Hello and welcome to this lecture on introduction to computer and network performance analysis using queuing systems. I am Professor Varsha Apte, I am a faculty member in the department of computer science and engineering IIT Bombay. So in the previous lecture, we had done a lot of discussion about shared resources and queues. We had discussed that delays are basically a result of contention for shared resources and we had discussed that resources in computers and networks include things like network links, web server threads, CPU and we had also made a list of pairs of resources and their user or customer entity. Remember that user here is the entity to which the resource is directly given. So we humans are of course the original users of everything, but when we say users we mean the direct entity that is scheduled, so the schedule level entity. So for CPU it is threads, for cellular network channels it is calls, we had gone all of this through the previous lecture. For the wireless medium it is frames, for the link it will be packets and so on. And we left off discussing that performance as we defined it in the last lecture, which is basically how well something functions given that it is functioning. That performance is something that we can talk about, we left off asking that can we be a little specific, can we say something more about these resource and users other than it is slow or it is fast. So again this is a reminder to have a pen and paper ready because it will be good if you also write some thoughts down as I ask. So before we get into discussing more parameters and metrics, let us define it very clearly. So metric is the attribute by which is a quantitative attribute by which we describe some quality of the system. So it is a quantity for describing some quality. So for example you might say that this person is very fast, he runs, you can just say this person is very fast, that is just a qualitative attribute. What is the metric? Then you will have to say that this person runs 1 kilometer in I do not know 5 minutes or 3 minutes or something like that or somebody is if you say this person is very strong that is a qualitative metric. Then how many kilograms can they lift? Is it 50 kg, 100 kg something like that people bodybuilders can lift? That will be a metric that this is as many kilos as this person can lift. So it is a quantity, it is a quantitative measure for describing some quality and that is metric. And when the metric, metrics can be for anything I just told you a metric for a person being fast, a person being strong, a metric to describe a car, recall from the previous lecture a metric for describing an efficient car could be how many liters of petrol does it consume? How many kilometers does it give for 1 liter of petrol? That is a very quantitative metric to describe an efficient car. The metrics that we will talk about are for computer performance of course, computer and network performance. So that is why we call it a performance metric. It can be a reliability metric also remember again from the previous lecture we had reliability or dependability, how many times car broke down in the last 5 years is a reliability metric. But again we will only talk about performance metrics in this class. Now what is a parameter? A parameter is something about the system or about the thing about which whose metric that you are talking about, it is something about that that affects the metric. So again recall in the previous lecture we talked about speed of the resource, how many resources, workload intensity all of these the quantitative versions of this. So quantifying an influencing factor, a metric influencing factor that is basically a parameter. And basically the metric is going to be a function of the parameter. And this is just a general graph. This is not any particular metric or any particular parameter. But this is what we are, what the relationship is, we will generally plot a metric as a function of a parameter. In this case whatever this metric is it is increasing in this way as the parameter increases. So let us talk about performance metrics in computer systems and in general also actually there are two types of metrics, the system metrics and user perceived metrics. So what are user perceived metrics? These are actually very easy to think about. These are metrics that are visible and are felt by and are of interest to the user of the resource. For example, the waiting time is something that is felt by the user of the resource. All the previous examples that we gave outside of computer systems and networks, clearly these are how much time you are waiting at an escalator, how much time you are waiting in a queue. This is something that a person actually experiences. Similarly, in networks and systems the waiting time will be experienced by a packet. Now the packet is not a person, it will be something that the network administrator will have to measure and so on. But it is a metric that belongs to the packet and is indirectly experienced by the human who is sending the packet. Similarly, the waiting room is full, meaning the packets came to the network buffer but were dropped. So they did not even have space to queue. So that could be this kind of something that the packet will know, if the packet was a person the packet would know that it was dropped. But at least it is something that the packet has experienced and maybe the sender of the packet will note that the packet was dropped. So one way or the other it is something that it concerns the user. A system metric is something that is visible and of interest to the owner of the resource or the operator of that resource or the resource herself or himself if the resource is a person. So giving the example of the pole booth worker which was a person, how busy they were, you know they were maybe they did not even get a break for lunch or something. That is something that will be experienced by the resource itself. If it is a computer or a network link that we are talking about, how busy it is which is called the resource utilization or how many packets per day, how many threads per second is a CPU processing, how many packets per second is a link transferring. All of this is something that the owner of the link or the owner of the CPU, they will know the person who is submitting a job to the CPU or who has sent packets to be sent on the network link, they will not know in fact, they are done when their packet goes over the link. Like again giving the example of the pole booth worker, the person who is the voter who is queuing for the pole booth, they will not know how many persons per hour came through this voting station today. They only know that I had to wait for 2 hours. The pole booth operator will know how many persons per hour came. So these are the system and user metrics and in fact, they are often in conflict with each other. System owners want their resources to be utilized. Now imagine for example, the escalator, if somebody installs some 2-3 escalators and they are not being used, that means you did not estimate the number of people that are going to come to that station or the mall or whatever would be, you did not estimate it properly and you put in too many escalators and you are spending so much money. So that is not good. Now so system operators often want their systems to be highly utilized, their resources to be highly utilized, users like the resources to be idle so that they do not have much waiting. So there is a bit of a conflict between what a system owner wants and what a user wants. Now coming to parameters also there are 2 types, system and workload. Here this is much more straightforward. As we discussed earlier, a resource has a speed, you know how many packets per second can this link carry, what is the bits per second bandwidth of the link, how many links are there or how many CPUs are there, how many poll workers are there, all of these are the parameters. We already discussed that these will actually impact the delay and the performance in general. The sharing policy, we discussed this previously also it is definitely a factor. This is actually a qualitative factor, this is hard to quantify, this is a general attribute but it is a parameter nonetheless. But these are all characteristics of the resource or of the system. Now regardless of this, the performance will be influenced by the workload parameters and as discussed earlier workload parameters will be like arrival rate, how many packets per second, how many jobs per second are coming to this resource and each user, how much work are they bringing to the system. And so if there is a ticket vendor, one person may just want to buy one ticket quickly and go but the next person might come and they might spend a lot of time choosing the seats and so on. So it is a different amount of workload that came to the ticket vendor. So how much unit of work is coming to the resource that will also be determining the metric. But it is a workload parameter, it is not the characteristic of the system, it is the characteristic of a user. So can we name some, in the instances that we saw for example for a network link and a packet which is the user, can we name some metrics. Can you go ahead and write some in your notebook. For example for this there can be packet waiting time, in fact it is called queuing delay, how much time did the packet spend in the queue. There can be packet drop probability, then in terms of let us say the web server system. So this one is of course, this is a user metric, this was also user. So the link utilization, what fraction of time was the link busy. This is a system metric, the web server again request response, request delay, how long did it take for the request to finish, this is one metric. Then average, we can have like average number of busy threads, this can be some metric. What could be a parameter, parameter could be rate of arrival of requests. So let us go ahead and look at this whole table that is here of various metrics and parameters. I hope you took some time to think about these things yourself. So for example CPU, let us start with the metrics, what is it, what are the questions, what are we interested in. So the resource owner will like to think in terms of so many jobs per second were done on the CPU. Let us say it is a high performance computing system, in those kind of systems, actually these large jobs are actually submitted for processing. And if you are owner of that kind of system, you will really want to be processing lots of jobs because maybe you have given it for rent to some users and you make more profit if more jobs per second are done by the CPU. So you really want as a system owner, you always want these things to be high.  From the user's point of view, of course you would love it if there is nobody else using the CPU in its only for you because you would be interested in the job completion time. What will affect these metrics, it will be affected by the speed of the CPU, the number of cores, these are system parameters. The more the cores and the more the speed, of course you can do more jobs per second. Other lot of very technical things like cache size, of course the scheduling policy, it is very important in terms of some of these metrics. We know for example that there are some scheduling policies which are better for job completion times, other scheduling policies are worse for job completion times. You can recall your operating systems undergraduate material and we will discuss this in some other lectures. Then there is a workload parameter, right. Each job is bringing how many instructions to the CPU and of course the job arrival rate itself. In cellular channels, we have the system operator, the cellular network owner will be interested in what is let us say in a day at between 11 am to 12 noon, what is the average number of busy channels. Then there is call volume, what is the calls carried per second, how many calls am I, successfully completing every hour for example or every second. The user will be interested in the same thing, blocking probability, blocking here means network busy, what is the probability that I tried to dial something and I got network busy. The parameters of course will be number of channels. If there are fewer channels then actually you cannot carry that many calls because many people will get network busy. This is the parameter of the system and then from the user's point of view, how long are users going on talking on the phone that will directly impact how many calls per hour you can actually carry successfully, right, you can complete successfully. So, this is for the cellular channels. For web server threads, wireless medium is all very similar. You will be interested in requests completed per second, average number of busy time, request response time, connection refuse rate, these are the metrics, parameters will be number of threads, scheduling policy, arrival rate, how much time does each request take. Similarly for the wireless medium, the bandwidth as we say, right, sorry, this is the metric in terms of the performance metric, how many bits per second is this Wi-Fi channel actually successfully carrying per second. That is a very important metric from the system owner's point of view. Then what fraction of the time was actually it being used, otherwise like I said again is it a waste, is it being used, collision rate, recall from your wireless network material that there is something called collisions that can happen on Wi-Fi. So, what is the collision rate, from the user point of view again it is delays and sometimes it can also be how variable is the delay that is also a metric of interest and maybe collision probability for the user also. The parameters will be data rate which we say bandwidth, right. If the bandwidth is higher, the frame transmission delay will be smaller. Then this is very important, protocol rules because usage like I said there is a resource sharing policy, right, whenever there is a resource, there is a sharing policy. So, this in networking, these policies are determined by protocols. In case of wireless medium, there is an access protocol, right, access protocol. So how are you going to access the medium because if many laptops are using the same medium, there needs to be a way to share that medium. So, that will itself be a qualitative parameter and then again we have frame arrival rate and frame size. In this table, by the way, the hash sign is for number, ok. So, this is number of instructions, number of course, number of threads and so on. Now, how do we calculate all of these metrics, ok? It is, you know, seems fairly dizzying as to all kinds of metrics are there, you know. Before we go into how, we may want to ask why should we calculate all of these metrics? Everything should have a purpose and you should never believe that something should be done just because I am saying in this lecture that it should be done. So, how do we calculate? Why should we calculate? Why is it important that we know all of these metrics, ok? Then finally, really what is all of this that we are doing, ok? Before we ask, answer how and why, let me just define what this is, ok? This material that we are actually talking about just like the name of the course is basically called performance analysis, ok. And what is performance analysis? It is a process by which we methodically analyze the performance of a computing or networking system. And do I mean by analyze the performance? Essentially what we will be doing is we will determine the relationship, remember I said metric is a function of some parameter. What we want to do in essence is to determine this function, ok? We want to determine the relationship of the performance metric to a system or workload parameter, ok? Now that we know what it is that we are talking about, the next question has to be why? Why do we need to do this? So, there are many reasons, ok. One is sizing. What is sizing? Sizing means being able to determine the number and speed of resources that you need for something. So, for a cellular operator for example, the cellular operator may want to know how many channels they should arrange for in a particular cell. For that they may need to estimate how many calls per second they need to actually successfully carry or they may need to estimate that if I only give say 10 channels in this cell then what will be my blocking probability? How many times how frequently will I be giving network busy to my users? If you calculate that then if it is too much then you might be able to say that no I should have 10 channels. Secondly, setting configuration parameters. What is the configuration parameter? One example is the number of threads a web server should have. This is something that is typically there in a configuration file in the server. Again, same thing might happen. I should not have too few threads so that the requests are queuing. I should also not have too many, I mean I should not have like 50,000 threads on a 4 core machine because all of you know again from your undergraduate operating system too many threads may cause what is called thrashing right we can have thrashing. So we need to perfectly set the configuration parameter. Choosing architectural alternatives meaning you can you might have to design a network let us say a campus network somebody is designing they would need to know what should be the packets per second or the bits per second that the network should carry. What kind of switch architecture remember we saw a picture of a network and link architecture what should that architecture be so that my performance is good. Then comparing resource allocation of or scheduling algorithms this is very important I have let us say a CPU core and then I have so many threads and processes using it. Again from your undergraduate operating systems you would have learned that there are so many different scheduling policies right. There is shortest job first, there is round robin all of these will result in different delays and if sometimes it can lead to different rates at which jobs are completed also. So based on what my I should be I cannot just propose some new policy other than these two without doing the performance analysis of it. Suppose I have some new idea for a scheduling policy I cannot say that I think this is going to be good please use it you cannot do that you will have to do a very very formal performance analysis ok. Determining bottlenecks this is another very interesting thing when you have multiple resources multiple types of resources that are used by any user to actually complete their job in that case sometimes different resources will see different use. So let us say in the network example I have you know so many switches and these are the links but this could be the switch to which many links are connected and this is a bottleneck the switch or the link this is the link on which lot of packets are coming in and this link becomes the bottleneck. So then I will I need to know that this is the bottleneck and maybe I should put some extra links here and increase or just put another link there with higher bandwidth. So I need to know what my bottleneck of my if I am this network owner this whole network I own then I need to know what my bottleneck is so that I can fix it right. Finally I need to do performance analysis because I may need to give service guarantees which is what is service guarantees suppose I am creating a website which I am promising to my customers that the loading time will be less than a second or less than half a second. How do I know suppose I am I have my customer is actually another business that needs to be very fast and I have a contract with that business that tells that my web their web page should load within a second. So I need to analyze my system right before I can be sure that I am giving that quality. So determining whether service guarantees will be met is the reason another reason. So how do we do this right how can we do this there are many ways one is you can just measure if the resource that you are doing this performance analysis for is already operating you can actually just use some monitoring logs or you can actually have some probes and some programs that are actually measuring the performance of the actual service or you can set it up in a test bed. So let us say you are a network operator you could set up a test network in your own premises and have some laptops and devices on it which are just sending lot of artificial lot of doing lot of downloads and uploads and while doing all of that you measure the performance using some software and that is how you measure you do lot of measurement and analysis and you get done with it. The other the last thing here is the other two methods actually are in the category of modeling. Now what is modeling? Modeling is what you need to do when you do not have the actual system to measure or it is not possible to measure. So here basically you create an artificial representation of the actual system there are two ways to model anything one is by simulation and another is analysis.  So switches and links and packets are basically represented by data structures and the program logic behaves like packets going from one switch to the other and so on and then you collect statistics and then you are able to estimate when you model things you can only estimate the performance. So one way to do it is this. Another way is to use just mathematical reasoning just reasoning and some probabilistic and mathematical calculations with pen and paper to derive some very good things about the system. Now there is a bit of a advantage disadvantage relationship between these methods. So analytical modeling one of the biggest advantages of it is it can give you some insights because this can sometimes result in some formulae and there is nothing like a little formula that gives you some very deep insight about the fundamental behavior of a metric with respect to the parameter. So more insight in this direction of course analyzing mathematically needs a little more expertise like you will have to do this course before you can analyze these things mathematically. But once the expertise is there actually you can get very quick answers it is just a formula sometimes you can just plug in some numbers there and you get the answer. As opposed to that measurement requires will rarely give you insights very deep insights you will have to do lot of you have to plot lot of graphs and everything and only then you will get you will get some insight of course by measurement. But it is a little harder to derive that insight rather than from a formula and simulation is somewhere in the middle. Similarly, but measurement gives you complete you know maximum flexibility ok maximum flexibility in a way because you can set up a very very complicated infrastructure and measure it. If the cost is not a problem right you can get flexibility but there will be lot of costs also and why is there less flexibility with analytical models? It is because analytical models are mathematical and they need lot of assumptions and this will be more realistic and again because mathematical models need to be simple there will they will be less realistic ok. So these are the trade-offs of all of these methods. Now in this course our focus is this last method which is analysis with pen and paper with and mathematics and just reasoning. So just last closing couple of thoughts ok. If I say that I have to use mathematical models to estimate these metrics in terms of these parameters these are metrics and these are parameters. So if you want to if you want to do this analysis you may wonder do we have to do it separately for each of these things and then hundreds of other resources that are also there in each system. There are different scheduling policies there are different metrics do I have to go through the maths for each of these systems? So that seems very daunting right how do we carry out this analysis? As it turns out actually you do not have to do this ok. If you stare at this table long enough and these metrics long enough you will realize that there is a lot of similarity in some essence between all of these things. So for looking at the metrics for example here I have jobs per second I have calls carried per second I have request completed per second I have successful bits per second in terms of user metrics I have job completion time I have request response time I have waiting time transmission delay here I have some collision probability here I have blocking probability in terms of parameters I have job arrival rate call arrival rate I have holding time I have processing time I have this arrival rate as the same as this arrival rate this number of threads corresponds to this number of channels corresponds to this number of cores. So there is something similar here right it is not that every system is different ok. So the insight that allows an analytical approach is that in essence all metrics and parameters are similar and we can try and generalize this view ok which brings us to the last slide here which is that this generalized view is what is called queuing systems it is a universal mathematical model to represent queuing for shared resources and for analyzing performance of such systems ok. And I will be explaining what these diagrams mean in the upcoming lectures. So from the next lecture I will introduce queuing systems and the rest of the course is largely about using queuing systems to understand and carry out performance analysis Thank you.


I mean, Shug was not one to mess with and it was easy, as I say, who first warned me. I had not heard of Shug and so this court case that they'd asked me to take part in and on the night after it, EZ had called me from LA and was like, thank you so much. I was so grateful and I was like, listen, I've just been honest. I've said, I was agree with what you say and some of it is incredibly disparaging towards women. But I do understand the context of where you're coming from. And he said, I want to just tell you about one person you've just got to watch out for. And he said his name, Shug Knight, and I'd never heard his name before. And I was like, what? And he's like, he's poisonous. He's got in with Dre, they're threatening me. And they just went off on this whole long list of stuff about how Shug Knight was a danger. Shug Knight was only interested in brutalizing people, getting involved in music to brutalize people. And I just like filled my head with all this stuff about somebody I'd never heard about. And in no time at all, Shug suddenly became somebody that everybody knew because he made himself very known very quickly.


Welcome to ToffeeTV, it is the Everton News Daily sponsored by Unibetter. Today's video isn't enough transfer news for you. Make sure you head over to Unibetter blog for all the latest updates. There's news breaking there all the time and I have a bunch of really good writers to check it out. The link is in the description. Well, all the talk today from Evertonians seems to be about Wilford Zaha. It doesn't matter you've just announced a new stadium. Everyone is talking about Wilford Zaha. Sky continuing to link him with us. Sky sources saying that there's a bid imminent of around 60 million with a player going the other way. That player has been hinted at being shunned. There's also talks of people saying that the player would be interested to come to Everton. We'll have to wait and see. It's a really, really interesting one. It's one that's come out to nowhere in the last few days. Zaha, obviously linked with Arsenal or Summer. Arsenal don't seem to have the money. The player himself is nearly 27. Hell of a price on him. He said he wants European football or Champions League football. Everton can offer neither of those things. I don't know. Is this applied by the agent or by Crystal Palace to get Arsenal back into negotiations? I'm not really sure but we'll have to wait and see on this one. It just feels a little bit not too good to be true but just a little bit like that's not what we're all about. So we're gonna have to wait and see on that one and see what happens in the next few days. Everton have also been linked with Jean-Philippe Gabon. I'm going with Gabon. That's what I'm going for. Who would be a replacement for the outgoing addresser Ghana Gay. The rumors are again that Everton will not confirm the signing of Ghana till they have a player in. That could happen over the weekend with Everton being in Germany, playing obviously in the Ogre Cup against Mainz and against Seville. So that's something that could be hammered out over the weekend. We'll have to wait and see. I'm sure Arsenal's bands are working hard to get players in the door. It looks like we need at least three to come in. The squad does look a little bit stretched and we'll have to wait and see whether whether he is one of the players. We've also been linked with Mario Mina from Southampton, another midfielder. Again he's been linked with Manchester United as well. Southampton said he's available and yet he's getting linked to clubs like Manchester United and with us. So we'll have to wait and see. Moise Ken as well. There's rumors out there that his ageing, so Juventus, sporting directors have come over to England to try and fresh out a deal with Everton. We've got just under two weeks and I don't know whether that's a good thing or a bad thing but we certainly do need players in. We've got the tournament tomorrow, a friendly against Bremen and then obviously the Premier League starts against Crystal Palace away in a couple of weeks. So a lot of work to be done but let's throw we know that that work could be getting done under the surface as we speak. So hopefully something will happen in the next few days. Lots of talk about Everton's new stadium with the designs out there at the moment. I'm waiting for the app. I've got my VR goggles but the app is not available as yet on Android. I'm just waiting to watch them. If you haven't got goggles or you want goggles, get down to the road shows, fill in the consultation and pick up a set of these. There won't be long left very long. Really nice like just a really nice actual souvenir as well. You can put your phone in there and away you go watching. There's loads of VR stuff on so you know get yourself one of them. The roadshow was in Liverpool today. That mice was there talking to people. Make sure you get yourself down to that consultation and you fill it in because the club have said already they want people to get down. Fill it in. Make sure this stadium gets through planning permission as fast as possible and you can help with that by taking part in the consultation. The build will take three years from whenever and get the planning permission. Hopefully if the planning permission is successful and only takes nine months to a year, then we can have it built by the summer of 2023 and ready to play football in the stadium by then. This consultation will be a really big help in getting that over the line. Now you've seen the stadium. The first part of the consultation was about everything really. Now it's home down on to the stadium. What you think of it and what you like and what you don't like and what you'd have or what you'd take away and that will all help out with our planning permission. So make sure you get that in. You get that done whether it's online or at one of the roadshow locations which if you go on the People's Project website Everton's website you can find that out at social media and stuff. So make sure you do that. Anyway, this has been the Everton News daily. Everton play twice tomorrow. So make sure you check that out. If you're in Germany or you're going to Germany, enjoy yourself. It should be a great day. Thanks for watching. We'll be back next week. See you later.


Martin Vashilik off the inside in red, Patrick Kudak gate two in blue, Fredrik Lindgren from Sweden, right for Walberhamsen in the Premiership in the UK, gate three in white and Jason Doyle at the Swindon Robbins in the SGV Premiership. He's off the outside in yellow, the inside gate in red. Lindgren now is going to go wide, Doyle is going to try the inside run. Here comes Lindgren round the outside for Vashilik, it's already well clear. He's on a flying machine here, Lindgren is going to give him everything. He's got to be careful not to give it too much as Kudak comes through. He's in third and Doyle in the back, but Martin Vashilik is riding superbly in his 19th Grand Prix. He's been in two previous finals, this would be three and this would be a second Grand Prix win. Well, what a start for Martin Vashilik from the inside, really he's been rocking away from the take, got himself to the first corner and had enough advantage to get across the first turn into the third and he's just wrought away out in front. Lindgren there just didn't quite get the smooth run around the first corner. He was looking for, got himself to second place through the third and once again, gate four really has proved so difficult to win races from and Doyle's out in the back. Martin Vashilik on the verge of a second Grand Prix victory. 16 Grand Prix points, he's back in the Grand Prix series and he's back in some style. It's a fantastic performance from Martin Vashilik with his second Grand Prix victory of his career in only his 19th GP. It's his third final and he's won two of them, what a record. 16 Grand Prix points, Lindgren finishes second in the final and second in the Grand Prix, but also collects 16 Grand Prix points, what a performance and he's having some fun now. It's many congratulations to Martin Vashilik. Congratulations from the team, they really must be tough to be, it's great effort from Lindgren. Here we go again, what a start he makes, he absolutely nails that, absolutely nailed it and the bike drove away, he must have been so chuffed he had enough room there to roar right across the first corner and there as a consequence he has so much speed down the back straight. Lindgren gave it absolutely everything as he charged down the back straight on the opening lap. Here we're seeing it again, this is what wins the Grand Prix for Vashilik, the bike just powers to the first corner. He has enough racing room to allow the bike to go right to the outside, he's in the right place at the right time and then he powers away in front, Lindgren in to second place, Doudette back in third, Doyle out the back but for Martin Vashilik that is some way to come back into the Grand Prix series and a terrific win for him.


Court, just good evening, everyone. This is from city of Fort Worth. And we are here today for the public meeting for. Bargain, straight improvement of a sidewalks from Mitchell to 1, the project number is 1, 0, 4, 7, 6, 1. And the project is in council district 8 and 11. I'm sure I'll I'll be the project manager on this project. And with me, I have today Chad Allen, he's our engineering manager. Laura Ingram, she's our communication specialist and we have Rachel. Rachel, do you want to introduce yourself? Sure, happy to this is Rachel. I'm a new district director in the office of council woman, Janet Martinez. This does cover district 11 as Shweta mentioned. So, happy to listen in hear any concerns and comments on this meeting and our office is here to serve the residents of district 11 and hear any comments from our constituents. Thank you so much. Happy to have you all on and thank you city of what we're team for being on tonight. Thank you Rachel. We also have our project sponsors, Marisa Conlan and Chelsea's includes with us today. And our design engineers are consultants. We also have our design team with us James Allen and. Go over a brief agenda in our meeting today to cover the project background, the location of the project project schedule, and usually some frequently asked questions for the sidewalk project and the project contact information. Going to the project background as a part of this project, we would be improving pedestrian mobility by installing sidewalks and 80 ramps. Along will barger from Mitchell Boulevard to 1 below 1. And this will be on both sides of will barger both north and south. And we will also be including sidewalk on 4th street from will barger to child rest. The existing sidewalk in some of these locations would be left undisturbed unless it has some cracks in it, then we would go ahead and replace it. And so it goes with the drivers to if the drivers existing drivers are compliant. That means they have like at least 4 feet of working surface. We will leave it in place. Not then we would have to redo the drivers this project would improve safety and access for pedestrians to access the schools, the churches that are on. Will barger and also some public outside stops the project is funded by 2020 to 1 program funds. This map shows the location of the project that we are referring to it's on will barger from 1 Boulevard to Mitchell. It's right south of 287. This shows the location map in detail where we will be installing our sidewalk on both sides of will barger. From Mitchell to 1 and also on 4 from will barger to child rest and that would be on the west side of the street. So, we would be approximately installing 9,500 feet a linear feet of sidewalk as a part of this project. Coming to project schedule, we are currently at a design and we are we are estimating to start construction in summer of 2025. The duration for construction would be 6 months and the current estimate for construction is 1.6 million. Coming to some frequently asked questions about the sidewalk projects that we usually get in these public public meetings. First one is what would be a typical width of sidewalk. So, city standard is to do a 5 feet sidewalk when it is detached from. Or do it as a 6 feet sidewalk when it is right back back of curve, but there are locations on will barger where we have some major trees. So, just in case to preserve those trees, we will we will be reducing our sidewalk with the 4 feet so that we can keep the trees in place. Next question is will we be impacting any drivers as part of this project and it so will the property owner have access to their property. So, we might be impacting some of the drivers just to reconstruct them to meet the requirements and in that case, the property owner would still have access to their property at all the time. So, we will be doing it as a partial reconstruction. So, the property owner can still access their driver at all times. The next question is will any existing trees be removed. So, city, city, stay along with the engineer, work the site wise, and we also work the site with our city or just to make sure if we can keep the trees in place. So, city would do their best to keep the trees in place as they are, but there are some locations where they are in conflict with our sidewalk alignment and we might have to remove them. So, this line shows the properties that we are proposing that is to be removed. And we will be contacting all this property owners personally to meet with them before we finalize our plans on free removals. Will traffic lanes be temporarily closed or we don't anticipate any detours or strict closures our contractor would be working with the street open and just the lane, the right side lane would be partially closed. But other than that, we don't anticipate any details. Will the existing irrigation system or grass be impacted as part of this project? So, if there is any existing irrigation system or sort on that location that we are impacting as part of our project, our contractor would make sure to relocate that irrigation system to back of sidewalk. And also put back the sort as it was before construction. So, city would be making sure that we will be leaving the place in better condition than it was before. The next question is, will the construction materials and equipment be left on site during construction? Our contractor might have some materials that he might be leaving on site during construction, but the contractor will be cleaning out the site every day before the end of this book. So, this is my contact information. Again, I'm Shwetha Rao project manager on this project and here's my phone number and email ID. And also James Allen is a design engineer with consultants and here's his phone number and email ID to this slide is for any future projects that you want to see as part of city of footwear improvement. So, you could request any projects or if you have any concerns, you can reach out to city of footwear using my footwear app for both Apple and Google, or you could text hello to 817-835-69-39 or you could call the city call center at<PHONE_NUMBER>. That is all we have for this presentation today. This presentation would be recorded and will be posted on city's website along with the presentation. So, if you have any questions, we'll go ahead and pick them up, but do you know, do you have any question? Just curious about how the segment of Will Barger was determined. I think it's a good thing. But what I'm getting that is there are other segments of Will Barger going east that also either do not have sidewalks or have partial sidewalks. So, how do we move forward with getting attention to those other segments of Will Barger? And I'm specifically speaking of going east by that Miller. Will Barger intersection, it does have some new sidewalks as part of that project in there, but then it stops. And then when you start proceeding eastward toward Village Creek Park. Eugene McCrae those areas are either they do not have sidewalks or it's just sporadic. So, Patrina, I think we have received a request to install sidewalks on Will Barger along the location that you're mentioning. And me and Marisa, we spoke about it a few days ago. Marisa and Chelsea, do you want to update us on if there's been any movement on that project? Hi, everyone. It's Marisa. Can you hear me all right? Perfect. Yes. So, we have been evaluating the section on Will Barger between Miller and Village Creek Road. And we've been considering that one. So, for right now, what we've done is we have evaluated it and it is on our list of potential projects for the next bond location. But again, this is only on a potential list. It is not, it has not been made a determination to move forward. This is Chelsea, Patrina. I'll just address your initial question about how this segment was selected. So probably about 2 or 3 years ago, the Glen Park neighborhood association was just. Ramping up and so we had started, started communicating with the neighborhood association about needs in their neighborhood around that same time. We began our annual sidewalk. Implementation program to fill sidewalk gaps, prioritize in the active transportation plan. And so, through working with that neighborhood and identifying some of the sidewalk locations that were particularly priorities for the neighborhood. Will Barger emerged as 1 of those priorities. However, that wasn't a sidewalk that we could complete. In our annual pay go program, you know, based on all of the factors that Shweta talked about in her presentation. And so at that time, we were developing the 2022 bond program. And so at that time, you know, we put this list, a list together of all of the requests we've received over the time we've had the sidewalk program. And looked at those that we weren't able to complete due to utility, right of way issues, driveway issues, et cetera. And because of the high ranking of will Barger in the transportation plan, as well as it been a neighborhood priority, that's how. This location was selected and we had also done some sidewalks. I believe on Michel Boulevard and will Barger specifically for safe routes to transit. And so we were focused on making those connections to transit as well as well as the school. I've had 1 elementary. Okay, thank you. Okay, and just another. I guess, question or comment. This is close to Glenn specifically where they notified about this meeting. They seem to be pretty active in things going on in and around their neighborhood. Yes, we sent the mailers out and they might have a safe deadline. 2 weeks before this meeting to quarter mile radius along this corridor. Thank you, Shweta. This is Laura. I'm not seeing any questions in the chat. We'll go ahead and the meeting. Thank you everyone for joining the meeting this evening. All right. Thank you. Goodbye. Thanks for whatever job.


This is covering the spread part of the Fandall podcast network For those of you who love having sports on and during work today is going to be a glorious day for you because of course the PGA Championship is teeing off right now, but also for separate baseball games throughout the day for today We're gonna talk about some bets you can sprinkle in across those four MLB games I'll talk about the two games coming up tonight and break down some NASCAR in North Wilkesboro For what should be a fun weekend. Let's dive on in now and get you ready. What should be a fun Thursday? Welcome on into covering the spread. That's right here on the Fandall podcast network and number fire calm My name is Jim Saunas. I am a senior writer and analyst for a number fire here to break down today's NLB Slating also talk about NASCAR at North Wilkesboro We'll dive on into all that here in just one second But first a reminder to make sure you're subscribed to the covering the spread podcast Wherever you get your podcast our pregna stakes podcast with Christina Blacker is up now breaking down Christina's thoughts on this year's field her thoughts on whether mage can get the second leg of the triple crown And also her favorite win bet for Pimlico on a Saturday to get that check out the Vandal YouTube page Or check out the cover in the spread podcast feed If you like what you hear leave us a thumbs up on YouTube or leave us a five star rating over on Apple podcast The second leg of horse racing's big three is here and Fandall is the best place to bet the pregna stakes Because right now all customers can get a no-sweat pregna sped up to $20 That means you'll get up to $20 back if your win bet doesn't win bet the pregna With America's number one sportsbook just visit racing dot Fandall dot com for your chance to get a no-sweb Precna sped up to $20 this Saturday. That's racing dot Fandall dot com Age and residency restrictions apply offer valid on first win wager refund issued is non-latch rollable Racing site credit that expires on June 12th, 2023 Restrictions apply see terms at racing dot Fandall dot com gambling problem call 1 800 gambler Let's dive on it now to the MLB slate for today because it does kick off here in pretty in pretty short order There are just four games in the day for today So again want to go through those and outlines and spots we could potentially get some value for your daytime viewing Starting with the early slate I do like a couple of bets in the first game on the slate that is the Orioles and of the Angels I like the Orioles money line. It is now minus 156 It was minus 146 earlier on today But something there's value in that number and then the other one is Tyler Anderson You can get him under four and a half strikeouts That is currently at minus 108 over at Fandall sportsbook If you want to pair those together via a same game parlay that is plus 174 right now Don't mind that again, not a huge same game parlay guy But I think the odds on that one actually are pretty enticing. Let's start things off here by breaking down the money line for the Orioles I've got their win odds for today at sixty four point seven percent So the implied odds at minus one fifty six sixty point nine percent still a big enough wiggle room there for me to Feel good about the Orioles here the Angels starting Tyler Anderson who again we're talking about the strikeout department and He's been trying to rekindle last year's magic that he had with the Dodgers and He has been getting better results his past four games He's been cutting back on his forcing fastball throw more cutters I believe change ups as well and the results been better But the underlying number still pretty rough in that sample across those four starts Anderson as a five point seven two skill Interactive era his strikeout rate very low in that time too, which we'll talk about with the strikeout prop here in one second He's facing the Orioles. Their active roster has a 126 WRC plus against lefties since the start of last year So when you add in that Tyler Wells on the opposing side actually has pretty good underlying numbers I think that having confidence in the Orioles here does make a lot of sense It is a bummer that has shifted to minus 156. I still think there is value in that number so to me The Orioles a good bet for today to win this game on any money line minus 156 if handles sportsbook as always the caveat is shop around to see if you can get a Minus 146 or better still out there for them But again my number here 64 point seven percent on the Orioles as far as Anderson specifically He has been getting a bit better recently. Look at the game logs may strike out perspective He has games of six and seven strikeouts across his past three games Which is interesting especially with the number being decently low here at four and a half but one of those high strikeout games came against the Brewers who With like it's their job against lefties. So you can kind of discount that one and The other one a six strikeout game He had one strikeout in the other two games with this new approach that he's had here So I don't think he's fully fully back yet and when you pair that with the fact that He's facing an Orioles active roster with a 20.7 percent strikeout right against lefties this year It's not a great matchup. He's on the road here I expect the Orioles to do some damage with their bats So they're multiple paths from under here. He could just be a low strikeout guys He's been for most this year and was for last year as well Or he could get knocked around by a very potent Orioles offense and get chased in this game I think when you have two paths to an under that's something I want to take at minus 108 So again Anderson under four and a half strikeouts minus 108 at Vanduul sportsbook. The Orioles money line is minus 156 Pretty good bets if you want to tie them together in the same game Parley odds on that are plus 176 right now at Vanduul sportsbook not totally opposed to that but again prefer route is to go with Individual bets personally another strikeout prop I like here on this early slate is in the Mets game That's taking on the Tampa Bay Rays for today and obviously that's a tough matchup and that does play into the handicap here I like Tyler McGill under four and half strikeouts currently plus 116 at Vanduul sportsbook McGill so far this year has struggled to get both strikeouts and whiffs It's we're still the point in the year where you can see guys getting more swinging strikes than you would think based on their strike area Which could imply they're due for positive aggression That's not really the case with McGill his swinging strike rate is 8.9 percent with a 17.3 percent strikeout rate as A result of those numbers McGill has gone over four and half strikeouts just once so far this year that was back on April 1st So his first start this year AIDS active roster as a 20 or the Rays active roster has a 21.8 percent strike area against righties and Similar to the Orioles they are a threat to chase a pitcher early because they are so potent across the board When you combine How good the Rays are the fact that they are a low strikeout team with the fact that McGill not a big strikeout guy as of right now I have McGill projected for 3.9 strikeouts. I think that makes you under a pretty easy call here So McGill under four and half strikeouts plus 116 at Vanduul sportsbook I think there's good value in that number again similar to Anderson multiple paths to the under hitting and that to me is a Attractive thing with a bet so McGill under four and half 116 at Vanduul sportsbook Final strikeout prop I like for today is going to be on Trevor Williams He's facing off with the Marlins and the Marlins not a great offense Which is good for strikeout props because it should allow the guy to get deeper in the game The problem is with jazz chism out from this game The Marlins are a lower strikeout team than they otherwise are so I like Williams under four and a half strikeouts at minus 146 right now at Vanduul sportsbook. I have Williams projected for 3.5 strikeouts So well below the 5 he need to hit the over here Williams is at five strikeouts just once all year and you know It's worth noting that wasn't his most recent star because his most his most recent full start Start after that was a post or a suspension due to weather but It's not as if we're seeing Williams trend up here in the strikeout or pitch count department He just happened to have five strikeouts in that one game. So the small ones offense They're obviously not good and they do lose their best bat with jazz chism being out But they also lose one of their higher strikeout bats So when you remove jazz chism from the active roster, they have a 21.2 percent strikeout rate against righties so They become a lower strikeout team they become worse team So the odds of Williams goes deep in this game are still decently high But will he get strikeouts while going deep? That's where I run into some issues being super high in the situation So to me Williams under four and a half strikeouts minus 146 I think that makes a lot of sense and a spot in one to go So again the bets that like on the early slate are the Orioles money line at minus 156 Tyler Anderson under four and a strikeouts and minus 108 Tyler McGill under Four and a strikeouts plus 116 and then Trevor Williams under four and a strikeouts minus 146 Clearly, I am pessimistic for today taking all unders on those three strikeout props as far as the night games go The one number I like the most is the Cardinals money line at plus 128 right now at Vandals sportsbook They're taking on the Dodgers and this pitching matchup here It's Julio Rios who is pitching very well against Adam Wainwright who just came off the IL Struggled in his rehab stint and has struggled so far or two starts in the majors So that may make you ask why on earth what I want to bet the the Cardinals money line here against the Dodgers I think it's kind of baked into the number pretty fully and as a result Even if I account for Wainwright struggling or Rios being very good stuff like that I still have the Cardinals win odds at forty seven point eight percent the implied odds here 44% Wainwright again, I'm not super high on him Based on what I've seen so far But I think this could be a situation where people see the names of castee or that they see Urias They see Wainwright and realize Wainwright has been having it so far and maybe they just kind of be behind the Dodgers so Plus 128 again forty four percent implied odds I then at forty seven percent the Dodgers deserve to be favored in this game despite the fact it is on the road and This bet will hit less than 50% of the time if my numbers are correct But I do still think that uh, we can find some value in the Cardinals here So of the nightgames favorite bet for me is the Cardinals money line at plus 128 I would give some thought to the the blue jays money line at minus 130 if we got news that Vladimir Guerrero Jr. Is going to play I don't think he will based on the report that we got But let's say hypothetically We get to four o'clock The blue jays lineup comes out and Vlad is in there and the money line is still minus 130 If all those things happen I would be okay taking the jays because I have some value there if I assume Vlad is in if I take him out though It's less so so Keep an eye on the jays lineup if we get Vlad in there I think that minus 130 a very fair number for them I don't think he'll play which is why I'm staying away from that for right now But I would check that out later on uh Cardinals money line at plus 128 the bet I like later on So hopefully I could see some some good bets for today across major league baseball as you're watching during work Hopefully stealthily, but I think it should set us up for a fun day of baseball Let's talk now about the NASCAR because I think it's a pretty fun weekend in the NASCAR side of things They're at North Wilkesboro And this is the first time that the NASCAR cup series has raced here Since 1996 which was before I was a NASCAR fan. I started watching in 1999 so I've never seen a race in north wilkesboro But we can still handicap this race because we know exactly what to expect here in terms of Archetype and that to me is the biggest thing what kind of bucket does this track fit into and for north wilkesboro? It is a short track about 0.6 miles. It is a flat track in terms of the banking There's actually some weird elevation changes which are kind of fun but then it's also the key characteristic here is that there is a lot of tire fall off and That to me is the defining characteristic of this track And it's going to be the defining characteristic that I use when trying to bet the NASCAR all-star race For those of you who do not know about the NASCAR all-star race having it right up on the format for this year They're going to set the starting order for the heat races all on a friday They're going to have a pit crew competition which will set the starting order for the heat races There'll be two separate heat races and the heat races will be similar to if you remember Daytona The dual races where one dual race at the inside row one dual race at the outside row And that's how they set the field for the race So That'll be the way the starting order is set and then also during the race It's actually a pretty straightforward format where they'll have a like a half time break 100 laps in but it's a 200 lap race There are no like weird inverts or anything like that That means relative to other all-star races I believe this one is probably easier to handicap than others even though It is taking place at a track. We have not seen again since I was five years old So I actually think this one is pretty easy to handicap What's interesting about that though is that I believe bookmakers are viewing this as being a Unpredictable race because look at Kyle Larson. Uh, he is the favorite now right now at fandall sports book he is seven to one and Larson has been you know Six five to one or so the past couple of weeks. So you are getting a discount there even though the field is smaller There will be 24 cars in this field after the open qualifiers advance to this race and I have dummy cars in there in my model Basically the three best cars in the open race are in my model for the all-star race to kind of give me some Cover in case the worst-case scenario happens in the three strongest cars advance I want to know okay worst-case scenario. What will cal larson's win odds be for this race and When I run my model I show value on a couple guys now when I was taking notes on Uh prepare my notes for today last night I thought I'd be unwilling byron because he was 10 to one at the time of fandall sports book I thought that was a great number was willing to take that Overnight he shortened to plus 750 which could be a bummer That could be a bummer because it means that Byron. I don't believe is any longer a value for me At 10 to 1 now he is our 750. So he's no longer a value for me there However, fandall as a good book maker would do Lengthened odds of other drivers in order to account for the fact that Byron's odds are shorting They weren't just increasing the hold on you So a couple drivers lengthened one of those drivers was kyle larson out to seven to one I think that even with a lot of uncertainty and even with practice to come on friday The heat races I want to take the seven to one right now on kyle larson the implied odds At seven to one for larson 12.5 percent. I am at 14.2 percent So almost two percentage points of edge on larson Which means even if things don't go perfectly for him in the pick crew competition or in practice on friday The odds that i'm still showing value are pretty high The reason my numbers love larson is he is very good on slick tracks. That's kind of how I view Tracks that are like this where the tire fall off is so great He comes from a dirt racing background Which means when the car gets tougher to handle larson will be very much. Okay We saw him have a great car in darlington as he always does great car He's always great in homestead, which is another track with a lot of tire fall off runs well in fontana He had a good race in richman this year Even though it's not traditionally been his best track definitely not a bad track for him, but Shown improvement there So basically every track with a lot of tire fall off is one where larson has a threat to win He also did win in martins though, which is another short flat track if you want to skew more that direction For this race So larson has had terrible luck so far this year. He's still won. I think twice Despite his awful luck. He could have realistically five wins already so far this year so Getting him at seven to one here. I think is a gift and it's a gift that I want to take so to me right now Kyle larson seven to one a good value and it's a nice way to Make up at the back. We couldn't get William Byron at ten to one Larson is one of the guys his odds lengthened. He was a plus six fifty He lengthened to seven to one the other guy who lengthened it's also now a value for me That guy is resting at 14 to one at vandal sportsbook And I was going to take chesting to podium in this race. He was three to one He's actually still three to one to podium But now that he's gone from 12 to one to 14 to one to win I'm going to take that that pushes him his implied odds to win down to 6.7 percent I have chesting winning 10.5 percent of the time That's a huge gap and the reason that my numbers are high on chesting is that he had a good car in darlington Obviously he and larson decided to Tangle toward the end so it did not pay off and chesting has not won since talladega last year He's not won on an oval non non drafting track ever in the cup series So maybe i'm dumb being as high on him But he was also good beyond darlington and richman in fontana as well I think he's probably going to be starting off pretty high in the heat race because his picker is among the best in the sport right now So the picker competition friday night should put him in a good spot for the heat race Should be able to maintain track position there I think that this number is too good to pass up so If I were forced to pick between betting chesting at 14 to 1 and larson at 7 to 1 I would pick chesting at 14 to 1 Because I think the odds is the odds his odds get longer or pretty low larson might I doubt it But like he might whereas chesting I don't think that's going to happen So to me for the all-star race the main event on Sunday night I like kyle larson 7 to 1 Ross chesting 14 to 1 if you can still get fire in 10 to 1 which I doubt I would take that but Based on the current fandal odds larson and chesting are the first bets now Fandal also does have odds up for the all-star open race and I do show value right now in tie gives tie gives is plus 360 to win at fandal sports book I have tie at 25 percent to win The all-star open which might seem like a lot, but it's a joe gibbs racing car Gibbs has showed a lot of speed recently not a ton of great competition in this event josh barry is there and josh barry Is well suited for this track. I would think and he's in a hundred car But I prefer I think gibbs is better personally so I do show value in Gibbs the reason i'm not taking it at plus 360 is because The picker competition will set the starting order for this race And unlike the all-star main events there are no heat races for the open Which means if gibbs's team has an issue in the Qualifying or in the picker competition He's gonna start in the back if kevin harvick messes up his team messes up in the picker competition He can make up for that in the heat race on saturday. There is no safety net here for the open drivers so I don't think gibbs's odds will get shorter should his team be fast in the picker competition Let's say he starts first. He's probably still going to be Roughly plus 360 but the downside here is pretty big so If you need a reference point in terms of betting gibbs later on I have his win odds at 25.6 percent He is 52.5 percent to podium and 41 percent to advance via finishing first or second not via the fan vote not that he'd win that anyway, but if you can find markets available 41 percent to race's way in 52.5 percent to podium 25.6 percent to win based on my numbers for ty gibbs in the open race He is the one guy i'm primarily focused on michael mcdowell is a slight value for me He is at 16 to 1 rather wait till we get the numbers from practice uh on friday before diving into him so I think gibbs is a guy i'll probably bet i've not done so yet But I would bet that I will wind up there at some point I just want to wait until after the picker competition and case things go poorly there to safeguard myself We also have the truck series racing here on saturday at north wilkesboro and this field is disgusting It has kyle larson. It has ross chest eight. It has bumblewalls. It has william byron christopher bell all on top of the truck series regular So this field is absolutely loaded, which means the odds are flatter than usual for the top end guys So we have to account for that when we're trying to decide which guys want to bet And even with the field being loaded I'm still showing value christopher bell at six to one to win this race and I'm willing to take that on bell bell six to one byron plus 350 larson plus 270 and the interesting thing for me is that I view larson and bell as being in somewhat similar equipment bell's driving for hatori one of the Toyota teams over in the truck series tyler anchorman the primary guy there And anchorman's a guy I've bet a couple times this year. I think that he's actually okay So a decent equipment prior on hatori. It's not great. It's not kbm which Byron is in but I'm not sure what to think about spire because They've had good races like last year at martinsville. William Byron is in the spire truck started dead last with no practice No qualifying and won the race But outside of that they haven't had any like pop pop performances So i'm a little bit lower on larson's equipment I think than the books are when they have my plus 270 and I've even being in somewhat equal equipment to bell But the betting odds skew pretty heavily towards larson as for Byron I do have him as a favorite for this race in the kbm truck because that is the best team in the series Byron's win odds for me 24.5 percent is implied odds are 22.2 So he has a value based on my numbers But bell is the bigger value at 17.1 to win versus the implied odds at 14.3 percent The reason it's high in bell is because he is tremendous on slick tracks similar to larson has that dirt racing background and He's great on short flat tracks, which is again where north wilkesboro falls into you look at his xfinity series record at New Hampshire Richmond phoenix stuff like that. He has been phenomenal and in the cup series. We've seen that translates to a lesser extent as well So you put bell down the truck series put his odds at six to one I think that's pretty enticing. So I will take bell six to one To win the truck series race, uh, I think that's the best bet as of right now Value on on Byron, but not quite there as of right now as far as other bets I like in the truck series race. No other outrides. I want to take a faddle sports book But looking elsewhere you can get some top five bets I have like ross chest aim plus 225 and steward freason at four to one. This is I think the third straight week We've been on freason, uh, but it's worked out so far. He finished runner up last week to cash At four to one his implied odds are 20 percent. I have freason at 22.4 percent So it's not a huge value, but I like his talent like uh his skill a lot, especially on slick tracks He is a dirt racing background. Again, I kind of like that a lot at this kind of track As for chest aim things have not gone well for him so far in the niece racing trucks But a lot of it's been equipment related or uh been, you know Attrition related. I still think that he's good enough to win in this equipment So I actually have chest aim at 44 percent to finish top five. Uh, he's again He's plus 225 to finish there at at other books I doubt there are 31 percent so I'm well above market on chest aim as I have been Several times so far this year, but I think I'm okay with that He might not be able to beat Byron bell and marsen But I think you can get a top five, especially when it's out there plus 225 So bets of the truck series bell to win six to one chest aim top five plus 225 freason top five Four to one and then also taking uh larson to win the all-star main event at seven to one Chest aim to win at 14 to one and monitoring tie gibbs likely taking him But I want to wait till post pit crew competition before doing so That is all that we have here for today on covering the spread again should be a pretty fun day checking out the pga championship Watching some baseball and then uh watching nascar for tomorrow I can always get on board with that kind of work day Do not forget to subscribe to the covering the spread podcast feed and check us out over on the Fandall youtube page you get the preqs preakness stakes podcast with christina blacker getting her read on this year's field If you got questions for me, I'm on twitter at jim sonnis j i m s a n n e s you can also follow the fandall podcast network at fandall podcast I want to thank you all for tuning in for today. Good luck to you with your mlb That's for today. We'll talk to you once again tomorrow This has been covering the spread right here on the fandall podcast network


r3, let's make a definition. So a co-bordism, let's call it sigma from l0 to l1, is a smoothly embedded orientable surface sigma inside of r3 times i with the boundary of sigma is l0 times 0 union l1 times 1. So it's hard to draw a really good picture of this, because we don't have four dimensions available. But roughly speaking, you should think that it looks kind of like this, where down here I have l0 and up here I have l1. So if I have a co-bordism like this, then I could look at kt, say that's sigma intersect r3 times t. So usually this will be a knot. There'll be some values of t for which I get a sort of singular thing. But generically, it'll be a knot. And I could take dt as a diagram of kt. So if I want to keep track of what this co-bordism looks like, I could look at this diagram and watch how it changes. And if I picked a generic projection here, and I set up the surface around just a little bit, I'd see that the diagram changed really in one of two different kinds of ways. So let's try and make that precise. So we'll call this, there's a movie. So I take some of these dt's. So my original diagram, d0, is dt0. And then it goes to dt1. And then after a finite number of steps, I get to dtn, where each dt0 to dt1 is either a righto meister move. So let me say what those are. So I could have something that looks like I have an arc. And I add a little kink. Two, I could have two strands. And I could pass one strand over the other, or three. I have, I'm supposed to draw a big. So let's do three over here. Three looks like this goes to this. So what I've done is, let's see if I managed. Yeah, and I've drawn these two wrong, haven't I? Yes, OK, so I should have this and this. OK, so what I've done here is I've taken this crossing here and passed it over this strand, OK? So that's one option. And so theorem of Kovanov says that if d, d prime differ by a righto meister move, there exists a chain homotopy equivalence, say ckh of d, to ckh of d prime, OK? So this is how Kovanov proved that the invariant that you get only depends on the underlying link and not the diagram. OK, so that's one thing that can happen. Let's see, have I managed? Let's see, I've drawn all of these going the wrong way. OK, there we go. Sorry. OK, yeah, OK, good, right.  OK, so you get these by looking at the orientation on your link L, but I'm going to be lazy and not say what these are. That's one sort of movie move that I can see. The other sort is that I can have more smooths, where the topology of KT changes. So I could add a 0 handle. I could go from sort of having nothing to having a little circle. I could add a 1 handle. I have a bit of my link that looks like that. I could add a 1 handle along here. And then I got something that looks like this. Or I could add a 2 handle. And so here I have a circle, and I cap it off.  So let's note that if d goes to d prime is a Morse move, then for every vertex in the cube of resolutions, so I get a co-bordism, say dv goes to dv prime. There's a little co-bordism, which is just given by this handle addition. So let's say a of dv goes to a of dv prime by a of s. So this induces a chain map from a ckh of d to ckh of d prime. So both of these types of movie moves give me chain maps between the covena of complexes associated to them. So what does that mean? So it means that we can define, let's say, a map phi sigma. Remember, sigma was my co-bordism from l0 to l1. Find phi sigma going from kh of l0 to kh of l1. So phi sigma is the map induced by the composition of these little individual maps. So let's say phi n minus 1 composed with phi 0 star, where phi i maps ckh of dti to ckh of dti plus 1. Now at this point, there's a question you should really ask yourself, which is, how do I know this is well-defined? So if I give myself a co-bordism, there are going to be lots of different ways to cut it up into a movie. How do I know that I get the same answer? And the answer is that just like there are these Reitemeister moves, which relate different diagrams of the same knot, there's a set of movie moves which relate different movies of the same co-bordism. That's a little bit bigger. I think there are about 23 elements. Kovanov looked at the number 23 and thought that it was big, so he didn't bother to check whether this was well-defined when he wrote it down. But Jacobson did, so there's a theorem of Jacobson that says that phi sigma is well-defined, well, not quite, up to sign. So there's really a genuine sign ambiguity in the way that this is defined. OK, so maybe let's summarize what we have here. Is we could think that we have a category whose objects are oriented links in R3 and co-bordisms in R3 times i. And what Kovanov homology does, well, up to this annoying sign is it provides a functor from this category to the category of Z-modules and Z-linear maps. So really what we've done is we've taken this 2 plus 1 dimensional TQFTA that we started with, and we've upgraded it to a kind of relative TQFT for links in R3 and co-bordisms in between them. So that's kind of interesting. Another thing that's interesting is that we can think about deformations of this chain complex. And let me explain by what I mean by that. So what if we use another TQFT A prime instead of A? Well, the whole complex, the whole construction, with these chain complexes work the same for any TQFT. Really the point where A was needed was to prove this theorem of Kovanov that the answer that I got didn't depend on which diagram that I picked. Now there's another exercise that says that if you want something that's invariant, you better choose dim of A prime of S1 is 2, which means that I should think about deforming the ring, let's say, A, which was Z of x as the multiplicative ring of my original TQFT to another ring, A prime, which is say Z of x mod x squared mod x squared minus Ax minus b. Let me just write down what the multiplication and co-multiplication maps look like for that TQFT. So I have 1 tensor 1 goes to 1, 1 tensor x and x tensor 1 both go to x and x tensor x now goes to Ax plus b. Now remember, this had grating minus 2, this has grating minus 1, and this has grating 1. So whatever I get when I do this is no longer going to have that Q grating on it. It's not going to be a graded TQFT. Similarly, the delta looks like this. 1 goes to 1 tensor x plus x tensor 1 minus v of 1 tensor 1, and x goes to x tensor x plus A of 1 tensor 1. Again, this has grating minus 1, this grating has gone up, this is grating 0, this is grating 2, this is grating 2. So what I see is that on the other hand, minus 1 and 1 aren't equal to minus 2, but they're both bigger than minus 2. And 2 is not equal to minus 1, but it's bigger than minus 1. Actually, what I have here is a filtered TQFT. So in fact, this is essentially the only A prime that I can have given that it's two-dimensional as a vector space. Good, OK, so we're requiring two-dimensional because if you don't, then you immediately see that you don't have an invariant, OK? So that's an exercise that you should do after this lecture. So what should we say here? So A prime is a filtered TQFT with associated graded. So the associated graded TQFT, I get it by throwing out all the terms that raise the Q-grading. OK, so this means that the chain complex that I would build is a filtered chain complex with associated graded chain complex, which is just the original CKH of D, OK? And so that means that I get a spectral sequence from the homology KH of D to this deformed homology, write the spectral sequence this way, KH A prime of D. OK, so now on the other hand, it turns out that this deformed homology is easy to compute. So there's a theorem, which is due originally to leave, but let me also cite Turner that says as follows. So if this polynomial x squared minus ax minus b has distinct roots in some field f, then the deformed homology with coefficients in f always has dimension 2 to the number of components of my link. OK, and the homological gradings are determined by linking numbers of the link l. So in particular, if K is not the dimension of KHA prime of K is 2, and we get a bonus invariant by looking at the filtration gradings of these two surviving generators. So the filtration gradings of the surviving generators in the spectral sequence, well, you can prove actually that they always differ by 2 are, let's say, s of K plus or minus 1. Take that to be the definition of the bonus invariant s of K. So another way that you can think about this, what does this really mean? i.e. this number s of K plus 1 is the maximum value of q of x such that the class of x is non-zero in KHA prime of l. And now, if I have a co-boardism, say, sigma going from K0 to K1, well, this induces in much the same way a map phi sigma from KH of KHA prime of K0 to KHA prime of K1. And this satisfies, so, q of phi sigma of x is bigger than or equal to, since this is a filtered map, q of x plus the Euler characteristic chi of sigma. So now, you can prove that if sigma is connected, phi sigma is an isomorphism in much the same way that you prove this theorem of Lee and Turner. And this means that s of K1 is bigger than or equal to s of K0 plus chi of sigma. So now, if I give you sigma mapping from K0 to the n-lot, it's easy to compute that s of the n-lot is 0. So this equation here says that 0 is bigger than or equal to s of K1 plus chi of sigma. This is minus 2g of sigma. So I get that 2g of sigma is bigger than or equal to s of K1. So you can tell from the noise outsize that I should be done. Let me make a definition state of theorem, and then I'll stop. So the definition says that I could think about what's called the smooth four-dimensional slice genus of K. So this is the minimum of g of sigma such that sigma, let me just, since I'm short of time, let me say it this way, sigma is a co-bordism from K to the n-lot. Then what we've done, plus the fact that s of minus K, so if I take the mirror of K as minus s of K implies that, actually, this invariant gives a bound on this smooth four-genus. So I get that 2g star of K is always bigger than or equal to the absolute value of s of K. So this is an interesting theorem because it tells us that Kh tells us about the topology of smooth surfaces inside of our four. So let's remark. So I could consider g for top. This is the popological four-genus. It's the same thing. But now I just require that sigma is, let's say, locally, flatly embedded. So every point has a neighborhood where the neighborhood is homeomorphic to r4. And the surface intersect the neighborhood looks like r2 inside of r4. This is another reasonable kind of surface that you might think about. And these two numbers are not the same. So I could look at s of that p minus 3, 5, 7 pretzel knot that we had at the end of last lecture. This is 2 and just compute this since Kovanov homology is very combinatorial. But the theorem of Friedman says that g for top of this knot, in fact, of any knot with Alexander polynomial 1 is 0. So this manifold bounds topological disk, but not a smooth one. OK, so I'm going to stop now. Sorry for running over. And yeah, so we'll come back in the afternoon and we'll talk about Kovanov homology for tangles and how that helps us prove Reitemeister invariance. OK.


target because the dogs get locked in on us and also he creates that prey, that happy play drive with the dogs. Let me know if I'm too close for you. No, you're fine. You're fine. So what he's wearing, this is the bite. We have the pants to match, so when we have the pants on the dog is actually able to bite anywhere between them.


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