall. Okay, so I'm gonna be using the 16 millimeter lens on the Sony. It's kind of a guide, I guess you could say, to try and figure out the frame lines for my 120 millimeter lens. This isn't bad. I kind of like the light coming through the door. I wish we'd see a little bit more of that. Maybe there's a way I can frame it.  I think this would work pretty well. Yeah, with the mountains up top, let's do it. I found my first composition and began setting up the beast. Your first shot is never anything too special so I wanted to get it out of the way and I had the perfect way to kill two birds with one stone. The one sheet of Ilford FB4 that I had loaded up was essentially a test sheet. The box was given to me by my friend Joey and he'd mentioned it would be kind of funky and he didn't really know how it would look. It expired in 96 so it could go either way. As a joke, I threw on the 120 millimeter lens and started setting up the shot a nice ultra wide angle with the subject, more or less being this light pleasantly splashing through the doorway. I mean, is it anything groundbreaking? No, but I think we both know I'm not capable of that anyway. Okay, I think I got some light metering off my phone today. FB4, I have one sheet. We're just getting it out of the way. It's expired. So I'm shooting it at 100. Did I miss a step? Il loaded the Pentax 67 really, really fast apparently. So the shot, it's not half bad actually. At first glance, it's conceptually all there but there's something definitely going on with the film. I can't really imagine I loaded it wrong or mishandled it but there are these like wavy crinkles burned into the edges of it.  I do really like the lighting and I do like how the black and white kind of mutes the amount of graffiti to some degree. It feels very layered all the way, you know until infinity, which is nice but overall this shot is more or less a discard. I guess I never really had super high hopes that it would work out which is what all my parent teacher conferences sounded like from outside the room. Onto the next one. I found the next one. It was literally where the camera was just a second ago. I'm gonna shoot that on the wide. Anyway, after spitting on the lens like all the pros do I set up another ultra wide of the entire gymnasium or whatever the hell this building was. I never really personally liked the reverse images you'd get from systems like Hasselblad or Mamiya 645 if you're using the waist level finder. I always just confused my little caveman brain but for some reason on the eight by 10 I don't really have that issue which really could only mean one thing.  I mean all the levels say it's flat. Doesn't seem, oh I see what's throwing me off. The roof is like slanted so I was kind of looking at the lines of the roof as like horizontal lines. There we go. All right, let's lock it down. It was time to shoot my first sheet of HP5 and I wasn't about to waste it. Oh, but we're gonna do it at 1600. Yep, I was gonna give this HP5 the old film photography special. I was gonna push it two stops to 1600. Bit unusual for large format because when you're kind of forced to use a tripod ISO really starts to matter a whole hell of a lot less. Really I just wanted to add a bit of contrast and a decent amount of, I guess, textural grain. Eight by 10 is so high resolution that it'd be nice to have some break up. Always get so scared pulling out the dark side. One, two. That is it, the fun was over. I had shot two sheets of eight by 10 and spent something like $450 already so it was time to just pack it up. Just kidding, hoes. You think I'd go down that easy? We do have three hours to get there and it'd be another three hours to get home so we're definitely gonna make the most of it. That might be a pretty good shot. I don't know, do we do it? So I ultimately decided that potential shot would be a little too similar to the FP4 shot that I took first. So I proudly said that I'm not an artist who makes duplicates of my own work and then realized I've made 137 nearly identical videos. This location is pretty well known and I've shot it before but it changes quite a bit every couple of years. Several years ago when we were here everything was pretty intact but now all the windows and doors are kind of bashed in. So it's a prime opportunity to shoot some interiors before they turn into graffitied meth holes. I decided to check out this garage thing off to the side. I couldn't really tell what it was a garage for. It seemed like somebody was maybe disassembling train cars out of it potentially. But speaking of locomotives I decided to run a train on some dank-ass 8x10 in here and there was definitely one obvious choice. That might be a shot right there. What do you think? Kind of interesting. A truck camper cover thing in the corner and some beautiful lighting splashing onto it from the side. Anyway, after blatantly disturbing the scene a little bit with my footprints I set up heavy and low for the angle. For this one I used the Nikkor 240 millimeter to punch in a little bit and go for less wide angle distortion.  So I quite like this shot. I guess I see it as a bit of a still life or like an environmental portrait. The lighting is good and it feels three dimensional which is the key here. The glow on the window is a little bit distracting if I could go back in time and stop myself from adding the promise I would have. But honestly who knows what catastrophic series of alternate events would have transpired if I even had that ability. I'd like to also give an honorable mention to the Nikkor 240 millimeter lens or maybe just eight by 10 as a format because the back corner here is slightly out of focus separating it from the camper top quite nicely. Sometimes photography is just all about separation. It's like divorce in that way. It was all over for me and I finally headed towards the light. But after that we decided to check out the main attraction, the destroyed cafe itself with a hidden wiener graffiti all over it. On the other side of the wall. Going a little further, go further. There were definitely plenty of shots in here for the taking on eight by 10. I think sometimes you just gotta find a one that stands above the rest. And for me, that shot was hidden in the back rooms where the light was pretty dim but coming in from kind of a nice angle and hitting this cash register looking thing on this desk. There's definitely gonna be a tight fit for the eight by 10. I had to shimmy and shimmy it in between a punched out window. The hallway and office were definitely a lot smaller than the wide angle lens on my Sony would have you believe. That and they were also quite destroyed probably by someone with rage issues. Well, if I'm gonna do color, I don't need a promise. I threw on the only choice really for this image the 120 millimeter. The lens, not the term for medium format that everyone gets wrong. I also committed to shooting color for this one. I felt like it would help differentiate the scene a little bit. And I wanted to grab those orange wood tones, you know, paired nicely with the green paint of the wall that was probably filled with lead. Portra 422, I'm gonna do 15 seconds. With reciprocity is 34 seconds. Okay, no problemo. One Mississippi, two Mississippi, three Mississippi, 34 Mississippi. So this shot isn't bad. It's definitely super wide and I love the detail.  I definitely think I would have changed some things up if I could. A lower angle, maybe it would have been kind of nice, but there was a cabinet here that definitely would have blocked the drawers of the desk and we wouldn't see all the papers littered all over the floor. Maybe a push in frame right and a tilt up might have solved that. The shot is possibly a bit overexposed as well. I probably could have taken, you know, a stop or two off the top, but I like the photo for what it is, plunger bong and all. My next shot was also going to be a tight one, you know, butthole-wise. If I thought there wasn't any room to work on the last shot, well, it was definitely in for a challenge here. The space was cramped in, darker than a well digger's ass, but I was riding high off as best as fumes probably, so I went for it anyway. Today's special, tuna casserole, super salad, Texas toast, all for $4. No wonder they went out of business. In fact, I had to take the whole eight by 10 back off the camera to load the film because I was kind of like sandwiched against a door frame and the bailback couldn't really open fully. I have to wiggle this one a little bit. Oh, because you can't get it in because of it. It wasn't all the way in, man. So somewhere in between F16 and F22, and we'll do one second, test exposure. Yeah, it's working. All right, one, two. In the end, this shot is just okay.  The other thing about it just kind of feels off balance to me and it doesn't really read as a kitchen for some reason. Anyway, with the hot water tank mocking my attempts at photography, I broke down and left. Broke down the camera, not my emotional state. Yeah. There was definitely a lot more to explore in the back. Time was kind of starting to run out. This one was sitting behind this like mountain and it was looking more and more like we were gonna get, you know, maybe five minutes of golden hour light. So our next moves had to be carefully calculated.  Why am I so obsessed with asses today? We may never know. Is that a comp? It might be. I don't know. We got time for like one more eight by 10 shot. Maybe get some sunlight. I think this is the shot, but is this the shot? I spent far too long trying to find, you know, it, but whatever it was, I didn't. There were shots here that could work well, but eight by 10 demands more and the clock was definitely ticking. All right, lighting is good. Got a rush though. Eventually I made up my indecisive mind and pointed myself towards the light, which is super poetic or whatever. I had one sheet left of Portra and two sheets of HP5. So I chose black and white, counting on it to just absolutely slay the drama of the scene. And to help inch it along, I threw on a red 25 filter on the lens. Yeah, here it is. Probably my favorite shot of the day. It's very moody and the subject feels distant and just overall kind of isolated. I do love the detail of the smashed in windows and the way the shadows fall off in between the buildings. So with no real time left to deconstruct, I threw out my scoliotic back, carrying the eight by 10 over to kind of a reverse angle of the cafe sign that was being lit up quite nicely. But for how long? Literally only another two minutes as it would turn out. So I hot swapped the back to vertical. I tried to quickly straighten out the lines of the building, threw on the red filter, then remove the red filter because I forgot to meter, put the red filter back on and I pounded out the last sheet of HP5. While I had the setup, well, already set up. I figured the lighting wouldn't get much better than this and I wanted to kill off my last sheet of Portra. Portra 400 at 320, 1 eighth, F 22. Almost didn't take the red filter off. We did it. I think the last three shots were pretty rushed, but it wouldn't be eight by 10 on this channel if I wasn't rushing eight by 10, huh? I don't think I screwed any of them up, but maybe. Definitely feel like I'm gonna be feeling this in my back tomorrow. You know what I mean? It's gonna be hurting. So how did those last two shots look? Here's the HP5 pushed two stops to 1600 with the red filter. It's pretty good, but it's also pretty cheesy, I think. I don't know, maybe I should be proud of this shot, but it's kind of an angle that's been taken, you know, 30 billion times by people passing through. So it's not exactly something refreshing, but frankly, my dear, it's not like I give a sheet. Here's the Portra that I shot at 320 ISO. Also not too bad. I think I like it more than the HP5 here. It definitely held onto the shadows more elegantly, which is to be expected in this case. The light is pretty solid and the colors are warm and pastel. What more can you really ask for? I don't know. The composition is still cheesier than Chester Cheeto, but overall I dig it. Speaking of things that I dig, I'd like to quickly take a moment and thank today's sponsor, Squarespace. If you're new to Squarespace, let me introduce you. Squarespace is an all-in-one website building platform that turns over the control to you and your own capabilities to build a website that surpasses even your wildest dreams. Start with one of hundreds of professionally designed templates and get to work building your visionary website with the knowledge and ability for you to scale up later, if necessary. When I eventually start selling prints of your work, no problem. Squarespace features a plethora of nodes and custom modules for building a seamless online webshop. I've personally been using Squarespace for years now to host my own photography portfolio and now that I have new commissioned work coming in, I'm gonna get to work rearranging my own website to show off my favorite pieces from that project. As a photographer trying to emerge in the industry, I'd personally say having an online portfolio is one of the most important steps towards getting hired and spreading your work out to the masses. Additionally, if you reach a point where you'd like to begin building a community centered around your brand or just your work in general, Squarespace makes it easy and convenient with its member areas architecture, a monetized way to give access to exclusive content through your website. So what are you waiting for? If you're ready to build a website, you can start a free trial today at squarespace.com slash grainydays. If you use the code grainydays at checkout, you can get 10% off your first purchase. Anyway, that was the end of the end, but also the rebirth kinda.  Caleb and I drove back to LA in complete silence as per usual and it sure gave me time to think about eight by 10 quite a bit, especially after taking quite a long hiatus from it. I do really love shooting the format as a whole. It's wonderfully rewarding at times. I mean, it's a lot of work for eight photos, but they're eight photos that I think came out really well. Well, okay, six photos that I think came out really well. The scope and breadth of detail in these shots make them quite a lot of fun to zoom in and stare at for just hours on end. Unfortunately, I don't really have hours on end to do that because I'm busy toiling away all my remaining time editing these videos, but you get the idea. Like I said before, this is probably my favorite shot from the day. It just worked out well and captured the mood I was looking for. It feels very, I don't know, post-apocalyptic. I'll definitely be doing a lot more eight by 10 this year now that I've kinda got my groove back a little bit and I even MacGyvered an eight by 10 film holder out of popsicle sticks, which has made scanning this stuff just a whole hell of a lot easier. Of course, I basically had to give myself diabetes to acquire all those popsicle sticks, but if you aren't dying for your art, then what are we even doing here?


We turn to First Minister's questions. Question number one, Ruth Davidson. Ruth Davidson 1. Thank you, Presiding Officer, to ask the First Minister what engagement she has planned for the rest of the day. First Minister. First Lady, can I welcome Ruth Davidson back from Birmingham? I hope that she is thoroughly ashamed of the xenophobic rhetoric that she has been surrounded by over the past few days. Later today, Presiding Officer, I have engagements to take forward the Government's programme for Scotland. Ruth Davidson 1. I assume that even the First Minister would acknowledge that I made my positions at a party conference perfectly clear. Presiding Officer, today's report from the Fraser of Allander Institute spells out plainly the challenges that Scotland, along with the rest of the UK, will face over the coming years as we leave the European Union. Like most members of this chamber, I didn't vote to leave the EU, but the question now is about how we maximise opportunities ahead and, yes, of course, mitigate risks. The report says that the focus must now be on areas such as food and drink and on manufacturing. Can I ask what work the Scottish Government is doing to ensure that these two sectors get protection from risks and take advantage of opportunities? First Minister. It is about rich to be asked what this Government is doing to protect Scotland from the risks when these risks have been created by the Conservative Party that Ruth Davidson is a member of and leader of here in Scotland. As I have said repeatedly in this chamber and outside this chamber, this Government will do everything in its power to protect Scotland's interests and to mitigate the serious risk that Scotland now faces, risks that are set out quite clearly in the Fraser of Allander report today. We are working intensively with all sectors across our economy. That work has been led by our economy secretary and by Mike Russell, whom I have appointed to deal specifically with the Brexit negotiations. It is not just manufacturing and food and drink. This week, I sat down with the financial services sector to discuss the real concerns that they have, not just about Brexit but about the growing indications that what we are heading for under the Conservatives is the hardest of hard Brexit. Unlike Ruth Davidson, my position has not changed. I continue to think that Brexit is a bad idea, and therefore I continue to think that it is my responsibility to do everything that I can to protect Scotland from it. Ruth Davidson. Let's talk more specifically about things that this Government could do to drive Scotland forward as we go through this period. The First Minister's Government is today expecting an announcement on underground coal gasification. Let me quote Graham Blackett, the head of bigger economics and a member of the First Minister's own growth commission. He says that, subject to the robust planning and regulatory process that we rightly have, there are major advantages in being the first movers in this technology and becoming a world leader. I know that the First Minister is restricted in what she can say, but her own adviser thinks that we could use this type of new technology to boost thousands of jobs and add billions of pounds to the Scottish economy. Does she agree? The First Minister. I am sure that Ruth Davidson is aware that the United Kingdom Government is also looking carefully at the issues around UCG right now, and I am sure that she is aware, perhaps more aware than I am, of the direction of travel that they might be going in as well. Ruth Davidson, as she did last week, seems to want to suggest that we should actually ride roughshod over evidence and over the reports that we ourselves have commissioned. Paul Wheelhouse will make a statement to this chamber this afternoon. He will report on the work that we have asked Professor Campbell Gemmell to undertake on our behalf. All members of this chamber—indeed, everybody across the country—will be able to look in detail at that work. Paul Wheelhouse will confirm the conclusions that the Government has reached as a result of the work that we asked to be undertaken. I think that that is the responsible way to proceed, because it is putting the concerns that people have and the interests of our environment and our economy front and centre and reaching balanced judgments as a result of that work. That is the way that we will continue to proceed on this important matter. Ruth Davidson. In the same way that people can still, by going on the Scottish Government website, look at the last report that you commissioned on fracking, whose advice you did not take. We have moved to another sector that is emphasised by today's Fraser of Allander report, which is food and drink. Whiskey producers tell us that Latin America, a market of 600 million people, has a potential for massive growth in the coming year. Yet south of Texas, Scottish development international has only one tiny office. Like me and the First Minister, the Scottish Whiskey Association did not want us to leave the EU, but they now want us to focus on developing opportunities. What action is the First Minister taking to expand our trade footprint around the world? The First Minister. Let us walk ourselves step by step through that question. Those who know what they are talking about around UCG and fracking will know that Ruth Davidson managed to switch between the different technologies there. I do not know whether she did that in full knowledge, or whether she needed to do a bit more homework. What we are talking about today is underground coal gasification. That is a very, very different technology to fracking. Before she comes to this chamber to ask questions about that, I would have thought that she might know and understand that. Secondly, on whisky, I met the Scottish Whiskey Association last week or the week before. The issues that they wanted to raise with me were firstly the success of the Scottish whisky industry, but also the real concerns that they have about Brexit and the likely impact on them of that decision. On our international presence, I am sure that if anybody was to go and do a quick Google search, they would find plenty of examples of the Scottish Conservatives criticising the international presence of the Scottish Government, saying things like, it is nothing to do with us, we should leave these matters to the UK Government. Thankfully, we do not listen. As well as the excellent work that SDI is doing, and of course we are considering carefully how we make sure that SDI is properly equipped in the climate that we have now been put in as a result of the recklessness of the Tory Government. We have also announced recently the opening of new investment hubs in London, Dublin and Brussels, making sure that we are not reliant on the likes of Boris Johnson to represent us overseas. We have the ability to do so ourselves. Ruth Davidson The First Minister seems more interested in discussing my position than her Government's own. I do not believe that I have ever hidden it. My position is to say that people from the EU and elsewhere are welcome here and that this is their home. My position is to retain the closest possible trading relationship with our European friends and neighbours while expanding trade abroad. However, my position is also to face up to the realities ahead of us, to mitigate risks and to take advantage of opportunities. This Parliament now faces a choice about whether to put the lion's share of its efforts into examining practical solutions or simply complaining about the results. Which is it to be, First Minister? Ruth Davidson is perhaps protesting a bit too much. She says that I am more interested in her position. I have to say that if anybody can work out what Ruth Davidson's position is on these matters any more, then they are doing better than me because she has flipped and flopped and flipped and flopped over and over again since the referendum result. I commend her for it. She said yesterday that what I stood up and said the morning after the EU referendum that people who have chosen to make their homes here are welcome here, they make a contribution. We want them to stay and continue making that contribution. Unfortunately, the difference between Ruth Davidson and I is that she wants control over immigration to stay in the hands of the xenophobes. I want it to come into the hands of this Parliament so that we can put these sentiments into practice. Lastly, Scotland finds itself now in a situation that we did not ask to be in. We are in this situation facing all the risks that we face because of the recklessness of the Conservative Government at Westminster. My job, and the job of this Government, is to protect Scotland's interests, and that is exactly what we will continue to do. To ask the First Minister when she will next meet HIV Scotland. As an organisation almost fully funded by the Scottish Government, officials of the Scottish Government have regular contact with HIV Scotland. Indeed, the Minister for Public Health and Sport last met the chief executive of HIV Scotland on 23 August. Across Scotland this morning, tens of thousands of people stood on station platforms as they started their daily commute. As Minister for Transport in October 2014, Keith Brown said that the new franchise agreement awarded to Bello was a world-leading contract to deliver for rail staff and passengers. Not only that, but it was a contract that will benefit the whole of Scotland. Does the First Minister believe that those promises to passengers have been kept? The contract was awarded because it was considered that it was the contract in the best interests of passengers across Scotland. However, it is absolutely incumbent on Bello as the holder of that contract to continue to make sure that it delivers services that meet the expectations of the travelling public. The Scottish Government will continue to liaise on an on-going basis with ScotRail to make sure that that is the case. Indeed, I am delighted that the recent dispute around driver-operated doors has been settled and that the public does not have the expectation of further industrial action episodes as a result of that. I doubt commuters on the morning train from Dundee to Edinburgh, or North Berwick to Edinburgh, or the nightly commute from Cumbernauld to Dalmure. I agree that Scotland has a world-leading contract, or indeed that the expectations of the public are being met. In the past few months, Scotland's rail passengers have faced cancellations, delays and overcrowding. New figures this week show that a third of all routes in Scotland have services that are late more often than they are on time. At the same time, Abelio rydw i'n rhaid i'n 1 million pounds a month of profit from that franchise. Does the First Minister agree that, although Scotland's rail network might be working for the transport bosses, it is certainly not working for Scotland's commuters? Kezia Dugdale is right to raise concerns with the travelling public, because the travelling public has a right to expect services that run on time and that they can rely on. It is because the Scottish Government is so firm in that commitment that Kezia Dugdale, I assume, is aware that, under the contract terms, the Scottish Government requested from ScotRail on 26 August an improvement plan, which was then received on 16 September. We are absolutely committed to working with ScotRail to deliver a quality service to passengers. That is our responsibility and we are serious in making sure that we discharge that responsibility. Kezia Dugdale, that is interesting because I have that improvement plan in front of me. In fact, it is a boast of a press release from Humza Yousaf this week, £3 million worth of extra investment to improve passenger comfort and accessibility on our railways.  I suggest to the First Minister that she just gets on one to appreciate how overcrowded the trains are. I need to be honest about the experience that is faced by passengers, because here is the thing. Since 2011, the average weekly earnings of commuters rose by only 6 per cent. However, the Scottish Government's cap on Russian rail fares increased by over 23 per cent. Let me make that absolutely clear. That is a rise four times faster than earnings. Those who travel to train for their work every day are paying more for a shocking service. Scottish commuters are fed up of the First Minister's excuses. That is her responsibility. What is she going to do to get things back on track? I do not think that anybody listening to this exchange will have heard me make any excuses. What I have said is that it is our responsibility working with ScotRail to make sure that quality service is delivered. That is exactly why the transport minister has been taking the action that he has been taking, and it is why we continue to invest significant sums of money in the rail network to make sure that that responsibility is discharged. I do not quibble at all about Kezia Dugdale's right to come to this chamber to raise these concerns. I understand the concerns of the travelling public, but my job and the transport minister's job is to get on with fixing the problems, not just to cart from the sidelines. The First Minister confirmed that she is aware that HSBC is intent on relocating around 200 high-quality jobs. Does the First Minister agree that that will have an obvious impact on individuals and the local economy? Given that disappointing news, does the First Minister also agree with me that that strengthens the case for sterling to successfully secure a city deal based on their excellent business case? Of course, I am aware of the situation at HSBC. I fully appreciate how anxious the time this is for the company's employees and their families. The Scottish Government will do all that it can to support those affected at this time. Scottish Enterprise is already engaging with HSBC to explore all possible avenues for supporting the business and its workforce. Of course, in the unfortunate event that any redundancies do proceed, our PACE organisation will be fully engaged. In terms of the sterling city deal, I had a brief conversation at another event with the leader of sterling council about this yesterday. I understand that these discussions are progressing well, although no conclusions have been reached. I hope that Bruce Crawford will see from the experience in other cities—Glasgow, Inverness and Aberdeen—that the Government is committed to taking forward city deals where we can. The First Minister will be aware that, on 23 October, First Glasgow will make substantial changes to bus routes. That will affect many of my constituents and bus passengers on her constituency and the transport ministers, too. Under the Government, the number of bus passenger journeys is down 74 million since 2007, and routes have been cut back by 66 million kilometres over the same period. How many more bus services have to be withdrawn before the Government backs any form of regulation? At the very least, does the First Minister not think that it should not be so easy for bus companies to walk away at short notice without any formal consultation from the communities that we represent? I think that First Glasgow and indeed all other bus companies should consult very closely with local communities before making any changes to local services. That is what I would expect of First Glasgow. As a local constituency MSP representing the south side of Glasgow, I regularly have discussions with First Glasgow about services that run in and through my constituency. I know that other MSPs will do likewise. Those are important issues. People in our constituencies depend on them, and I would expect bus services to take their views into account when reaching decisions. Will the First Minister join with me in welcoming to the galley today a delegation of campaigners from the Denun to Gwric ferry action group from my region? Can the First Minister confirm that it is the policy of the Scottish Government to provide a vehicle and passenger ferry service between Gwric and Denun town centres? Was David McBrain limited, which is wholly owned by the Scottish ministers, instructed to tender under the Gwric to Denun procurement exercise? First, I would welcome the campaigners for the Denun to Gwric ferry service to the chamber. I know many of them well as, in one of my previous Government jobs, I had the responsibility for taking forward this work. I absolutely appreciate the strength of feeling around the town centre vehicle service issue. I know that the member will appreciate that, now that we are in a live procurement exercise, there are strict limitations on ministerial involvement in that tendering exercise and what I am able to say at this stage. I hope that he will appreciate—indeed, the campaigners will appreciate—from my previous involvement how serious we are in seeking to make sure that there is a service running in that route that meets the expectations of those who rely on it. 3. Willie Rennie To ask the First Minister what issues will be discussed at the next meeting of the cabinet. Matters of importance to the people of Scotland. We have heard the Conservative international trade secretary branding European citizens working here as cards in an EU negotiation. We have heard the Conservative Home Secretary advocating listing foreign workers. Those cards are our neighbours and our friends. They are our family. People who voted for Brexit across the UK did not vote to send their friends home. So what can she do to ensure that EU citizens are treated with respect and dignity in those negotiations? The First Minister The first thing I can do, which is what I did do in the morning after the EU referendum, is say unequivocally that people who have come from other European countries or indeed from any country and chosen to make Scotland their home and make a contribution here are welcome here. This is their home, this is where they belong and it is where we want them to stay. All of us have a responsibility to say that as often as we possibly can. We have also, since the EU referendum, taken steps to liaise with the community of EU nationals living in Scotland. The cabinet held a question and answer session a number of weeks ago in order to hear directly their concerns. We have taken some practical steps, for example, around university tuition fees to give some reassurance to EU nationals where we can. We will continue to look for other areas in which we can do that. Unfortunately, it is a matter of real regret to me that I do not have the power to guarantee the right of EU nationals to stay here in Scotland. I hope that I will have the backing of every single person in this chamber when I say that. That is to call on the UK Government to stop using human beings as bargaining chips and to give them the guaranteed right to stay where they belong here in Scotland. Many of those European citizens work in places like Amazon. They deserve decent treatment, too. This week, Amazon celebrated recruiting more people below the proper living wage. It was described as a bonanza. I have raised this issue before an action was promised by the First Minister but nothing has changed. This week, the Scottish Government did not utter a peep—not one word of criticism. This is Amazon that has had millions of pounds of Scottish Government grants paying poverty wages. Does she still intend to do anything or has she lost interest? I think that that is a really unfair criticism for Willie Rennie because he knows—I know that he agrees with this—how seriously we treat the issue of the living wage. We encourage and I would go further than that and say that we expect all companies where they can to pay the living wage. We have taken a real lead in that. I wish I had the power here in Scotland not just to guarantee the right of EU nationals to stay but to legislate on minimum wage levels so that we could raise the statutory minimum wage to the level of the living wage. Let us argue not just for companies to do the right thing. Let us argue for having some of those powers in the hands of this Parliament so that we do not have to simply call on the UK Government to do the right thing for us. The First Minister will share my concerns at today's news that a hard Brexit could cost Scotland 80,000 jobs. The Fraser of Allander Institute report shows that the weaker our economic integration with the EU, the greater the negative impact. Does the First Minister think that it is high time for the Tories to drop their bluster over leaving the single market and at long last reveal a plan? The Tories should have had a plan to deal with this before the referendum. It is absolutely shocking that they did not have that. It is equally shocking that, three months on, we still have only the sketchiest of details about what happens now. Unfortunately, the details that we do have suggest that we are heading down the road of a hard Brexit, which, as the Fraser of Allander Institute report says today, will cost people in Scotland in terms of lost wages and lost jobs. That is completely and utterly unacceptable. What I think has been really clear from the Conservative conference this week is that decisions by the Prime Minister are being driven more by her desire to appease the Tory right than they are by the genuine interests of the country. I think that that is wrong, I think that it is regrettable and I think that it is deeply irresponsible. Douglas Ross Thank you, Presiding Officer. When Andrew Flanagan, the chair of the Scottish Police Authority, was asked yesterday about public concern over sex offenders and violent criminals being tagged, he said, and I quote, I think that that worry would be understandable. Can the First Minister assure the public that her Government will not use the extension of electronic monitoring for those criminals, given the very real concerns that have been voiced by the public and victims of crime? Public safety is at the heart of all of those decisions. As I have said previously in an exchange just a couple of weeks ago, it is not for politicians to decide sentences, it is for courts to decide appropriate sentences. But when a court is deciding the appropriate sentence in any case, whether that is prison or an alternative to prison, including the use of electronic monitoring, then risk assessment and issues of public safety will be absolutely integral to that decision. That is right and proper and the public would expect no less. Daniel Johnson Thank you, Presiding Officer. As the First Minister is no doubt aware, two weeks ago today, there was a very major rupture in the water main supplying Edinburgh that occurred in Liberty in my constituency. The destruction that was caused was very substantial. Many families have had to vacate their homes. Frankly, the only reason there wasn't a loss of life was because an elderly couple are currently in a care home where the greatest destruction took place. I had a very constructive meeting with Scottish Water in Tuesday this week, but it was revealed that the main regulating valves for the supply of water to Edinburgh are causing serious issues for Scottish Water to the point where they are supplying 24-hour supervision. The same valves are also used to regulate the supply of water to Glasgow and the Malgi. Will the First Minister assure me that her ministers are looking into this matter and detail to the Parliament what steps they are taking to make sure that the issue is remedied? The First Minister First, I am aware of the disruption and concern that was caused to the member's constituents as a result of the incident that he has talked about. I know that Scottish Water will deeply regret that inconvenience. I am more than happy to ask the minister with responsibility to raise the particular issue that the member has brought to the chamber today with Scottish Water and ask him to correspond with the member when he has Scottish Water's feedback on that. Is the First Minister aware of the turmoil in the Crofters Commission caused by the intolerable behaviour of the current convener? Does she know that other commissioners have asked for his resignation and that the previous chief executive, Katrina McLean, left because of the convener's behaviour and the pressure that is being placed on commission staff? In those circumstances, will she and her rural secretary now take action to make the commission work for crofters across the Crofting counties without the disruptive presence of the convener? The First Minister Tavish Scott raises an important issue. The cabinet secretary for the rural economy has already welcomed the apology from the board of the Crofting commission, but it is disappointing that the convener was not a party to that apology. It is important that we get to the stage of being able to draw a line under recent events. The resources that were spent in dealing with those issues by the commission would, in my view, be far better used and be an effective regulator in contributing to a sustainable future for crofting. I note that crofting commissioners have unanimously called on the convener to resign. The Scottish Government has requested further information from the convener in relation to last week's events. Although the Government would not ordinarily intervene in the internal operations of an independent statutory body, the legislation does give the Scottish ministers power to act if required, and I can assure Tavish Scott that the cabinet secretary continues to monitor the situation very closely. We will be very happy to discuss it further with Tavish Scott. Thank you very much, Presiding Officer. To ask the First Minister what the Scottish Government's response is to the recent Scottish social attitude survey, which shows that levels of prejudice in Scotland are falling. I welcome the findings from the survey. It is encouraging to see that Scotland is becoming a more inclusive society with more people embracing and valuing diversity. However, we should not be complacent. It is completely unacceptable that some groups in society still face prejudice. We need to continue to work together to eradicate discriminatory attitudes in Scotland. I can assure the member that this Government is absolutely committed to doing so. I thank the First Minister for that answer and that commitment. This week's Tory party conference saw the most disgraceful display of reactionary right-wing politics and living memory, with the Tories hinting that they will target foreign workers and name and shame businesses for not hiring British employees. We perhaps saw an early glimpse of that from the Scottish Tories in recent weeks, when they questioned Christian Allard's right to take part in public life. How will the First Minister work to ensure that we build a tolerant, inclusive Scotland, where people are judged on the contribution that they make to our society and not by the place that they were born? We do that by standing strong and, I hope, united in defence of that inclusive, tolerant society. We should value people by the contribution that they make here, not by where they were born or, indeed, the colour of their passport. I think that that work is undermined by some of the rhetoric that we have heard from the Tory conference this week. Yesterday, Theresa May's speech was endorsed by Marine Le Pen, the leader of the French far-right. Nigel Farage said yesterday that virtually everything that Theresa May said in her speech were things that he had said over the last few years. I think that all of us have an obligation to stand up against intolerance, against prejudice, against discrimination and against xenophobia in all of its forms, and I hope that everybody in this Parliament will do so. The First Minister has already called out the hateful, disgusting rhetoric that came out of the Tory party conference this week. Perhaps the most sinister of their proposals was that from Amber Rudd, the Home Secretary, that companies will be forced to disclose the proportion of their workers who were born outside of the United Kingdom. Will the First Minister and the Scottish Government support businesses in Scotland who refuse to comply with that disgusting proposal? I would absolutely stand full square beside any company that refused to comply with any request to publish details of foreign workers. What I found particularly offensive was the idea that companies would be named and shamed for the foreign workers they employed, as if there was something shameful about employing workers from other countries. It is absolutely disgraceful. I know that Amber Rudd went on the radio yesterday morning and tried to roll back from this proposal by saying that it was not something that the Tories were definitely going to do. I think that, as about time, the Tories stood up and said this that it is definitely something that they will not ever do, because it would be downright disgraceful and disgusting, and this Government would have absolutely nothing to do with it. First of all, can I associate myself with the comments that the First Minister has made about the Tory party conference? I think that all of us on this side would be in full agreement with her on that point. We welcomed the broad findings on the social attitudes survey, as well as the figures out last week that showed that hate crimes in Scotland had fallen over the last year, but we cannot be complacent, First Minister. We still have bad things happening in Scotland too often. For example, in the last year, islamophobic hate crimes have increased by 89 per cent. Prejudice and hatred have no place in any of our communities and certainly not in any part of our society. What specific action will we take to highlight the issue of islamophobia and to reduce hate crimes such as this? Firstly, I agree absolutely with Anas Sarwar's comments. Indeed, I did say in my first answer to this question that we should not and must not be complacent, so there is no disagreement whatsoever from me on that. We do see a rise in islamophobia. The Government continues to work with faith communities and, indeed, through all of our equality work, to combat discrimination in particular, to combat the rising trend of islamophobia. We have seen that. I was speaking at an event at the end of last week in Friday night, an interfaith event organised by the Alibate Society, where I made specific mention of the need to make sure that we continue to welcome the fact that hate crimes have fallen, but not in any way be complacent about that. I know that Anas Sarwar is very familiar with the range of work that we do seeking to work with communities to bring people together to make diversity something that we celebrate as a key strength of our country, not something that we should fear and exploit. That will always be the way that this Government behaves and conducts itself, and I hope that, in doing so, we will continue to have the unanimous support of everybody in this chamber. To ask the First Minister what steps the Scottish Government is taking to tackle the rise in the number of drug-related acute hospital stays. While drug-taking among the general population is falling, and indeed the number of young people taking drugs is at the lowest level in a decade, we remain determined to tackle problem drug use. With our partners and supported by an investment of more than £600 million since 2008, we are working to reduce the harm caused by drug and alcohol use. The rise in the number of hospital stays is the result of an ageing cohort of drug users. The reality is that, as they get older, they become more vulnerable, and that means that they have a greater need for the support and care of the NHS. We will continue to work with third sector groups to identify and understand the current and particular needs of those individuals. The First Minister will be aware from the recently published drug-related hospital statistics report that general acute emissions increased by almost 500 in the last financial year. The same report showed that around half of those patients lived in the 20 per cent most deprived areas of Scotland. Will the First Minister accept that the Scottish Government needs to do much more to reduce serious drug misuse in our most deprived areas? Of course I will. While we still have a problem of drug use, there will always be more that government needs to do. I would genuinely point the member to some of the trends that I highlighted in my opening answer. We are now seeing the number of young people taking drugs at the lowest level in a decade. That would suggest that the initiatives that we are taking are having some success. Coupled with that, it is right to say that we are seeing an increasing trend of hospital admissions, but that is related to the ageing cohort of drug users. As people become older, having had a lifetime or substantial parts of their lifetime taking drugs, then they do more and more need hospital treatment, and that is the explanation behind that particular trend. Drug use in any community, but particularly in our most deprived communities, is something that we should not and cannot be complacent about and we must continue to do everything possible to combat it. Does the First Minister agree that drug-related acute hospital stays are often related to illegal drug use? Can she confirm that drug-related crime has fallen dramatically since the SNP came to office with a fall of 45.7 per cent in North Ayrshire alone from 1,235 cases a decade ago to 671 last year? I certainly would welcome in point to the recently published recorded crime figures, which highlight the reduction in drug offences in North Ayrshire and reflect other positive trends in that area. North Ayrshire routinely exceeds a national performance standard that expects 90 per cent of people in need of drug or alcohol treatment to access it within three weeks. However, as I have just said in response to the earlier questions, we know that there is no room for complacency. We know about the vulnerability of an ageing cohort of people who have been using drugs for many years, and we must deal with that. Kenny Gibson is right to point it out. There is also cause for optimism. Nationally, drug-taking among the general population is falling. As I have already said today for young people, it is now at the lowest level that it has been in a decade. There is cause for optimism, but we must continue to tackle the problem because it is one that affects too many lives and can often affect those lives in a very dramatic way. To ask the First Minister what impact the breaching of EU spending rules has had on the funding of infrastructure projects. In 2015, the European Commission suspended three European structural and investment fund programmes. The suspensions prevented the Scottish Government from being reimbursed for money that it had already spent for the duration of the suspensions, but there was no impact on the projects themselves. All suspensions have now been lifted, with the final one being lifted in September of this year. I think that the First Minister has been badly advised in her response, because I am talking about European Statistics Authority regulations in relation to infrastructure projects. She has answered perhaps a different question. The First Minister will hopefully now be aware that there are at least four major capital projects that breach EU rules on funding. The Aberdeen Western Peripheral Route, the Edinburgh Sick Kids, Dumfries and Galloway Royal Infirmary and the National Blood Centre. The total capital required for all four projects will be at least £900 million. According to Audit Scotland, capital was transferred from housing, and capital was transferred from Scottish Water, and £300 million was borrowed last year to fill part of the gap. What further borrowing will be necessary to finance those and other planned projects? What is the opportunity cost if we still have to find the balance of the £900 million, and what projects will be delayed? I now understand that Jackie Baillie was talking about the ONS reclassification. I am not sure how anybody could have taken that from the wording of her question. Nevertheless, I am glad that we now have a meeting of minds on the question that we are answering. As Jackie Baillie knows, the ONS reclassification and there are a number of issues. We have seen one in recent weeks about housing associations where the ONS reclassifies from private to public. The UK Government also has similar issues to contend with. In terms of the capital projects that she talks about, the Scottish Government has made full provision for those. There has been no interruption in the capital projects, and we continue to make sure that our capital programme is taken forward to deliver the infrastructure that the country needs and deserves. The Auditor General's report last week tells us that a sum of £14 million has been lost from the Scottish Government's accounts due to its financial incompetence and its inability to comply with EU accounting rules, which projects have been cut or delayed because of the incompetence. I see that Murdo Fraser made the same interpretation of Jackie Baillie's question as I did, so I should say that my previous answer to Jackie Baillie stands in respect of this. In terms of the suspensions, the effect of the suspensions that have all now been lifted is to temporarily prevent the Scottish Government from being reimbursed for money that we have already paid out to the projects. There is no impact whatsoever on the projects concerned. We learn lessons that, as other Governments do, the European Commission regularly and routinely audits projects under those funds. We learn lessons and we have applied those lessons in terms of the current rounds of structural funding. I would say, of course, that it is the actions of Murdo Fraser's party that is putting the future of structural funding under so much stress. To ask the First Minister what the Scottish Government's response is to the proposed deadline of March 2017 for the triggering of article 50. It seems clear that the decision on the timing of article 50 is being driven more by the Prime Minister's desire to appease the Tory Eurosceptics than it is by any rational consideration of what is in the best interests of the country. I think that that is deeply irresponsible. As we have already heard in this session of First Minister's Questions, we can see in the report by the Fraser of Ireland Institute this morning that the damage that Brexit, especially the hard Brexit that the Prime Minister now seems to favour, will do to our economy. That is why the Scottish Government will continue to do absolutely everything in our power to protect Scotland's interests. Emma Harper I thank the First Minister for that answer. Given the timescale that it has taken for the Prime Minister to set a timescale, what is the First Minister's best bet on how long it will take the UK Government to come up with a plan, or any substantial notion of what Brexit means? Well, I have no idea how long it is going to take the UK Government to come up with a plan. They should have had one by now. What I am more concerned about with every day that passes is the direction that the UK Government seems to be going down, not just exit from the European Union but exit from the single market. Let us be quite clear about what that will mean. That will mean tariffs and non-tariff trade barriers to our companies who export to the European Union. It could mean our financial services companies losing their passport rights. It could mean all of us having to pay for the privilege of travelling across Europe. Those are real implications for each and every single one of us. That would be bad enough, but it is even worse because Scotland did not vote to be in this position. I hope that everybody in this chamber will unite behind a call from the Scottish Government to stay in the single market. I do not believe—notwithstanding the result of the referendum—that Theresa May has any mandate to take the UK out of the single market. How many times did we hear the leave campaign say that leaving the EU did not mean leaving the single market? I hope that Ruth Davidson will go back to one of her previous positions and again get right behind the Scottish Government when it says to Theresa May, keep the UK as a whole in the single market and stop putting the interests of the Tory Eurosceptics in UKIP ahead of the interests of the country. To ask the First Minister what discussions the Scottish Government is having with the governing bodies of sports, contact sports, regarding head injuries. First Minister, on behalf of Parliament, can I take this opportunity to convey sincere condolences to the family and friends of Mike Tewall, who sadly lost his life following a boxing match in Glasgow last Thursday? The British Boxing Board of Control is investigating the circumstances of the incident, and it would be, obviously, inappropriate for any of us to comment on the details at this time. On the broader issue of concussion in sport, as Liz Smith is aware, we were the first country in the world to introduce standard guidelines for dealing with concussion in sports when the Scottish Sports Concussion Guidelines were published in May last year. Those guidelines were developed with a range of experts, including the chief medical officers at the Scottish Government, Scottish Rugby and the Scottish Football Association. They have been made available to all sports clubs and coaches for both contact and non-contact sports. Liz Smith, I thank the First Minister for that response. I also thank her for the helpful letter that she sent to me this time last year following another FMQ that I raised the same issue. In that letter, she says that she fully recognised the seriousness of the issue and intimated that guidance would be updated on a regular basis. I wonder whether those updates have taken place and whether consideration has been given to the fact that there is currently different guidance for serious concussion injuries in different sports. For example, in boxing, the suspension from the ring is a minimum of 28 days, whereas in rugby the minimum is seven days away from the sport. Would she agree that the medical expert panel to which she referred in her letter might like to look at whether there should be a standard approach? As I said in my original answer, we have introduced standard guidelines for dealing with concussion in sports. However, as I said previously, when Liz Smith last raised this issue with me and was raising it, I think that at that time the prospect of legislation, which the consensus among medical experts appears to be at this stage that legislation would not necessarily be helpful. However, when I said what I will say today, we need to make sure that we keep this under review and that, as we do so, we are informed with the best medical opinion. So I am very happy to take the comments that Liz Smith has made today and make sure that they are discussed by the panel of medical experts that inform those decisions. I will be happy to enter into further correspondence with her when we have done so. Thank you. That concludes question time today. We will now move on to members' business in Liam McArthur's name. We will just take a few minutes to change seats.


Diagonal matrices are actually very convenient, they are very easy to understand and for instance if you have a diagonal matrix, its eigenvalues are the diagonal elements and so on. There are so many nice properties that diagonal matrices have and so in general we want to know if a given matrix A is similar to a diagonal matrix that is to say that the matrix A belongs to a certain equivalence class and does this equivalence class contain any diagonal matrix in it. So that is the following definition is diagonalizable if it is similar to a diagonal matrix. So when is a matrix diagonalizable? We have the following result is diagonalizable if and only if it has an linearly independent eigenvectors. So that is the requirement that it must have n linearly independent eigenvectors and we have already seen that if a matrix has distinct eigenvalues then the corresponding eigenvectors will be linearly independent and so any matrix that has n distinct eigenvalues will necessarily be diagonalizable. Of course a matrix could have repeated eigenvalues and still be diagonalizable and the identity matrix is an immediate example all its eigenvalues are equal to 1 it has n repeated eigenvalues and it is already diagonal so it is diagonalizable and in this case you can also see that any non-singular S is such that if I do S inverse times the identity times S gives me a diagonal matrix. So the matrix S that transforms the identity matrix to a diagonal matrix can be any non-singular matrix S. So that also shows you that this matrix S that defines the similarity transform connecting A and B to matrices it need not be unique. Okay so let us just see how this is proved so if there are n independent linearly independent eigenvectors x1 through xn then let the matrix S just be a stacking of these vectors not right here with commas x1 stacked with x2 xn so this is an n cross n matrix we will show that this matrix works okay it will reduce A to a diagonal matrix. So all we do is we consider S inverse AS which is equal to S inverse times A times this matrix x1 through xn and this matrix so if I expand this product I will get S inverse the first column of the product will be A x1 the second column will be A x2 A xn and because these are eigenvectors of this matrix A this A x1 is some lambda 1 x1 S inverse times lambda 1 x1 lambda 2 x2 up to lambda n xn and if I consider a diagonal matrix with lambda 1 through lambda n as its diagonal entries then I can write this as S inverse times x1 xn times this matrix lambda where lambda equals it's a diagonal matrix okay this is just rewriting this product here but then this matrix is just S and so I have S inverse S which is the identity matrix which is equal to lambda so we've shown that the matrix actually gets diagonalized so what this shows is that if there are n linearly independent eigenvectors then the matrix A is diagonalizable by a similarity transform I've reduced A to a diagonal matrix since it's an if and only if condition I need to show the converse also so if what it what we need to show is that if A is diagonalizable then it must have n linearly independent eigenvectors so if there exists an S such that S inverse A S equals lambda where lambda is some diagonal matrix then it means that A S equals S lambda I'm just pre multiplying by S so this just if I write out what this means in words this means that A times the ith column of S is equal to but lambda is a diagonal matrix and so that will be so the ith column of so this will be the ith column of A S so A times the ith column of S S is equal to the ith diagonal entry of lambda times the ith column of S which means that the ith column of S S is the eigenvector of A associated with the ith diagonal entry of lambda as eigenvalue okay so so basically what this means is that the columns of S are essentially eigenvectors of this matrix A and the diagonal entries of lambda are the eigenvalues of this matrix A and of course since by definition A is similar to a diagonal matrix this S is a non-singular matrix so since S is non-singular there are or A has n linearly independent eigenvectors so that completes the proof so basically this result that A is diagonalizable if and only if it has n linearly independent eigenvector so in principle this is a way to diagonalize a matrix if it is indeed diagonalizable so all you need to do is to find eigenvalues and eigenvectors of the matrix A and then you check whether the eigenvectors are linearly independent and if there are n linearly independent eigenvectors then you can just stack those eigenvectors together and that gives you the matrix S which is a diagonalizing similarity matrix okay so this is one way to find how to diagonalize a matrix A so again coming back to our previous example this matrix 0 1 0 0 is not diagonalizable okay what it means is that it does not have two linearly independent eigenvectors so I mean if if this was actually diagonalizable then there must be a matrix S such that S inverse times 0 1 0 0 times S is equal to a diagonal matrix containing the eigenvalues which is the all zero matrix because both its eigenvalues are zero but then this implies that if I pre and post multiply by S and S inverse it means that 0 1 0 0 must be equal to 0 0 0 0 which is not possible okay so this matrix is not diagonalizable and in fact this matrix has only one one eigenvector corresponding to lambda equal to 0 which is the main the vector 1 0 so if I multiply this vector this matrix by 1 0 I will get 0 0 so that is so 1 0 times this matrix is equal to 0 times 1 0 and so 1 0 is an eigenvector of this matrix corresponding to lambda equal to 0 and I cannot find any other linearly independent eigenvector of this matrix A so we see that the number of linearly independent eigenvectors of a matrix that you can find corresponding to an eigenvalue can be less than the multiplicity of the eigenvalue okay the multiplicity of the eigenvalue 0 in this matrix is 2 okay it is an eigenvalue of multiple 3 2 but the matrix has only one linearly independent eigenvector it does not have two linearly independent eigenvectors corresponding to lambda equal to 0 so basically not every n cross n matrix will have a full set of n linearly independent eigenvectors okay so here is so here's another direct consequence of what we just saw if a in c to the n cross n has n distinct eigenvalues then a is diagonalizing this is an immediate consequence because if it has n distinct eigenvalues then it has n linearly independent eigenvectors okay and so we just saw that result a has n linearly independent eigenvectors which implies that a is diagonalizable okay obviously the converse need not hold that if a is diagonalizable then it need not have distinct eigenvalues and I already gave you the identity matrix as a as an example okay it does not have a distinct eigenvalues all its eigenvalues are equal to one but it's of course diagonalizable okay so now you've seen that this similarity matrix that say diagonalizes a matrix need not be unique so a related question is is it possible that there is a single matrix similarity matrix that will diagonalize both two different matrices so we say that a and b are simultaneously diagonalizable if there exists a single matrix s such that s inverse a s and s inverse b s are both diagonal okay what this and in words means is that there is a basis in which the representations of both these linear transforms are diagonal okay so both these are diagonal they need not be the same matrix the same diagonal matrix all you need is that s inverse a s and s inverse b s are both diagonal okay in other words a and b need not be similar to each other but they can be simultaneously diagonalizable here is one result which I won't prove but it's nonetheless true is let a and b be n cross n matrices okay and so suppose these two matrices are diagonalizable okay then a and b commute that means a b equals b a if and only if they are simultaneously diagonalizable the proof is not difficult it's just somewhat long and so I don't want to do that in class it uses an induction argument on the matrix size to show that they commute if and only if they're simultaneously diagonalizable okay there's one other important result which which we will use quite quite a lot in this course and it's also a very useful result so that is this result so let a in c to the m by n now no longer square matrices and hello sir yes sir what do you mean by a and b will commute even there I just said it in words but okay okay please m less than or equal to m okay then has the same eigenvalues as a b counting multiplicities together with an additional n minus m eigenvalues is equal to zero okay so in another way to say it is that that is if I look at the characteristic polynomial p b a of t that is equal to t power n minus m p a b of t so this has n minus m extra zeros because t equal to zero is a repeated eigenvalue zero of this polynomial with repetition n minus m times so there are additional n minus m zeros of course the matrix b a okay is of size n by m n by n and this is a matrix of size m by m and m is smaller than n less than or equal to n and so this has more number of eigenvalues it has exactly n minus m additional eigenvalues more on top of whatever are the eigenvalues of a b but the there are the m eigenvalues of a b will also appear as m eigenvalues of b a and in addition b a will have n minus m extra eigenvalues which are all going to be equal to zero and if m equals n and at least one of a or b is non-singular so the both square matrices of the same size then a b is similar to b a okay so this is one example where from this result we see that if I apply this result to the case where m equals n then a b and b a will have the same eigenvalues but we've already seen that two matrices could have the same eigenvalues but not be similar to each other but what this is saying is that if at least one of these two matrices is non-singular then these two matrices will be similar to each other okay so this is one example where having the same eigenvalues is actually sufficient in for the matrices to be similar but provided two other conditions are satisfied namely that m equals n and at least one of a or b is non-singular okay of course yeah the thing is we are only comparing checking whether a b and b a are similar okay so there isn't time to see the proof of this in this class so we'll see the proof in the next class which will be Wednesday of next week that's all for today


last 24 hours how good does it feel at the team found a way to win. I'm just glad for the guys that they were able to get back on the floor get back to what they enjoy doing love doing competing and playing the game of basketball so at the end of the day that was the best part of getting together and competing today. What was the message to the guys after this one? We got a road trip coming up Chicago gave us a little dose of aggressive teams and our ability to take care of the basketball on the road take care of each other put us in a position to get some wins on the road. Jack it seemed like last week you guys had made some steps in the right direction with the turnovers and then today had so many just what we kind of went into that number today. Not completely sure you know I we even end up changing the basketball throughout the course of the game which is doesn't happen too often so we complained that it was a little bit too slippery in Chicago did too and they changed the ball so I think that was the first seven the other 21 will have to look at tomorrow but overall they're aggressive team and they always force you to not be casual and I think we were casual at times with the basketball so good tests for us especially going out west. Coach would you think of DeAndre's performance today and then did you use him any differently today than he's been used throughout the rest of the season. I thought first of all both bigs were really good in their roles today. DJ's minutes were extended that first and I thought it just gave us a presence and a some stability at the rim. I thought we had some great verticalies throughout the course of the night and he was part of a lot of them. Coach you said before the game you hoped the guys would play for each other. It looked like there's a little more assistant coaching going on there from the guys themselves. DJ was kind of hyped up again. Did you feel like they were helping you coach and congrats on the first one. Thank you. I appreciate that. I wanted all and I think you have that communication throughout the course of the game even when we went small at the end being able to communicate that to the guys is important for us. We'll start implementing defenses that if you don't have the communication that they won't work. And so it was good to see us at least for the first three quarters communicate too many points given up in that fourth quarter. Coach Kobe White came with an inches of tying it. Is that your general philosophy not to foul in the closing seconds when you're up three. We talked about on the bench. That scenario presented itself that we weren't going to foul. But there'll be times analytically where we will file. But this situation we chose not to. Jack Harris went four six from three and he was saying the other night that you know lately he tried to be more aggressive just get more threes off. How much have you seen that part of his game develop the last month plus. Yeah. When he's making threes he's really really hard to defend. You know he has the knack to get to the rim get to the basket create contact and finish. And when he can get his defender to inch up on him that just gives him more opportunities to get downhill. I think he's playing with the extreme amount of confidence. And when you have confidence multiple parts of your game are able to blossom which was just happening for Keras. Coach you're the lead assistant for the past few years. Was there anything from watching Kenny that you utilize today. Without a doubt. The overall whether it was substitution patterns that we had talked about. We were a very collaborative staff. And so on both ends of the floor. So definitely whether it was sub patterns whether it was some play calls that guys were familiar with. Overall they're definitely some familiarity because of Kenny and I being together for these years. Was just your general assessment of the gameplay in that fourth quarter in terms of effort level in terms of execution. You guys are leading by 13 I think in the third quarter and then they got pretty close. Yeah I think we took a few possessions off where maybe we didn't get a 50 50 ball. We didn't box out. I use the word casual. And I said that to the guys in the huddle. The ability to lock in each possession is going to be a challenge for us. Good thing we locked in at the free throw line and made some free throws that definitely helped. But the rest of the game we have to be locked in. Coach Wilson was plus 21 even though he only scored six points. What does he do out there that allows him to have that type of impact on the game. Somehow you want to put him on the floor. He's going to give you all that he has. We appreciate that. He's stable like each game. And that's a great place for a coach to be and where you can count on that individual. And he gives the coaching staff confidence. Thank you. Okay guys. Good night. You know it's interesting.


Hi, so what are you doing here in Curita and where are KEDA? KEDA is one of the bosses of Qtron and we are here because we are one of the members of the Qtron community Contribute to Qt and work on Qtron-related products like Qtron Automotive Suite, we are shown here together with the Qtron company in KEDA which is a specialized version of Qtron for users in the automotive industry via AI systems for example showing the Qt3D integration that we contributed to Qt and the gamma ray tooling integrated into Creator that allows you to do high level one time introspection of your Qt application running on a remote target So could you just emphasize on how useful this is for the developers? Well, the tooling that's the main part we contribute to the Qtron Automotive Suite that enables you to diagnose problems in your application on the same level you design it with so rather than using the instruction level debugger to step through your state machine for example you actually get a visualization of what's going on and you can like, what do you find out if you learn to use IoT deploy to an embedded target so it saves you a lot of time and makes your life a lot easier by working on the same level you actually need to think when you sign on the code That is wonderful and thank you Qt for supporting us like forever and we hope we will continue to do that Thank you for being here


Nestled opposite the old houses of Delhi's civil lines, one could pass it by as just another city garden. It has a quaint charm that leaves one to sink in its surroundings the way they feel best. The one-kilometer walk through the outer circumference would take the time you pace yourself at. But as you enter, the original gate to it still stands and reminds you that this is after all Kutsia Bagh. The former garden complex and palace of Kutsia Begum, Mughal Emperor Mohammad Shah's wife. It takes a historian to point out, however, that her abode is also an example of lesser known women in history that did a commendable job of rising to power well before the Fortune magazine list came out. This garden, Kutsia Bagh, was commissioned by Kutsia Begum, the mother of the Mughal Emperor Ahmad Shah. She was the real power behind the throne with the title of Nawab and a high Mansab rank of 50,000, unprecedented and unheard of during its time. Unlike most royal ladies, Kutsia Begum was not born to privilege. She had been a dancer who became the concubine of Ahmad Shah's father, Mohammad Shah. It was by the dint of her own personality that she grew to enjoy such power and influence. Kutsia Begum used her part wisely. She paid close attention to affairs of state and was famous for her generosity. We have many more examples of such women from Delhi's history who rose from relatively humble origins and made a name for themselves. One of them is Begum Samru, the ruler of the state of Sardana. The other is Mubarak Begum, the wife of General Octolon. If you can brave the traffic on the ring road on the other side of Kutsia Beg, then do cross over to the Ladakh Buddhist Vihar. There is a footbridge down the road for the less adventurous. An old market with a monastery and a Dharamsala, the Thukpa, Digmo bread and curry and other Tibetan food in their little restaurants will be a satiating ending to the walk in the Beg.