This meeting's not just about giving you kind of the good things going on public safety. We want to talk to you about some of the challenges as well and we're going to hit some of those challenges today. But before I begin with talking about one of the challenges we want to talk about is I want to give you an update on the chief of police search and where we are with that at this point. I have this week literally met with over according to individuals have been with me and also talking to the PPA. We believe I've met with at least a third of all sworn workforce at this time. I have another roll call to go to today and I'll be meeting with sworn and civilian employees later this afternoon. It is extremely important for me as a director of safety and leading the search effort for the mayor to make sure that we hear from our employees. Those employees are on the roads every day. They're in the communities every day. They know what issues that we're facing. We need to know what they want their police department to do in the future and also need to know some of the challenges that they think that they have during their jobs and how we can help them with their jobs and what they're looking for in their next police chief and how that chief how he or she could help them be successful. Also equally important actually more important because we take an oath in all of our departments specifically this time the police department to serve the public is will be having four community meetings. These meetings will be announced. I'm hoping to begin those meetings the week of the 14th. But some of this is still in the work. So please if that changes we will let you know but hopefully we can have the first meeting the week of May the 14th. We're working on locations now and we want to think it was important to have a facilitator someone that is trained in facilitation that can get to the certain points and to get community input and understanding of what once again communities are facing what issues they'd like to see their police department address any challenges that we need to address and moving forward. So those meetings will be forthcoming. How this process is going to work is that the information received from the community meetings and the information received from our employees will be reviewed. It'll be reviewed by me. It'll be reviewed by some others. It'll be reviewed by a third party that I'll talk about in a moment. And we will develop questions during the interview process. Some of the questions will be directly from the community and from the workforce. The priority is going to be as if we see the community is saying something at every one of the meetings and it's a continual theme. And we're also hearing it from our internal personnel. Certainly that's going to be a question. If we see a continued theme throughout the community that is certainly going to be a question that we pose to applicants for the position of chief of police. It's important to me to do that and to include the community and their voice and their questions because that police chief is responsible to the mayor and myself. But ultimately he or she is going to be responsible to the citizens of this great city. So with that said talking about the mayor is establishing a panel and it's going to be approximately 14 to 15 individuals that panel will be announced by the latest early next week. I am in the process of doing some follow up calls with them today and tomorrow. I'm about halfway through and I want to make sure that they understand the process thoroughly and that they're still on board to participate in reviewing the applicants. The posting for the position will go out sometime next week. Are we still in line for that daily. So sometime next week it will simply consist of a resume and a position paper. The position paper will be based on a question that we will ask each applicant to answer. Those resumes and position papers will then be forwarded. Hopefully we're working on this process today. We had some phone calls this morning on a potential third vendor an outside party that will receive all applications and all resumes. We're looking at a couple of vendors right now. Both of them have extraordinary records of finding doing searches across the nation. And let me be clear they are not handling the search for us. We are only taking applications from within the Denver Police Department or individuals that have retired. But what I want them to do is bring their national expertise and looking at the resumes looking at the background doing anybody looking at the position papers doing anything they think they need to do the properly vet. But my request to them is simply going to be this out of the applicant poll that we receive. Give me individuals that would be competitive for any national position of chief of police. So any major city across America I want the people that we review. I want to know that they would be competitive in any process across this nation. I say that with confidence that we have a tremendous amount of people with that background and the ability to run this police department and having a third party that does this constantly that is reviewing candidates on a daily basis fulfilling some of the largest cities police chiefs needs. I think it's important for us to have that third party in that perspective as well in ensuring that our next chief is committed to best practices and understands best practices across the nation. Once we have that list that'll be given to the panel the panel will review that list will have a probably a pretty lengthy meeting and from that initial meeting we will start setting up interviews of those candidates that we think show the most potential. Once that is concluded the mayor will make a decision from that panel recommendations on who he would like to interview. He could interview as few as one person. He could interview as many as all the individuals that'll be up to the mayor and his decision at that time. An aggressive timeline but a thorough timeline I might add would be that the mayor could do some interviews sometimes by the end of June or early July would be my preference. But first of all we need to make sure we have a thorough process. Some questions that I have received is why are we looking just inside Denver and not doing a national search. I've been here for a short time but I've worked on a national level for quite some time and I can tell you without a doubt we have a tremendous amount of talent within the Denver Police Department that has grown dramatically over the last six ten years and I think that they need an opportunity to participate this and I certainly believe that the best candidate for this position even if we did a national search is going to be an internal candidate so that's why we're committed to doing that. I do want to add this about the meetings that I've had with the employees of the Denver Police Department. I've had media, I've had people on the street corners, I've had individuals internally say those are going to be tough meetings. I don't know why the perception is that those will be tough meetings or could potentially be meetings that people were aggressive. I have found the opposite to be true. The employees have been very thoughtful in their approach. The employees have been very professional in their approach. The PPA opened up their doors for us the other day in addition to the road calls to ensure that people had an opportunity to come there as well, receive great feedback, receive some very positive things that were said about the department and also quite frankly receive some things they believe that we can improve upon. But one of the things that was a common theme from our employees is their commitment to the community and their commitment to ensuring that we continue to develop partnerships, partnerships that will help us in the future because realizing that the job of policing is difficult and everyone has to have a responsibility in that position. With that said, I'm going to move on to some other issues in a minute. Can I answer any questions about that now? Would that be okay? Is that or do you want to go to the end? Any questions regarding the search? You know, I haven't, no, well I should have thought you would ask me that and I haven't really thought about it quite frankly. Let me, okay, right, I, well I'm sure. Let us talk about that. We have not, we have not had that discussion but we will and we'll, we'll go from there. Okay, thank you. All right, so second thing today is and when I said earlier that these are not about just positive things that's going on within public safety, this is something that's a big concern to me. If you know my history, one of the things that that I was concerned about and brought on a national level a few years ago was some of the violence we were seeing in inner cities across America and then when I arrived here in November and started looking at some of the scene sheets and different things that I was seeing in violence within the city, I became a little concerned obviously but I want to make sure that there was trending in that direction, understanding that a little bit more. Well, we're, we're through the first quarter of this year and our murders are up. They're up from 17 last year to 26 this year. That is a concern for me. I have had good conversations with the police department and I can tell you setting through their data meetings, listen to their approach. They are very thorough. They are doing the best job that they can do. Obviously, there's always room for improvement but I've set through a lot of data meetings. They're, they're making all the right contacts. They're hitting, hitting and talking to the people that they need to be talking to and addressing these issues, not just on a global area but on the street level. However, we still have 26 homicides or murders, I should say. 26 murders as compared to 17 last year. Nine is an increase. I'm going to turn this over in a moment to the commander but I want to say this to the public and you'll hear this from the commander in a moment. We are not seeing a spike because of a certain topic. Sometimes in the past it's been, if you go years ago, there's a spike in violence because of crack cocaine. Then there may have been a spike in violence because of methamphetamine. There may be a spike in violence and it's usually associated with, with a drug of choice. What the police department tells me they're seeing now is not uncommon that we're seeing in some cities across America is that people are using guns to settle arguments, settle beasts with one another. And what I would say today as you get the updates and you hear some of the numbers that are not very positive, obviously, know that your police department's working hard but also that citizens can take an active role in helping reduce this number and this growth that we've seen in the first quarter. If citizens see people in a simple argument, remember they need to have civic, be civically responsible and call their police department and have us look into that as an agency DPD. Helping officers identify individuals that are angry, having trouble, that have a beef with a neighbor, something along those lines, you could be preventing a murder, you could be preventing an aggravated assault. That is extremely important. Also, I will say that detectives have done a very good case or a very good job of developing cases on many of these murders so far but there's about 30% of those where they have very little or no information and the second ask I would have of the community on behalf of the police department is if you know something about any of these cases, no matter how small that information is, please notify the police department immediately. So with that said, I'm on turn over to Commander Archer for her to give you kind of a deeper overview and I'll pass this down to you Commander. So good morning. I'm Barb Archer. I'm the commander of major crimes. So as the director has said, we do have an increase compared to last year of nine homicides compared to last year at this time. We were at 17 this year or 26. Out of that, we have 26 victims with 23 incidents and it's important to note these incidents are not related. They're independent. There's no connection. We have not had any retaliatory acts connected with any of these. Guns were the weapon of choice in 21 of these murders. Knives were used in four and bodily force was used in one of them. One of the things that's unusual for us this year is we have three incidents where we have two victims. We have the 38th and Chestnut that happened in January, a double murder again on Leedsdale and then another one 13,000 block of East Elgin Place. Obviously that drives our numbers up a little bit more. Five of these cases are gang motivated. We've determined through our investigation. Two of them were domestic violence related incidents. Of those 26 cases, 17 of them we have suspects identified. We've made arrests or we have warrants issued and I want to praise the work of the detectives who have pursued every opportunity of any piece of information, any lead to develop these cases into the point where we could make arrests. That also goes along to say we've had great cooperation from witnesses in some of these cases which can be difficult and some of that information has come from crime stoppers tipsters which is super important for us. The 10 unsolved cases that we have include our five gang motivated homicides this year. Gang homicides are difficult for us with witness cooperation. We encourage crime stoppers as a resource for people to provide us information especially on those types of cases where people aren't comfortable coming forward based because they're in the neighborhood or they know the people involved. Three of the cases I want to bring up that we would really look for crime stoppers tips on is 38th and Chestnut. This was back in January. We two males were found shot in the parking lot at the new Welcome Inn Bar. We're looking for information on the murder of Guillermo Ornelis and Jose Herrera Cabral. The next one we're looking for information on was on January 30th. Donnie Howard was found shot and laying in the street in the 2100 block of Arapaho. Love information on that one as well and then the other one I'm going to make a plea for happened in February at 8282 East Colfax. The victim Richard Young who goes by the nickname of Panic was found shot behind the Regis Motel at 8282 East Colfax. So again these are crime stoppers bulletins that we have put out but the public can contact us contact crime stoppers through their phone number 720913 stop. They can text it to 274-637. They can email it as well. We really welcome any piece of information anything that you think might be useful. It could be a person something you've overheard. It could be a vehicle that you saw leaving the area or somebody some other conversation that you're hearing in your social settings that would help us. Prevention of these things is tough. The community members there's a valuable contributors to our investigations witnesses eyewitnesses ear witnesses anything that you think is useful we really want you to reach out and contact us you know to go back to the kind of famous phrase now if you see something say something reach out to us give us a call. The Denver Police Department does a lot to direct efforts at addressing violence. We have weekly meetings where we discuss trends being seen across the city at our core meetings. We adjust patrol resources based on what the deputy chief sees and the needs that he can provide. We have some technology that we have at our fingertips now called ShotSpotter that helps us identify evidence and maybe witnesses. Unfortunately gunfire has become too frequent and a lot of people don't call it in anymore so the ShotSpotter technology has helped us get to scenes quicker and I'd like to think that that is helping interrupt some potential violence if we're in the area quick quickly. So as we address these issues we work with some of our partners we work with federal and local law enforcement agencies we work with other city agencies parks and rec Denver Public Library. We created a whole set of community opportunities for people using the faith-based community Denver Public Schools. We also work with GRID, the Gang Reduction Initiative of Denver and Director Kellan-Ann is here to speak about that. So any questions that I can answer on the homicide? They are not. So we have 26 murders. We had 17 murders last year. We have 17 cases that we've identified suspects and there sometimes are single suspects sometimes are multiple suspects. Ten or I'm sorry you're right nine. Yeah 26 and 17. Yeah last year we had 38 of them involved firearms. 38 total. Yes last year we ended with 57. Last year also included blunt objects, bodily force, asphyxiation, knives, and a motor vehicle. Anything else? Okay I'll turn it over to Paul Kellan-Ann. Good morning my name is Paul Kellan-Ann. I'm the Director of the Gang Reduction Initiative of Denver. I just want to take a couple moments and talk about what the city is doing in response to the gang elements of the current violence that we're seeing as well as what we've been preparing for over the last couple years of developing in a sustainable model to address gang violence. Since 2012 the city has been partnering with the U.S. Department of Justice and the network of state and local agencies in developing a sustainable gang violence reduction model. The model focuses on enhancing our collective efforts in the areas of enforcement, intervention, prevention, and community mobilization efforts. In addition to exploring how we can leverage our existing resources, federal funding has allowed us over the last couple years to implement and design and test some innovative programs as well as replicate some proven and promising programs that have been effective in other cities. To give you some examples of some of those efforts, since 2012 8,000 elementary middle school students have completed the gang resistance and education and training program. This is a law enforcement taught life skills program that helps kids avoid gangs and violence. Approximately 500 high-risk individuals involved in the gang culture have received coordinated case management services from MDT teams that are comprised of Denver's best treatment service agencies. The purpose of these teams is to guarantee direct services and immediate access to services to these individuals as well as 24-hour support system. To compliment that, about 5,000 case managers across the city that work with youth and adults involved in the gang culture have been trained in understanding Denver's gang structures and dynamics and how to better effectively work with gang members. We recently implemented a specialized juvenile court gun project to take a look at are we providing the most advanced or most effective intervention and supervision programming to youth that have been arrested with firearms. We've worked with community coalitions and developing community designed short-term and long-term projects where the community can get involved in reducing efforts. Some of you might be familiar with the 2014 summer safe holly effort which involved a coalition of agencies, community-based organizations and neighbors in northeast Denver holly area where for 90 days they declared a safe zone of a hot spot within the city and for that 90 days there wasn't a single incident of of the shooting. So we've proven that on the short term that community residents and groups coming together can have an impact. In the long-term projects with the community we're working with the coalition out in Montbello right now called RISE, I believe it's a respect to intervene, support and and I forget educate. But what that coalition of community groups are doing is looking at how to develop a long-term sustainable program specific to the Montbello area that involves heavily community involvement. To intercede in some of the violence between gangs that we've seen over the last couple years, we've embarked on some innovative programs where we worked with individuals that used to be involved with gangs that serve as violence interrupters across the city that have a unique ability to reach out to those groups and individuals that are involved in the violence and try to mitigate some of the conflict that is going on. We all know that violence in our community inflicts wounds and scars. People are frustrated, they're angry, they're hurt, they're scared. The level of secondary trauma leads a long-lasting impact. In response to that, June of last year we kicked off a program in partnership with our faith-based partners around the city who are combining their efforts with our mental health partners and providing a critical incident response to gang shootings. And in not so what they do is after a gang shooting in the city the church closest to that shooting will open a store for a period of three days. Mental health specialists will help staff that facility for the three days and it's an effort where people in the community who are just angry or frustrated have a safe place to go to get some spiritual or emotional assistance. If they need some more services then those are extended to them. To date we've implemented 18 safe havens across the city and over 1500 residents have taken advantage of those services. We believe that's the coordinated efforts of all that are involved that are going to reduce violence and keep gang violence in check across our city and we're beginning to see the results of that. Between 2015 and 2017 we saw 65 reduction in gang related homicides. Between that same time frame we saw 22 percent reduction in overall gang violence. However gang violence is very dynamic in its nature and we continue to be vigilant in what we do. This year ends our in 2017 ended our financial relationship with the feds. A large number of our federal grants ended where it came incumbent upon the city to sustain many of the proven models that we've put in place. At the beginning of the year we were short a little bit of funds for our secondary prevention area but the Department of Safety was able to reallocate some funds to ensure that the full model is funded throughout the rest of the year. Gang violence is difficult to address. There's a lot of factors that have impacted gang violence. It's a wide spectrum of influencers across the board. But we remain vigilant in what we do and when we look at numbers and we look at reductions we take a step back, we breathe and then we move forward with optimism and what we're doing is correct. If we see numbers that are going up we take a step back, we breathe and then we refocus our efforts on what we need to do better. It's too early this year to tell where gang crime is going to go. Every year we're faced with comments about we're going to go back to 1992-93 with the summer of violence. We hear that every single year of the last three or four years we have not seen that. I don't anticipate that we're going to see that this year because I think we have a sound model in place. The difference between today and maybe 10 years ago, 15 years ago, is our approach to addressing gang violence is consistent and it remains coordinated on a daily basis rather than a fragmented approach or a knee-jerk reaction. Thank you. I'm wrapping that part out just like you know we have 26 murders. The challenges of the police department are not just the murders as significant as they are but remember the city is growing us our recent study 1% per year. We are having more events, we are having more people come to the city, we have more visitors, more individuals looking for employment. The difficulty of the police department are when you look at all this combined has increased and so they're making some different changes adapting to it, looking at staffing, hiring civilians, more civilians. That work needs to continue and it really pulls these two stories regarding homicides and murders and the chief search together because these are some of the challenges that the chief is going to have when he or she arrives. How to deal with this type of violence is this a going to continue to be a trend that has to be addressed. Is it something we can get ahead of as a department and as a community and then how do we address the rapid growth? That is a challenge for this police department that is not a challenge for most departments across the nation. So far they've handled it very well and we need to make sure that momentum continues in the future. At this point I want to turn it over to our fire chief that has some updates on some important things that have matters that have occurred within the fire department recently. Chief. All right thank you. So luckily I get to talk about some positive news here today and I think the first thing we're going to talk about is fairly exciting is that we were able to appoint a new division chief of administration recently. Wendy Motor here will be our new division chief of administration. She is the first female to ever hold that position within the Denver fire department and only the second female to hold the rank of division chief. So with that news I'm going to let her introduce herself to you and give you a little bit of her background. Thanks chief. Good morning my name is Wendy Motor. I've been on the Denver fire department for 22 years. I've been in several different divisions in the department. I've worked in our dispatch. I've worked as a captain in the EMS division. I've worked in arson, a captain in arson and IA. I've also worked in the fire prevention division. I've been in operations in district three mostly as recently as a roving assistant chief and as in two weeks ago I was appointed to the division chief of administration. Anybody have any questions for Wendy before I move on? All right seeing none. So the next is probably what I consider to be exciting news. Hopefully you guys will share that excitement. We recently went under an audit from the insurance services office who gives every community a public protection class rating which then ultimately helps to set the insurance rates for homeowners, residential and commercial insurance. They grade fire departments, their water supply system and their ability to respond to and to mitigate fire hazards in a city on a scale of one to ten with one being the best. Denver fire has traditionally received a grade of two which is extremely good. However after this last audit Denver will now be a class one rate at city and so I can see you guys are all looking with tremendous excitement wondering what that means. So let me just tell you right now insurance services offices, they help insurance companies underwrite their policies by providing them data and ratings for 14 of the 15 largest insurance companies. For each point of improvement you see up to about a 5% reduction in insurance rates both commercial and residential. So for our homeowners in Denver and our business owners they have the potential of receiving either a discount next year or depending what insurance rates maybe their rates don't go up as high. This is something we worked really hard for over the last almost 10 years now is when we got our last audit we looked at every area that we had lost points or not received maximum points and put a lot of effort in there with the goal of receiving the ISO rating of one. I can tell you we actually did it one year early. They typically do those evaluations every 10 years. We had reached a point where we thought we had met most of those goals and so we voluntarily submitted for an audit and we were able to receive that positive rating. They do about 46,000 ratings across the world and of that only 241 cities last year were at that ISO one so that kind of shows you where we fall in that spectrum so I'm very proud of that rating and all the credit goes to the men and women of the Denver Fire Department that are truly dedicated and bring their A game every day so along with that rating we also looked at an area for improvement and one was in our arson division and through a partnership with the ATF we now have a new accelerant detection dog. It is a black Labrador and I invite you guys to come to a badge pinning at one o'clock at Denver Fire Station number one at 745 West Colfax where we'll be pinning a badge on our dog which happens to have the name of Cora and no we did not pick the dog and I see see I finally got some excitement out of you guys there we didn't pick the name the dogs come with their name so unless anybody has any questions I'll give it back to Troy. All right well thanks for attending I also want to say you look around the room and there's a lot of individuals here and here's what impresses me about Denver I've not asked any of these individuals to be here I've asked these individuals to be here I've asked Eileen to be here as the chief of staff but it just goes to show the commitment that our employees have and I've said this numerous times I've worked across this nation I've consulted I've never seen a group of such talented individuals and compassion individuals and I'm really excited about the future but with that any have any other questions or anything about anything else we can answer while we're here or I can answer. So the murders this year are pretty evenly spread across the city in our police districts I have four in district one five in district two five in district three seven in district four five in district five and four in district six


Hello, this is Laptop Media, and today, we will show you how to open the HP 470G7 and what's inside of it. Once again, HP has tried to hide most of its precious screws with the help of the rubber stripes. However, they are easily removable with a flat head screwdriver, or preferably a plastic tool. After you do that, remove all of the Philips head screws you see. Then, turn the laptop around and open the lid. This is where the prying process happens. Next, make your way around with a guitar pick, and remove the bottom panel from the chassis. Inside, you'll see a single, thick heat pipe, cooling both the CPU and the graphics card. Despite the fact we are talking about energy efficient hardware, it is usually not a great idea to connect your two main heat sources. In terms of upgradeability, the 470G7 is well packed. There are two RAM Sodom slots, which support up to 16GB of DDR4 memory, working at 2,666 MHz. Storage wise, you can see an M.2 slot with PCI-EX2 and SATA support, as well as a 2.5 SATA drive bay. As of the battery, there is a modest 41Wh unit, powering the huge 17-inch screen. If you'd like to see more disassembly videos of the latest notebooks we would highly appreciate if you hit the like button and subscribe to the channel.


Hello, everyone. Welcome to CNSafe Wasm Day. My topic today is WebAssembly class application runtime, brings a new area of fast. My name is Jason Song, and currently work for Onto Group. I'm now mainly focusing on Cloud Native and the microservice areas. We have deployed a large service mesh cluster in our production environment up and running for two years. The sidecar is named as Mohsen, which is written in Golan and provides similar features as Envoy. Now there are more than 200K parts in the service mesh cluster, and the service mesh has solved our challenges in service connectivity areas well. However, as a company with a lot of business scenarios, we are still having challenges in other areas like cache, message queue, etc. As the diagram shows, they are tightly coupled with the application code. For example, if we want to migrate the cache from Redis to memory cache, we need to upgrade the SDK on the application side and require the application to change its code to use the new API. Another problem is the cost of multi-language support. Since we need to develop the logic of protocols, codecs, load balancing, disaster recovery for each language SDK, the cost is very high. In early 2020, Belgian Abram published an article called Multi-Round Time Microservice Architecture. The main idea is to abstract the various distributed capabilities into multi-round time so that the application no longer needs to rely on specific SDKs, but will interact with the runtime over defective standards, such as HTTP, GRPC, which then solves the challenges just mentioned. And that brings Laoto. As shown in the diagram, Laoto is built on top of Mohsen. It provides a unified standard runtime API with various distributed capabilities. Developers no longer need to care about the differences in the implementation of the underlying infrastructure, but only need to focus on what capabilities they need and just call the standard APIs. Speaking of the runtime API, we know that it is not easy to define a set of APIs with clear semantics and wide application scenarios. So we are now working with DEPA community and Alibaba to build the API, hope it could be a standard in the future. Here are some excerpts from the API definition. We can see there are APIs to invoke services, get set of cache, publish messages, et cetera. In addition to normal applications, we are also exploring the fast area. WebAssembly, aka Wazam, was introduced to web browsers to address performance issues with JavaScript. However, its near native performance, sandboxing and portability features also makes it attractive for fast scenarios. With Wazam, Wazam provides a high level model for accessing system resources. However, in real cases, there are many other resources required to make a normal application work. For example, invoke services, get set of cache, produce or consume messages, et cetera. Lack of these features makes it hard to host a service applications in Wazam. As Lioto abstracts a standard API, so we think why not deploying Wazam modules with Lioto so that Wazam modules could consume external services via course to Lioto sidecar? However, as Mosan also has the capability to host Wazam modules, we then think, why not we go further to combine them together? Then we have this diagram, the Wazam host, Mosan, and Lioto are all logical components in one process. Wazam host, like Wazam Edge, is embedded in Mosan to host Wazam modules, and Lioto is used to provide distributed capabilities such as invoking services, reading cache. These capabilities are exported to Wazam as API, similar to Wazi. We wanted to develop a demo to prove this concept. So we did some research and found there has been some exploration about how to integrate Kubernetes with Wazam. The basic idea is to develop a container D-shame plugin so that when it receives the request to create a container, it will hand over the actual creation logic to start a Wazam runtime to host the Wazam module. However, since we want to verify the non-no process architecture, so we did some customization. As the diagram shows, we first start a Lioto runtime on the node to serve as the Wazam host and provide distributed capabilities. Then we customized the container D-shame plugin so that when it receives the request to create a container, it will let Lioto run the Wazam module instead of creating a container. With this solution, we could reuse most of the Kubernetes capabilities and yet achieve the effect of running multiple Wazam modules as non-no processes in Lioto and can also take advantage of Lioto's distributed capabilities. We also reuse Docker to package Wazam modules and submit them to Docker Hub for distribution. Here's a demo showing what we've accomplished so far. There are two Wazam functions. The first function receives a HTTP request and extracts the book name from the request. It then calls the second function to query the inventory of the book. And finally, we'll return the inventory information to us. We defined the invoke service API with function ID, method, and the param so that Lioto could use this information to locate the function and do the invocation. And here is the second function. When it receives the request, they will use the book name to query Redis for the actual inventory and then return the number to the caller. We defined the get state API with store name and key so that Lioto could find the correct backend store and query the value. Now let's build the programs to Wazam modules. Then we could use Docker build to build them into Docker images. We also need to register the runtime class to enable our custom container runtime. After that, we could deploy the Wazam functions with normal pod definitions. To make the query work, let's pre-configure the inventory to 100. Let's check the function status. Now let's query the inventory for book one. We can see it works. Let's change inventory to 99. And yeah, it returns the latest value, cool. And finally, let's clean up the resources. I hope this demo explains our idea clearly. With this demo, we proved this idea could work and we believe with the fast development of WebAssembly and application runtime, the possibility to bring a new area of fast will eventually come true. Okay, that's all for my talk. Thanks for watching and you may check out our GitHub repository for more information. Have a great day, bye-bye.


Hi, everyone, Joe for jaspyscasebreaks.com coming at you with this is this is actually not correct Just redo this on the fly. This is not break six. This is actually break four ladies and gentlemen I know I wrote six there.  There there you go there break four of 2020 prism football mega box edition with five Football mixer spots the high-end three box mixer that we have on the site five spots being given away at the end of the break So we'll do the break itself first and then we'll re-randomize your names in a different dice roll We'll see who wins those spots, but for the break big thanks to all of these lovely people here for getting into the action Thank you very much. All teams are in. Let's roll it. Let's randomize it three and a six nine times one two three four five six seven eight and Ninth and final time Jack down to Nicholas three and a six nine times for the teams one two three Four and ninth and final time after nine. We got the Colts down to the Lions Lions, I thought the Lions would be all in on Robert Sala as Robert Sala is from Michigan. I thought they'd go real big on on Robert Sala, but Guess not. I'm sure Jets fans are happy though Big thanks to all of these folks for getting in there. The team is right there Jack with the Dolphins Bangles for Zack chargers for Matt No trade windows in these little filler breaks Just a reminder folks always look at the break schedule to see which fillers we need to accomplish for particular breaks Let's drop frequently into the chat if you're watching live Let's print and rip. There's the mega box right here the neon green pulsars are the The exclusives in this Good luck. I think someone was saying earlier. Is it anciller saying early at the Falcons got their head coach squared away? I think it's the Titans offensive coordinator So the coaching dominoes the head coaching dominoes are starting to fall some green pulsars up on top There's Stefan digs and There's Kenneth Murray for the chargers chargers need a head coach too. What are the chargers gonna do? That's Matt McLaughlin with the Bolts. There's AJ Dylan Green pulsar Ryan Kerrigan Michael Pittman Jr. Had a nice game. I think he's gonna be hopefully he'll become a future star for the Colts That's gonna be for Jack AJ Dylan. Is he gonna have a big game raise his stock? Matthew and the Packers Ryan Kerrigan really solid and we've got the Rams is Terrell Lewis A lot of people are now Are on the Rams to beat the Packers at least cover. I don't know. I think I'm getting a lot of that Here in LA. I'm getting all that LA sports talk radio bias Filtering into my head people around town getting me thinking the Rams might actually beat the Packers outright It's JK Dobbins. Will he raise his stock this weekend Daniel Katz It's Jalen Johnson Anthony Barr, there's cam acres cam acres definitely raises stock last week This is for the Rams. This is gonna be for Mike Leone. If the Rams win I think it's if this guy's gonna have to be a big part of it cam acres and Jared Goff's got a bum-thumb Cold-weather Goff. Everyone knows that that's that narrative So if the Rams do anything it will most likely be because of cam acres Can't wait for tomorrow folks. I'll be here tomorrow So we'll watch the Saturday games together as we do some more group breaks Okay, now let's give away some spots From Dustin down to Raymond and everybody in between. Let's put you in a new list and some new dice Four and a two six times. So it's gonna be top five After six good luck One Two and six in the final time so Once again, it's top five right and so From six down to 32 Sad times my apologies Remember we do have to do a couple more of these. So if you want to try again I would encourage you to do so jaspys case breaks calm another spot or two just to see let's see what happens Thank you though for trying top five Congrats Kenneth Mike Matt Zach Brian Congrats to the five of you You are in the action in that three box high-end football mixer I think flawless impeccable and another nice box that go and get it jaspys case breaks calm Thanks for watching. I'll see you next time


A film in three minutes, another round. The ancient Greek comic play writes Yuboulos once said of wine, the first cup is to health, the second to love and pleasure, the third cup to sleep, the fourth to violence, the fifth cup to uproar, the sixth to drunken revel. And I suspect I don't need to continue for you to guess where Yuboulos was going with this, but four friends who sadly didn't get the memo are about to find out in Thomas Vinterberg's 2020 drama Another Round, a cinematic exploration of inebriation, masterfully directed and featuring stellar performances that will make you marry with delight before leaving you with a killer hangover. Set in Vinterberg's native Denmark, a country with some of the highest rates of teenage drinking in the world, Another Round, or Druck in Danish, which literally translates to binge drinking, follows the lives of four middle-aged educators whose enthusiasm for their profession is found wanting by their soon-to-be-graduated students and their parents. Depressed and bored with life, the four men learn of a paper penned by Norwegian psychiatrist and professor Thin Skaldäø, who theorises how humans are born with a blood-alcohol content deficiency of 0.05%, and that if such a level was raised, then people would be more creative and relaxed. Upon learning this, the teachers decide to embark on a social experiment of their own by drinking at regular intervals and then logging the results. However, what begins as a tipsy first foot into this world of empirical intoxication slowly descends into an all-consuming self-destructive addiction. If you are of a creative mind, then you'll probably be no stranger to the positive effects moderate alcohol consumption can bring at times. It's no secret how many successful artists, writers, politicians, teachers and all-around geniuses have existed throughout human history, who are also completely slashed. But despite the film's initially comic interpretation of drinking, Winterberg's unsympathetic camera quickly captures the darker side such half-in-the-bag behaviour contains with chilling effect, never flinching from the ugly, depressing and all-around terrifying reality that resides at the bottom of every drink as the experiment goes off the rails and the price the four men pay steadily becomes dearer. Madd Mickelson achieves the best performance of his career, playing a character who conveys the bitter lessons that marriage, family, career success and even friendship don't necessarily bring us the happiness we are all told it will, with a nuanced pain and ecstatic joy that has to be seen to be believed. So, the next time you decide to imbibe that beloved gift from Dionysus, perhaps take a moment to reflect on your own relationship with alcohol and ask yourself if you truly need another round.


So we'll discuss that more as it approaches. Let me review this little bit and then we'll take a question that you might have. So let me review a little bit of what we were talking about. So we discussed a very important idea, the distinction between coherent superpositions or quantum superpositions of different alternatives and statistical mixtures of this mode. That's the language we use and it has an important operational meaning. So if we think about, for example, a spin-1-2 particle, as well we've really discussed it, to date. So if we have a pure state, we've said that could be described by this ket, which generally could be in a coherent superposition of the two basis states. And we know from the Born rule how to calculate the probability of finding one of the outcomes in a projective measurement. And that's given then by the squares of these amplitudes. And if we look at, for example, the probability of finding a spin-up along x, as we've said from the very first lecture, there's an important contribution to this probability which doesn't follow from classical logic. So this probability has pieces in it that we would argue from the point of view of logic. There's some probability to find spin-up along x given that the spin was spin-up along z. Times the probability it really was spin-up along z. Plus the probability that we would find spin-up along x given that the spin was really spin-down along z times the probability that it is spin-down along z. And then there are these terms. These terms which have no classical, logical analog. They are the quantum interference terms between those two alternatives. And that's the hallmark of the fact. The fact that these interference terms are there is the hallmark of the quantum superposition. The fact that these two alternatives were not locally real. We just didn't know which one they were. They exist in some quantum limbo state that we don't really understand and that has impact on this probability. For example, if those two probability amplitudes were, say, equal to one over root two, then the probability of finding spin-up along x would be one. We would definitely get that outcome. And we can think about that as there is constructive interference between those two alternatives. In contrast, if the amplitudes were equal but there was a minus sign there, then the probability to find spin-up along z would be zero. There would be complete destruct interference between those two alternatives. So that's the superposition, the coherence of the superposition, and that's being contrasted with what we call the statistical mixture. What we say is that the preparer, we imagine this scenario, which is a possible thing that one can do and one does do in some, say, quantum communication protocols where the preparer has the ability to send you, the receiver, to be called Bob, not to be called Alice, because they're A and B, and they're the names you'll receive. So Alice prepares either this or that, and she doesn't tell you what she's doing, but she does so with a coin flip, that coin that may or may not be a fair coin, it has some probabilities. What we showed last time is that we could describe the state of the system in that case, not as a quantity reposition of these two alternatives, but as a statistical mixture, which is represented mathematically by this thing we call the density operator or we can call it the state operator. It is our representation of the state of the system. It's the thing that we use in order to calculate probabilities of measurement outcomes. And the way we do that, the generalization of the Born rule to the case of statistical mixtures is that the probability is given by the diagonal matrix element or the expectation value for light of the density operator in the state of consideration. So if we wanted to find the probability of finding spin up along x, this is the rule, okay? And doing that, we find this, and that's just the classical logic piece. It doesn't have the interference. So what distinguishes the statistical mixture from the quantity reposition is the lack of interference between those two alternatives, okay? That's the key point. And you can, any state of the system, whether it's a coherence to reposition or a statistical mixture, is a density operator. So the density operator is the most general way of writing a quantum state. So you can have all possibilities, quantum or classical kind of statistics, all right? And so, for example, a pure state is a state which is just given by this outer product between a ken and a bra for some particular state in Hilbert space. And I just wrote this out as an example in the context of writing it in this basis, so I expand it side in this basis, which I can always do. And when I do that, I'm going to write out all the terms, you see explicitly that this density operator has diagonal elements which look like the statistical mixture of spin up and spin down, which is just like this. But then it has octagonal pieces and those octagonal pieces are the things that we call the coherences. They express the potential for observing interference between those alternatives. Does co-operation be negative? Sure. I mean, in this particular case, they're generally complex numbers. They generally have real unimaginary parts. And they generally, they're positive or negative. I mean, for example, what we showed, excuse me, pardon me, this boo-boo, how we mistake. That should have been that. In this case, these coherences would be negative. Right? This would be minus a half and minus a half. And that was the case where we had destructive interference. It could be pure imaginary. It could be anything, any complex numbers. But the trace of the density operator for a pure state must equal one. Right. We'll get to that in a moment. So these are real numbers. Because they are the absolute squares of complex numbers. How long does it have to equal one to the state's volume? It's normalized, indeed. We'll get to that in a moment. So what we have here is that we said that we have just so statistical mixtures, we could have whatever we like. We could say we can have an ensemble of possible pure states, of pure states side by side. They don't think we could have as many as we like to prepare with probability. So we have this picture of the preparer sending us a pure state but not telling us what she's sending us. She just tells us the probability she's going to do it. And the state we would assign if that were the case, would be this. If she sends, if she tells us she's definitely going to send one state with probability one and all the others with probability zero, it's a pure state. Otherwise it's a mixed state. So this is generally what we call a mixed state. Not all the probabilities are there only. If any, the probabilities aren't one and zero for all the rest of it, it's mixed. Otherwise, it's called a pure. And moreover, we have the, so in a basis, let's just talk, we're talking generally now, not just about three and a half, let's just say we have a heat dimensional elements, then, and let's just say we have a basis, the alpha, to be. Then we can look at the matrix elements of this operator. So just to emphasize the facts, the diagonal elements, the probability, thine, the alpha, you know, projected measurement, that's the more rule. And the off diagonal elements are what we call the coherences. They are the, they in some sense represent the potential to see interference between alternatives, the alpha and the beta. That's how much interference you might see in some, and again, if I look at this from the point of view of the statistical mixture over here, then this is equal to sum over all the members of the ensemble in this guy. That's that, right? So I'm just waiting, this would be the more rule for a particular pure state, but I don't know which pure state she sent me. So I have to average over that. Clear? And that I could write if you like, as this side, or this particular I form I is equal to the sum over alpha c alpha to the right guy. The off diagonal element here, data, that is equal to the sum over, so let me just write this as the ensemble average of that for all those guys. That means average over the ensemble. Now I have this c alpha on here, and this is c data stock, which is, if I write this, each of these complex numbers as having a magnitude at a phase is, I just wrote each of those complex numbers as having a magnitude at a phase. And so, again, to emphasize the key point of the coherences they have something to do with the phase relation. Coherence and phase are intimately related. I mean, you know that from, maybe you know that from the notion from wave interference and classical wave theory, say in optics. And we talk about a coherent coherent field. That has a well-defined phase. And the fact that the phase is well stabilized means that you can see interference between different wave paths. But if the phase is jiggling around in some way and not well-defined, then you don't see interference between the waves, right? And that's what this is saying over here. This coherence is the ensemble average of this old guy over all the members of the ensemble. And if the phase relationship is not well-defined between all members of the ensemble, then it will tend to average out to zero. So there's this intimate relationship between the well-defined phase between the probability amplitudes and whether or not you can see interference between those alternatives. So let's say a few more things now about the density operator. What are its properties from a mathematical perspective? What can we say? Well, if we look at this operator over here, the density operator written this way, this writing again, firstly it's clear that this is her mission. Why is that clear? A mission operator is one which is selfish. Why is that obvious? Because P is real. These are real numbers. We have an ensemble of possible states with sums of one. And when you take the editor to this, this goes back to itself. So it's her mission operator. The other thing I can say is that it's a positive operator. It's one where the expected value of rho is not negative for all possible factors. Is this the case? Sure, because this is equal to the sum over i, P i, and this is a positive number, or it's something that's not negative, it could be zero. So, it's a weird thing. We call them positive operators where we should realize you call them not negative operators because it could be zero. That's just the jargon that we use. All right. And as that means, of course, that means that two things. If it's a her mission operator, then we need a normal operator. And so that means that rho can be dangle. Its eigenvalues are non-negative. Those are two things that have to be hitting follow. Right? So that what that means is that in dimension D d eigenvalues and its eigenvectors can always be chosen. Right? Discuss in the first week or so class that her mission operators have can be diagonalized. It has D, in this case real non-negative and that we can always choose that to be orthonormal. If they're for different eigenvalues we can always, if they're not, we can always find their orthogonal basis within the degenerate space. So let's call the eigenvalues of rho to the eigenvectors R and we call them u lambda and the eigenvalues. And we can always express rho in the basis of its eigenvalues. In the basis of the eigenvectors I should say. So what can you tell me about this representation? How can I interpret this? Well, it looks just like that. Okay. So rho is always can be thought of as a statistical mixture of its eigenvectors with mixing probability given by its eigenvalues. Now here's an important point. These guys need not be the same as these guys. Okay. Now let me explain why. I can tell you what I'm mixing. Here I am, I'm Alice.  I can send you whatever I like. And the vectors I send you don't have to be orthogonal vectors. And I can send you a million of them. Okay. I can send you a million different possible spins. And I can tell you beforehand so this ensemble of decomposition doesn't have to be an eigen decomposition. It could be whatever it likes. One thing you learn from this is that there is not one unique ensemble for a given state. In other words, there are many, many, many different ensembles. In fact, an uncountably infinite number of different possible ensembles which all lead to the same density operator. You could now tell the difference. That's one of the things you're going to see in your homework. And that's because the classical probability and the quantum probability are kind of getting mixed up. So the ensemble decomposition is not unique. Now we can ask what are the conditions on the ensemble such that the same density matrix. And we can quantify that. We can say these two ensembles would give the same state. It is a very positive thing. Now, of course, the eigen decomposition is unique up to degeneracies. So if all the eigenvalues are non-degenerate there is a unique way of thinking about this as a statistical mixture of the eigenmetrics. Yeah? Is this related to a previous question where you can keep back lines that you continuously rotated into that or you could change any into a diagonal matrix. That's not necessarily that matrix. And the reason is if they're not orthogonal. Okay? So the example I gave here goes back over here. This density matrix is in its diagonal representation. Okay? But let me come back over here and say I suppose this is a probability here that you're homework. Let's say I have rho is a half spin-up along z and a half spin-up along y. Okay? That's a possible perfectly good density matrix. A perfectly good density operator. That is not these are not the eigenvectors of this operator. If I look for example what happens if I act this on this? Well I get in this case a half spin-up along z plus a half spin-up along y times that, which is 1 over 2. Right? And so I don't get that the same vector. That's not an eigenvector. In fact you can see it also in a matrix representation. Suppose I wanted to express this operator as a matrix. As a 2 by 2 matrix in the basis that of choice. Here's the basis. Let's say spin-up has been down along z. So what does this operator look like in that basis? A matrix. 0, 0, 0, 0. Everyone see that? This is in the basis so in the basis up and down along z that's the projector. What does this projector look like in that basis? Well that's a little trick here. So the way to do it is there's lots of ways to do it. One way to do it is to write this as rows and column vectors. So this vector if you remember is 1 over root 2 that's the column that oh actually sorry this is that's the wrong list again. So it's a superposition of spin-up along let me do this more slowly.  Let's sign it. This let m be this I want to write a matrix representation of this in the basis. There's lots of ways to do this. How do we do it? Well we can insert it in the set right on the side or we can just write out the matrix elements we can say this is this column, column do it in a somewhat systematic way that we can remember anything else. Why in terms of z basis? That's what we're doing. There's lots of ways to do it. Just write it out systematically if you remember how to write an operator in basis. There's lots of ways and I'll show you the other way just so because we have different approaches and I don't think we can change that depending on which is the most convenient thing. So what we remember is that we have to look this up or remember it which I do remember because there's just a few of them that you can remember so with that said this is equal to this operator over here this is equal to this is equal to this and this is equal to that right? So this is equal to what? This is equal to a half on the diagonal ok? This is the square root of those opportunities and then I have this times the column here and this ok? So and as I was saying just a moment ago I could write this and this is what was being suggested and this is how I originally didn't do it because if it's just an outer product of two vectors I can I don't have to go through all those tedious steps I could just say this guy is equal to this is equal to 1 over root 2 I over root 2 and then have the bra and then I take the outer product of doing it you have to learn how to use these different techniques and which one is the most rapid convenient ok? So what was the point of this exercise? The point of this exercise is this is not an diagonal matrix so you know we write this out this is this plus this it's not an diagonal matrix even though it's it's a statistical matrix of these two things it's not the diagonal what does that mean? but coherences between what? they're coherences between spin up and spin down in the z basis and that's because this state although it doesn't show interference between these alternatives it shows interference between these alternatives and that's what's being captured in the diagonal elements see if you have a question so I mean when I first saw it the state the odd angle would be zero but that's not true so we're going to there's a degree of mixing this we're going to talk about that for a completely mixed state so there is a continuum of possibilities perfectly pure they have odd angle element and then in some basis and then we have maximally mixed and those states have no of that in any basis and then you have partially mixed partially pure as we said you can always think about it as a statistical mixture of its eigenvectors and in some ways you can up to degeneracies now let's see what I want to say let's see sort of bringing out a pure state of partial mixed states matrix I mean how can you tell what's rich by just looking at the matrix good question we'll get there very soon it's an excellent question it's an excellent question I would say one thing you can't necessarily talk about looking at the matrix because that's a basis dependent property and we want something that's independent of basis it's a property operator not the representation in a basis it's important to understand that distinction between basis dependent properties and basis independent properties we'll get there in a moment alright do do do do do do okay yeah oh yeah that was a point I forgot to mention that was the point you raised earlier normalization so density operators are permission operators they're positive permission operators we can also normalize them and the same way that we said that when we talked about cats we said we typically normalize them so that we can easily calculate the probabilities okay so we're normalization chosen so that this equals the probability of one trip okay and so that what we mean then is that if we have a basis I guess I was calling it alpha so what we want if we have a basis the alpha then it should be the sum of all the leads choose the probability to find one of the alternatives should be one right but that's how it states normalize and as we saw this is just the sum of the bag which has a name it's called the trace so this is the trace over so we choose our density operators to be normalize by setting their trace to be one now the appointment of course is that we can always normalize afterwards okay so if some reason we had some operation where we got a density matrix that wasn't normalized we could always re-normalize in the same way that when we did projected measurements or measurements in general on cats we had to re-normalize right in our bays and stuff like that so we just find out what the trace is and divide by it so that the trace is one after alright so now I want to say something about pure versus mixed states so for pure state we said there is some cat such that row is then just the projector on that cat right what can you tell me about the eigenvalues and eigenvectors of this state so remember it's a cat and it's a normalized cat if this is a normalized right so the normal of this that matters much but I just wanted to remind you that is this a normalized that's the trace of this equal how do you tell well remember we proved in problem sets that the trace of an outer product is equal to the inner product that's a very very useful tool and I always think about it as outer products with inner products and you always put a little to remind myself that I'm clicking them together when I do the trace I make the same so what is the trace of this it's just that no it's equal to 1 as well because the trace of a so let's say we have a mixed state and let's say I wrote it as I can write it in any ensemble decomposition I like I'll write it in there's some ensemble decomposition I don't care whether it's the eigen decomposition or any other decomposition I want what is the trace of this mixed state that's the trace of that this is some of the traces traces of linear so I can bring it inside this sum that's one of the things we proved and the trace of this is 1 and so this is the sum of all the probabilities in that with 1 so for a mixed state the trace of 1 is as well a state the state is normalized mixed for pure now the question I really for a question I wanted to get to is what are the eigenvalues and eigenvectors of pure states so here's my state it's pure what is can you see one eigenvector eigenvalue in one what about the eigenvector to psi psi so psi is an eigenvector that's obvious because if I operate this on this I get it back right and the eigenvalue is 1 so that's one of the eigenvectors and that's one of the eigenvalues what are the other eigenvectors if it's a d-dimensional space what are the other eigenvectors and eigenvalues well let's just say we had a basis and this was one element of the basis and then we have all the other d-1 basis elements all of which are orthogonal to this what happens when I hit row pure on those you get 0 so all the other eigenvalues are 0 so for a pure state and we can see that over here this is the general form of the density matrix or the density operator written in its decomposition in terms of its eigenvectors and eigenvalues and if it only had one term if it's a pure state then one of these eigenvalues is 1 and the rest are 0 then it just has that one term so for a pure state and that's important there's only one eigenvalue that's 1 and the rest are 0 so for a pure state let's put that on the front board it's important not for the size but somehow we have this eigenvalue is 1 eigenvalues or eigenvector other eigenvalues are 0 and it doesn't matter but choose any eigenvectors we like that are orthogonal complement to this anything that's orthogonal to that is an eigenvector it doesn't matter it gets weighted by 0 so question what is the matrix representation of this pure state in the basis of its eigenvectors what does it look like one of the diagonal places wherever psi is in the basis we just write that one as the first basis element and then all the others some sign doesn't matter and it's back and it's 0 everywhere else now this comes to a point z that you were raising this is a pure state it's at the most coherence that you can have but it's the off diagonal matrix elements are 0 this is a point I'd like to re-emphasize the it's not right to talk about the off diagonal matrix elements it's off diagonal matrix elements with respect to a basis if it's a pure state that means in some basis it will have very big off diagonal matrix elements it doesn't mean that in every basis it will have big off diagonal matrix elements and in fact in the basis of its eigenvectors there's 0 because there's no interference between those different alternatives because there's only this alternative good so now I want to come to the question that Steven raised, he's not here at the moment but maybe he'll come back let's see and that is how do we distinguish because we can't just look at the matrix and look at it unless we're somehow and he says about matrices generally and know whether this was a pure state or not because this one I can see it's a pure state because it's got one on one diagonal and zero that's pure but generally if I looked at that matrix I wouldn't know offhand how pure it makes that work if I add those things together so what is it a defining feature of the density operator that is a function of the state itself and not the basis with which we use to represent the state so let's consider the square of the density let's just consider that well I can always do a function of an operator by expressing it in terms of its bag of representation if it's a permission operator and then just do the square on the eigenvalues that's what we learned so this is the sum over all the eigenvalues of the density matrix so what is the trace of rho squared well that's one so this is equal to the sum of the values of the square so what can you tell me about that if it's a pure state what is the trace of rho squared one so if it's a pure state the trace of rho squared well what if it's mixed well if it's a mixed state what can you tell me about the eigenvalues I guess I should have said that over here what can you tell me about that well there are positive numbers because we said it's a positive operator and it's normalized and it's normalized the trace means it's the sum of the eigenvalues the trace of rho is equal to the sum of the eigenvalues and that sum has to equal one so what can you tell me about each of the eigenvalues they have to be less than one right they can be zero for a mixed state all of these are less than one but they're not necessarily the probabilities they're not necessarily they are the probabilities of a mixing in the eigenvalues but they're not necessarily the probabilities in the original mixing okay so the eigenvalues which are properties of the operator are all less than one if it's a mixed state so what does that mean about the trace of rho squared he's talking about this sum it's got to be less than one so the tell-tale sign of whether or not the density operator corresponds to a pure state or a mixed state is by looking at the trace of rho squared I mean you can look at the eigenvalues but the quick way to do it is to look at the trace of rho squared and this has a name this is called the purity of the density operator you can call also the mix in this but it's typically called the purity and so if it's a pure state then the trace of rho to the purity is one and if it's a mixed state the purity is less than one if it's a statistical mixture of some kind so what if it was maximally mixed go to question what does it mean to be maximally mixed excellent question, I said mixed let's do it let's find that out that's exactly where I was at so in max what do we mean by a maximally mixed state if it's maximally mixed that is what we mean by that is an equal statistical mixture of the orthogonal states that says mixed as you can be for example 50% spin up along z 50% spin down along z that's completely mixed so all the lambdas would be equal? indeed so what are all the lambdas in this case the quick excellent point so what are the lambdas in this case they're all equal and what they have to be they have to sum to 1 1 over d excellent so the lambdas are 1 over d for all lambdas so how could I write then a representation of the density matrix for maximally mixed well to sum over all the eigenvalues each eigenvalue times the eigenvector and the eigenvectors could be anything I like that are form of basis now since it's independent of lambdas bring this outside the sum and so that's 1 over d the sum over lambdas but this is familiar object what is that that's the identity so a maximally mixed state is just proportional to the density I mean to the identity it is 1 over d times and moreover this state it looks the same in all bases this is always what the matrix looks like which means this off-diagonal matrix is r0 absolutely 0 in all bases so the matrix is in 0 but it's off-diagonal matrix 7 it's r0 in all bases if it's maximally mixed so it doesn't matter whether I thought about it as so here is the point for a point I'm Alice I'm going to send you either spin up along x or spin down along x I'm going to do that with a fair point I'm Alice number 2 I'm going to send you spin up along z with probability or spin down with z with probability you couldn't tell the difference you would get random results no matter what you did your result would appear random to you it would be completely a random 50-50 no matter what measurement you did whereas from Alice's point of view she kind of knows if you do a z-measurement but you don't so those are exams of 2 ensembles with your statistics of exactly the same so now what is the trace of rho squared so for a pure state this is 1 for a mixed state it's less than 1 but what's the smallest possible value of purity you can have 0 no it's a good guess 1 over d so let's let's just look at this we have to do this sum over all the eigenvalues I'm saying for dimension d it's not, it's dimension d well it would be the sum of 1 over d squared and then you have them d times so they'll just be d over d squared again which is d 1 over d excellent so the minimum value of this the purity at smallest is 1 over d rho is max so you can't get 0 the purity is always something but that's just the number we get but the off diagonal elements are absolutely 0 for a maximum mixed state so the purity is a measure of how mixed the state is now I should just before there's something I meant to say earlier but I hadn't but let me just say it now some of these concepts are not this is not purely a quantum mechanical idea this is something that you might be familiar with if you study optics and that's the notion of partial polarization and polarization suppose I have the line that's coming out of slide and I looked at it as polarizing and analyzing if I looked at at say vertical half the intensity would come through if I looked at it horizontal no true no we come through but it's not a coherent superposition of vertical and horizontal it's a statistical mixture of those it's not polarization at 45 degrees because if I put it at 45 degrees still half would come through so it's completely mixed polarization now partially polarizing the light that reflects if you studied optics you know that when you reflect some part of it reflects differently than the other and it would be partially polarized so these concepts are classical wave concepts as well where they become quantum is when we think about them as events and probabilities rather than fractions of these okay next so another thing we want to talk about here is so we have we can calculate probabilities if we have a density operator but what about expectation values so what we said here was that given or so this is the probability to find eigenvalue a associated with eigenvector a of some term so this is the problem I could rewrite this in a way that is useful this is equal to the trace of rho with that projector because so another way of writing this probability is the trace of rho with the projector on that this is the projection operator now if I have a remission observable decompose it in terms of its spectral decomposition in terms of its eigenvalues now I can even allow those things to be degenerate that projector could be onto a degenerate subspace associated with that eigenvalue it could be one deep projector like this or it could be that way so the expected value of a eigenvalue well that's equal to the sum over all the eigenvalues times the average value by definition that's what we mean by the expectation value it's the average value and this is equal to this that's what we just said and the trace is linear so I can bring it outside the sum rho doesn't depend on A so I can be and this is equal to this I brought rho trace outside the sum and then I could rho outside the sum and this is the observable A so the general way of expressing the expectation value when I don't have a pure state but I have a general state which might be mixed is to look at the trace of the observable with the state okay and the boardable can be expressed as by a projective measurement the probability I'm going to see that outcome is the trace of rho with the projector can anyone guess if I have a general POVM with POVM elements what is the probability of seeing an outcome what do you think my trace of rho exactly terrific I mean when we had it as a side we wrote it like this now this is the generalization so now you know the most general form of Born's rule that this is the board rule this is really really it it takes into account the fact that your state might not be pure and it takes into account that your measurement might be preprojected that's the most general form and that's the most modern way of saying side star side in the last two plus whatever minutes I wanted to say a couple of one thing about now time evolution so what we said was when we had a if we have a closed quantum system pure states are mapped a unitary operator I'm going to change my notation a little bit I'll fix it in the notes because that's the notation I prefer to use let's say we have the state at time t zero I want to know what is the state at some later time t they're related by a unitary operator which I'll just put these two okay t greater than t zero so this is a unitary operator how does this look just from the point of view of the density operator so the state at time t zero was this the state at time t is a pure state and that state is given by u in depth and this in between was is this so we have for this evolution on a pure state that the state at a later time is this unitary map on this okay, the unitary transformation for a general mixed state which could be in any in some of the confidence in my life then what is the state at a later time if it's a closed quantum system well each one of these guys evolves like this and then that could be brought outside the sum so it's the same thing so if I had a closed quantum system then this is the evolution of the state no matter what it started at okay, this is what we call unitary evolution now what about if I have a closed quantum system what happens to the purity how does the purity change as a function of time it doesn't and how do we do that the trace okay, we want to find what is the trace of the state at a later time that's what we'd like to know so let's plug it in that's equal to the trace of u rho at t0 u dagger times the same thing again and now u dagger u is 1 right? so this trace of rho at time t rho squared at time t is the trace of u rho u dagger we know because we need the homework that you can do the cyclic permutation right? so that's the trace of u dagger u rho squared and that's the identity yay, yay when you have unitary evolution the purity is unchanged and that's what we'd expect that's sort of how we define the fact that the evolution of the close quantum system was unitary because we wanted to say pure states are pure states but moreover whatever mix-it-ness you have that mix-it-ness is unchanged and that's because we're neither losing information nor gaining information okay, what we'll talk about briefly to conclude this discussion next time is that of course not all the evolutions present are purity because for non-states we have to get a thermal state when we take the silk ground that's coming out of the other so we want to talk briefly about that then we have to deal with these