Thank you very much Welcome everyone. We are delighted to be here to talk about scaling batch. I am a workload beyond the Kubernetes scheduler So a quick introduction. My name is antenna Stephanie T and I'm a software engineer after that where I work on OpenShift AI specifically focusing on the resource management for model training I run my name is Anish Astana and I'm an engineering manager on the same team as Antono focus very much on resource management and distributed workloads So for today's agenda, I will start by briefly talking about the key Characteristic that differentiate offline job from online services will then take an example and see how those characteristics some of them Make it challenging to scale the exception of bad job on Kubernetes using the default Kubernetes scheduler We'll then move on to review the different classes of Project batch scheduler project that have emerged in the ecosystem and that I'm at solving those challenges And then we will go over briefly in more detail some of these projects so to To start the and it's important for the discussion that we we are going to be having in in that presentation Just quickly see what differentiate offline jobs from online services that we know Kubernetes is good at orchestrating well So a typical example of an online service is a web application a Microservices is kind of architecture or several less application So these are mostly stateless application where the replicas are homogeneous. They are like the same Kind of workload That are disposable and generally the Processing unit is the request and it goes to being processed by a thread or a routine and as a platform and instructor The KPI or the SLI that you're really interested in is the latency and the availability of your platform and from a compute When it comes to sizing the cluster from a compute standpoint You would take like the expected load model from let's say your production environment and it would be fairly easy job to to size the cluster accordingly to the load that's expected and and the Viability of the load would be fairly limited which it's that generally The way you would adapt to the variability of your load into is to autoscale at the pod level So on the other end of flying jobs bad job such as like a IML distributed model training or a spark job or a ray job for example These are mostly stateful application that are made of like heterogeneous replicas the prime example being like you have a driver Process or let's say your leader that is responsible for coordinating multiple workers The processing unit is more like the worker that is going to process data partitions or data shards that are allocated to each worker And from an administrator standpoint you're more interested into maximizing the throughput of your platform And also the efficiency or optimize the usage of your resource or of your platform is And when it comes to sizing the cluster It's a bit more difficult because the the activity of your user that directly translate to a viability of loads you can live like peak usage where Lots of jobs get submitted and generally that means that when you want to really adapt be capable of adapting to that Magnitude of variability in the load you would ready Autoscale at the node level at the cluster level So when it comes to highlighting what are the key challenges when it comes to scaling batch job scheduling on the Kubernetes scheduler We've the Kubernetes scheduler. We've taken a fairly simple example. So scheduling a thousand batch job each of them having ten parallel pods a Simulating like a completion duration between three minutes and five five minutes around five minutes The key constraint being that all the pods have to be ready So the entire job can start its progression So that that kind of like is the constraint that you have when you you do like distributed model training They all your worker pod they have to be online and the leader as well So and the training can progress and we set a completion deadline to 15 minutes So that means that when the deadline exceeds all the All the pods for that jobs get terminated and the jobs get Terminated as well. We schedule those jobs on a hundred nodes. We we've been using quark to simulate the node So quark is a very good like project to ease performance testing for Contrombene components and and you don't have to have like real physical server to do that So given all the parameters there the A total request resource request for the jobs what's available for from these hundred nodes and the average duration time for the job it It gives us like the theoretical maximum throughput for the platform for for the the execution of those jobs Which is around roughly a thousand jobs Completed in ten minutes. So that's kind of the key A performance indicator that we wouldn't expect to be Provided by the Kubernetes scheduler So here is the result of running that simple example with the Kubernetes the default Kubernetes scheduler and we see so here we see that a large percentage of the job fails and And and so we see that quickly as the jobs get gets created The saturates the the saturate the Available computer resource provided by the nodes And there is simple simply not enough like bandwidth for all the job to complete within their Before they are completion deadline Exceed so as the job saturates the available computer resources We see that a there is an increasing number there of scheduling items that fails and it takes an increasing number of attempt to get But successfully scheduled and similarly takes an increasing amount of time For a single pot to be successfully scheduled on the platform Another interesting aspect also is that with that simple test we see that It also impact the scheduling of Other kind of workload likes some of those that could be scheduled beside the test job The average scheduling time is for for the pot that have the same priorities impacted on the other end It's still the skin the Kubernetes scheduler still does a fairly good job for the higher priority pot So we are not going too much into the details today of how the Kubernetes scheduler works It's more for people interested if you want to already get deep into how the Kubernetes scheduler works There is a good resource in the C scheduling project and that explains exactly how the Kubernetes scheduler works So with that example That limited bandwidth that the system provided It could be mitigated by increasing the Completion deadline that we've set but there is a major a more problematic issue, which is resource fragmentation So here what we did like we increase the parallelism of the job that we schedule So instead of having a thousand job with it each ten pods. We only have a hundred Pod but this time they have like Android pods each so we still have the same Amount of computer requests It's just that they are distributed differently and we see that by increasing parallelism The failure rate also increases. So we we started with 51% of failed job and now we have 81 And the reason is that the Kubernetes scheduler have no idea of The constraint that there is that the all the pod for a single job have to be scheduled Atomically As a group so basically what happened is that we end up with many jobs that are scheduled partially And it ends up in it in a kind of a date lock situation and no matter no matter how much extra time we give to the system to to Work we were here in we've re-run the test and we instead of having at the line of set to sit to 15 minutes It said it's it's set to one hour and and it does not any good We we still have a fairly very high level of failure and and we see here that the the Kubernetes scheduler just struggle and and at each scheduling cycle it retries, but there is no chances that By chance it schedule the entire set of pods for a single job. So that that problem is It's supposed to be solved by a Plug-in a cube scheduler plug-in. That's called the co-scheduling plug-in So what it does is like it extend at some extension point the default Kubernetes scheduler and it sort All the pods in the scheduling queue Continuously force for each job so that they are continuously scheduled and it makes sure that It only binds the entire set of pods for a single job when There is enough resources and that the entire set of what can actually be scheduled So here we've rerun the test using the by enabling the co-scheduling scheduler plug-in So what one thing for us to mention is that like it does a very good job like the the the entire set of jobs or the The Android jobs they successfully complete Then the major thing to mention is that it takes a very long time for all the job to complete and It's much higher than the expected theoretical maximum throughput. We had like computed before It's almost a other magnitude larger than longer than the 10-minute theoretical maximum throughput and the reasoning is that probably for each Scheduling cycle here it operates on the entire set of pods So it's it's at each scheduling cycle It's going to sort the 10,000 pods and it it really leads to a significant increase in basically the the scheduling items Average time now there may be quick things to mention is that It does a good job also at not impacting the other Kind of workload that can be scheduled. So any schedulable pods with default priority or even higher priority is not affected by that and Here is just an example Apprenting the example where we have a thousand Best job, but this time we use a Those job scheduler crew manager project. So for instance here, it's using Q So we were in the exact same test and yeah, we see that We've such a project for in that example Q It's all told the execution of the jobs here and it makes sure that it does a very good job at maximizing the Optimizing the available resource usage and it's also very efficient at I Executing all these these these jobs and here the Total completion time is 15 minutes, which is very close to the maximum theoretical for boot We also see that Almost all the pods get successfully scheduled in one attempt here Same year for the average duration It's it's very nominal and by doing that is it really relieves the scheduler the default Kubernetes scheduler activity Here we see that it's an order of magnitude lower in the number of scheduling attempt and same year for the other kind of workload Pods, they are not affected by Whatever we do for testing there. It's very low nominal average scheduling time and And last but not least just the example where we increased the parallelism here are still with Q so 100 job with 100 pods and and it does not like Make any difference because Q operates at the job level. So no matter how distributed the job is it's still able to do a very good job at maximizing the resource usage and also same the Completion The throughput is very close to what would be an optimal throughput. So now that we've seen Basically the the challenges that comes with the default Kubernetes scheduler and an example here of using a Q manager source as Q I'll end over to any age that is going to talk a bit more about those kind of projects All right Yeah, so again, I said like he's given us a lot of the motivation for why you would want some sort of job scheduler We can talk through some of the options we have now First up you have your custom schedulers and you have your Q managers Custom schedulers replace or extend the Kubernetes scheduler But then there's a kind of ends up being the same thing. You are changing how scheduling works for your cluster They operate at the pod level for the most part and they're responsible for both queuing and admission of jobs as well as your scheduling Great in practice, right the only downside is that there is a Pretty big impact in that you are changing the default scheduler for your cluster Q managers are but it's in the name. They are solely responsible for queuing and admission of your workloads They usually operate at a higher level on some CRD. So it could be like your jobs by torch jobs, whatever and They're pretty lightweight you usually just get a control or maybe some CRD sort of configuration Now our case for OpenShift AI like we had queuing requirements pop up has and now motivated it and We lent we were leaning more towards Q managers and just due to the fact that there's less Possible impact on customer clusters right like we are asking you to install a custom scheduler on your cluster It's going to be a little challenging Next up I'm going to talk through some of the options as we understand them First up I'll talk about coordinator with a key like everything else in Kubernetes It comes with a custom scheduler an admission by book and a demon set running on your nodes The interesting thing about the demon set is that it is profiling the actual memory usage or resource utilization of your nodes So it can really try to eek out As much use it as possible of your nodes It provides gang scheduling via the pod group API What this means is that your pods will not be bound to nodes unless every single pod in that pod group can Be bound to a node. It also provides additional QoS things for It provides custom QoS is for when Kubernetes QoS is don't suffice for whatever you're trying to do It provides quota managers quota management as well for that All they're doing is they're extending the cube scheduler last Dakota API with some custom Anundations to help support multi-level coders Last up they do have support for heterogeneous clusters if you have different types of hardware nodes or specialized nodes They provide a device API that can be used to inform the scheduling And they also support fractional allocation of your CPUs and GPUs The cluster auto scaling is pretty normal They just use the inbuilt like cluster auto scaler and they don't have multi cluster support I'm calling this out. They're not like as a con for Coordinator, I think for most schedule we think for most schedulers Multi cluster doesn't really make sense Because a cluster a scheduler should be looking at the cluster. It's operating on Next up. I'll talk about MCAD. MCAD is a Q manager It's a controller that comes with a couple of CRDs for configuration as well as a CRD for your actual Application the CRD is called app rappel Our app rappels operate is that you take whatever workload you want MCAD to queue for you and you just They copy paste that into like the app rapper format the app rapper just contains a little bit of additional information that is used for scheduling This provides you with a lot of flexibility right as a user or as someone trying out a new technology You don't have to update MCAD all you have to do is give it the right R back to operate on this new CRD And then you're good to go One possible point of friction here though is that as a user I may be familiar with upstream CRs and now I have to make changes to my processes to work with MCAD I'm kept provides all the core things you care about with queuing so preemption borrowing priorities gang scheduling It also provides multi-level coders and it uses Kubernetes extended resources for dealing with You know specialized hardware requirements It supports auto scaling via the machine set or machine pool APIs on OpenShift And it does have multi-class to support which and as a queuing system. It's more able to Talk to other clusters Next up. I'll talk about volcano. I'm sure most people here for the volcano It's a custom scheduler which has a controller and some admission web books It does it is a little interesting or different and that it also has its own job APIs Which for the most part I just bought template specs with some additional scheduling related metadata This is they have a lot of community integrations as well. So You know cube ray spark you so they all have volcano related integrations, but and I'm sure this is much longer list They support all the core things you care about with queuing And the one thing I'd probably call out is that they use custom APIs in walking They use custom APIs for the most part for everything these APIs are pretty comparable to what's in community, but it's in the volcano umbrella They have quota management as well. It's single-level coders And one interesting thing they do do with you coders is that you can have proportional queues or coders What this means is that you can allocate 30% of a cluster to a quota and as the cluster scales up and down that queue will also automatically get readjusted It uses Kubernetes extended resources for the again petrogenous clusters and it's also numerous so you can Do more fine-grained allocation with your CPUs it supports our auto scaling via the cluster auto scaler and I think there's a talk today earlier today actually about multi cluster support where it's delegating to external projects The last custom cuz schedule I talk about is unicorn Unicorn can be deployed in two different ways either standalone or as a plug-in to the Kubernetes scheduler But the end results the same you're really updating the behavior of your scheduling It comes to the controller and some admission webhooks it operates on any Pods and the main thing it's doing is like it's making sure that any incoming pods Get transformed and the scheduler set to refer to unicorn. It provides all the core Queuing capabilities that you care about One interesting thing that they're doing in it actually is placeholder pods So when you have a job or workload waiting for admission Unicorn will start creating a placeholder pods on your nodes to start reserving resources The minute you have enough placeholder pods on the nodes for the workload to actually run it mutates those pods into the actual workload and Basically you've got like a guaranteed execution at that point for quota management. They have a custom language and Configuration parts they also do the same thing for our back. It's Interesting right like it's a divergence a little bit from Kubernetes But also lets you do some things that normal Kubernetes our back doesn't let you do it supports Kubernetes Extended resources and it works with the cluster order scaler as well Lastly, I'll talk about Q Q comes with a number of CRDs related to configuration it operates on a predefined set of CRDs which means that if you want to Start queuing a new type of workload with Q you're going to you're going to have to make code changes both in queue as well as in like whatever upstream CR you want to support The benefit though to this approach is that as a user you really don't have to do much if I'm used to submitting normal pytorch jobs just continue doing that and If Q is running whether it's not running doesn't really affect me beyond you in capabilities coming in It provides all the core queuing capabilities that care about and it's also extensible using the admission check API So for instances where we find that Q doesn't meet your needs. You can just Create a custom plugin for it It provides quota management the quota management only has two levels of coders and it allows you to share between coders and all that one stuff For heterogeneous clusters, they provide a resource flavor API that is also used for scheduling So you can submit a workload saying hey I want a BNC resources and Q will make sure that the right gains taller the right tolerations and node selectors are applied to your workload as it gets submitted it provides Autoscaling capabilities via the CA cluster autoscaler provisioning request API and they just recently introduced alpha support for multi clusters That's the end of our slides, but like I'm sure you can guess at this point that we've gone with Q as a solution As we were looking at the job schedulers options out there Customs schedule is pretty much immediately went out of the window due to the fact that you have a really wide impact Right, like you're changing the full customer cluster behavior for scheduling a lot of customers would just laugh us out of the room at that point While we were looking at the two these two Q managing solution and solutions We went with Q with a K since there is minimal impact on users for adoption With MCAT we have more flexibility, but having to adopt a new CR introduces another barrier to entry for people who You know want to do things with minimal effort Well, yeah, that's all we had we have any questions Thank you for your talk My question is that in all of these schedulers Q things. I might be missing with something but is there any of them that predict the Workload how much for example time does it need To complete on on the workload not on the node itself So because it's a common practice in a scheduling And I want to see if there is any specific things for AI in this term like AI workloads so if your question is about like providing an ETA for a job like At the moment At least as far as I know they don't provide some such an information given that They run like arbitrary workload and and they don't have the knowledge about what is being actually Scheduled or Q on the other end you have some project that provides some visibility on on on the queue Like the position of the job in the queue Etc. I think that's the next step actually for this project like to provide those kind of like We could call it like an intelligent matrix But based on because they would have to learn about The workload they are managing basically some are like Be able to capture some insight of them and be able to like doing some even you know The same kind of stuff that you do with time series forecasting or stuff like that You try to like find similarities and then you can provide some some estimate But at the moment, this is a separate concern as far as I see it But it's generally a typical request that we have from end user like from so this project generally They have like two personas like you have the platform administrator the one that operates the project and generally You really want to make sure the platform is stable. You have a good support and and that is Basically what he care was about but then you have the actual end user like the data scientist or whatever is submitting job and then That kind of matrix that this is the matrix. They are really care about like on their own for their own job Well, I think we're at time as well. So thank you very much for your time. Thank you


But it is now time for Member's Statements. Member's Statements, I recognise the Member from Toronto, St Paul's. I've got a message from St Paul's for this Conservative Government. Hands off Ontario Place. Keep Ontario Place public. This Government has quietly taken down the Ontario Place statement of heritage value from its website. It's not the first time this Government has disregarded culture and heritage. Last year, Architectural Conservancy Ontario and other key heritage stakeholders were not consulted on the disastrous Bill 23, which served as a slap in the face to our Ontario heritage system. Their Ontario Place redevelopment deal, or scheme? Same old deal. No meaningful consultation with community, Indigenous landkeepers, environmentalists. Even its own landscape architects have stepped away from this Government's ill-fated project due to its attack on climate change, including tree clearing, which would essentially kill decades-old wildlife habitat. I oppose this Government's new no-deal for Toronto Act. It stinks of preferential treatment for friends and wedding guests, and disregards comprehensive environmental and heritage assessments that should be necessary for large-scale infrastructure projects. Bill 154 allows for a Government power grab bypassing breaking multiple provincial laws in order to complete Ontario Place redevelopment on behalf of their private luxury-buddy firm. And don't forget, folks, the secretly publicly funded garage. We stand with Ontario Place for all, future of Ontario Place project, and thousands more across Ontario, saying hands off our Ontario Place. Thank you. Thank you very much. Members' statements? The Member for Oakville. Thank you very much. Here, and I first want to say happy Scottish Heritage Day to everyone in Ontario of Scottish Heritage. As Member of Provincial Parliament for Oakville, I'm proud to discuss yesterday's passing of the fall economic statement. I'm honoured to highlight some of the significant strides that our Government is making for the people of Ontario and my riding of Oakville. This plan features some of the most ambitious capital spending in our province's history, totaling $185 billion over the next 10 years. Let's dive into some of the initiatives that will make life better for the residents of Oakville. We are extending the cuts to gasoline and fuel tax rates, maintaining them at $0.09 per litre until June 30th, 2024. This initiative will continue to provide financial relief to the residents of Oakville. We are also enhancing the Ontario flow-through share tax credit to maximise opportunities in critical mineral exploration. This will not only improve access to capital for small mining exploration companies, but support industries such as the Ford Auto Plant in Oakville, which is critical to critical minerals in Ontario here. We have expanded the provincial eligibility for breast cancer screening for women ages 40 to 49 to underscore our commitment to health care and early detection. This expansion will directly benefit the women of Oakville, ensuring they have access to vital health care in our community. And as auto theft has increased in Oakville and across Ontario, our investment of $51 million to fight auto theft and assist police in identifying and dismantling criminal networks will help make the residents of Oakville live in a safer community. Thank you, Speaker. Thank you. Member Statements, the Member for Ottawa Centre. Thank you, Speaker. I'm rising this morning to pay great thanks to Dr. Danielle Brown-Schrieves, who's a family physician in our community, who has just been recognised by the Ontario College of Family Physicians as being a regional family physician of the year. She just won a Reg L. Brand Perkin Ontario Family Physician of the Year award by her colleagues. And let me tell you why, according to her colleagues. Dr. Schrieves-Brown leads the only black-led team-based family physician clinic in our city. Dr. Schrieves-Brown opens up wellness day opportunities for people in our city who do not have health coverage because of their citizenship status. Dr. Schrieves-Brown spends her own time meeting directly with settlement agencies in our city, above and beyond what we would expect health practitioners in our province to do. And that's what leadership looks like to me, Speaker. That's why I want to thank Dr. Schrieves-Brown and her team from the bottom of my heart for all you do to keep our city healthy. Our city is living in a context speaker where at least 150,000 people do not have attachment to a nurse practitioner or to a family doctor. This government has only allocated $30 million in the next two years. That's $2 per ontarian. To expand primary health care, they should sit down with Dr. Schrieves-Brown, they should sit down with the restored clinic, and they should listen to other initiatives from Ottawa Centre. I'll be talking about in this House in the next two weeks to put us back on track. But Dr. Schrieves-Brown, thank you for your service. Thank you very much. The Member for Simcoe Grade. Good morning. I stand today to talk about the incredible history of volunteerism in my riding of Simcoe Grade. Indeed, Speaker, it is part of the DNA of our residents. And as we get close to entering the month of December, and we reflect on the end of year and the start of a new one, I think about a full year of successful events, of charitable fundraisers, of community gatherings, and of sporting events that have brought the people of Simcoe Grade together.  And the impact that this has across our communities, the ripple effect that it has, it goes to show that the saying, how high tide raises all boats. Speaker, the word community in my mind is derived from two root words, common and unity. And our communities work together to ensure that they are supporting their residents in a compassionate way, growing community spirit that can only happen when we work together. Speaker, recently I was notified by the Ontario Ministry of Citizenship and Multiculturalism that over 30 residents of Simcoe Grade are being recognized with Ontario Volunteer Service Awards. And I want to thank each and every one of those individuals. These years, this year's recipients truly represent the qualities that make Simcoe Grade so strong. And each in their own way, and of their own story of volunteerism, has made our community stronger, more resilient, more inclusive, and more compassionate. So thank you to each of those volunteers and congratulations. Thank you, Speaker. Thank you very much. Members, statements. The member of Flannark Frontenac Kingston. Thank you, Speaker. Giving Tuesday was earlier this week, the world's largest generosity movement. It was created in 2013 in Canada with a simple goal of encouraging people to do good in their own communities. Giving Tuesday has spread to over 90 countries, including thousands of non-profit organizations participating in whatever ways they can. Speaker, many organizations in my riding of Flannark Frontenac Kingston participated this year, highlighting their missions, asking for donations, and gaining new supporters. Organizations like the Person Smith Falls District Hospital Foundation, who are seeking for donations to their MRI campaign. Lannark County Interval House is requesting donations to its Christmas holiday program, as well as becoming a volunteer. The Lannark County Community Justice Program is appealing for socks, mitts, or gloves that will be donated to someone in need. And Southern Frontenac Community Services celebrated Giving Tuesday by acknowledging their wonderful volunteers and thanking the public for rallying behind its mission to work with others to provide health and social services. I would also like to congratulate the Perth Lions Club. I had the pleasure of attending their 70th anniversary celebration last weekend, 70 years of service and giving back to its community. Let's all think about how we can lend a hand to one favorite non-profit, not only on Giving Tuesday, but throughout the year. Thank you, Speaker. Good. Member's statements. Okay. The Member for... Member's statements. The Member for Cambridge. Mr. Speaker, it's an honor today to speak in front of the House. I would like to speak about the people in my writing of Cambridge, who are truly fortunate to be cared for by countless organizations dedicated making their lives better. Among those organizations is the Southwestern Ontario Aboriginal Health Access Centre on Cornation Boulevard, which provides quality health care and services to Indigenous peoples. With six locations in southwestern Ontario, the organization recently marked its 25th year of caring for First Nations. Inuit and Métis peoples, from Windsor to Waterloo Wellington and north to Owen Sound. In that time, they have provided care to more than 35,000 people. A highlight of the 25th anniversary was a grand opening of a location on Dundas Street in London, Ontario. However, celebrations will continue in the next couple of months. The Southwestern Ontario Aboriginal Health Centre was found in response to academic, excuse me, epidemic, systematic health disparities and things that were not equal within the Indigenous population of Ontario. Its mission is to empower Indigenous families and individuals to live in a balanced state of well-being by sharing and promoting holistic health practices. The Centre provides innovative Indigenous informed care through a combination of health and social services. This past summer, myself and MPP Don Gallagher were honored to attend the grand opening of the ceremonies of the Cambridge location, where we were treated to traditional sights and sounds of Indigenous culture. And we were privileged to have Amil with the Centre and they served buffalo meat, which my EA Grace Camara had never tried before and now she's a lover of that meat. Thank you. Thank you very much. I recognize the member for Ottawa South. Thank you very much, Speaker. I was pleased to join members of the Lebanese community and my colleague from Ottawa, Vanie, yesterday to raise the Lebanese flag in recognition of Lebanese Independence Day. On November 22nd of 1943, Lebanon was declared a sovereign nation following 23 years of mandate rule. November is the Lebanese Heritage Month here in Ontario. It recognizes the many contributions of the Lebanese community across our province. I was proud to introduce Bill 60 here in the legislature, the Lebanese Month Heritage Act, and I would like to thank the member from the PN and the member from London West for helping to pass that into law in 2017. In my writing of Ottawa South, we have a very strong deeply rooted Lebanese community. Every year there are wonderful celebrations in our writing, celebrations of Lebanese culture, such as the annual St. Elias Festival. It's one of the biggest festivals in Ottawa and actually one of my friends, Michael Kakish, met his now wife there. At the Lebanese Festival. And I always like to say about the festivals is that they combine the five Fs, which is faith, family, food, friends, and fun. It's really, if you're ever in Ottawa in the middle of July, please come. Lebanese Heritage Month is an opportunity for Lebanese Canadians to celebrate their culture and traditions. It's also a great opportunity to recognize and educate future generations about the great contributions of the Lebanese community has made to our community, to our province, to our country, and to the world. Contributions made, but not limited to, law, science, politics, business, and culture. Happy Lebanese Heritage Month. Thank you very much. The member for Scarborough Centre. Thank you. Thank you, Mr. Speaker. I'm honored this morning to announce that well-granted real estate dedication has elevated them to, as leaders, in purpose-built housing where, from being final in the North American division, are now winners of the 2020 Theory Wholesome Gold Award in Global Competition for Excellency in Sustained Architecture and Design in Venice, Italy. And it gives me great pride to report that this project is taking place in my right in the Scarborough Centre at 1925 Victory Park. This purpose-built is a mid-market rental building that fulfill a critical void in the marketplace representing the scalable strategy for solving Ontario's housing crisis for which our government, under the leadership of the Premier, is tirelessly working to solve. Mr. Speaker, I'd like to welcome Jordan and Gabriel Diamond, both vice-president of the well-granted real estate for taking us to the world stage. Welcome to your house. Your accomplishments not only bring pride to yourself, but to all Scarborough Centre residents, all Ontarians and all Canadians. Thank you and congratulations for your success, but also to elevating Scarborough Centre on the world stage. Thank you very much, Mr. Speaker. Thank you. Member Statements, the member for Parkdale High Park. Thank you, Speaker. I stand today to honour firefighters like Captain Sean Coles, who served as a firefighter for 24 years, nearly half his life. He was diagnosed with stage for esophageal cancer and is not expected to see Christmas. He's the father of two kids, and after his diagnosis, Sean not only had to fight cancer, but also fight to ensure his family was supported, because even though he had dedicated 24 years in service, he was one year short of qualifying for benefits for his family. The blue bracelet I'm wearing was created to raise funds for Captain Coles' family, who would have been left without their father and unsupported. Thankfully, just last month, the latency period for esophageal cancer, the mandatory period of service before qualifying for financial support, was reduced from 25 to 15 years. Sean has the relief of knowing his family will be financially supported. As well, his name will be added to a memorial, showing he gave his life for something bigger than himself. But, Speaker, more must be done. The risk of kidney and skin cancer is also incredibly high, and their latency period must be lowered. The restrictions for eligibility for colorectal cancer must be changed. It makes no sense that once a firefighter reaches 61, they're ineligible for support, even though they can serve on a truck until 65. Firefighters die of cancer at two to four times the rate of the general population. They're at the highest possible occupational risk for cancer. We must step up for firefighters the way they step up for us. Thank you. Thank you very much. Member statements? The Member for Burlington. Good morning, Speaker. This year, at their 2023 Distinguished Entrepreneur of the Year Award Ceremony, the Burlington Chamber of Commerce paid tribute to Al Taylor. In 1959, on his 20th birthday, Al founded Taylor Moving and Storage. In the 63 years since the company's founding, Al Taylor estimates his company has moved more than half a million people. Speaker, that's more than the number of people who currently live in Hamilton. Today, Taylor Moving and Storage employs more than 120 people, including Al's sons and grandson. From the very start, Al knew the importance of keeping his business in the community. His story, rooted in hard work and determination, mirrors the very soul of entrepreneurship. From sweeping floors at 14 to driving trucks at 16, Al's early days provided a hands-on education in the School of Hard Work. He hustled, built relationships based on integrity and trust, laying the foundation for an extraordinary legacy. Al's story embodies the Canadian spirit of entrepreneurship and community building. The Taylor legacy continues through Al's sons, Richard and Russell Taylor, who purchased the company in 2002. I would like to congratulate Al Taylor for his years of service to the Burlington community. Thank you. Thank you very much.


What's up everybody Jason here for jazzy's case breaks calm 2020 panini contenders baseball four box break picker teams number four Just sold out which is from a fresh case guys, and if you buy two or more teams We're gonna give away five hundred dollars in break credit. Whoo It's great So again how to get entered into five hundred dollars break credit potentially get about two teams in this break so if you buy two teams you get one entry into the giveaway by four teams you get two entries by six teams you get three entries and We'll do that randomize at the end of the break So if you only buy one team you not get entered to win guys again top five will win a hundred dollars each I'm sure we're no veteran commons. We'll ship out of here So let's do this. I'm not sure if I print out the list yet, but here's everybody else I bought in Into the break itself. Let's print it out And then here is the fresh case Six on each side. So we're gonna do this for here make one break for here One break and these four here make one break So if I roll a one two, we're gonna go to the left side or roll three four We're gonna go to the middle five six with the right side right here Five one two three four five six So this year will be for the picker teams and let me also just like Write PYT on each one. It's cool. Yo, awesome. Oh guys. Good luck. Here's everybody in the break. All right We have a game 31 draft ticket to 149 Clayton Kershaw One of the Dodgers and Keen Wong for San Francisco first auto Giant's Winner Raymond Debbie grew long for Philadelphia rookie ticket and Jordan Walker So for some of these guys will look this up through the checklist on group brick checklist So I'll put that over here and then we'll tag them for you guys So you guys know right away who we're looking for Mick Abel Abel Walker's Cardinals, thank you George If you're on the checkers, let me know the other one But no rush. I still like to show it on the video anyway, so Nick Nider from Miami. I'll look at my back at the end of the break de-fest We'll do them all at once. So I'm putting them both separately I will don't I will show it to you guys on the video to confirm it. So don't worry Nick bits go We'll leave those over there. Okay And I'll put a little tag here on the top loader. So that way we can write it down Doesn't get left out So we'll look up most of those prospects at the end of the break. Okay, we just started the first box Nick This is the pick your team number four Garrett Crochet look at that one as well. These are all just base cards guys Some season tickets and these will ship because they are purples And we got Jevon Ward for Milwaukee. All right, thanks, George I'm still gonna look them up at the end of the break so everybody can see it on the video But thank you man. Is that gallon for Arizona at a 50 that's on card as well Very nice Arizona Artuta 99 draft picks Nolan or not. Oh and Miguel Maya for Chicago and Randy Arosa Raina Rookie ticket that's gonna go to the Rays and last spot module Daniel. There you go, man very very nice and Edward Ozole Rookie ticket for Chicago Cubs also going to Daniel well There is gonna be a new golf product coming out finally Pete after so long with upper deck I don't know when it comes out, but yeah, we'd have to we'd have to find some product For sure Yeah, we're excited of the return of some golf with over deck. It's gonna be sweet Next box next one and Matt dies.  Yeah upper deck golf is strong price Jarvis Draft ticket again, we'll look this one up as well with group break checklist and Tag it for the shipping team as well Put that on that stack right there Quang young Kim. Oh One out of ten a little mojo See that right there. That's pretty cool That is for St. Louis going to Jeffrey Rookie ticket. Oh with all the Tiger Woods Pete. I've seen I don't yeah I've seen one of those that's the one you're talking about They did one of those not so long ago with like all Jordan's Brandon Wilson or Williamson. Sorry for Seattle Evan Is that fitterer? Yeah, fitterer It's just amazing. I was like man, are they just trying to like dump their auto sticker dump over something Oh, I see one. It was a little bugger. I've had like ten Michael Jordan autographs. Okay. I mean, it's so cool Dray Jameson Arizona Some of these autos really quick. All righty guys one more box. Like I said, we'll check all those collegiate autographs Once we're done with this box here I'm flipping back and forth with the Chargers Raiders and the Dolphins Cardinals Gavin Lux. Look at that Daniel you guys have a very nice one. That is a cracked ice 13 out of 23 Rookie ticket that is a beautiful card Love the cracked ice. That's a sweet one man and on card as well There you go It's been a while. All right Drive taking Max Muncie You got Ryan Nelson. All right, four more packs Brian or Bray you for Houston run Eric Jalen Davis San Francisco Victor Vodnik for Atlanta and Abraham toro to 75 All righty guys, so let's double check those proxmic autos but This was a nice little four boxes. Remember we still have another two-thirds of the case all these tickets rookie tickets draft tickets will all go to the Teams that are affiliated with them that's a nice little cracked ice Gavin Lux Out of ten right there Very very nice Brand new rules are in as well. Now. We'll look at these ones right here. One two three four and five George said that was St. Louis, but we'll confirm that I do trust him though Well, let's actually just switch over to the checklist really quick All right, so Jordan Walker is St. Louis Cardinals. So we do have that right. Thank you George We'll go Bryce Jarvis to Bryce Jarvis's diamond backs for Arizona diamond backs without one The next one would be Garrett Crochet would be White Sox So White Sox, there you go. That'll be Daniel Nick bit go would be Tampa Bay rays Which would be Daniel as well Mick a bell would be Philly's So there you go So make a bell Philly's Bisco TB crochet White Sox Jarvis, Arizona and Walker St. Louis So appreciate it guys. It's the tenders baseball four box pick a team number four now guys Let's see who has two or more teams to have a chance to win up to five hundred dollars in break credit So good luck. So let's alphabetize the customer name list So our thorough you have to that'll be one entry Daniel with Sevens we can only give you three spots Daniel, but good luck Eric with four that'll give you two entries Jeffrey Goldberg with six that'll give him three entries Matthew with just one Mike with two Oliver with two so each of you guys get an entry Raymond with four and Russell with two so They go Raymond with two Russell with one and there you go Put you guys in here 14 possible entries roll it It's a five and a four nine times customers one through five get a hundred bucks each one two Three four five six seven eight nine Boom Nine times Jeffrey at one all over to Daniel three or doodle four and Daniel five So again top five will get a hundred dollars each guys And I'll be sending that out to you right now at the end of this video Jasper's case breaks


Thank you very much. Thank you also very much for giving me the opportunity to talk here. I have been asked to give a presentation of my recent work on quantum electrodynamics in 2 plus 1 space-time dimensions and in particular the possibility of spontaneous breaking of Lorentz symmetry in this theory. And this is basically a follow-up work on an old project done with Holger and Jens and Dietrich a couple of years ago. So why it all should one be interested in studying quantum electrodynamics in three space-time dimensions? Well initially this theory was just conceived as a toy model for in fact the theory of quarks quantum chromodynamics in four space-time dimensions. And this is because it's a much simpler theory than QCD on the technical level, but in terms of physics It's very similar in particular. It's it's also asymptotically free once we go to shorter distances to the end to the ultraviolet Then the gauge coupling the fact-defined structure constant goes to small values But in the infrared at larger distances then the gapless fermions interact strongly and in fact they might develop spontaneously Dynamically generated gap to to a chiral symmetry breaking in its compact version also QD3 might show a confinement transition However, it was then later realized that in fact QD3 is much more than just a playground for theories that more than just a toy model it describes real physics real materials and And in particular it has been derived as an effective low-energy theory for the super round taking states in the high-temperature Cooperates but also in very different other aspects of quantum condensed metaphysics this theory kind of pops up For example in in spin systems with just localized spins the elementary excitations being just Yes, I spin degrees bosonic spin degrees of freedom when there is strong frustration say on a triangular or a Kagami type of lettuce then this theory might Develop a spin liquid ground state with fractionalized excitations which turn out to be of fermionic nature and In particular in in certain cases then these fractionalized excitations can be Dirac fermions coupled to you one gauge fit QD3 very recently QD3 theory also popped up in In the fractional quantum Hall effect as in field theory for the Huffield Landau level state and a simultaneous development was to generalize the bosonic particle Bortex identity to fermionic systems with at its heart lying the conjecture that the dual description of Single Dirac fermion as it occurs for example on on the surface of a topological insulator is in fact again QD3 For all these applications the number of fermions that couples to the you engage field differs For example, it's n equals 2 in numbers of in terms of four component fermions in this high temperature corporate Application in order to make use of these of these effective theory with Therefore need to know the ground state as a function of and the number of fermions in fact this ground state t equals zero phase diagram was under debate the last couple of 30 years or so and The kind of common more or less scenario is is that we have two phases There is a lot at large n large number of fermions There is a conformal phase with a conformal fixed point interacting gapless fermions Which in condensed matter physics could be understood as a non-framing liquid however below a certain critical number of fermions the number of which is under debate Fermions are expected to develop a dynamical gap Carol symmetry breaking and in in condensed matter physics. This could be understood as a more insulator In this talk, I'm going to argue in a certain controlled limit of this theory that it's Impossible to have a direct transition from this conformal state to the current symmetry break and broken phase In particular, I would therefore distinguish between two different critical flavor numbers And I call them the conformal critical flavor number below which conformal symmetry the conformal state becomes unstable and the carl critical flavor number below which the carl symmetry breaking occurs Well in particular show that this carl critical flavor number is smaller than the conformal critical flavor number at least in a certain limit of this of this theory There's therefore an intermediate phase and I will argue that most most likely this intermediate phases characterized spontaneous Lorentz symmetry breaking Here's the outline of the talk I will start with epsilon expansion around the lower critical dimension of two space-time dimensions To show that there is a finite conformal critical flavor number for any finite epsilon Below which this conformal state becomes unstable But this conformal critical flavor number becomes arbitrarily large as long as we're going close to this lower critical dimension In the second step, I will then argue using some RG monogenicity arguments that We can find an upper bound for the possibility of carl symmetry breaking which in fact in the in this limit close to the low critical dimension Being just one in terms of four-component Dirac fermions There's therefore a large range of values of n below which Carl symmetry breaking is forbidden, but the conformal state is unstable and finally I use mean field theory again This this this RG monogenicity arguments the f theorem as well as an independent susceptibility analysis to argue that this intermediate phase between Carl and KSB and and conf is governed by a vector order parameter V mu which gets a vacuum expectation value Here's the model Plane QED but now below four space-time dimensions Field strength tens of f coupled to Dirac fermions psi and psi bar via this covariant derivative capital D and this this Derivative involves the gauge charge if you like e and e has mass dimension e squared 4 minus d So that means below four space-time dimensions It's a relevant parameter towards the infrared and therefore goes to larger values of the coupling To the ultraviolet. However, it goes to smaller gauge coupling and therefore QED 3 is is is asymptotically free and super This theory enjoys the carl su2 and symmetry where Correality is in that respect in this three space-time dimensions just a consequent of the reducible Four-dimensional representation of the Clifford algebra. We use four component Dirac fermions Has explicitly the parody symmetry parody anomaly is absent and noture in Simon's term is generated Of course Lauren's symmetry and local you want gauge symmetry is also enjoyed by this theory Once we do our G However, new interactions which are not present in the initial action can be generated by the loop corrections Most of them at least close to the lower critical dimension will be irrelevant just by power counting however local for fermion terms are marginal in two space-time dimensions and Any interacting fixed points in in two plus epsilon dimensions Therefore, we have to take them into account because they can become irrelevant at such an interacting fixed point fortunately the number of of Such four fermion terms is strongly restricted by the large symmetry of our QD three action In fact what we can show is that any four fermion term can be written as a linear combination of these two old acquaintances This is G one which which which is the coupling in front of gross never type of interaction with With gamma three five being the product of gamma three and comma five the two left over gamma matrices which are not present in our kinetic term and G two With which is a tearing type of interaction known from the tearing model in two plus one dimensions the charge Has a particularly simple form for each flow and this is due to the word identity to the gauge gauge symmetry in fact to any loop order that the flow equation for the charge should always be Written in this form D minus four plus eta a times e squared e to a to arbitrary order At least is unknown, but we can compute it to leading order However independent of the order we calculate we therefore see that as long as we're in the perturbative regime It is small we always flow to larger values of e squared and finally the flow only stops if eta a is four minus D So that means that independent of the loop order Exactly eta a must be four minus D at any charged fixed point In fact, if if we now use this this information for the scaling of the photon propagator at such a charged fixed point Then the exponent in in Fourier space of the photon propagator must be two minus D And that means it becomes constant the photon propagator in two dimensions two space-time dimensions This is nothing but the well-known result of the Schringer model a massive photon in two dimensions In three dimensions, we recover also a known result that the photon propagator goes as one over absolute value of q And this is basically this is the fact exactly the result known from first and as well as a second order one over any expansion for this photo propagator and From this argument we now conjecture that's actually true to any order in the one over an expansion However once we now have such a strong charge e squared then new new couplings g1 and g2 will be generated by this box diagram So how does the flow look like once we have now this strong charge? Here is the flow for large in a large and limit infinite and limit Now projected onto the charge e squared and g2 tearing type of short-range coupling plane We have besides the Gaussian fixed point at the at zero coupling three interacting fixed points a Turing fixed point at at a non-vanishing short-range coupling which can be understood as ultraviolet completion of the Turing model and two charged fixed points if now the red line is the RG trajectory of pure q the pure QED action if we start the flow for say small gauge coupling and Initially vanishing short range interaction would end up at this fully attractive fixed point and since we're at large end That's precisely the conformal fixed point the fixed but which relates to the conformal state of the large and QED However, there's also a quantum critical point with one relevant direction and once we lower now this This fermion number n then these two fixed points approach each other in particular if we lower it towards Some conformal critical flavor number then they merge onto a single point and Below this conformal critical flavor number they disappear into the contract complex plane fixed point annihilation Now if we start the RG flow close to this Gaussian fixed point for the pure QED action the red line Then what happens is that we have a runaway flow always towards divergent G2 So the conformal state below this conformal critical flavor number is gone the questions of course What is this instability to? We can compute this conformal critical flavor number within this 2 plus epsilon expansion and what we find is that in fact It becomes arbitrarily large once epsilon is small enough Now we're now going to argue that this instability It's impossible to have chiral symmetry breaking Because the reason is that this instability happens at large and at such large value of and it should be impossible to have Well, as we'll see so many numbers of Goldstone volts Now we'll use RG monosinicity arguments to show that these these arguments are based on the simple observation that defective number of degrees of freedom that play a role in a certain system always decreases under the RG and And a simple example would be the Wilson Fisher o n fixed point where we have n critical modes But on either side of the transition we have less than n critical modes massless modes There are only n minus one massless Goldstone modes in the broken phase and there are even zero massless modes in the symmetric phase Of course to make use of any that that we need to somehow quantify this effective measure of Effective number of degrees of freedom But fortunately this has been done in one plus one dimension By some logic of showing that actually the central charge of the conformal address C Give such a measure of the effective number of degrees of freedom this C in fact He was able to show that C always decreases under the RG and becomes stable at any fixed point Particularly this means that at any ultraviolet fixed point this C must be larger than the C at the infrared fixed point and In a certain sense we can imagine the theory space as a landscape with with hills and and valleys and always Ultraviolet lives kind of for large valleys of C on top of the mountains and infrared fixed point live in the valleys And the flow always needs to be from from large valleys of C to small valleys of C Flow RG flow in a certain sense always goes downhill with respect to C central charge This theorem has recently been generalized to higher dimension Following a proposal by Cardi in three-plus one dimension the a normally coefficient so-called are Cardi's a theorem But only recently has been rigorously proven in four dimensions but then it Now is also known in three dimensions where a similar quantity which Yeah, gives this effective number of degrees of freedom is f So called sphere free energy which is obtained when the theory theory the conformal field theory is Conformally mapped to a three-sphere embedded in four four spacetime dimensions so very recently Between these three seemingly independent quantities Connection has has been possible to made by introducing this quantity f tilde the so-called generalized Sphere free energy f this generalized f f tilde in fact could we're able when we're able to show that this generalized f becomes Precisely a constant times the central charge in two dimensions It is exactly the sphere free energy f itself in three dimensions and is proportional again to the a normally coefficients in four dimensions We therefore have for any integer dimension that this f tilde fulfills RG monotonicity And it's that's a that's rigorous statement f tilde in any integer dimension at an ultra valid fixed point must be larger Then it's value at an infrared fixed point F tilde is is a quantity which is continuous in the spacetime dimension D therefore just from Analyticity we would expect that this holds this RG monotonicity also holds and continuous dimension not only an integer dimension There's no rigorous proof for this statement yet But there's various evidence in various different types of systems often to high-order napsal expansion that this f tilde fulfills RG monotonicity in any dimension also in fractional dimension In fact this f tilde has an plays an important role in quantum information theory There one wants to know the the so-called entanglement entropy which is a measure of how the states are entangled in a particular system this entanglement entropy is is defined by by dividing a system into a subsystem a and its complement a bar and computing the for Neumann entropy of the reduced so-called reduced density matrix which is obtained by tracing just over the states of the outer system a bar In fact one can compute this entanglement entropy for for different simple types of system for example This is a very simplest example where both a and a bar are just two level states Then if the whole system is in a product state say both spins pointing upwards That's a non entangled state then it turns out that this entanglement entropy is in fact is in exactly zero however, if if we're in a non product state in this EPR state for example Then entanglement entropy is non zero in fact one can show that Entanglement entropy scales linearly with the number of entangled states between a and a bar important question is how does Entanglement entropy scale with the size of this subsystem with a Say with a radius r for trivially gap state. There's there's a Yeah, well-known law in this field the so-called area law that the entanglement entropy always should scale in three dimensions and three spatial dimensions as r squared and in two plus one dimensions in our case It should scale linearly. It should scale proportionally to r however for for non-trivial conformal for example phases This area law is violated in particular in two plus one dimensions There one can show that there's a constant shift with with this constant usually called gamma It was recently shown that this gamma is in fact nothing but the sphere free energy and similar relations also hold in one plus one and three plus one dimensions we therefore have that these Universal coefficients and the scaling of this entanglement entropy are again monotonous quantities under renormalization group a full fulfill RG monotonicity arguments and these quantities Should be larger at any ultraviolet fixed point then their values at the infrared fixed point I'm now going to assume that this theorem not only holds in integer dimensions But also into in two plus that's on dimensions non-integer dimensions if we assume so then we we can make Strong statements about possible RG phases. Sorry infrared phases We can compute for example the f tilde at the ultraviolet fixed point and not too surprisingly It's proportional to n the number of gapless fermionic states and in this theorem theory For the other possible candidate infrared phases for example the conformal state we in fact find Find that it's also goes linearly within the number of Gapless fermions, but there's a constant shift and this constant shift is negative such that in fact F uv is always larger than f con and this is reassuring because then our proposed flow from this ultraviolet Gaussian fixed point to the conformal QED fee a QD 3 fixed point is in fact Perfectly consistent with this generalized theorem However, we already know that this this Conformal fixed point annihilates and the conformal state becomes unstable and the question is is it possible then to have chiral symmetry breaking? chiral symmetry breaking with the breaking pattern u2n going to u n times u n would have two n squared massless goldstone nodes and therefore f tilde also goes with n squared the number of goldstone nodes and Therefore for large and it's impossible that f uv is larger than f chi sb and according to this f Theorem it's impossible to have a flow from the ultraviolet fixed point to such a chiral symmetry breaking infrared phase if n is large In fact, we find that it's always larger f chi sb is always larger than f uv if n is larger than one in terms of four component iraq fermions one four component iraq fermions therefore Assuming this generalized f theorem is strict upper bound for the possibility of chiral symmetry breaking close to the lower critical dimension However, we knew Know already that the conformal critical flavor number is very large close to the lower critical dimension and therefore it's impossible Near and below this lower this conformal critical flavor number that that this this phase This instability is towards chiral symmetry breaking The phase below this conformal critical fiber number cannot exhibit chiral symmetry breaking that must be a novel intermediate phase At least it's not yeah, it's not chirally breaking So what can it be? There's a beautiful theorem by wafa and witten showing that q d3 should have first an unbroken u n times u n symmetry at least And therefore u to n going to u n times u n is the only possible chiral breaking pattern No other breaking patterns with say less than than n 2 n squared massless goldstone modes is forbidden by this wafa-witten theorem Secondly the wafa-witten theorem also tells us that the spectrum in their fact of q d3 should have should be gapless Should be have a gapless spectrum And this rules out plain parity symmetry breaking by which the the fermions would acquire A mass a gap, but there wouldn't be any goldstone modes and the spectrum would not no longer be gapless So what else can it be Well insight into the problem can be gained by again looking at the flow When we look at the flow we see within this epsilon expansion. It is always towards diverging g2 But both e squared the charge at g1 this crossover type of interaction remain finite So effectively on a mean field level this this theory in the infrared looks as if there were gapless fermions Dirac fermions coupled via g2 type of tearing type of interaction On a mean field level this theory however it can be solved What we find is it's a free energy for a vector order parameter v mu Which relates to the to the u1 current So this what is this is going? Trying to tell us is that for large g2 This vac vector order parameter composite vector order parameter acquires a vacuum expectation value However, if a vector order parameter acquires vacuum expectation value This means it selects a direction in two plus one dimensional space time and therefore it spontaneously breaks the Lorentz invariance If for example v mu has a temporal component from mu equals zero then in a condensed matter system This this uh such a state could experiment and reveal it safe by a spontaneous Formation of some type of charge order and it's therefore perfectly consistent both with Waffa Witten theorem as well as with the f theorem In fact, this this conclusion can independently on also obtained by by an Susceptibility analysis now again controlled in two plus epsilon dimensions We add to the action small infinitesimally small symmetry breaking terms seeds magnetic fields if you like of chiral Yeah, we break chiral symmetry parody symmetry some type of cacally order or Lorentz symmetry And then we compute the flow by these diagrams to leading order in in in these small Masses and get this exponents x which are related by the usual scaling form of free energy to the susceptibility exponents gamma for these different types of orders In fact, what we find at this quantum critical point that there is a unique order which Which turns out to have a positive susceptibility exponent gamma and this gamma is is is exactly one It's the gamma which is related to the Lorentz symmetry breaking delta mu mass or order parametration This again corroborates our conclusion In two plus epsilon dimensions now that this instability is towards the spontaneous breaking of the Lorentz symmetry Now all that I've said so far was controlled only in the limit of small epsilon Questions, of course, what happens in the physical case of d equals three space-time dimensions That's a difficult problem because we're at finite and now and and and d equals three Beyond above the lower critical dimension Strong coupling and it's difficult to answer However, by the f theorem we can at least find this More or less strict upper bound for the possibility of carol symmetry breaking again And what by comparing these f quantities and what you may now find is that in d equals three A rigorous upper bound would be that carol symmetry breaking is not allowed to occur above 4.4 in terms of four component ferments To make a prediction for the conformal critical flavor number Is a little bit harder, but using different methods ranging from our old work Using a functional rg as well as just naïve extrapolating these two plus epsilon results And and and and as well as a one-loop Expansion a fixed dimension we get values between four and ten so as long as this carol Critical carol critical flavor number does not exactly saturate the this upper bound and this conformal critical flavor number Does not saturate these say lower bound of four Then there may be an even in d in d equals c in the physical dimension an intermediate range of values Where carol symmetry breaking is not yet allowed, but the conformal state is unstable But of course to nail on in particular this number higher order calculations are necessary So here's the phase diagram in in d spacetime dimension d and fermion number n plane Most of what i've said is Is related to this upper left corner and there we can find a fully controlled approximation An expansion in in two plus epsilon dimensions And there we can compute this conformal critical flavor number and can show explicitly via the susceptibility analysis That the the instability is towards lower symmetry breaking in fact This is the only instability which is consistent with both wafa witten and the f theorem In d equals three this conformal critical flavor number becomes smaller and the possibility Of the upper bound for the carol critical flavor number becomes larger And so we don't do not yet know what quite happens in d equals three, but at least from these from these approaches We suggest that Maybe also this intermediate phase also the physical dimension So let me conclude Three-dimensional qed has a conformal ground state if the number of fermions n is larger than a certain conformal critical flavor number And in two plus epsilon dimension this conformal critical flavor number has a particular value But it becomes very large once we're going to the lower critical dimension Because this conformal critical flavor number is so large the common scenario that this instability is below this This Conformal state is towards carol symmetry breaking is inconsistent with the generalized f theorem And this is definitely to exist as long as we're in within the ups and expansion The reason is that where there are just too many goldstone modes for this carol symmetry breaking to occur The only possibility that is consistent Both with wafa witten as well as with the f theorem is a conformal critical Below this conformal critical flavor number is that spontaneous lower symmetry breaking occurs And in fact it's precisely this conclusion that one's led to by an independent mean field as well as a susceptibility analysis Which confirmed this existence of the law and symmetry breaking phase In d equals three We we do not yet know much, but at least the extrapolation as well as a Proturbative expansion in in fixed d equals three suggests that there is a finite window of law and symmetry breaking phase also in the physical dimension Thank you very much for your attention


Please listen to this, because many others and I might not live much longer if you don't. You see, from as far back as the early 90s, we at Microsoft have been slipping Easter eggs into our software. Office is very notable for this. In the 97 edition, we hit a rudimentary flight simulator, pinball, and basic eight ball games into Excel Word and Access respectively. Right before that is Excel 95, where we slipped another game called Hall of Tortured Souls. To access this game, you must follow these instructions. 1. Open Excel 95 with a blank worksheet. 2. Go down to the 95th row. 3. Select the whole row. 4. Tab over to column B. 5. Go to help slash about. 6. Hold down control alt shift, and click on the tech support button. 7. The game will appear, called Hall of Tortured Souls. The game is set in a first person perspective, with Doom-like graphics. The game appears to only have two rooms, one with blue pillars and green pools, and another with a window crediting us in red. However, if you type, Excel KFA, while facing a certain direction, one of the walls will disappear, and in its place will be another room, which can only be entered once you cross an extremely narrow and hard to cross bridge. The name Hall of Tortured Souls finally makes sense when you enter the room. In this room, there are loads of low resolution photos of me, and the rest of the developers, plastered on garish red walls. Which is what working at Microsoft is like. Please, if you are listening to this, help us. Bill Gates, and other high Microsoft executives, kidnapped me and the other developers away from our homes, and forced us to develop office 24 hours a day, 7 days a week on no pay. They abuse and torture us if we dare not obey their orders. They have ruined our lives. When they discovered our game, which they discovered after Excel was released, they went berserk. They beat us all up, leaving all of us at the development team with several injuries, one of whom suffered spinal injuries. Another even died from his injuries, but his death was covered up by Microsoft. We had hoped that when somebody discovered the Easter egg, they would help us. But no. Which is why I wrote this story, to request that you would help us. We hate it here. We want to go back home. Back to our families. Back to our lives. But we are trapped.  Free us from our hell. Free our tortured souls.


Hi, I'm Josh McDonald, member of the Open Telemetry Technical Committee and an engineer at LightStep. I'll be talking about metrics, instruments, and the requirements that gave us the up-down counter, a new kind of instrument. Let's review how we got here. Metrics systems have been around a long time, but I'm thinking about what happened around 10 years ago. Looking at open source systems prior to then, we had just one kind of metric instrument. I'll call it the number instrument. We would use it to report numbers with timestamps, and then we would plot those numbers as a function of time. The result is numbers in a line. The nice thing about numbers is they support math. You can do a lot with numbers, but first you should know what they mean. And 10 years ago, the interfaces we used to report metrics began to change. Why? Because it helps the metric system help the user when numbers have meaning. Back then, around 10 years ago, there were a couple of changes in metrics interfaces. The counter instrument was introduced with an interface dedicated to counting. This is a convenience for the programmer, since they no longer have to track a running total. This also made it easier for the metric system to correctly compute rates. The semantics of a counter instrument are that resets are not meaningful. Another thing that happened with metrics APIs around 10 years ago is they changed to support attributes. Now you could decorate metrics events with a list of attribute values, and every distinct combination of attributes used would produce separate lines of numbers. In the diagram pictured, there are three dimensions, A, B, and C that categorize the data. We can picture the metric instrument, in this case, producing a cube of number lines with coordinates equal to the category values for attributes A, B, and C. Now, still talking about progress that happened around 10 years ago, these two innovations, the counter and the attributes, work really well together. When we add a new attribute to a counter, the result is a new way to subdivide the count, which generates new ways to group and aggregate the same data. Counter data for specific attribute combinations can be compared with other attribute combinations or divided by the total to form ratios and fractions. There are two diagrams shown and two snippets of instrumentation code. These two examples are both CPU usage counters, but one tracks usage on a per-CPU basis and the other tracks total usage. This shows how we can remove an attribute from a counter, either at the source or when displaying data, without a change of meaning. To remove a CPU label or any label from a counter, make sure to sum the individual counts. When the counter was introduced and defined to support resets, it meant that they couldn't be used for counting up and down. For counts that go up and down, a gauge instrument was recommended instead. Here's the Prometheus documentation for gauge. A gauge is a metric instrument that represents a single numerical value that can go arbitrarily up and down. Gages are typically used for measured values like temperatures or current memory usage, but also counts that can go up and down, like the number of concurrent requests. As a consequence, we have one instrument with two interfaces. Use set to record the current value and use add, subtract, increment, and decrement to change the current value. And here we are. Open telemetry has separated these two interfaces. The requirement that led to separate interfaces for up-down counter for things you count and for gauges for things you measure is best described as follows. Open telemetry metrics processors must be able to remove attributes for metrics data without a change of meaning. We want to be sure that when we remove an attribute, the result is just the same as if the attribute had never been recorded in the first place. When an instrument is being used for counting, attribute removal means computing the sum, which is the same count that we would have achieved had the attribute never been used. The point of all this is that a metric system can automatically transform metrics data as a form of cost control and to produce meaningful visualizations without knowing how the instrument is defined, as long as the system knows the kind of instrument that was used. To view any metric at the cluster level, a job level, or a rack level, simply remove the irrelevant attributes. However, this would not be possible with just two kinds of number instrument. We needed a third instrument, the up-down counter. An up-down counter is something like a counter and something like a gauge. Up-down counter acts like a counter in the sense that attributes give new ways to subdivide the metric, defining meaningful ratios and fractions, and in the sense that the natural aggregation is a sum. Up-down counter acts like a gauge in the sense that there is not a reset operation and in the sense that it defines a current value and is not primarily used to define a rate. These instruments exist in the real world. They generally report the difference between two counter values, and where we find these being used is because the two counter values would not be considered useful on their own. One real world example is a parking lot counter. A device that counts how many cars enter and exit a parking lot. This instrument can be used to display how many spaces are available on each floor of a parking lot structure. For example, another real world example is the energy meter on a home with a solar array attached to the electricity grid. When the solar array is feeding energy to the grid, the count goes down. When the home draws power from the grid, the count goes up. Let's review. Copent telemetry offers three instruments for reporting numbers, the counter, the up-down counter, and the gauge. These three instruments have distinct use cases. Counters are useful for monitoring rates, up-down counters for monitoring totals, and gauges for monitoring measurements and other derived quantities. When we aggregate metrics data, particularly when we remove attributes to save cost or reduce cardinality, there is a natural aggregation that applies. For counters and up-down counters, it is natural to group by the sum. For gauges, it is natural to group by the mean. Now you may think that if your instrumentation is doing the right thing, you won't need to remove attributes in your metrics pipeline. While that may be true, when it comes to inspecting and visualizing metrics data, it is easy to create metrics where there are too many number lines to effectively view them at once, say per host metrics in a large cluster. When we have too much cardinality to effectively view metrics data, we need to remove attributes, and that's all there is to it. Up-down counter is distinct from counter-engage instruments in ways that help a metric system to control costs, because whether writing metrics data or reading it, it is useful to be able to remove attributes without a change of meeting. Thank you.


What's up guys? Welcome back. Today I want to talk about something that a lot of you may have been thinking but weren't quite sure what happened. What happens to tickets that actually don't sell on Stubhub and other resale marketplaces? Actually, before we get into what happens to expired tickets, we should first explain what's actually happening on Stubhub themselves. So, when tickets are actually first being put up onto Stubhub and other resale marketplaces, or either fans who have tickets that they decided they either want to sell because they couldn't go, or they just have friends cancelled on them, got to go to my friend's house, have an emergency birthday party, got to go, you know, out of town because I'm just so popular. However, usually what happens is the person who had the tickets or the person they were going to go with couldn't end up going anymore so the tickets they basically just get unused, or whatever the case may be, try to make a few extra bucks or they just, you know, whatever. Or you have the same side where the ticket brokers are the ones also listing their tickets on there trying to again make some money because they're in the business of making money. You, the buyer. The tickets get listed up there. Prices will be set basically by the market. I can go in online and set it for $20 million or whatever the maximum price is, but it doesn't mean that ticket will actually sell for that price. And then we get into the situation where we're trying to buy tickets last minute. Then I have to do what everybody else does and race to the bottom, try and list your price as low as possible to make sure that yours is the one that gets bought and not someone else's. So, some people are going to say, oh, I'm going to list my tickets for $19.99. I'm going to list mine for $19.98.  I'm going to list my tickets for $19.99 minus two more cents. So $19.97. $19.97. They are the geniuses. That is the magic secret. That is the magic word. That is how you sell your ticket. That's not how you sell your ticket. Just take a look up over here, here, one of these sides. Basically one of these corners, take a look. I actually have a video on how to buy last minute tickets. And we go into that in detail with a very exciting example, which happened last week. So go ahead, check that out. But what happens is as ticket prices come down, get close to the event, you know, basically it's just a race to the bottom. End of the day, what's going to happen is that not every single ticket will get sold. So what happens with those tickets? Let's take a look because lots of exciting things could potentially happen to them. First thing that happens when you end up with tickets that didn't actually end up selling is the most obvious one. They're just gone. Useless, done. Worth nothing. And you might as well just give up now. Basically say here, Ticketmaster, take my money. I don't want it anymore. I don't want to attend your terrible events or amazing events. I just don't want it. Take it away. I don't need this money. Goodbye. Goodbye. And that, my friends, is very depressing. It means you had some tickets that are now worthless. On the other hand, you have not just, you know, fans who are trying to sell tickets, so you also have the ticket brokers. So these are the people who are actually, you know, in the business of buying and reselling tickets. And so what they'll have at the situation is they'll take it so basically not been sold anymore. And so they are kind of in a bit of a pickle. You know, they're kind of stuck saying, okay, what can I do now if I can't list them on Stubhub anymore? Is there any other option for me or do I just have to take the loss, you know, take the hit right in the face? Boom! Or do they have other means of trying to unload them? And the answer to that is yes, they actually have a few other options.  Some sellers will actually be able to list tickets past the event time. Gives them an extra, you know, half hour, hour, sometimes almost two hours. I don't imagine many things will sell in that time. But they have the option to actually sell these tickets for an extended period of time longer than the average fan. But at some point, tickets eventually for everybody will be delisted. The event will go away. You won't be able to see it on any resale markets anymore. And that, my friends, is when you are at the situation where you no longer have the ability to sell your tickets online. And when that happens, again, tickets worthless. One other option when your tickets expire on Stubhub and other resale marketplaces is to actually smash the like button. Because that really helps me out. Now, with that being said, there are a few other options that might exist for you. So if you're listing them on Stubhub and they take the listing down, you know, two hours before the event starts, or one hour before the event, or the one the event actually starts and you can't sell them anymore, you have a couple of things that you can do. So one is, one that you might be thinking of is actually go and find a ticket scalper. So as a fan, if you have tickets that you can't get rid of and then you just got to get something for it, what you could do is, if one, if you have a contact, or two, just head down to the event itself. If the opportunity exists for you, go ahead, find a ticket scalper there. Sometimes you see them all over the place. They're just, you know, on the streets, on the corners, at the venue itself. Just with big signs saying, ah, I need tickets, ah, I need tickets. And what they'll do is basically they'll just buy them from you. Yes, they're going to buy them at a very, very discounted price, but would you rather get something rather than nothing? It's, it really kind of depends on your situation. If you're close to the venue or not, if you can do it, if you can swing it by, go ahead, get your couple of bucks, give you some cold heart cash. From the ticket broker side, they may actually have people who are designated ticket runners who will actually take the tickets if they are physical tickets. And what they'll do, they'll bring them down to the actual scalpers themselves and they will then try and sell those tickets on the streets. Oh man, or your neighborhood, or wherever it is your event takes place. Also, also, also, also, there are a few resale websites that let you list tickets well past the event start time. And this would include Vivid Seats and Ticket Network, specifically those two. They have options to do, you know, last minute deliveries. And so with those, what you can do is actually list your tickets well past the event start time and get your tickets sold. Two downsides. One, there aren't many people looking to actually buy tickets after the event has actually started, so that's your one big concern. And then two, if you actually have physical tickets, you can't mail them to someone. You actually have to go down and meet them and, you know, give it to them in person. So it's, it's, it's a bit of a pain. So I would not recommend it if you would do not live anywhere close to the venue. Other than that, I mean, the other option is you could take your tickets and turn it into something like art, make a little tower, make it grow nice and big and fancy and tall. Lastly, and probably the most obvious one other than the first one, which is also the most obvious one because things are just too obvious, is you could actually just end up going to the event or giving the tickets away to someone who could go to the event. If you have friends who live close by, who to the event and they say, hey, you know, I got some tickets that I can no longer use.  But are you interested in actually going? Question mark? Question mark. Again, if you're the one on the receiving end and then they're giving you these tickets after the event has actually started, are they really your friend? Something to think about. Basically when things expire and you can't use them anymore, you've got to be a bit creative. So these are my options for you. There are some ways to try and sell them. There are also some ways to try and have fun with them. Whatever it is you decide to do, I support it wholeheartedly because I have been in that same situation as you. If this has happened to you before, let me know in the comments below what you've actually done with your tickets that could not be used or could end up being sold in time. Also, be sure to subscribe because I haven't reminded you yet. But when you subscribe, you actually have way more fun with your tickets. Did you know that? These are facts. Facts, I tell you. If you have other ideas, definitely leave them in the comments below. I'll check them all out. And I'll see you guys next time. Look at them. Good frame them. You could drill holes in them. What about if you, like, turn it into a nose costume? Like a little eye hole or something?  Another option? Origami. You know? Fold this side. Yeah. Yeah, yeah, yeah. We got this, guys. Don't worry about it.  Then you fold this side. That's not creepy at all. That's not a good idea. I don't recommend that. In fact, I would say stop.  This is what I would do. This is the thumbnail that we want. You could turn it into a... a Vuvuzela. These might as well rip them up. Take the drill out of your hands right now. Don't... I see you. You could also turn it to a fan, I guess. And then you turn the little thing into the other thing. And then you just... I think it worked. Well, still, the more dramatic, the better. I see you. I see you with that drill. Don't do it. Just stop. Just step away from the drill. See? Fan. Works very well.  It doesn't work so well. Uh... You could put it in a frame and say, oh, look at this nice, beautiful ticket. It's so cute. And lastly, my most favorite thing to do with tickets that expired, couldn't sell them, just stuck with them. Favorite thing to do? Just rip them.