Fel ai'n rhoi unig gan hynny, rydw i'n gwybod i dda i chi'n ddweud eu cynnigol i ddweud eu cymryd a'i cymryd wedi rhoi ei ddweud, ond mae'n gweithiau i ddweud o phas y lleiwgwyfo ar y cyfyrdd. Mae'n gweld ei ddatblygu i gyda ni'n ei ddweud i gweld eich ddweud o phas a ddweud ei ddweud i gweithredu llinwyr i ddweud. Mae'n gweld ei ddweud eu gofynu hynny i ddweud i ddweud, a o wnawn i chi ddweud i ddweud o'r ddatblygu'r eich cyngniaw hwyl. Felly, coleg chi'n brys Crawford i gael i ffiddiwethaf i niw Anabell Ewing. Mae gennynni Crawford yw 7 maen nhw, felly rae maen nhw? Rai, yn cymryd ddim yn fwy ffordd rai i gabi yn bryd i Anabell Ewing rwy'r pryd i'r ministeriaeth i commandeis ystyried y gallwn ymdyn nhw. Be iawn i ddodol i'r gweithio, a ddod o'r ddodol i gael i'r ddodol, those who have turned up to debate at this moment, but also to thank Annabelle Ewing for creating opportunity for me to lead the debate on celebrating St Andrew's Day. In my contribution, I particularly want to reflect on Scotland's place in the world. A stated in a motion, St Andrew's himself was a man who touched many countries. Of course, the obvious countries with which Scotland has links lies with our friends in the commonwealth countries across the world. It was in the commonwealth countries that many of our forebears chose to make new lies for themselves and the more recent past and, of course, vice versa. But Scotland also has centuries-old relationships with our Scandinavian neighbours, with Poland, Germany and the Netherlands. Scotland emigrated in numbers to these countries mainly in search of economic or military careers. Many, as we know from those countries, settled here. Again, it was the same for our neighbouring countries across these islands. Again, it was vice versa. Similarly across the world, in more contemporary times, in the first maritime and air travel, we have witnessed Scotland take her place as part of a smaller and more independent world. We know that in more recent times there have been people come to enrich your society, whether that has been the Italians and the Poles of the past or people from Pakistan and India, etc. In developing our place in the modern world, as a result of the many links that we have around the globe, we have become a much more ethnically rich and diverse country. That has helped us retain, I believe, a unique and outward-looking culture. I think that everyone would agree, and it goes without saying, that 2014 has been a year-like no other to celebrate all that is good about Scotland. Our referendum was a magnificent renewal of Scotland's national democracy with an enormous turnout and truly incredible levels of democratic engagement from our citizens. I happened to be in Fort William earlier on this week with the Further Devolution Powers Committee, and we had the chance to speak to many 16 and 17-year-olds who were involved in that democratic process. There is no doubt in my mind that what we have heard from the Smith commission for example this week and from all the parties in Parliament now that we recognise and value that the young people's contribution is part of the referendum process. I am glad that everyone is committed now to giving 16 and 17-year-olds a vote in our country. That referendum was a spectacle. It was watched in awe across the world. This week, the journalist Jack Wright wrote in his view from Scotland's column for the excellent addition to Scotland's new daily newspaper titles, The National, that our brand is stronger than ever in the United States, as he commented on the new-found interest in Scotland and our politics. It is more than just that, of course. We have welcomed visitors in the second year of home coming from all over the world. I met many of them at the Banachburn event myself, succeeded in organising and delivering the best common world games ever, as well as the magnificent spectacle that was the World Cup. Of course, we have had a wide range of culture events in which to reflect on and commemorate this year for Scotland. For instance, the historical heritage of our country included the hugely successful marking of the 700th anniversary of the Battle of Banachburn. However, the common world games in particular presented a golden opportunity to celebrate the diversity of family of nations and what the common world represents and the diversity that we found now in modern Scotland. Indeed, the former First Minister's description of the diversity of modern Scotland put it elegantly. There are many different colours and threads woven in to the Scottish tartan and we celebrate them all. I wholeheartedly agreed with those sentiments. As the richness of that tartan is reflected in the analysis work done for the 2011 census, Dr Andrew Smith, the senior lecturer in sociology at University of Glasgow, said that what our research in the centre on dynamics of ethnicity reveals is a picture of growing diversity within Scotland and of diversity spread across different areas of the country. He added that what the analysis also reveals is that Scotland's growing diversity is not producing polarised islands of different groups but a mosaic of differently mixed areas. Those findings are very reassuring in modern Scotland, but there is no room for complacency in this chamber or indeed in Scottish society in a wider general sense. We must always strive to ensure that a diversity of the society is celebrated and never something to divide us. As well as modern Scotland being about those from elsewhere who made their home here in our country, Scots have left the shores for opportunity and have made a huge contribution to the modern world. The USA and Canada are off-sighted examples where millions can lead claim to Scottish ancestry. Indeed, it is estimated that from this wee country of ours, between 28 and 48 million people may be able to claim Scottish descent. I was intrigued to discover recently that 80,000 people in Chile claim Scottish descent. I could not understand that number. It is more than many other European countries put together, but I discovered that it was mostly about sheep and about an admiral who went to Chile to create the Chilean navy from Scotland. Forgive me, I cannot remember his name. John Mason is now going to tell me his name. John Mason? When he mentions other countries, I was wondering whether he would comment or if he realises the connection with Jamaica, which also has a saltire in its flag. Scots were involved there and there is a huge number of Scottish names in Jamaica. I recognise that although it is a yellow saltire that goes through the flag of Jamaica, it goes further south. We also come into places like Guinea, where lots of Scots went along during the times of the sugar plantation. Scots have a significant contribution in that part of the world. It is a pity that the bobslayers from Jamaica are better than our bobslayers. I was reminded yesterday by my American Indian Heidi Brown that Thanksgiving Day is being celebrated in the United States as we speak. This national holiday gives families a day off to rejoice in the co-operation between Native Americans and the pilgrims during that period. Americans mark this day by feasting, as they did after their first successful harvest in 1621, as well as giving thanks to the continued tradition of accessing gratitude to Native Americans. I want to therefore conclude my remarks by wishing Americans here in Scotland a happy Thanksgiving Day on their national holiday. The motion to which I speak also advocates the celebration of St Andrew's Day as a national holiday. I have no doubt that it is not beyond our wit to designate St Andrew's Day a national holiday and rearrange our calendar of public holidays to reflect that if that is what we choose. As I close, if there was ever a good reason to celebrate St Andrew's with a public holiday, it would celebrate Scotland's contribution to the world, but even more importantly, to celebrate and to raise a toast from all around the planet who has chosen Scotland as their home, enriching our culture and our daily lives. I congratulate Bruce Crawford on congratulating Annabelle Ewing in this debate, celebrating St Andrew's Day and our patron saint in Scotland, not just of Jamaica, but of Greece, Romania, Russia and some others. I am good to see Jamie McGrigor in the chamber. I know that he will be speaking later, speaking from the Conservative benches, but I have to say, Deputy Presiding Officer, I have to remark on the fact that there is nobody in the Labour benches, nobody on the Liberal benches to speak to the motion celebrating Scotland's national day, pretty disgraceful. Raising the profile of our national day is undoubtedly due in this part to this Parliament reconvening some 15 years ago, and not least to Dennis Canavan's act, the St Andrew's Day bank holiday Scotland act of 2007, though it is not a full national holiday, as Bruce Crawford alluded to, and not as celebrated yet as, for example, Burns night. Google, at one time, displayed the saltire on its homepage on St Andrew's Day. I hope it does it this year. I would suggest that those members who are not in the chamber and that's most of them will pay attention and suggest to Google that the St Andrew's flag is on the Google page on 30 November. It's good business for Scotland and it's appropriate. St Andrew gave us the saltire and flags are at the beating heart of a nation. It is symbols of nationhoods such as our patron saint and the flag emblematic of his crucifixion that have carried the heart and the hopes of Scots in good and bad from the confrontations and football pitches to those on battlefields. When is that symbol of our patron saint more distinct than in our flag the saltire, which was inspired by the vision that Athos Stamford in 832 AD, where King Angus, Angus is my oldest son's name, there's DNA for you, Angus led the Scots in battle to defeat the Angles. The night before battle, St Andrew appeared before King Angus assuring him of victory and in the morning a white saltire against a blue sky appeared to both sides. It scared the Angles to pitch their lost confidence and were defeated and that has been our image ever since. The saltire was also used in the nation's coinage when it was introduced by King David I in the 13th century. It therefore has an ancient and noble lineage. On St Andrew's day in our capital city, however, there is the opportunity to fly the St Andrew's flag prominent position over the castle. Why not? Why is it not flying over the castle? There is a false argument that the castle is an army garrison. It is not. It seems to be a garrison in 1920, and the army is now there largely in a ceremonial capacity. I'm thankful that Historic Scotland saw the light last year and didn't put Olympic rings on it, but I have a suggestion. Why not project a large saltire on the ramparts of the castle for November 30th? In commemoration of St Andrew's day, his flag may fly over Edinburgh Castle, it may or may not, but not in pole position, as I've said. However, the British Government, on behalf of the Ministry of Defence, designated it as an official flag-flying station. The union flag therefore takes precedence yet by the Scotland Act 1998, and by agreement between the Crown, the state, commissioners and the Scottish Office, ownership of Edinburgh Castle and other historic buildings, transferred from the Crown to the Secretary of State for Scotland and hence to the Scottish ministers. The transfer of 26 properties took place in 1999, in fact. It included inter alia Edinburgh Castle, the Government through its ministers, now the owners, and therefore the landlords to the MOD. The MOD is merely our tenant. It's time for the landlords, on behalf of the Scottish people, to tell the tenants to take down the union flag and fly the saltire in its place, not only because it symbolises our nation and its patron saint, but because, frankly, if it's good enough for recruiting Scots to fight in the legal wars, it's good enough to fly all the year round. We know that, despite the narrow mis of independence, or perhaps because of it, because of those 1.6 million Scots who voted yes in the face of a unionist tsunami of negativity and the now baby steps taken under the Smith commission and substantial and cohesive and home rule have all been redefined, and we now know the definition of a vow. We all know, wherever side you are in this Parliament, that Scotland's story has not yet been told, that ending remains unwritten, and then the saltire will fly everywhere. Many thanks. Nercle and Jamie McGregor to be after which moved the closing speech to the minister. Thank you, Deputy Presiding Officer. Referring to Christine Graham's remarks earlier, I'm too astonished as nobody from the Labour benches. Oddly enough, there was nobody during the Ukrainian debate the other day, which I thought was rather odd. Perhaps they've all been rendered speechless by something. And I congratulate Annabelle Ewing on securing today's debate, and I'm very glad to take part in it because it's important. Christine told the story of the Scottish saltire and the legend of St Andrew, which I was about to tell you, so that's taken away some of my speech. But I have to say, I was very glad to learn that it was St Andrew whose dream inspired the saltire. It's a beautiful flag owned by all the Scottish people, and of course it's part of the Union Jack as well. Quite why St Andrew's was considered to be the end of the earth, where St Rul was instructed to take St Andrew's remains, is a mystery to me, as I was considered in a very fine town with a great university and a marvellous golf course. But perhaps St Rul arrived on a bad day, which was made worse by a har or something like that. But he was lucky to get away with his life, unlike the Hussites who arrived at this one stage from the Czechoslovakia who were burnt at the stake in St Andrew's. But anyway, what celebrations St Andrew has inspired worldwide, particularly in Australia and Canada and in China, the Canadian Society of Beijing of which my brother was a previous chairman, holds a St Andrew's ball where an enormous amount of Scotch whisky is consumed. The Czech Republic, where the Hussites I spoke of recently came from, amazingly hold a St Andrew's night as well, which is very forgiving of them, I think. And in Saudi Arabia, they hold a St Andrew's night ball in Jeddah, but I don't think quite so much whisky is drunk at that one. Turning to, I suppose, slightly more serious matters, during my time as an MSP, I've spoken in many debates on St Andrew's Day and I argued before our position on making the day a full national holiday has been consistent and clear. And we've always been supportive of the desire to have St Andrew's Day as a bank holiday, but in exchange for another day, and not in addition to existing days, this was the approach adopted in the 2007 act, and we remain supportive of that. St Andrew's Day is correctly a voluntary public holiday, and this is what has happened. It is also what our Parliament does. Strangely enough, Eaton College celebrates St Andrew's Day as a holiday and has done so for hundreds of years. We didn't support the argument that St Andrew's Day must be a compulsory national holiday, as the cost of this inevitably falls on businesses, especially small businesses, and the taxpayer. CBI Scotland has in the past stated that more and more firms are moving away from closing on specified days towards a system where employees have an annual leave entitlement and decide for themselves in agreement with their employer when to take a holiday. We would be happy for employees to engage with their employers to discuss taking St Andrew's Day off instead of another holiday if this was appropriate, as it might be the case if the employer's spouse or partner or children have St Andrew's Day off. I just thought that the retail sector might benefit from a holiday at this time of year because it could boost sales leading up to Christmas. That is a good point. I agree with the motion that St Andrew's Day is a great opportunity to celebrate the diversity of our cultures and faith. We also recognise that tourism businesses can need extra promotion during the winter months, which is what my friend was talking about. We want to see a continued focus to boost winter tourism in Scotland. I am pleased that Historic Scotland offered free tickets to many of its properties on St Andrew's Day, and I paid tribute to all those enterprise businesses, shops and tourism enterprises in my region of the Highlands and Islands that seek to use St Andrew's Day to boost the trade. As a keen angler, I have always thought that it was very appropriate that our Scottish patron, St Andrew, was a fisherman from Galilee. I wish all those who have Friday off at St Andrew's Day that they have an enjoyable day and hope that some of them will do a spot of fishing or even enjoy some of our flesh-class shellfish in Scotland. We now move the closing speech from the minister. I want to congratulate Annabelle Ewing for bringing this forward, and then I want to congratulate her ministerial appointment as a colleague in government. I also want to congratulate Bruce Crawford for taking up the mantle somewhat last minute. I could think of no MSP more appropriate to have done so. I am delighted to be winding up this debate on behalf of the Government. I, too, am surprised at the lack of some opposition members here. Nonetheless, today's members' debate about St Andrew's Day being celebrated widely as a national holiday is incredibly important for a number of different reasons. However, I particularly want to pick up the point that Bruce Crawford and latterly Jamie McGregor mentioned about this being an opportunity to celebrate Scotland as an outward-looking nation that where Scots have travelled the world over, sometimes for good reasons, sometimes I would suggest when it comes to Jamaica probably not for particularly great reasons, but also a country that has opened itself up to migrants and been a welcoming country in that regard. St Andrew was the patron saint, as was alluded to by Jamie McGregor, of fishermen, fish mongers. I am certainly not looking at any members of this chamber, particularly behind me at all when I say that he was also the patron saint of singers, of spinsters, of maidens, of old maids, of women wishing to become mothers and perhaps a good thing for politicians, the patron saint for sore throats as well. Since then, it has been seven years since the Scottish Parliament approved the bill to have a national holiday on or around St Andrew's Day. As you know, since then, as has been mentioned, Scottish Government and public sector organisations such as Visit Scotland observe that holiday. Many local authorities do, but we hope more will take up that challenge. Indeed, the opportunity, as John Mason said, to take that holiday. You will also be pleased to hear that we have gathered some encouraging evidence that suggests that St Andrew's Day celebration is a gathering momentum. For example, in 2013-14, the Scottish Winter Festival's events recorded a total footfall of 257,884. That is an 8 per cent increase on the footfall the year before. The number of private sector organisations offering free or discounted entry on St Andrew's Day has increased 140 per cent between 2012 and 2013. Going back to Bruce Crawford's remarks about the global Scottish diaspora, it reminded me of a saying that you will have heard many a time. I am sure that there are two types of people in the world—Scots and those who wish that they were Scottish. It is estimated that, in that vein, there are 50 million people across the globe who claim Scottish ancestry. Many of those Scots and Scots at heart, wherever they are from in the world, from Beijing to Rio to Toronto to Brisbane, will be remembering and marking the national day. As they do, Hogmanay, as they do, burns night every year. People are quite correct to mention that St Andrew is also the patient saint of many other countries—Grease, Russia, Romania—and indeed, apparently, Barbados, which is fantastic. Although external affairs still comes into my remit, if the members of the chamber would want me to, and if I have to submit myself to the country to go on a fact-finding mission to Barbados in this regard, I am more than happy to do that. We are very much also working with our partners across the world to try to establish St Andrew's day as an important day to mark. I was delighted that we were working closely with the FCO, the Foreign and Commonwealth Office, to promote the celebration of St Andrew's day. I was having a Twitter exchange with the High Commissioner of Zambia, James Thornton, who was at the Caledonian ball to celebrate St Andrew's day just this week. Many examples, given by Jamie McGregor, were delighted that they are doing all that they can, and we are doing all that we can across the world to promote St Andrew's day. As well as members here who will be celebrating in their local constituencies. As the motion for this debate states, St Andrew's day is also an opportunity to celebrate the diversity of cultures, faiths and ethnic origins of this small country. I thought that Bruce Crawford made that point throughout his speech extraordinarily well. During this year, in particular, through all the events that we have had, including, of course, the Commonwealth Games, we have managed to bring those communities of Scotland closer together. St Andrew himself was an immigrant. He immigrated and travelled to many different countries—Ukrain, Romania, Russia, Greece and Turkey—amongst just a few. However, one of the programme of events that helps to celebrate that ethnic diversity on St Andrew's day this year is a fantastic event that is called the Multicultural Homecoming, which is being organised by Bemis Scotland, headed by Dr Rami Ousta and his team. That homecoming celebration is the finale of that homecoming celebration on St Andrew's night. The Cabinet Secretary for Culture and External Affairs will be representing the Scottish Government. I myself will be that day celebrating St Andrew's day with our vibrant Sikh community in Scotland. As we enter that winter festival season, it is important to remember that St Andrew's day is not the only celebration of these winter months. We have a fantastic programme where we will have Hogmanay a month later and then, as I say, Burns as well. I thought some of the ideas that came from the chamber on how we can celebrate it further and give St Andrew's day more prominence were very good ideas indeed. I think that Christine Graham has managed to volunteer herself with the saltire in her teeth to climb the ramparts of Edinburgh Castle to attach it on there. She says that if I get her the flag, she will do it, so I will certainly get her the flag, but I will also get a photographer on-site to capture that moment. On a very serious note on her point, I know that when I was in Stirling Castle most recently, the former First Minister had managed to secure the lion rampant flying for that for only the second time in 400 years. I am more than happy to explore the idea that she suggests and, indeed, even the idea with Google to find out if she will be advocating the saltire on her page. I am more than happy to ensure that we do that. It is my hope that our 2015 year of food and drink will sustain and build on the momentum generated by this year's homecoming and that all the chamber will be impelled to take part, helping to inspire the people of Scotland and our visitors to celebrate Scotland's outstanding natural lardar, to further develop Scotland's ever-growing reputation as a land of food and drink, and to promote and celebrate our nation's culinary achievements, not just on St Andrew's day but throughout the year. Perhaps the last thing that I would say is that there is a lesson in St Andrew's story for every single one of us. He was a man of great humility, as demonstrated even in death and persecution when he refused to be crucified in the same cross as Christ, so there are many lessons that we can learn in St Andrew's, but I think that the best lesson, as was said by Bruce Crawford, is that this is the national day that should be celebrated by all of Scotland's communities, but also all Scots who have chosen to make other parts of the globe their home. I hope that in that spirit of unity, in that spirit of diversity and that spirit of tolerance that each and every one of us has a very happy and enjoyable and festive St Andrew's day indeed. Thank you Minister, that ends members business. As the parties were so advised, we are moving straight on to the continuation of the


This Army presents The Big Picture, an official report produced for the armed forces and the American people. Korea today is paradoxically a house that stands divided. Slicing across the country is a narrow demilitarized zone, a bulwark of freedom for the people of the South. This DMZ strip and the freedom it protects were purchased at a cost beyond measure. Both are preserved by the continuing effort of men of many nations. Meet one now, Sergeant Clint Walker, just back from Korea. Let's talk off the chatter. Out of some of you men, this trip to Korea is just going to be so many months of drudgery. To others of you, it's going to be an introduction to a people and a way of life that you've never known. Now technically, the state of war still exists. You're being assigned there to maintain the truce and to make sure the war doesn't become a real one again. The way you will work and live will depend a lot on where you're assigned. There's a big difference between the forward areas and the rear areas such as around Seoul or Busan. But wherever you will be, it will take a man to do the job. Now we're stationed on a DMZ. It conditions all our thoughts and actions.  It is under constant patrol by United Nations forces on the South and by the communists on the North. Our forward units are composed of Americans with a few Catooses, Korean Army troops attached to the United States Army, some Turk and Thai troops, along with a rock army which covers over 80 percent of the line, and they are some of the best troops I've ever known, and we're lucky to have them. The rock army is the fourth largest in the world. It's tough, it's determined and alert. It's equipped with modern arms and ready for any emergency. Individually, the rock soldier is tough too. This is a form of judo called Tang Soo. It makes plain why the Korean troops are sometimes called hard rocks. You never get a chance to forget that the enemy is just across the ridge, and he's tough, but so are we. That's why you have to be ready all the time. Anything less than 100 percent qualification is just sticking your neck out. Your first warning of enemy action may come from an observation post to patrol, in which case you may have as much as an hour before the enemy troops could reach your battle positions, but you may be only seconds away from their artillery shells. So there are a lot of alert drills, and you will never know when it's the real thing. Because of this alert status, only a few troops can be away from the post at any one time, so the off-duty facilities are varied enough to suit everyone. Incidentally, a lot of you may find this a good opportunity to increase your education.  Because the Catooses will live and work with you, you will have a good chance to get to know them as individuals, but it may take time. Kim was a member of my squad. He was a good soldier, but I didn't really start to know him until one day we were making the courier run together. I was fresh out of the States, pretty green. I was getting near dusk, and we were climbing through some of those vertical mountains on our way back to the DMZ. Kim was driving, and I was riding shotgun. Suddenly, we began to look like a Stanley steamer, and I knew we'd had it. The old radiator had let go, and we were in the middle of nowhere, well, at least almost. Leaky radiator, no water. Without water, we couldn't get through the mountains before dark, and one of these villages didn't strike me as a kind of place to spend the night. After an eternity, he reappeared, and with reinforcements. The nice people, sure I like. You come from around here? No, my people live on the other side of the mountain, but many cousins on both sides. Kim, tell me, what was that stuff you put in our radiator? Oh, I bought more, like voice cars. Be prepared next time. It doesn't taste like flour. We call it Tapsakaru. Nice flour. Flour got good, so we get home. Have to clean out good, then. Or, Lieutenant, befriend me? Where'd you ever learn something like that? Oh, pick it up. When I was kid. You shouldn't figure on him teaching me anything. But what I learned from Kim that day was just the beginning of my education. That is, Sergeant. Sergeant Walker, you know why I sent for you? You proved yourself as a combat leader, and also you've taken a tremendous interest in the civic affairs of our area. I'm asking you to take on an additional duty. Yes, sir. So from now on, you'll be working with me as a member of the Community Relations Advisory Council. Thank you, sir. Now, you're familiar with our area, but let's take another look at it. You recognize this map, Sergeant? I think so, sir. Well, this map shows our sector of responsibility, the Imjin Meeon. A Meeon is equivalent to one of our counties at home. We have about 2,000 men to carry out defensive operations. Around us, there are approximately 10,000 people who live in these 16 villages. Now, obviously, it's terribly important that we maintain good relations with these people. I don't think we can know our Meeon too well. In the event of a shooting war, we have to know who to evacuate and who to arm. As a matter of fact, their good will and their active assistance may play a major role in our defense of this area. In a broader sense, Sergeant Walker, we must defend the free world by promoting democratic ideals right here in Korea. There was a lot of hard feeling last week in our advisory council over that Jeep accident. You remember that? Yeah, I remember it, sir. It was clearly a case of reckless driving, Sergeant, and the people in the village had every reason to get sore. However, after they learned that we don't condone such misconduct, that the man was punished, they were at least reassured that we had a sense of fair play. Yep, one eight ball, one careless stack, can last up our whole operation over here. Now, today, the shoe will be on the other foot. At our crack meeting this afternoon, we're going to take up the difficult problem of conditions in the villages. The village of Tongni has made a real effort to get rid of those undesirable elements that congregate around our camps. I want to give them all the help we can. You may have some ideas of your own. I have a few, sir. Good. Let's go. I've been to town before, but I've never go through it with such a sense of importance. The Honor Guard was sure to spit and polish, and I was proud that our outfit had helped with the uniforms. The representatives on the mayor's side included a merchant, the head of the orphanage, the minister, chief of police, the doc. Well, I suppose I'd seen all these people before, but they were just Koreans then. Now I was meeting them as people. Some of them I would get to know a lot better. Together, we, the leading citizens of the entire community, met to discuss its problems. Mr. Yeondae. Thank you so much for visiting our office today. Oh, look at this. The students of the school are drawing. Yes, this is the best way to do it. I gave them the first place. Colonel, it is my great pleasure to have you and your men visit us in my Myeon office today. You will see around us a picture made by school children for the safety campaign. It will be our duty later to select the best one for a prize. But the discussion didn't linger on the subject of art contests for children any longer than courtesy required. Once a friendly atmosphere had been established, the civilian representatives brought into the open the things which really concerned them. The practical everyday problems of community life. These embraced everything from relations with the armed forces in the area to general aspects of the local economy. And in a country largely agricultural, it is not surprising that one of the most pressing topics was one that happened to be right up Sergeant Walker's furrow. Well, sir, my folks are farmers back home, and I'm pretty well acquainted with this problem of a cash crop. What I think these people need is a more diversified farming. Well, now this may be way out in left field, but... Left field? What is left field? Well, that means a revelant. It doesn't make sense. It's just a baseball expression. Well, down south, I've noticed the farmers have livestock, and up here the people don't have much. Now, if we could start a program like, well, at the 4-H club, maybe we could not only increase the stock, but we could improve the breed. Before I knew it, I was a 4-H club expert, complete with members and livestock. We also managed to get some calves to improve the local stock. Well, I was really getting around the countryside, and Kim and I had become a pretty good team. Through Kim, I was getting a better look at Korean country life, but there was more to come when we went to Seoul. One of my buddies was stationed there as part of the United States Army Advisory Group, Korean Army, and Korean Army. He was one of a small group of Americans who were allowed to have their families with him. I was anxious for Buck Armstrong to meet Kim. Please come in, we're a little bit cool. Yeah, let's get out of here. Talk to how long have you been here? Long time. Ah, I don't know. Wow. Mr. Kim. Yes. How long have you been here? I've been here for 6 months. I've been here for 6 months. Ah, really? Yes. Nice to meet you. Thank you. For crying out loud, where did you learn this lingo? Oh, the language school, the army language school in Monterey. Anybody that's going to be over here on a long term has to go there first for some study. And then, too, it's a command order that all the two-year men here have to study on duty time. How are you doing, Kim? Very good. Why don't you all sit down if you're more comfortable? Oh, a little, that looks wonderful. Thank you. Oh, boy, you sure surprised me on this language bit. I sure wish I knew that much. Well, you'll learn some of it while you're here. After all, it isn't such a difficult language. Only just don't be too discouraged at first. After all, any attempt is better than none at all. Isn't that right, Kim? Just right. People will try to understand. And you know you'd be surprised how many Korean people can speak English, especially if they've been to high school. And they're always looking for a chance to try it out. A number of the fellas from the posts near Seoul are teaching English to small groups of Koreans. These are very industrious and ingenious people. You've probably noticed the many Jeeps converted into taxi cabs and even fancier bus bodies. They're old truck chassis, and the bodies are hammered out of discarded oil drums. Seoul was particularly hard hit during the fighting, and almost all manufacturing facilities were destroyed. These people have had to start over from scratch and are past masters at improvising all sorts of things from whatever can be salvaged. Most of Korea's industrial strength was originally in the north and is now in communist hands. Through American aid, many new factories are now being built in South Korea. There's also great emphasis on technical training, which can help raise the standard of living for these people. I've learned to admire the spirit of the Korean people. That may be because, in many ways, they're a lot like the Americans. My father is looking forward to meeting side and work, huh? Perhaps we go to it yesterday? I'm looking forward to it also, Kim. Like we were on our way there, Buck. I just wanted to stop by and make sure it was you. William, it's been great seeing you again. Well, it's been wonderful seeing you again, Cliff. Come back again. We will. You take care of this look, huh? Oh, I sure will. Come on, buddy.  But then he looked like a pig. Nice to meet you. My son speaks good language in the near future? My father says, that my brother has told us about your many goodies in the village near your camp. He is very proud to know you. Well, Kim deserves about half the credit for everything I do. He speaks to the people for me. Besides, I was enjoying myself. You are very modest. Some soldiers do not make so good impressions, trying to enjoy themselves. My sister is too serious. You see? What education does to a pretty girl? Forgive me, Sergeant. These have been difficult years for the girls to glove in. Many families do not allow soldiers to meet their daughters. It is a sincere compliment to you that my father has allowed my brother to bring you home. I also am happy that he did. I understand. But I hope that you will help Kim show me around your town. A model is of another generation. I will be glad to go with you. If you will excuse me, I will change to street clothes. After the discussion at Kim's house, I felt pretty privileged at having a queen like his sister showing me her city. I found that her education, far from ruining her, had made her a very mature and attractive girl. She understood both her own people and the tremendous changes that the war had made in their lives. These solid old rock walls once held out in vaders, but that was long ago. They are capital cities only minutes away from the communist jet airfields. Gates and walls have lost their protective strength. Most of our homes were destroyed in the bitter fighting that led the full length of our country. Over three and a half million refugees pulled in from the north. But now great progress has been made in health programs and in new housing projects. But perhaps the most significant progress is being made in education. That is why I am so proud to be a teacher and have a part in building the future of our nation. Here is where I work with 80 little girls and boys trying to help them learn all the things they need to know to become our future citizens. Sometimes I can take them to the shrines where the past greatness of our country can be remembered in the beautiful palaces of ancient rulers. Scholarship is one of Korea's finest traditions. In the 15th century, one of our scholar kings developed a simple alphabet and began one of world's first encyclopedias. As a matter of fact, Koreans invented movable metal type at least 50 years before anyone in Europe did. Today this hungle alphabet serves as well since it is written across the page instead of down like other Oriental characters. Now Koreans can read many books in their own language. There are also many universities, 20 future teachers and other leaders for our country. There are yet many problems to be solved but we trust with friendly understanding that your people will take from Korea memories of what is best about us. Just as we will remember the great strength and the kindness that is America. Miss Kim, my friends in Moonsanee and perhaps most of all Kim himself had opened for me a side of Korean life which I would have never appreciated had I stayed in camp and I was grateful for it. In spite of the hardships there are many opportunities in Korea. Whether you are stationed with a Korean people or on the DMZ, be a good soldier. Live up to your responsibilities as a citizen of a most fortunate country. Democracy protects individual liberty but it will only protect us so long as we protect it for all men everywhere. The Big Picture is an official report for the armed forces and the American people. Produced by the Army Pictorial Center Presented by the Department of the Army in cooperation with the State.


This is going to be a joint work with my colleague, David Gossett, who is an organizer of this conference and Robert Koenig from the University of Munich. And so let me begin with some motivation for why we are interested in shallow circuits. And suppose we want to build a quantum computer using noisy qubits and noisy gates. And then basically we have two options. Option one is to encode each qubit using some quantum error-correcting codes, say the surface code, and perform logical gates on encoded qubits. Then they know that in principle we can perform arbitrarily long computation as long as our error rate is below some constant free-shot value around 1%. And option two is to apply gates directly to physical qubits without error correction. And this completely avoids the quantum fault-orderance overhead that can be quite large. But now there will be a certain limit on the maximum size of a computation they can do. And the first approximation we can use this rough estimate, and basically it says that the average number of faulty locations in our circuit is upper bounded by inverse error rate. And so the total number of locations that can potentially be faulty is just the number of qubits n times the number of computational step d, or circuit depth. And so n times d is upper bounded by inverse error rate, and this is a constant, but hopefully this constant can be quite large, perhaps 1,000 or even 10,000. And somehow this bound leads to interesting trade-offs. So we can try to do very long computations described by deep circuits, but then we can only afford a few qubits. And of course any quantum circuit acting on a few qubits can be efficiently simulated on a classical computer. So in some sense this is a boring regime. Alternatively, we can consider shallow circuits with a small depth, and now we can afford much more qubits, perhaps 100 or something of this order. And it is strongly believed that such circuits are impossible to simulate classically. So the question is whether we can realize any useful computation using shallow quantum circuits. And so the study of shallow circuits was pioneered by Barbara Terchel and David Devenchampso back in 2002 when they were here at IBM. And they gave convincing arguments showing that even constant depth circuits with depth 3 or larger are hard to simulate classically. And quite recently people developed some ideas of what can we do with shallow circuits. So we have heard from Eddie Talk about approximate optimization algorithm. And if we apply this algorithm to problems such as Max-Cut on bounded degree graphs, it can be realized by constant depth circuits. Then we can try to do variational quantum eigen-solver. And this may have applications in quantum chemistry simulations. And quite recently there was a lot of work on complexity of sampling problems that we can realize with constant depth circuits and for indications that somehow such sampling problems are hard for classical computers. So we can achieve this quantum supremacy. Now if we increase the depth from constant to something logarithmic in the number of qubits, we can do much more interesting things. For example, if we allow ancillary qubits, we can realize a short factor in the algorithm. And we can implement any circuit composed of Clifford group gates. Then there are interesting variational states called Mera that can be prepared with logarithmic depth circuits. And this Mera states is a good approximation to ground states of gapless spin systems. And perhaps we can even study, we can learn something about quantum gravity. In particular, it's known that random logarithmic depth circuits exhibit a property called information scrambling and these reminiscence of dynamics describing black holes. And of course, if we allow depth polynomial in the number of qubits, we basically have universal quantum computer. So we can realize anything in BQP. In this talk, I will restrict myself to constant depth circuits. And so let me start from some terminology. So a circuit of depth D consists of D time steps such that each time step is a product of these joint gates. So this is an example of depth five circuit composed of two qubit gates. And so this circuit has some classical input and classical output. And say input is just k bit stink and we initialize the first k qubits in 0 or 1 according to this input stink. And there could be some ancillary qubits that we initialize in 0. And at the end of the day, we measure some subset of qubits in 0, 1 basis and this defines output stink of the circuit. And so the main object we are interested in is this output probability distribution. It tells us what is probability of observing some output Z provided where the input is x. And so what I mean by constant depth circuits is actually an infinite family of such circuits parameterized by number of qubits n. And the depth of the circuits is bounded by some constant independent of n. And I'm going to consider a fixed gate sets also independent of n. Now I guess the most important question is there's a constant depth quantum circuits can outperform classical computers. That is solve some problem which is hard for polynomial size classical circuits. As I said, we believe that probably the answer is yes, but we cannot hope to get unconditional proof. Because if we can prove that the answer is yes, we can separate complexity class BQP from the class BPP which would imply some major breakthroughs in classical complexity theory. For example, we would separate p-space from p. And somehow here we ask perhaps a simpler question. We ask whether constant depth quantum circuits can solve some computational problem which is hard for constant depth classical circuits. So we are comparing quantum circuits and classical circuits, but in both cases we restrict to constant depth. And we will see that this is a much simpler question. But it turns out that the answer depends on what exactly do we mean by a computational problem. And usually in complexity theory people study decision problems. So what it means is that input of the problem is some b string x and output is just a single bit z which tells whether x has or doesn't have some property. But it's not hard to see that if a constant depth quantum circuit can solve a decision problem, it can also be solved by a very simple classical circuit. And basically we can use causality to show that somehow this output bit z can only depend on a constant number of input bits. So you suppose we have some constant depth circuit Q that solves a decision problem and then we can compute probability distribution of z by measuring expectation value of some single qubit observable or say acting on the first qubit on the final state produced by the circuit. And so this expectation value is given by this equation. And so you can see that this operator, well if u is a constant depth circuit this operator acts only on constant number of qubits. So this is some quantum circuit which has only constant size. And of course we can simulate it by a classical circuit of constant size. So somehow for decision problems the answer to this question is no. And so next let's consider search problems. So here the input is still a b string but the output is not a single bit it could be a set of some n bit strings. So for each input there are many possible outputs and each output is a bit string. And one example of such search problem would be a combinatorial optimization like solving a three set problem. So here input x describes some system of equations with binary variables and a set of solutions z is just a set of bit strings that satisfy all equations. So these search problems appear naturally in many areas. And we can say that a quantum circuit solves a search problem if for any input x it outputs a valid solution perhaps with some small error probability epsilon. So we want to have this condition for any input x. Remember that this thing is the output probability distribution of the circuit. And so this is a summary of our results. So I will show you one example of a search problem that can be solved with certainty by a constant depth quantum circuit. And moreover this quantum circuit only requires nearest neighbor gates on a two dimensional grid of qubits. On the other hand we prove that somehow if some classical circuit solves this problem with non-negligible error probability such circuit must have logarithmic depth. So in the quantum case the depth is constant and in the classical case it's at least logarithmic. And in the classical case somehow we allow arbitrary gates to have to be nearest neighbor or geometrically local in any sense. But as usual there is some fine print. You can probably not read this. But what it says is that this problem can be solved classically in polynomial time. So somehow we don't achieve quantum speedup similar to Schur's algorithm. But this is a quantum advantage if we restrict both quantum and classical to a constant depth. Anyway, and this is the plan for the rest of my talk. So first of all I will formally define this problem. We call it hidden linear function problem. Then I will show you a constant depth quantum algorithm that solves this problem. And in the rest of the talk I will sketch the proof that basically gives you a lower bound on the depth of a classical circuit that solves this problem. Okay, so let me define what is hidden linear function problem. So suppose we are given some binary matrix A and it has to be symmetric. Then we can define several things. We can define null space of this matrix. And this is a set of n-bit strings that are annihilated by this matrix modulo 2. So just the usual null space, but it's defined modulo 2. And we can define a quadratic form. So here we take the argument of this form is n-bit string. So these variables are binary. And so here I use matrix vector notations. So x is column vector and this is x transpose is a row vector. And for technical reasons I evaluate this form modulo 4. Now let me just illustrate this by example. Suppose we have three variables and we have this symmetric binary matrix. Then what is the null space of A? Well, we have to solve this system of equations. And well, it's not hard to check that the null space consists of all zero vector and all one vector. And the quadratic form associated with A would be given by this equation. So this x1 and x3 comes from diagonal matrix elements. And because x are binary variables, say x1 is the same as x1 squared. And the purpose of this example is to illustrate one distinction between real-valued quadratic forms and binary ones. So say if x is a real vector which is annihilated by A, then of course this quadratic form evaluates to zero. But surprisingly, this is not the case for binary quadratic form. Say if you look at this example and we pick x as all-month vector, then this quadratic form evaluates to something non-zero. And more generally, one can easily show the following property. If we take this binary quadratic form and restrict it to null space of A, then we get some Boolean linear function. So more precisely, we can represent q of x as 2 times some Boolean linear function L of x, and this is true for all x in the null space of A. And any Boolean linear function can be parameterized by this secret bit string z. So the linear function is just in a product between z and x, up to this factor of 2. And the problem I'm going to consider is defined as follows. The input of the problem is a binary symmetric matrix A of some size n, and the output is just with a secret bit string z. So we ask that if we restrict this quadratic form to the null space of A, then it coincides with linear function just in a product between x and the secret string z. Yes, so this is the problem that I'm going to consider. And the first thing we can note is that for a given matrix A, there are many solutions z. Say if z is one solution, we can pick any vector of y from the binary orthogonal complement to the null space of A, then z plus y is another solution. So this is what I call a search problem. For a given input, we have multiple solutions z. And another property is that this problem can be solved classically in polynomial time using just basic linear algebra. Say we can first compute a set of basis vectors for this null space of A, and then we just need to solve a linear system of equations modular too. So it turns out that this problem is closely related to this Bernstein-Vazirani problem. And in the Bernstein-Vazirani settings we also have some hidden linear function parameterized by a bit string z. But this linear function is given to us as an oracle. And the oracle implements this unitary operator. So here the goal is to find this secret string z using as few queries to the oracle as possible. And in the quantum case, we can find z using a single query. We just need to implement this simple quantum circuit. But in the classical case, we need to evaluate this linear function at least n times to learn z. So the only difference between our problem and Bernstein-Vazirani is that in our case there is no oracle. So the linear function is specified by this quadratic form. And the quadratic form is given by a list of coefficients. And I'm going to consider a certain restricted version of this hidden linear function problem defined on a two-dimensional grid. So we assume that these variables x live at sides of a two-dimensional grid with n sides. And matrix A basically is adjacent to matrix for some subgraph of the grid. So we only allow non-zero matrix elements if i and j are nearest neighbor sides. And then non-zero matrix... non-zero of diagonal matrix elements correspond to some subset of edges of the grid. And non-zero diagonal elements correspond to some subset of vertices of the grid. And so in the rest of the talk, I'm going to consider this two-dimensional version of the problem. So next let me show a quantum algorithm that solves this problem. And the algorithm is actually quite simple. So we are going to have two registers. One register consists of n qubits and it's initialized in zero state. And the second register is basically classical and it stores the input matrix A. And then we implement this quantum circuit. So we have layer of Hadamars and then we have a layer of CZ gates. But each CZ gate controlled by this classical register. So if we have a pair of qubits i, j with non-zero matrix element of A, we are going to apply a CZ gate. And then we do similar layer of control S gates. So for every qubit with diagonal matrix element of A equals to one, we apply the S gate. And finally, we measure each qubit in zero one basis. So we get some output and bit string Z. And what we can show is that this Z is always a solution of the hidden linear function problem. And moreover, the output distribution of this circuit is the uniform distribution on the set of all solutions. And so you can see that the gate set used by this circuit consists of only of Clifford gates. But most strictly, these are classically controlled Clifford gates. This is not too important. And moreover, all gates are geometrically local on a two-dimensional grid. So we only use nearest neighbor gates. Now, let me give you some intuition why this algorithm works. Well, it's not hard to compute the output distribution and it turns out to be given by this equation. So it's Fourier transform of a phase function controlled by this quadratic form. And this is very similar to output distribution of IQP circuits that we saw in Michael's talk on the first day. And using the fact that QFX is a quadratic form, one can show that basically we can restrict this sum to new space of A. And if x belongs to the new space of A, we know that this quadratic form becomes some linear function L of x. And this expression looks very similar to output distribution of the Bernstein-Wazirani algorithm. So basically if z is not solution of the problem, some terms in this sum are plus one, some terms are minus one, and you have cancellations. So the sum evaluates to zero. But if z is solution, then you have constructive interference and the probability is not zero. Now let's move to classical circuits and just some terminology. So a classical gate basically computes a Boolean function. So we have some number of input bits k, which is called fan in of the gate. And we have some number of output wires called fan out of the gate. And the function computed by the gate is copied to every output wire. And I'm going to consider circuits with bounded fan in. So the number of input wires is bounded by some constant k. And a depth D classical circuit basically consists of D time steps. And like in this example, we have just two time steps. And each time step is a product of this joint gates. And so this is our main technical results. So this gives a lower bound on the depth of a classical circuit that solves two-dimensional instances of the hidden linear function problem. And this bound grows logarithmically with number of qubits n. And this constant depends only on fan in, which is some constant. Now, here I'm considering probabilistic circuits. And what it means is that the circuit takes as input this binary symmetric matrix A and some random bit strings are, which can be drawn from some arbitrary distribution. And then we apply some sequence of gates. And what we can show is that if the output of this circuit is a solution of the HLF problem, this high probability then the depth of the circuit must be logarithmic in n. Sorry, this capital N should be actually little n. And to prove this result, we exploit the fact that input-output correlations of this HLF problem exhibit quantum non-locality, which is very similar to quantum non-locality in Bell experiments or JHD experiment. And on the other hand, we will show that classical circuit will input-output correlations of classical circuits cannot somehow achieve this form of non-locality. And the proof proceeds in several steps. So I will start from completely local classical circuits, which are basically local hidden variable models. Then we shall consider classical circuits with geometrically local gates. And then finally, constant depth classical circuits. And just let me give you a few definitions. So suppose we have classical circuit with some inputs x and some outputs z. Then we can look at some output bit and find all input bits that are causally connected to this output. So this subset of input bits is what I call the light-con of this output bit. And in a similar fashion, we can look at some input variable x1 and consider a set of all output bits causally connected to x1. So this will be the light-con of x1. So let's start from completely local classical circuits. And I'm going to use this jg-type relation. So suppose we have a classical circuit, these inputs x1, x2, x3, and outputs z1, z2, z3. And suppose that input-output correlations of the circuit are there with jg-t relation. And here I assume that output variables are plus minus one instead of zero one, but it's not too important. Then what can we say about locality of such circuit? They're known that it's impossible to satisfy with jg-t relations using these local hidden variables. And what it means is that each output bit is a function of the corresponding input bits and some shared random variable h. And more generally, one can prove this result that if a classical circuit obeys this jg-t relation with high probability, then the light-con of some input bit must contain a distinct output bit. So in that sense, the circuit cannot be completely local. On the other hand, if somehow we allow shared entanglement, we can just take 3 qubit jg-state distributed between these three parties, and then each party measures its qubit of jg-state in either x or y basis depending on the value of the input variable. And one can check that the measurement outcomes always satisfy this jg-t relation. So in that sense, quantum non-locality bits are completely local classical circuits. And in the following, I will consider more complicated relations like this one. And I will write such relations in a compact form. So we just have some relation that depends on inputs x and output z. And we want it to be satisfied if input bits sum up to 0, modulo 2. So let's move to geometrically local classical circuits. And instead of jg-state, I'm going to consider these graph states defined on a cycle or a ring of n qubits. So we start from O0 state, apply a layer of Hadamars, and then we apply a CZ gate for each nearest neighbor pair of qubits. And now I define certain pattern of measurements on this graph state. So I'm going to pick some triple of qubits, u, v, w, that are measured in either x or y basis. And all remaining qubits are measured in x basis. So this defines these input-output correlations. So I have three input bits that determine measurement basis at u, v, and w. And I have n outcomes z that determine measurement outcomes on all n qubits. And we are going to use a nice result from this paper by Barrett et al. So they showed that these input-output correlations obey a certain relation, which is a generalization of jg-state relation. And I'm going to call this a cycle relation. And this relation, I'm not going to write it down explicitly, but the rough intuition is that if you can see the reduced state of qubits u, v, w, after all other qubits have been measured, this is actually the jg-state. And there is some power correction that depends on this measurement outcomes z. So what we can show is the following result. So suppose we have a classical circuit that satisfies this cycle relation with a high probability. Then we can find some input variable xi, such that its light cone contains a distant output variable. Say this could be x, y, could define measurement basis for this qubit. Then its light cone would contain some remote output variable. Now, how is this related to our hidden linear function problem? So let me remind you this quantum circuit that solves a HLF problem. And you can think of the first half of the circuit as preparation of a graph state defined on a certain graph depending on A. And this is basically the graph with adjacency matrix A. And you can think of the second half of the circuit as a bunch of single qubit measurements, and we measure each qubit either in x-bases or y-bases depending on the diagonal matrix element of A. So this is actually very similar settings to what I showed you before in this one-dimensional graph state. And because we are free to choose this adjacency matrix A as we like, we can choose it as adjacency matrix of one-dimensional cycle embedded in this grid. And we can choose diagonal matrix elements, such that we have this triple of qubits, w located on this cycle, and these qubits are measured in either x-bases. So if you have some classical circuit that solves all two-dimensional instances of the HLF problem, it must also solve all instances of this one-dimensional cycle problem. Okay, and finally, let's consider general constant-depth classical circuits, and such circuits have the property that the light-con of each output variable contains a constant number of input variables, because the circuit has constant depth and each gate has constant number of input wires. And we use this property to prove the following result. So suppose this classical circuit has depth sufficiently small, then we can find some triple of vertices on this grid, u, v, w, and we can find a cycle gamma that passes, that contains u, v, and w, such that light-con of input variables associated with u, v, and w do not contain any output variables that belong to gamma and are located far from u, v, and w. And basically this property implies that such classical circuit cannot solve, cannot satisfy this cycle relation on this red cycle. And this implies that it cannot solve all instances of two-dimensional HLF problem with high probability. So this basically proves the desired low-bound on the depth of classical circuit. Now I want to conclude with some open problems. So as I mentioned, we know that this HLF problem has polynomial time classical algorithm. And basically one way to get such algorithm is just to classically simulate a quantum circuit that solves the problem. So the quantum circuit uses only Clifford gates, and we can simulate it using, say, Aronson-Gottesmann algorithm. And using the fact that all gates are nearest neighbors on a grid, you can do this simulation in time n squared. On the other hand, the quantum circuit has a constant depth, so it runs in time linear in n. And we conjecture that actually n squared is the best classical algorithm that we know. So it's possible that we actually have a square root quantum speedup for this problem. Then you can ask whether this quantum advantage that we observed is robust to noise. And for HLF problem defined on a grid, the answer is probably no. But it would be interesting to consider the generalization of this problem defined on other sparse graphs. And you can also define, well, the question is whether we can define the generalization of this problem by replacing a quadratic form with some more general function, say, cubic polynomial. And yes, so there are interesting open problems related to this complexity of sampling. So if instead of considering all possible inputs, we can try to restrict the circuit to a single input and ask whether we can sample the output distribution using constant depth classical circuit. And let me conclude here. Thank you for your attention. Questions? Is this working? Good. So thanks for the talk. It's like a very beautiful result. I wonder if the original work of Barrett has sort of this connection to bounding the communication in these non-local correlations. Is there a way to turn this into one of these classes of Bell inequalities with communication? So we write down a normal Bell inequality says local hidden variables won't work. Is there a way to immediately take this and sort of write down an experiment that people can run that sort of say that in order to simulate that experiment there'd have to be this much communication? Yes, so I think this was the motivation for this work by Barrett at all. And we tried to, as you said, we tried to generalize local hidden variable models to the case with some bounded communication. And so this cycle relation is basically a generalization of the Bell inequality to this setting. So I guess you probably, I think in that paper they had to restrict their classical communication to the nearest neighbors. And your result sort of implies that a model where you can broadcast actually can still result in that. Is that correct? Yes, I think you're right. Thank you. Other questions? I have the mic. Is this working? Yeah. So you show that classically this problem is in polynomial time and there's an n-squared time algorithm. Do you know what is the smallest classical complexity class into which you can put this 2D HLF problem? Like is it in log space or something? Well, it's basically it amounts to solving a system of linear equations modulated to. So I don't know the answer to your question but my conjecture would be it's probably in NC class because we know that linear systems can be solved in NC. We have time for one more question. Okay, so another question. Let's thank Sergey. Okay.


When we talk about the other side, the Seattle Seahawks, there's a lot that went wrong in this deal form for fantasy purposes. DK Metcalf's value went from probably a wide receiver one to more wide receiver two-ish, mid to low end wide receiver two. If Drew Lock happens to be the quarterback this season, the Seahawks did get first round picks, so they probably are gonna invest in a quarterback. I anticipate Drew Lock to at least be starting a few games early on in the season. Tyler Lockett's value is now at a wide receiver three, putting him in the boomer-bust category when it comes to wide receivers. No longer having that deep arm. Russell Wilson there, the dependable arm, now gonna have Drew Lock or potentially a rookie coming into the fold. No offense, it's gonna remain about the same. Mid to back in, tight end one there with the Seahawks, but they did get him, they wanna use him. We'll see what his value is.


Yn 2014 ac 2017, rydyn ni wedi'i gweld y projech yn ymddiadau ar ysgolwyddiadau, sydd wedi'u gwneud y cyfnodau a'r legosi yng Nghymru yn ymgyrch, ac mae'r ffyniau yn ymgyrch yn ymgyrch. Yn ymgyrch ymgyrch yn ymgyrch yn ymgyrch yn ymgyrch yn ymgyrch, mae'r ffordd yma o'r model ymgyrch yn ymgyrch yn ymgyrch. Nid ymgyrch yn ymgyrch yn ymgyrch yn ymgyrch yn ymgyrch dan 19 yr ymgyrch yn ymwyf yng nghymru, ac mae'n gwneud ar gyfer yr ymgyrch yn ymgyrch gan ymgyrch yn ymgyrch yn ymgyrch, mae felly mae o'r fewau i'ch vinell. A ymgyrch yn ymgyrch yn ymgyrch yn ymgyrch yn ein bethau, ynglyn â gydych chi'n amli gwych hefyd, ac allan yn ymgyrch yn ymgyrch yn ymgyrch yn ymgyrch yn ei ffyniadau. Byddwch yn y cyfnod y gweithio y ffordd ar y cyfnod, byddwn ni'n meddwl ydy'r 350 ymgyrch yn 27 ymgyrch yn 5 ymgyrch yn ymgyrch ar Ymgyrch Egynfod Argyllidol. I should emphasise that such a widespread distribution of archaeological finds does not reflect an inherent interest in the ancient Egyptian past. Bear in mind that much of this material being sent out is pottery, pottery fragments, bronze fragments, small amulets. Instead, it reflects far more recent geographies of cultural authority, power and knowledge. So, in trying to look at the history of these collections, and I'm particularly interested in finding out why would Japanese universities want Egyptian objects? Why would they end up in Ghana? Why would they end up in Canada? I've tried to establish a far greater sensitivity to the historical conditions that shape and enable these interests. So central to my argument is something that we've termed the object habit. This is basically a shorthand for referencing society at large's interest in things, its attitude to material culture, affecting what got collected, when and why. So in other words, it's not just about museums and their ideological practice or their agents, and it's not just the intellectual thrust of archaeology as a discipline establishing object value. Both of those exist not on a vacuum but in society, and how does society, what does it make of things? And so in order to kind of try and demonstrate this point in the short time I've got here, I want to compare and contrast two periods in Britain's collecting. On the one hand, an almost insatiable desire to acquire Egyptian archaeological finds between 1880 and about 1925-1930. And then contrast that with an increasing disinterest and indifference towards antiquities after the Second World War. It's a really profound change coming with modernism and futurism. And at this time we see collections being disbanded and dispersed and I want to try and explain why. So starting in 1882, this is the founding of the Egypt Exploration Fund and this is the newspaper headline announcing the founding of the organisation. And you can see the title there, Egyptian Antiquities. That's the draw, that's the interest. The rhetoric within the column is appealing to biblical and classical narratives. It's within wider trends, imperial and colonial rhetoric around preservation. And you can also see in their names like H.R. Lainard who of course was famed in the 1850s for his work at Nineveh and which provided the British Museum with a wealth of monuments. And clearly that headline is hoping to reflect that ecology of images in the Victorian public's mind. But the very last line of that column says it must be distinctly understood that by the law of Egypt no antiquities can be removed from the country. So how come all of this material ends up leaving Egypt? Now this is quite a complex story, I'll just give you a very brief overview. Partly you could say from an intellectual point of view it's Flinders Petrie. That archaeologist that we line eyes for promoting the value of the small and the everyday signs. And that his interest is in contrast to those Egyptian antiquities laws which more readily recognise the colossal, the monumental and the unique as subjects for state control. But it's not just the essential qualities of things here. This is opportunistic. And Petrie has to negotiate value of these objects with Gaston Maspero, the French head of antiquities in Egypt. And this is a letter from 1883 where they negotiate partage whereby Egypt can retain first choice of objects and the foreign excavator can then remove objects from the country. And Petrie essentially argues that these trinkets, trifles and ornaments, they're of no interest to Egypt but they will be of value to collections in England. So we've got mechanisms for moving objects out of Egypt and we've got an indication here of the context in which they are then absorbed which is the rise and development of museums across Britain. The Egypt exploration fund was founded at a time of peak growth of regional museums so beyond the British Museum there's now a whole host of other institutions more than willing to have less than monumental pieces of Egyptian culture and that's largely because of industrialisation. So there's a broader society context we have to understand. And so several industrial town museums were putting on displays of modern equipment, modern technologies of production and the ancient finds that Petrie is bringing out resonates with that. So somewhere like Sheffield which is an iron producing town is absolutely thrilled by the offering of four iron knives, a nail and an iron hook. Thrilling. So you've got mechanisms for objects coming out of Egypt. You've got new context for their absorption. But why would the Victorian public care? Why would you even want to see these small and incidental finds? Well for that we have to look far more broadly at the Victorian attitudes to things and those attitudes had also been shaped by industrialisation especially from the 1880s onwards as tastes were nurtured by developments in advertising and department stores. And so within Victorian affluent Victorian homes we've got domestic spaces becoming more museum-like.  But the key thing is that these collections in Victorian homes they're not just about showing off status. They are absolutely vital to understanding in the Victorian world. I just point you towards the literature of the period. Take Ryder Haggard for instance, famous Victorian author. His novel She has 12 pages devoted to describing single pottery shirt. Objects in these tales are fetishised as sources of power and meaning. Even a fragment or small relic offered a seductive possibility of an unmediated connection with the past. And this power of objects to tell and reveal things permeates all areas of life. Sunday schools are desperate to get small museums and collections because objects are stamped with divine approval and authority. Other schools are trying to create museums themselves if you're really rich like the private school of eating you can fund the Egypt exploration fund and get original objects. So we start to see that this period is more than just an epistemology of things. People like Chris Gosden have argued that knowing the world was mediated through objects but I would argue it's far deeper seated than that. There's a greater ontological value in things in this period than if we contrast it with what happens after the Second World War. Now the physical devastation by the Second World War across Europe was only one of the threats faced to collections. Far more insidious was a widespread society change in attitudes to things. And I'll just give an example. Flinders Petrie's wife in 1949 writes to dozens and dozens of UK museums offering material that before they had been keen to acquire and every single one declines. Curators replied that interest in archaeology is long dead. There's no public interest. But actually most telling is the fact that as Britain's empire fragments after the Second World War the ideology of expansion precedes regional institutions start to define themselves far more closely by their regional collections. They're not interested in exotic antiquities from elsewhere. Fortunately I suspect we're seeing similar trends today. But not only are museums not collecting this material anymore they're getting rid of it. They are thinning of their displays. They don't like this clutter anymore. Quick examples here are UNESCO putting out rhetoric museums association saying clear out the clutteration of your collections make your museums bright and cheerful. This new rhetoric is not just an initiative of the museum sector. It's far more broadly and I'll just mention two factors briefly. First, modernism. Now modernism had taken root on the European continent in the early 20th century things like Le Corbusier's machine for living in, shoes ornaments. We don't want fussy. We don't want clutter. And Britain lagged behind those developments until the Second World War when rationing and post-war austerity cemented a distaste for ostentatious display. And we get a wider embrace of continental trends.  After the bleakness of war this is a promise of a fresh aesthetic. Decluttering was as much a general shift in society as it was the result of the internal dynamics of museum practice or the disciplinary focus of archaeology which itself had stopped being as interested in objects as new field techniques were taking off. A second broad trend that undermines the status and antiquities in museums is the rise of the post-war future boom. Nuclear science, the Cold War Space Wave Wraith and other sorts of big science enterprises were catalyst to a widespread interest in the future on its visual high tech iconography. Now I should emphasise that this scientific mindset it's nothing new. The Victorians were very interested in the future but it was far more strongly grounded in the historical field. I'm thinking for example of pit rivers and sequences of objects from primitive to complex. So those sorts of cultural evolutionary ideas were based on incremental change and it could be mapped out using well-ordered museum collections. But the science boom of the 1950s that meant that instead of collection and enumeration its experiment and theory that are now considered fundamental to understanding. And so we've got a widening conceptual difference between the past and the future that renders the past totally foreign. So just to end with one final, more positive perhaps note these objects can be repurposed because we've got quite dismal picture here and many of the objects that were disposed of from museum collections in Britain ended up in decolonising nations like Ghana. On the eve of independence in 1957 the National Museum of Ghana opened using a vast array of objects collected including Egyptian objects particularly because they were seen to tap into narratives about a glorious pre-colonial Ghanaian past and that was seen to emanate from the civilisations of Egypt. And that was important also to the modern politics at the time where the leader Kwame Nukrumun's radical pan-Africanist politics were attempting to overcome tensions, national identities, royal authorities and other local issues. So for example we've already heard about the Aswan mission by UNESCO this is an example Ghana got involved and here's a series of stamps produced in 1963 juxtaposing Egyptian monuments with the Ghanaian flag in effect putting Egyptian royalty next to Ghanaian nationalism. Now I don't have time to unpick all the other nuances in these histories of collections so if you'll forgive me a horror of blatant plug for my forthcoming book Scattered Fines that should be out in January will be free to download. So just in closing I think it's suffice to say that when we're examining these histories of collections I think it's not just about trying to understand where objects come from to give us more insight into the ancient past. They are much more likely to provide us insight into more recent and contemporary worlds as they are for any ancient reality. Thank you very much.