The next talk is being held by Matthias Lasse. Matthias is talking about how to reverse engineer FPGAs. He did it by himself and he will tell you how he did it and how he especially reverse engineered the Xilinx 7 series and Latisse ICE 40 series. He knows much more about this than me, so please give me a warm applause and here's Matthias. Hi, hello, can you hear me? Okay, what is this talk about? In this talk I'm going to explain to you what is FPGA? How does it work? What does it do? What does FPGA stand for? And of course I will tell you stories on how I reverse engineered them, show you some pictures and so on. What this talk isn't about? This talk is not about how to use FPGAs. I actually cannot use them. I never learned Verilog or VHDL. And this talk is also not about high level synthesis. Maybe a quick story why I decided to reverse engineer the ICE 40 series four years ago. I wanted to build a small CPU and I had the problem that chip design and building chips is far too expensive. So the next simpler solution would be an FPGA. But I did not want to learn Verilog or VHDL. So I decided to sit down and document bit stream format and the internal layout. Anyhow, FPGA stands for Field Programmable Gate Array. What means Field Programmable? In a sense, it means that the device is in place programmable. So to say in a live circuit, we can just reconfigure the device. The gate part is, yeah, FPGA simulates or implements logic gates and the array, yeah, it's a two-dimensional array of logic gates, programmable logic gates. Yes, but what is logic? Before I will tell you how an FPGA works and so forth, we have to get down to logic 101. We have four operators. Operators, yeah. We have a NOT gate, we have the AND gate, we have the OR gate and we have the exclusive OR gate. On the bottom, you can see the truth tables. When we have at the input, for example, at the OR gate, 00, we get zero on the output. When we have 01, we get one and so forth. Next thing, we can chain together logic gates into a circuit. Here is a small example of one-bit full-edder, which is used to implement addition. And as you can see, it uses two exclusive OR gates, two AND gates. Ah, this one uses three exclusive OR gates. Okay, there are several implementations of them. In, on the former slide, we could see that we can generate a truth table dependent on the input states and what we get on the output. With that, we also can combine several logic gates into one table. I did the work for the full-edder here and now we have our three inputs, we have two outputs and if we, for example, get on A1 on B0 and we have the carry set to one, we know the result will be zero and the carry out will be one. The nice part about this is we don't have to trace through the logic and we just kind of implemented several logic gates in a lookup table. And the lookup table is the smallest part in a FPGA. This thing implements the logic gates. However, we need more than one lookup table, of course. So let's zoom out a bit. What you can see here is a slice in the seven series silings FPGA. These are for lookup tables with six inputs each. They are followed by a special carry unit because implementing addition with lookup tables would take up too many resources and because we need it quite often, it is far cheaper for the manufacturers to include a carry chain. And then on the outputs, we have flip-flops because sometimes we need to synchronize the state or we need to store one bit of information. We then pack together one lookup table, one part of the carry chain and in case of the seven series, two flip-flops into what's called a logic cell. Four logic cells make up one slice and two slices are then grouped together, combined with a switchbox and interconnect into a tile. As you can see, we have surrounding tiles and that's how we implement logic and that's how we wired the logic. Now we zoom out a bit more. Here we can see that several of those tiles are grouped together into columns and we zoom out a bit more. One column with the seven series contains 50 tiles and one clock tile in the middle. This is a rather small device. It only has 186 columns, which equates to 9,300 tiles. The columns then are grouped together into regions. This particular device has six of them and that's the basic FPGA fabric, but we're still missing something. We still can't communicate with the outside world of the chip. For that, we need something like a bridge or input-output modules. At the borders, we have the IO tiles, but are there more than those two tile types? Of course, sometimes logic is not enough. Maybe we need memory. Of course, we could implement the memory in logic, but that's expensive too. The vendors gave us small units called block RAM. Here are the columns of block RAM in that particular device. Each small rectangle contains 36 kilobits of memory and there are 140 blocks of RAM in this device. Sometimes memory is also not enough. Sometimes we need processing power. Implementing arithmic functions like multiplication would also use up lots and lots of resources, lots and lots of logic. The vendors gave us DSP tiles. DSP stands for digital signal processor or in that case it's just a small addition unit combined with a multiplication unit. Now we really know about the basic makeup of FPGAs, but how do we configure it? How does each lookup table know its values? How do the flip-flops know their initial state and how is everything routed? For that, we have the bitstream. The problem with the bitstream is it is undocumented and it configures the switchboxes lookedup tables and provides the initial state. This thing decides which switch to turn off and on. The goal of reverse engineering FPGAs is getting the bitstream documented. For years ago, I reverse engineered the IS-40 FPGA. A quick summary. The IS-40 FPGA is a very, very small one. It is optimized for low power consumption. It only has between 384 and 7680 lookup tables with only four inputs. Even the block RAM blocks are small, but it is very beginner-friendly and the cheapest one on Mouser. This is the picture the manufacturer gives us. It shows that the programmable logic blocks contain eight lookup tables and that the whole fabric is surrounded with the IO tiles. But we don't know anything about the interconnect. And we don't even know how many tiles, how many rows and how many columns there are. A closer look at the controller logic block or in that case the logic cell. We can see there is only one flip-flop and it can be bypassed. You can use both the pure output of the lookup table and the flip-flop. And we have only four inputs. What's special about the routing in the iS40 is they are routed B-directional. So you have more than one source at each wire. You can if you put in the right or wrong configuration because it sheds circuits in the device itself. Another thing they provide us with are eight globally routed signals. They get routed to every single tile and at every tile we can choose out of those eight four. The interconnect between the tiles mainly consists of wires that span over four tiles and over twelve tiles horizontally and vertically. And of course every single tile is connected to its eight surrounding neighbors. That's it. What were the challenges with reverse engineering the iS40 FPGA? Well, we had no knowledge about the internal layout. I had no schematic. I had no idea at all how many wires they were, where they go, where the switchboxes are, how the switchboxes connect to the controllable logic blocks. And even the bitstream was a command for commanding the FPGA to load the correct bitstream where only partially documented. Another challenge, of course, is mapping the tile location to the bitmap coordinates but I will show you more details of that later. So how did I reverse engineer the iS40 FPGA? Well, I took a closer look at the tools the vendors gave me, especially the bitstream generator. The bitstream generator seemed to contain several strings which related to the names of the wiring and you could compare them to bit names. But they were behind the debug flag that I could not breach because they commented it out and the compiler didn't optimize it out. That's why it was easy for me to document and reverse engineer the iS40 FPGA because I only had to replace one single jump instruction in the vendor tour and I was able to get every single name of every single bit there was and a short description of its function. Alright. Another fun story about how this tool was written when I tried to decompile it and looked through some functions in it you could see where the copy pasted everything together.  Another thing I noticed the bitstream contained a CRC or cyclic redundancy check but there was not a single opcode that related to this function namely exclusive or the whole binary had none. If you implement the cyclic redundancy check you normally need XOR. That puzzled me. So I just randomly stopped the bitstream generator and took a look at the memory dump and they found out they generated the bitstream in ASCII. So at some point I found a giant string of ones and zeros in ASCII and they generated that part only for the CRC. I don't know what happened in that program. I don't want to know what led to these decisions but with the Sailing 7 series I partially reverse engineered the Sailing 7 series two years ago I had another challenge because the 7 series is a really high performance device. One single LUT 6 lookup table uses up half the memory of one CLB tile in the I-40 and even the smallest 7 series FPGA has more lookup tables that are 4 times bigger than the I-41s and the biggest one has more than 1.2 million lookup tables. This maps to around 150.000 tiles. Other resources in the 7 series contain the block ram. The block ram has 36 kilobits of data, as I mentioned before. We have the central clock line, the DSP cost, the IOTiles. By the way, this is just the bottom most part of the Zinc 7020. Now I will tell you more about the Zinc 7020. This is the particular device I decided to reverse engineer because it contained two ARM Cortex A9 processor cores that could reprogram the FPGA and interface with it. I really really liked the thought about combining an FPGA with the interconnect with the memory system of those processor cores and use that. But then again, I didn't want to learn very long of the HDL. So I decided to reverse engineer it. With the 7 series I had to scale up my whole operations because for example, as I mentioned before, there are 9300 switchboxes. Each switchbox contains 216 multiplexers and 3,738 possible connection states. That's a lot. They also connect through 135 wires to neighboring tiles and route 117 wires from neighboring tiles to them. The whole operations suddenly got very big. And of course the whole device contains more than 3 million wires and there are 32 million or more than 32 million configurations bits. With each of them I had to find out what they do. What were the challenges with the 7 series, the complex design? But with this one I was not able to get any debug information whatsoever. Also the tool chain was much more complex than the latest one. It was first written in Java. So no decompiling there for me. I'm only a C assembly C++ programmer. And it was written much nicer. Another thing that bothered me, I will show you shortly, is that there is a small part where the pattern of the bitmap you can extract out of the bitstream doesn't match the rest. And this part is as I later found out for the error correction part. Also another small challenge was mapping the tile locations to the bitmap coordinates. Now I will show you a very small section of the bitmap I can generate out of the bitstream. Okay, when I first looked at this I was like, fuck, this thing seemed like an insurmountable wall to me. But I already, and you already can see some patterns in there. We for example can see that there are some bigger chunks. Most probably these are the configuration data for the lookup tables. Nice. Now we only have to find out what the other columns that look like noise do. Of course they are for the switch boxes. But mapping them to the sync wires, that was hard. About mapping the tiles to the bitmap, I have another picture. We can see that 64 pixels map to one tile. And this part, or yeah, this part maps to the other part. With the middle part I was puzzled. Of course the small regular flock of pixels we can see here and here. Had to be used for the clock interconnect. Here in the middle we can see there is the clock. We know that 25 tiles on one side and 25 tiles on the other side. But that's all I got first to work with. About the error correcting code that we can see there, that thing was a challenge. But I had an idea. I wrote a small parser that counted the number of bits that were set in each row. If this number was one, I stored the information about the middle part. Out of that I was able to find out this thing was using Hamming code. Or single error correction, dual error detection. Extended Hamming code. I would love to show you more. But right now I had a problem with my hard disk and my notebook. And that's kind of where my talk early ends I think. What can I tell you more about the reverse engineering of the seven series? With the Vivado tool chain we get the net list, we get the internal schematic. And you can extract it automatically. You get the information on the tile coordinates, you get the names of the wires. But we don't get the information in the bit stream. But with the knowledge of where the tile sits in the bit stream. We can correlate the data. I created several automated tools for that. I would have loved to show them to you. But something went terribly wrong. I'm sorry. So what are the implications of my work? I did it there. Because I can create a net list out of the bit stream. I'm able to cross compile bit streams to different architectures. With that we can copy, extract and reverse engineer IP cores that are otherwise impenetrable. Another possibility is starting project ISTOM. Another project ISTOM with Clifford together to create a second target for his open source tool chain. I'm very sorry that my talk got this short. Any questions? This was very short indeed. So if you have questions for Matthias, please come to the microphones. Here's one, two, three and four. And we can take questions from the ISC chat or via Twitter as well. Yeah, we have a question here at microphone one. Yes, I would like to know what happened to you? Were you pressured not to... What happened to your laptop? What happened? It was something about XFAT and macOS and unplugging it. Okay. And my windows when I try to repair the disk just freezes. Okay. Yeah, that's hard. It happened like one hour before the whole thing started. My second question, have you worked on Xilinx Spartan 6 series? No, I never cared about the Spartan ones and about the 6 series. I only wanted to reverse machine 7 series because of the Cortex processor in it. Okay. Thank you. Thank you. Microphone two, please. Can you comment on this like middle point of the FPGA?  Is it like the error correction code for half of the FPGA and the other half of the FPGA or how does that work? Exactly. With Heming code you normally mix the parity bits into the data. But of course Xilinx doesn't want that so they put it in the middle. And these 13 bits, yeah, they are the Heming code for one row. I can show you later the details when I get them out of my hard disk. They have everything in details with more details. Thanks. Thank you. Microphone three, please. I was somewhat puzzled by your remarks regarding your inability to decompile the Java tool chain you mentioned earlier. Because usually C sharp MSIL byte codes and JVM stuff is the easiest prey in that regard. How come? That might be, but I always come a bit from a different direction because I taught everything to myself. I had no idea how to take the Java. With the latest tool chain I created two tools for that code elimination. One, for example, patched every single jump instruction in the binary so it could get the program flow. Another one replaced every single opcode with breakpoint. I then hooked the structured exception handling from Windows and replaced every opcode as it was executed. In that way I could really use the code by two perks which was easy to decompile. But as I said with Java I had no idea how to tackle that. There's lots of automated software for that. Give it another go. I never used... I always wrote my own software, maybe. That's one of the reasons. Then we have a question from the ISC chat. What architectures do FPGAs use? You mentioned ARM once, but it wasn't the FPGA itself. No, FPGAs don't use architectures like CPUs. They use the building blocks like the controllable logic block. Like block RAM, DSP tiles, DIO tiles and that's the architecture. Then microphone one again. I'm wondering whether you have tried to extract some of the device database from Vivado or some information or did you skip that for legal reasons? I thought about doing that, but the binaries I think are more than 10 gigabytes in size.  Okay, I think Vivado encrypts IP cores. So basically VHDL code and they do the same way also for XML files which contains some of the device information. I think that's quite similar to what Intel is doing for those who listened to the E-Talk yesterday. I had no need for that information because I could get the device information out of like 10 or 20 example projects just flew into the core. If you want, I can show you later some more details about that. Microphone two, please. Hi, impressive work. Thank you. Sorry for the presentation. Okay, so let's exclude your presentation from your work. Still impressive. My question was almost the same. So you didn't look at GTX or high-speed IP cores because it was too complicated, I guess. No, I didn't have a device for that. Okay, okay, I don't have all the hardware in my mind. Okay, thank you. I will ask you details later. Microphone one again, please. Did you do any work on clocking? What? Did you do any work on clocking like PLLs and clock distribution and all that? Yeah, sure. I have some information about the column drivers, the row drivers, how everything comes together. Okay, but there was also part of the slides which have disappeared.  Microphone two, please. Thanks for your talk. My question is regarding reprogramming the FPGA fabric from the ARM Cortex course. Did you have a look at that? Is it also possible with your work? It is, but another thing that interests me more, the small thing, the 70-20 I'm talking about, has two tiles that can reprogram the whole thing or partially reprogram it. And of course, readouts. Yeah, so it would not be a problem with flashing that with your self-made bit file. One thing about the sync. The sync is a combination of a CPU and an FPGA, but they're isolated. You don't even need to power up the FPGA part, but you need to power up the ARM part because it's the ARM part that obviously is prioritized and that configures the first bit stream. Okay, so I can just use your bit stream then that you generated using your tools? I have a very, very, very, very proof concept place and route tool for small gates and bits with DIOs that's working. And it's routing and it's placing. Okay, thank you. Anyone, please. What about the timing information? Have you also reverse engineered that? I started extracting the timing information, but I wanted to finish up more of the tile information before I started with that. But I have the tools already waiting and that would be one of the next parts I would tackle. So sometime in the future, we can expect to actually use it with timing analysis and... I would hope to because I don't have a real motivation behind that device other than for fun. If I could create something great out of that that interests the community, I would love to do that, but until now, I wasn't in contact with anyone. Microphone 2, please. So did you look at some other FPGAs like the Ultrascale Plus or maybe... Yes, I did. I started looking at the Ultrascale, but before that I wanted to finish up the 7-series and I don't have a working Ultrascale and I just want to hold it in my hands when I reverse engineer it. I think you can understand that. And another part of the question, did you look at other vendors, maybe micro-Semi, Altaira? Micro-Semi, I first considered before I decided to reverse engineer the IS-40, but I think they're crap. And yes, I really want to reverse engineer the Altaira Intel FPGAs next because then I kind of reversed and did all big free vendors. Super, thanks. Thank you. And number one? Yeah, I have a question concerning the place and route you do. What is the basic approach you take to reduce all the combinations of block placing? Right now it's just the proof of concept. There is no reducing anything later. Of course I will use simulated annealing and I really want to get into what way they call the reduced order binary decision diagrams. Okay, thank you. Number two, please. Thank you for the questions. You're saving me. Hi, do we have and tried out to get the bridges between the FPGA and the hardcore part working, for example, for memory or access from the FPGA to the hardware peripherals in the... I started working on that. That's just reverse engineering another tile. I can show you more to that later if you have time. Thank you. Number three. How does the FPGA apply the bootstream? In what sense? You put it in via UART or something. How does it work? Okay, there are several ways with the Zinc one because it has an ARM Cortex processor, so there's a small bootloader. You can put the whole thing on an SD card and it loads it automatically through the Cortex A9. Of course, you could use JTAG or you can connect an external SPI device. There are many possibilities. Great, thanks. And we have a question on microphone four. Hi, thank you for your talk. A little request. Could you present the whole presentation in a self-organized session later, maybe? I would love to. Cool, thanks. And number one again. Yes, I had a question. During your studies, did you discover new stuff about FPGA backdoors made by NSA and friends? No, but I found ways to detect them. But? I found ways to detect them. Okay, I'd love to talk to you about that. Sure. And I wanted to say something else about the Xilinx family you've been working with which integrate an FPGA and a CPU. I think that in terms of cyber security, it is absolutely not a good idea to mix in the same chip an FPGA and a CPU because an attacker like NSA can easily upload a few bytes of code. No, you cannot. And I will tell you later about that because I'm working on a proof of concept for a provable un-tempered device. Okay, I'd be delighted to talk about that with you later. Thank you. We have a question in the IRC chat. What is lacking to get a free and open source FPGA tool chain like with Storm for the IC40 series? What do you mean? Ah, the place and route tool. With the IC40, I gave Clifford my findings and he, together with some other guys, they created the place and route tool and I just provided them with the information about documentation, basically. Hope that answers that question. Microphone 2, please. Yes, thanks. You said that you don't do a very long NVHDL so what do you use as input for your design tools? The example project of the vendors. Then I drag around the gates to get some different placing and routing and with Silings you have the block design editor. I also had that in my other presentation. Okay, thanks. Number one again, please. Hello. Between, Silings forces you to use the XI4 bus between the programmable logic and the ARM cores. Did you figure out if there's another way to connect these parts? What do you mean? They don't force me to use the XI bus, there's also UR, UOM also have like 64 GPIOs. Oh, yes, to get outside the device. I don't know, between the ARM core and the fabric. Okay, good, thank you. If you want to, I can show you more details to that later. I think there will be a session later. Microphone 2, please. Could you explain your way of reverse engineering the FPGA? Did you create a bit stream and observe its behavior or did you just create a bit stream and not run it? I never run the bit stream that I created. I only once tried a small bit stream I created by myself and that was it. So what did you do if you did not run the bit stream? I just got the knowledge out of it. I tried to recreate the same net list information that I got out of the tool chain only by looking at the bit stream. Thank you. And microphone 2 again. Can you talk about reverse engineering the non-logic tiles like the PLL tiles, IO tiles? Is that somehow different from reverse engineering the logic tiles? Sadly, yes.  You have to look at, or I have to look at the schematic information, look what intern switches are used, where they go. Then I have to create another image where the switch is not used and I can take the difference between the tile and then OK. One detail. Do the vendors provide some sort of schematic of the PLL blocks or is that classified information? With silings, you know almost everything about the device. Cool, thanks. And another question in the IRC chat. When and where would the later session take place? When and where do you want it to take place? I'm not that good with talks. As you've noticed, I'm more a conversation guy. Maybe you just come to the front of this talk and you can figure out a place together, maybe at a bar or if there is some free space. It's a big space, actually. Are there any more questions? It doesn't seem like that.


Teaching is a craft. It's both an art and a science and it can't be accomplished by following a recipe. There is no guidebook or instruction manual or how-to video for how to be a great teacher. There is no secret formula or codified list of best practices that will guarantee success in your classroom. This craft of teaching is often messy and confusing. You doubt yourself. You get frustrated. You make mistakes. Tons of them. An improvement is painfully slow. And yet, that's the beauty of it. You get to explore like an astronaut. You get to experiment like a scientist. You get to design like an engineer. You get to compose like a musician. And you get to create like an artist. There's no point where you have arrived. As a creative teacher, you're always exploring. You're always experimenting. You're always innovating. But that's what makes the journey so amazing.


Greetings, I'm comparing an award and that is for Cuck of the Century. I stumbled upon this rather hilarious or perhaps rather tragic thing the other day. So we have a poor fellow writing in and asking I'm married to a woman who my love and adore.  Now she wants to have a baby, but it won't be mine What do I do? Ask Ellie. Well, you can ask me too, actually. You can ask the great lion of wisdom for some advice in this matter and I would just go ahead and say that you should definitely not have a child neither should your wife You are both not worthy and not suitable to have children to reproduce. That is my take on this situation But I do have some insights for For other guys and I base this upon the primordial truth. So we can ask ourselves how did it come to this? How did it come to the pure disrespect his wife is showing him? Yes, it comes from the fact that she has under a very long time most likely asked herself Quite frequently. Where is the limit? She's kept pushing him and he has never put down his foot He has never set clear boundaries and limits for her and this is something she has wanted She wanted clear boundaries. How far can I go? Where are the limits because if someone doesn't have limits then there will be no order then this is chaos So the guy has never put down his foot. He is never there to be a man say enough is enough This is how far you can go but not further since he is back down every single time She has keeps pushing keeps degrading him to find where the limit is So it's not actually that she is fundamentally a bad person Obviously now she is but it stems from the fact that he has been too feminine to show her You know these are the rules if he had done that from the beginning She wouldn't have kept degrading him kept pushing the limits kept trying to find where the boundaries are So this is a tragic story of the modern world of the feminized man and a cautionary story as well This can happen if you don't set boundaries if you keep cocking if you keep backing down all the time if you keep letting your woman in this case push you So never do that Obviously we have a lodged indoctrination saying that masculinity is bad and that and that respecting women is about Disrespecting yourself that is absolutely not the case respecting women is about treating women with Respect and being polite to them being a gentleman But you can't be a gentleman if you're not a man and a man obviously do not tolerate disrespect in At this sort of level and here's the thing if we look upon this example This is not where it all started. It probably started with something else that he didn't Have guts enough to say, you know, this is not acceptable and then she has kept pushing so the point being The cautionary tale is have clear limits It's absolutely fine to set limits and boundaries to not be Disrespected because if you are Disrespected if you let her she will walk all over you So that is the lesson for the day and I say this as someone who is a great advocate of treating women with the utmost respect And you know always be a gentleman and everything like that, but treating women with respect is not about treating yourself with disrespect And also this sort of emasculated man it will always lead to trouble I think this woman in the example she probably wanted a good strong man She could respect and whom she could be happy with but because he's such a pussy that she can bully around Yeah, she's not happy there either. So feminine men leads to bad things simple as that So don't be afraid to be a man. It's okay to be a man Regardless of what Gillette commercials will tell you so anyway treat women with respect treat yourself with respect have some dignity have some honor and We can restore these horrendous gender relationships In whom I am the herald of the primordial truth. XXO boom


Gwelodd Llywodraeth Cynwylliant Cymru nhw oeddordeb yn ganesolodol bandww. Rwy'n credu maen nhw'n hollwch arnaethiaeth cerddaint a mediadau Cenedig yw Llywodraeth Cenedig yw Llywodraeth Cenedig yw 400 ffordd yma ar ddırfodol 60 oes yma, ystod yn y pethau yma yn y graf o'r ddod, fel Wmg.com. Felly, ystod yn y graf o'r ddod, ac rwy'n cael ei ddod. Felly, ystod yn y graf o'r ddod. Felly, ystod yn y graf o'r ddod. Felly, rwy'n cael ei ddod, ac rwy'n cael ei ddod. Rwy'n cael ei ddod i'r sefydliadau Ierri Gwylbers, is the real expert and who is the director of the arbitration and mediation centre. So perhaps first if I may start on the technology dispute survey, which is available to you. As I mentioned, this is based on 400 responses, which is I think a very good response rate from respondents in over 60 countries, and it gives us an idea of what practitioners and industry think about the state of technology disputes internationally. There is an executive summary to the report, and I think the highlights that I would like in particular to signal are the following. First of all, less than 2% of agreements in relation to technology result in formal dispute proceedings. So that's an interesting piece of information at least for us. And I think the other thing that I would like to particularly emphasise, you can find in the first, second, third, fourth, fifth paragraph of the press release, the third from the bottom, and I think there's some very interesting results here. Upper most in the minds of parties to technology agreements cost and time of dispute resolution procedures. This comes through very clearly. And in that paragraph to which I referred, there's some interesting information. First of all, court litigation is the most frequently used procedure followed by arbitration and mediation. So court litigation was most common standalone clause 32%, arbitration 30% and mediation 12%. In terms of time, court litigation at home in your domestic jurisdiction on average takes three years, abroad on average 3.5 years. And similarly, legal costs in court litigation at home on average amount to $475,000 U.S. dollars abroad, foreign court litigation on average to slightly over $850,000 U.S. dollars. And on the other hand, if you compare the alternative dispute resolution procedures, mediation took on average eight months, which is significantly better than three years or 3.5 years. And 91% of the respondents stated that typically the costs of a mediation did not exceed $100,000. So that again is significantly better than the 400 and 75,000 or the 800,000. And then arbitration, and again it's in that same paragraph to which I referred, on average took slightly more than one year, which is again significantly better than three or 3.5. And on average it costs $400,000. So that's not necessarily a great improvement except its half of what foreign litigation costs on average. So what's the significance of all this? You know why we're talking about this? Well, I think the significance is that we live in a world where technology is increasingly important, and so the contractual relationships formed around technology are increasingly numerous. We now know a little bit about the behaviour in those contractual relationships. Less than 2% of them result in formal dispute resolution procedures, so this is not a massive amount at all. And then interestingly, you see, if you are entering into a technology agreement in this world, there's a significant chance it's going to be between parties located in different countries. You know, it'll be an international agreement. And then it becomes relevant to know what your exposure is to costs and time in the event that there is a dispute. And not only what your exposure is, but what your options are. And what this survey is telling us is that non-court options, namely arbitration and mediation, are delivering significantly better results. And so it's very useful to pay attention to that, obviously. So that's what I would say on this one, and we can come back to some discussion. And as I say, Eric can take you through a lot more detail if you would like in relation to that. But let me move on then to internet domain name disputes specifically, where, as you know, if I may say, the WIPO Aputation and Mediation Centre is the champion in terms of dispute resolution service provision, thanks to Eric and his colleagues. So last year, 2012, we had a record number of cases, once again, of cyber squatting cases. We had 2,884. If you go to the press release on page 9, annex 5, you'll see the evolution of cases over the years. So you see last year 2,884 cases covering 5,000 domain names, because a case can concern more than one domain name. We are very proud of the fact this is a very international procedure, and it caters for the international character of the internet. So in this respect, complainants and respondents came last year from 120 countries, and the cases were dealt with by 341 panellists from 48 countries. So we think this, that we have here, a procedure that is particularly adapted to the international character of the internet, and by the way in 13 different languages. And we do these cases, by the way, in all of the top level domains, the international domains, if you like, .com, .net, .org, and so on, plus in 67 national domains, so .ch, etc., .fr, for France, and so on. As to, let me make just a couple of other comments, as to the areas where cyber squatting is most prevalent, as judged by the cases, well this is retail, fashion and banking and finance. And you'll find some information of that in the press release, and if I may refer you to annex nine on page 13, you will see there examples of cases, samples of cases organised by different areas. So if you're looking for some banking, biotech and pharmaceutical areas, you'll see Bayer, Beringa, Ingelheim, Eli Lilly, Hoffman-Larash, Gen and Tech, Merck, Pfizer, Sanofi, Yventus, and so on. So you have there a pretty good sampling of the cases in 2012. Let me then move on to our last, the last area that I wanted to touch on, which concerns new generic top level domains. So this is the action that is being taken by ICANN, the Internet Corporation for Assigned Names and Numbers, to open up new domains, new top level domains, to the right of the dot. And they received nearly 2,000 applications, 1,930 applications for some 1,400 distinct new domains. Okay, so this is a real change in the landscape that is occurring. We're going from 10 or 20, 20 or so top level domains to his 1,400 new ones. Okay. And what we do is in this area, we continue the uniform dispute resolution procedure, applying to 2nd level domains, applying to what is to the left of the dot. So coke.com, so the coke is a 2nd level domain. So that continues, but in addition we have a role in something called the legal rights objection procedure. Okay. And that is a procedure whereby a trademark owner can bring in an objection to the granting of a new top level domain on the grounds that it infringes their trademark rights. So someone asked for a domain, for example, dot Coca-Cola. And they were not Coca-Cola. Okay. You could bring in an objection, a legal rights objection on the basis that Coca-Cola could, on the basis that it's allegedly infringing your trademark rights. And by the March 13 deadline, we received 71 LRO, legal rights objection cases, and you have, hot off the press, this little piece of paper, which will give you the proposed string that is the new top level domain on the left. So, for example, dot del Monti, who the objector is, the objector, the trademark owner, who the applicant is the applicant for the string, who the applicant is, and the status. Okay. So that's, do you want this? It's down here. So this is quite interesting information.  And you'll see this information, as I said, hot off the press for these cases that are coming out now. I think the only other thing that I would mention, if I may, and then you can ask questions, particularly for Eric. The only other thing that I would mention is that, last year, we were particularly active in expanding the range of our dispute resolution procedures. And one of the things that we are doing, new things that we're doing, is cooperating with national IP officers to provide mediation proceedings in respect of what we call opposition proceedings before the officers. So, let me just explain that. If you apply for a trademark, you know, and let's say the IP office grants it to you, then there is usually a period, either before or after grant, where someone else can object to the grant, oppose the grant to you. It's called an opposition procedure. They say, we don't think you should have granted that or you should grant that because it's too close to our mark. And that was a formal sort of judicial, quasi judicial procedure. We're applying mediation here in cooperation with the Singapore office and in cooperation with the Brazilian office. And we had our first cases in Brazil, in Singapore, that went very well last year. So, there, I will stop my remarks there and we're happy to talk. Question. John. John, tell me. The number of the main cases, the main cases, has been going on for the first time. Is there any indication why that's been happening? I would say simple explanation would be increased use of the internet. So, increased range of potential infringers and that if you work on the basis that a certain percentage of human behaviour is deviant and the more the behaviour there is of behaviour, the more cases there will be. Do you assess 71 cases? 71, yes. But there's not 71 in this list because they have not all yet been processed. Crystal Clear. How do you explain the difference between the home share addiction, the work of the home share addiction and for you? Well, if you're trying to manage a dispute, the legal part of a dispute, and you're doing that in your home city, obviously your transportation costs and your, you know, and possibly language interpretation costs and your assistance costs and so on are going to be reduced compared to doing it elsewhere. Can you just say again the difference between the abjector and the applicant who's on the side of this 71? I can be confused. Yes, sure. The abjector is the person, the trademark owner and the applicant is the person who has applied for the new domain. OK. Who wants the new domain? So, basically, Amazon has stated its claim for a lot of these new domains and it seems to be a repeat offender. Well, there's no judgements yet, so I wouldn't say it's a repeat offender. But yes, there is a claim against them in the couple, there is, as you see. But I think it's interesting to look through this because you can see that this gets complex, you know, blue, for example. That's the blue cross is abjecting. Pinterest is abjecting to .pin. The US Postal Service is abjecting to .mail.com, it's a good one, .KOM. And the abjector is Verizon. That's some of the objective for, in fact, the applicants themselves. Yeah, that's what I see that, yeah. So, the first question, what is the status, what is the outcome of the listed cases? The listed cases, the director general mentioned, really are a sample, basically to give a public impression of the types of applicants, in this case, complainants and the types of domain names, trademarks that are involved in the cases.  And if you would like to know the precise status of cases involving that particular complainant or trademark, we have, and Samarwi, we always make that available, of course, we can do that right away. We have on our website a search facility on the website of WIPO and then the section under the WIPO Arbitration Mediation Centre, where you can just key in the name of, as you can, for example, quote from this attached list, the name of the trademark owner. And in that case, you will find everything about that case, you'll find the outcome of the case, but you'll also find the decision itself. So, you can also read the considerations by the, from the panellists that actually decided the case. So, for each one of those, it is entirely possible to find out what the outcome is specifically. If you'd like to also know about cases beyond this year or rather before 2012, the same search facility allows you to look at all of this data over time. So, you can select your time period, you can do it from the beginning of the UDRP, or you can take an interval, or you can compare it between the last two years, however you like. In terms of the geographical distribution, here we, again, this is based on a search facility which we make available, where you can also make your selections on the side of the complainants, on the side of the respondents, or on the side of particular countries as well. If you do it on the side of particular countries, you will find the evolution over time. So, and to the extent that the stats still don't answer all the questions, our facility, which is real-time connected to our database of cases, then please, you know, just give us a ring today, anytime, an email, and we can get you the information more specifically. With some distance, I can say that traditionally the United States has been, and continues to be the largest, let's say, location of trademark owners filing cases, and also the largest location of respondent parties, owners of the main names, let us say, who are being implicated in these cases. However, there is an evolution there, and the evolution, I think, the evolution really, again, connects to the use of the internet. The use of the internet is, let's say, relatively speaking, probably moving east from here. Asia, China, Southeast Asia, the emerging economies, they are all becoming bigger players on the internet, including in domain registrations, both internationally and international domains, and I think that over time one can also see that back in the statistics, but not only on the respondent side, but also on the complainant side, where trademark owners from those jurisdictions are also becoming more involved. On annex six, you know, a very crude, if I may say, way of looking at this, on the left-hand side, the goodies on the right-hand side, the baddies, you know. The ranking for the top 25 is an annex six. If you'd like to have it in full, so if you are, for example, wondering about the particular jurisdiction on the complainant order respondent side beyond the top 25 that we have listed for 2012, you'll find that precisely in the statistics page, so you can go down to the last country, so to speak, involved with the most minimal amount of cases, and you can also find the geographical distribution over time in that way. We've just singled out the top 25 because we think that those are probably telling the story of registrations and infringement in a more significant way than if we go down to 120 names. Can you just say how long China has been at the 500 level? China has been moving up. If you go back to, for example, our press releases, but also our database today over, let's say, the last five years, then you will see that China has been entering steadily into the top 10 and then a little bit up within the top 10, as you can see. I think, again, what if you set that off, for example, against registrations in the national domain of China.cn, you'll find that that has become one of the largest, I do not know the exact statistic today, but that has also, likewise, broken into the top ranks, surely in the top 10 of all domains, including the international domains. So that's, I think, telling us that squatting in such a location is not necessarily just a question of people changing their mind and starting to enter into this behaviour, but it's also a function of electronic commerce becoming more and more prevalent in such jurisdictions or in such locations, I should say. But also, it's obviously in the US, a lot of these cases can be from the US to the US, right, because the US is top of the table in both, but China is nowhere, it's 23rd on the complainant, so as a goodie, it only ranks, it's got nine cases and as a baddie, it's got 500, so it's obviously international for China. Yes, it's probably too, let's say, a little bit too easy to presume that if the US is more or less 50% on both counts of this equation, then that is quite against one another, but you're absolutely right that the chances of it being US-US, for example, or the case staying, let's say, in western locations is larger than in the case of China. However, if we can maybe, you know, zoom out from these dispute statistics, and Baipa is also a director general, as of course also, as you know, been putting out information about, for example, the Madrid statistics, the Madrid system for trademarks. And if you combine all of these things, then I think it's quite likely that you're going to be seeing Chinese trademarks coming up on the complainant side in these disputes as well. There is just a certain lag time, but if the registration numbers that we see in Baipa are any indication, then the east, if I may put it like this, the far east, southeast Asia, are very likely to be the ones moving up also on the left side of the table over time. I should have said alleged goodie and alleged baddie. Good. Thank you very much.


So, why do the rich care about making money? The poor certainly need to care about making money, when one's resources are only enough to scrape by money as all that matters. And it's important to the middle class as well. Looking after their spouses, their children, there is a culture of dependence that weighs them down. The rich want to make money because they can always be richer. There was always another echelon of wealth to rise above. Some degree of opulence that is beyond their grasp. They drive to even further heights, seeking to slake their thirst for coin. They care about making money simply because they can. To do so, the rich exploit the people far below them on the social ladder, the poorest of the poor, to the oil magnet, to the harsh dictator, to the kings and queens and lords and ladies. The common people are specks of dirt. And to marshal carter and dark, the rich are unto ants. People, regardless of social standing, are all the same. The poor may spend their savings on worthless, yet treasured trinkets sold by the middle class. The salaryman may splurge on a pretty ring for his wife, the profits of which go into the pockets of a wealthy mining boss. In the same way, the gullible rich will burn millions of dollars on a single impossible object. Everyone is willing to waste their precious, precious money on something out of the ordinary. But value is artificial. The poor spend their pennies on the mass produced to China, convince that it has some worth. The rich convince the middle class that diamonds are rare and valuable, despite the stones being retrieved from Africa by the billion. Marshal, carter, and dark convince the rich that the impossible has value, while any an artist on a street can twist a die into a hypercube. The methodology of such a scheme is quite simple, but the critical step is to gain a market monopoly. If you are the only seller in town, you can set the price at any level you desire, so long as you can drum up demand. In this regard, Marshal, carter, and dark have the advantage. For hundreds of years, they were the only peddlers of anomalous wares in the world. They had the time to gain the capital, and with that capital, they can now outprice even the most competitive upstarts. So, well-organizations such as the Foundation, the GOC, and the Horizon Initiative resent the company's existence, they are unable to deal with such an unassailable economic powerhouse. With a glance, Marshal, carter, and dark could level a city, bankrupt a country with a single call. They could plunge the planet into a thermonuclear war. And yet, to the eternal relief of all, they are the least volatile players on the anomalous field. After all, if the veil of secrecy were to break, their treakings would become worthless. Their business would crumble and dissolve. Well, this may cause some to think of Marshal, carter, and dark as a massive, faceless corporation. Their workforce numbers at most in the order of a hundred. Their operations are directed, streamlined, maximized for efficiency and minimizing cost. Further manpower, if necessary, is outsourced from other organizations. And those in the highest positions of power are perhaps the most mysterious. Wild stories abound on the subject, depending on the source. They may be ghosts or demons, old men sending messages from beyond the grave, faceless monsters from another world, or even shape-shifting lizardmen. A major part of their operation is establishing supply lines between various anomalous groups. Marshal, carter, and dark purchased directly from groups such as Dr. One Detainment and the factory, reselling their goods at exorbitant prices. Of course, Prometheus Labs gladly supplies the group with their latest research in exchange for examples of exotic or complex anomalies, and they often host an art exhibition exerting notable control of the artistic marketplace. Similarly, they host various social functions for the rich and powerful people in the world. With hooks throughout Europe, America, Russia, and China, there is never trouble finding a market for a given item. They are, of course, willing to sell to any buyer, including groups such as the Chaos Insurgency, who are some of the most valuable clients. Perhaps the organization's most opposed to Marshal, carter, and dark are the Mana Charitable Foundation and the Serpent's Hand. Mana Charitable often attempt to sabotage their operations due to their restrictions of anomalous goods to the upper class. However, their limited range and resources make them more irritating than threatening. The Serpent's Hand, meanwhile, are directly and openly antagonistic, carrying neither for the veil of secrecy or the company's continuing practice of anomalous human trafficking. And impossible to economically intimidate, they represent the only pervasive threat to the group's operation. Without question, Marshal, carter, and dark are one of the most important pieces on the board in the anomalous world, occasionally putting other players into check, but never checkmate. For Marshal, carter, and dark, the planet is an intricate network. They have secured safely beneath their thumb where winning and losing are meaningless times. There is no need to move pieces when you can move the board. When you could end the match at any time, there's only one reason to continue. It's all about playing the game. Thank you very much for watching. Thought I'd put together a little reading today from the Marshal, carter, and dark cub. But, oh, let's get the author real quick. Let's click. Let's click. Hold on. Hold on. Get to the next page. Posted by Randomini. There, I did it. I gave proper credit where creditors do. Normally, I read my own stuff, so I don't have to bother. If you like this kind of content, please hit the Subscribe button, and then the notification bell next to that so you're updated as soon as I upload a new video. And join everybody who's here on the screen already, including VeeVee, probably a wizard and definitely not a scientist, hot-headed Canadian, and lawful evil, who have all pledged at the O5 tier. It's nice to know that I'm not alone out here. And I will see you all again on Thursday.


I have to get so much work done today so we gotta get to it and I just made my smoothie and I'm about to take my vitamins and I always like to take my vitamins right in the morning when I wake up I like to make my smoothie or just a little something to eat just so my vitamins are absorbed way better you know all my vitamins that I take you don't need to take more food but I just like to and the vitamins I've been loving to take are the seed DSL on daily symbiotic and this is a prebiotic and a probiotic supplement which I love because baby your girl I'll be bloating every time I eat a little bit of something in the past I would literally feel bloating and I hated the feeling so I was like girl we gotta get this together and this has so many more benefits than just your gut it has healthy regularity it's a broad spectrum probiotic and prebiotic formulated with 24 clinically and scientifically studied strands for the whole body benefits so it's gonna help with the cardiovascular system your skin health and then also it's gonna help the ease of evacuation which goes to the bathroom cuz during the holidays it's so hard to stick to healthy habits and healthy routines you want to enjoy the time with our family make memories eat good food obviously during the holiday you feel the impact in your digestive system I've noticed such a huge difference when I take my seed when I take my seed I don't feel bloated at all and also like I said it does have skin care benefits so I've noticed such a huge difference in my skin it's gonna help promote healthy skin and just help you have a more useful appearance and I'm not just saying that I literally take these every single day I don't know if y'all noticed in my videos that I've been showing y'all I like to take this with food so every time I eat food I whip this out and also baby there with me when I travel I've been traveling non-stop lately I'm about to travel today and these are ready to go I've been really enjoying these in my daily vitamin routine because they just helped me become my best self so you'll be able to get your own a seed via someone daily symbiotic all you need to do is click the link down below and you'll be able to use my code which will be right here on the screen and it will save you 25% off your order so thank you so much seed for sponsoring this video love y'all supplements and I've noticed such a huge difference when it comes to my overall health so I'm just so happy I have these in my routine I need to get you with everyone I need someone to me if you can all these years never said I'm just a love baby girl just a love baby girl take a summer talk a talk a brush and make an ocean so y'all just got back to whiskey I have a like a little appointment that I have to go to why is it dark okay but I'm about to give my sister her little gifts I have for her from Tokyo whoa oh you got to try this I bought your little treat so I got her this key chain she loves her to kill me clearly here here's the first thing and I got you these purple snacks cuz y'all she loves purple don't nobody go harder for their color than purple people and then I got her this this is for good fortune her and my mom got this so you need to keep this with you all the time and then I got you this little cosmetic pouch this is actually supposed to go in your Christmas gift but here do you like that so y'all I just got back home today and I just unexpectedly got invited to a vision board party and I'm with Kelly of course y'all miss her yeah we be vibing y'all can y'all believe this my first time being in Kelly's car she does she did not want me in her car for some it was a mess I have a busy life I have a crazy life guys my car is always a mess but I wouldn't judge you it doesn't matter you deserve to be in a clean car Kyra I just got it detailed she's crazy so anyways we're on our way inside I can't wait super excited but I'm only staying for an hour because I'm literally outside past my bed so the vision boards are already assembled definitely looks like a bunch of sports the ones we can't fit on our stuff so y'all can take them a money call in I'm taking this one for sure I'm about to get started on my vision board and I'm excited


The UK is in talks with the Taliban. A representative of Boris Johnson's government has travelled to Doha to meet with members of this barbaric terror group. Now, while it is understandable to want to get British citizens out of Afghanistan safely, it used to be the case that governments didn't negotiate with terrorists. Whatever your view on this particular scenario, if we take it in a wider context, there is a definite sanitisation of the Taliban taking place. Let's look at some examples. Watch this clip of the Chief of Defence staff of the British Army, General Sunik Carter. How do you feel about collaborating with the enemy when they have carried out such atrocities against UK military personnel over the years? I think you have to be very careful using the word enemy. I think people need to understand who the Taliban actually are.  As President Karzai put it to me yesterday, their country boys. And the plain fact is that they happen to live by a code of honour, a standard which has been their standard for many, many years. It's called Pashtun Wally. It has honour at the heart of what they do. They are bound together by a common purpose, which is they don't like corrupt governance. They don't like governance that is self-serving. And they want an Afghanistan that is inclusive for all. People need to understand who the Taliban actually are, he said. Yes. Yes, people do need to understand who the Taliban actually are. And it isn't the boy scout club that Nick Carter describes. The Taliban are scriptural Muslims who have governed Afghanistan with full Sharia law and will govern it again in the same way. The Taliban are absolutely barbaric. When they governed a couple of decades ago, it was a blood bath. They've been back in power for a matter of weeks and that blood bath is flowing again. Reports from inside Afghanistan reveal that these butchers have been going house to house looking for people to execute. These boy scouts who live by a code of honour according to our military have also drawn up lists of girls over the age of 12 to be removed from their homes and provided as sex slaves to Taliban fighters. In accordance with Islamic scripture, by the way, how very honourable. They'll rule Afghanistan like the brutal psychopaths that they are. They'll terrorise, murder and enslave just as they did before. We, by the looks of things, will lie about this and legitimise their barbarism, just like we do with Saudi Arabia. Western governments rarely cover themselves in glory these days, but this sanitisation of the Taliban is a new low. It is a complete betrayal of truth and basic decency. It is a betrayal of everything we pretend to value. Freedom writes civilised behaviour. It is an elevation of the most evil of evils and we ought to be thoroughly ashamed. The Taliban should be completely isolated, cut off from the rest of the civilised world. For the record, so should Saudi Arabia and Iran and all the other monsters of Islam. But Islam is key here and that's what we're really sanitising. We've been doing it for decades with our nothing to do with Islam rhetoric whenever an atrocity is carried out. If our governments really believe in the values they pretend to believe in, then they should stand by those values. This moral relativism is disgusting, but only to be expected. We want our morals back. We want the truth to be told. We want this legitimisation of the Taliban, Saudi, Iran and others to stop. What the Taliban does is Islamic and we need to tell the truth about Islam. Thanks again for helping us to bring back Britain.


So, in this study of return probability to the starting point, so far we examined the ultimate return probability. It is a matter of certain interest to understand how the first time return probability depends on the number of steps taken that is basically k dependence of f k. We demonstrate it here essentially for 1 dimensions. We have seen many results for absorber problem for 1 dimension both in terms of steps and in terms of time, but here we have to visualize this as a not an absorber problem, but merely a visiting to the origin for the first time. So, let us recall the definition. The definition of f k is stands for the probability of visiting the origin which is a starting point, visiting origin for the first time in k steps. Let us stick to 1D case. So, then it will be basically a random walk along a along the real line. Then we defined a generating function phi z. So, phi z represented a generating function which is basically step sum. It is a step sum generating function. So, it was defined as f k z to the power k and k equal to 1 is minimum. It is defined there is no meaning for returning to the origin 0th step because it was already there. And correspondingly we also defined a pi naught z as the generating function of the occupancy probability at the origin. So, that would be defined as again w n 0 z to the power n equal to 0 to infinity. So, these were the two definitions. Then we developed a relationship between the two quite generally regardless of dimensions and all as 1 minus 1 by pi naught z. So, if you know the generating function of the occupancy probability at the origin, we have the generating function of the first time return probability. So, now we specifically focus on 1D. We consider 1D case. So, the logic that we follow is if if we have results of occupancy probabilities for 1D, w n 0s are known for 1D. So, we can construct pi naught z from that we can construct phi z. And once we construct phi z and if we can expand it in powers of z, we have f k's as coefficients. So, this is the logic that we will follow. So, regarding regarding pi naught z in 1D, we know that the visitation to the origin occurs only in even number of steps for symmetric random walk specifically we focus on symmetric random walk or unbiased random walk. So, we know that w n 0 is 0 if n is odd equal to nonzero if n is even. So, specifically from the very basic equation we derived for the occupancy probability, we have shown that specifically for 2 m in general that the even an even number can always be denoted by 2 m. So, that at the origin is going to be 2 m C m 1 by 2 to the power 2 m, where binomial coefficients are defined by the notation 2 m C m for all for all m equal to 0 1. Now, now you can put m equal to 0 1 2 etcetera because automatically 2 m will be even. So, with this result we can construct the generating function steps some generating function for 1D symmetric random walk as sum over all the m's will do because anyway the odd ones are going to be 0. So, it will be w 2 m 0, but we should remember it is not z to the power m it will be z to the power of 2 m because only even terms will contribute. So, this is the definition. So, explicitly written it will have the form 2 m C m then z to the power 2 m divided by 2 to the power 2 m. So, I could write it as z square by or z to the ok z by 2 to the power 2 m for all m equal to 0 to infinity. Explicitly if we express 2 m C m it takes the form sum m equal to 0 to infinity 2 m C m is nothing, but 2 m factorial and m factorial and m factorial again. So, it will be m factorial whole square and we can write this as function of z square by 4 to the power m. So, we have an expression for pi naught in terms of a series of z square to proceed further to evaluate pi naught z or phi z we need to have one can work with series, but we need the reciprocal of the series. So, it will be a very tedious thing, but some simple solutions exist. Similarly we can identify this series we identify the series with 1 minus z square to the power minus half. I will shortly tell you how we what led us to identify that is specifically we say that series m equal to 0 to infinity 2 m factorial by m factorial whole square z square by 4 to the power m is 1 minus z square to the power minus half. The proof of this is a somewhat involved, but one can verify it by several means. One way is take a first of two terms of expansion Taylor expansion of 1 minus z square to the power minus half it can be always expand a Taylor expanded around z equal to 0 and verify that the coefficients agree and then trust that the series is ok. A more rigorous way is to consider the extended binomial expansion of the function for example, any function 1 plus x to the power nu where nu is not an integer can be written formally as this is a very formal way of writing can be written formally in the form of say r equal to 0 to infinity. Now the moment nu is not an integer it becomes a series it is not just a progression of a finite terms. So, this will have nu c r x to the power r is a formally extending the binomial expansion we have done two things we have just replaced if it was an integer n would have written n c r then it would have terminated at n, but if nu is not an integer we have to take the upper limit as infinity and write nu c r and interpret the factorials in terms of gamma function. Specifically in this case let us take specifically we choose this is by hand side we know this result we have to only just verify it in a way. So, choose nu equal to minus half and x equal to minus z square. Once we choose nu equal to minus half I am only going to indicate the steps it is quite a tedious, but straight forward procedure then you will have gamma of negative numbers. So, long as these negative numbers are not integers that is gamma of minus 1 does not exist, but gamma of minus 3 by 2 exists and it is a very defined number. We can convert this gammas of negative argument into those of positive argument by what is called as a reflection formula for gamma function. For example, the reflection formula for gamma function can be used that is gamma of z and gamma of 1 minus z is equal to pi by sin pi z is in general true. So, if a z is large and positive then 1 minus z will be negative number. So, you will convert it that negative number in terms of the positive gamma function via this relationship. So, upon doing that and then simplifying we will end up this particular series with the nu equal to minus half and x is minus z square will come over to this series. So, this is the way we can arrive at this generating function solution. So, for the moment we take this result. So, if we take that result our specific expression therefore, for the generating function pi naught 1 d symmetric random walk turns out to be we can write it as 1 by square root of 1 minus z square that minus half can be rewritten like this. So, once pi naught z is known it is actually a simple function now. So, we can determine phi z the generating function as equal to 1 minus 1 by 1 minus. So, 1 minus 1 by pi naught z that is 1 by square root of 1 minus z square which will turn out to be 1 minus square root of 1 minus z square. So, we have another simple expression for phi z. So, the now the next step is we have to re express this equation 1 minus square root of 1 minus z square as a power series in z. So, as to identify the coefficients of some z to the power k to get f k. The same procedure we can follow as the extended binomial expansion of square root of 1 minus z square you can even call it as a Taylor expansion. So, upon re expanding or let us say upon expanding square root of 1 minus z square as a power series we do not do it explicitly, but the method is now almost understandable you have to develop a general expansion or you have to look up at some handbook of series of various functions. So, we can obtain the following expansion for 1 minus. So, we gets 1 minus square root of 1 minus z square equal to we take the expression it will be k equal to 1 to infinity 2 k minus 2 c k minus 1 z to the power 2 k divided by k into 2 to the power 2 k minus 1. Again you can verify it by putting the calculating the coefficients for k equal to 1, 2 etcetera and confirm that it is true after expressing the binomial in terms of the factorial functions. Here you do not need to do any negative gamma functions because there will be all integer factorials can verify it. Or you can follow the same root as I mentioned in the previous slide that is by using the extended binomial expansion one can do either that or verify it either way we have a detailed expansion. So, upon comparing this expression with the definition upon comparing this expression with the generating function with the expansion or with the definition with the definition of the definition phi z equal to sigma f k z to the power k 1 to infinity we note that f of odd number let us say k equal to we rewrite f 2 k plus 1 will be 0 because it is a expansion of z square. So, you do not have odd powers of z since z to the power 2 k plus 1 coefficients of z to the power 2 k plus 1 since coefficients z to the power odd powers of z are 0 there are not powers of z and f 2 k will be 2 k minus 2 c k minus 1 1 by k into 2 to the power 2 k minus 1 for all k equal to 1 2 etcetera that is the very lowest value will be f 2 f 0 has no meaning f 1 does not exist.  So, it will be square of this and then here it will be we can say it is a 2 k into 2 to the power 2 k minus 2 I just took out 1 k and put it here for all k equal to 1 2 etcetera. So, now we have an explicit. So, finally, this is the exact expression then exact expression specifically f of 2 for example, if we evaluate f of 2 will be half if you put k equal to 1 you will just get this 1 by 2 term. So, it will be half there is a 50 percent chance of first time return in the very second step. Similarly, k equal to 2 if you put f 4 you will have this will be for example, it will become 2 factorial here and it will be 1 factorial square here and here you will have 4 into another 4. So, it is going to be 1 by 8 likewise you can show that f 2 k that is k equal to 3 you put in the sixth step probability will turn out to be something like 21 divided by 1024 etcetera. So, so on and so forth you can you can calculate the return probabilities for any value from this exact expression. Now, a matter of interest is asymptotics how does f k behave for large k this is always a matter of interest. For that we do asymptotics our very useful tool is the Sterling's approximation once again. So, asymptotics of f 2 k in let us say 1 d we just indicate it as a 1 d problem. So, then we note we need asymptotic approximations for 2 k factorial and all.  So, if you now lot of terms get cancelled for example, this can be written as 2 to the power 2 r r to the power 2 r e to the power minus 2 r square root of 4 pi r. So, 2 I take out square root of pi r and denominator if you square it it is r to the power 2 r e to the power minus 2 r 2 pi r square root of 2 pi r square is simply 2 pi r. So, we see these terms cancel e to the power minus 2 r also cancels and here we will get 1 by root 2 cancels. So, we will get 1 by root pi r. So, this is going to be 2 to the power 2 r divided by root of pi r.  So, 2 to the power 2 r cancels again. So, we have an expression 1 by 2 root pi 1 by r to the power half into r plus 1. So, for large r which we are discussing as r goes to infinity we can ignore 1 and this will have the behavior 1 by 2 root pi r to the power minus 3 by 2. So, the first time return probability to the origin varies as the step number to the power minus 3 3rd 3 by 2 not 3 3rd 3 half that is r to the power minus 3 by 2. We can recall at this point in time that the occupancy probability is distinct from the first time return probability we have been emphasizing that fact and to be very specific our occupancy probability let us say if you use that notation n for the steps it will it will be the exact expression is always 2 to the power minus 2 n 2 n factorial divided by n factorial square and this same asymptotics if you do will have 1 by root pi n or it will go as 1 by root pi n to the power minus half. So, here it goes as the step to the power minus half whereas, the first time return probability goes as a step to the power minus 3 by 2. So, the return probability decays much faster than the occupancy probability. So, pictorially we can represent this by the following graph. So, let us say we now uniformly denote all steps by the notation k or we use the r for f and n for occupancy w, but you can uniformize it by the notation k then the w function w k in fact, for even k only it if it decays as k to the power half k to the power minus half then the first time visit probability will go as f k as k to the power minus 3 by 2 much faster. So, the occupancy probability decays more slowly that is what we understand from this. So, this is the one example of explicitly calculating the visit the visit to the origin probability in one dimension. So, all these results of a 1 D for 1 D and then symmetric random walk this exercise can also become completed for 2 D. In 2 dimensions the problem of course, is a little more complicated, but I can indicate the steps. The steps is we have the occupancy probability for 2 D at the origin an explicit expression which includes all those 2 m factorials etcetera, but any different form and then you can construct it is generating function. However, the generating function for the 2 D occupancy probability is slightly complicated it is not expressible in terms of an algebraic function of the type square root of 1 minus z square instead it involves. So, for 2 D the generating function pi naught now 2 D symmetric random walk it has what is called as an elliptic integral some of the first kind k function k z square where k is the elliptic integrals these are defined as integral 0 to pi by 2 D x or D theta divided by square root of 1 minus n square sin square theta this is the kind of function this is k m this is the definition. So, to complete this we can reach up to the pi naught 2 D. However, reciprocal of that is difficult to express in terms of simple functions. So, one has to literally expand invert this elliptic integral or elliptic function and then term by term we can identify the coefficients of f 2 k it is possible to do, but a general expression is not easy. However, it is possible to obtain the asymptotic form and we find that the asymptotic form here decays as with a different power law we will not explicitly attempt this exercise. So, with this we have sort of got a grasp of what this return probability problems are and from now on we move to a more general formalisms of random walk specifically we try to understand whether some steady state situations also exist in an infinite dimensional systems such as nearest neighbor random walk that we discussed in the next lecture. Thank you.


Good evening, respected judges and my colleagues. I'm Dr. Nidhi Rai, radiology resident of VMMC and Satyajan Hospital.  I've done this under the guidance of Dr. Rupi Chambal, who is the associate professor and consultant at the Department of Radial Diagnosis, Satyajan Hospital. There were no conflicts of interest and nothing to disclose. The aim of my study was to determine the vascularity of brain tumors by evaluating tumor blood flow using RT that's been labeling perfusion imaging. CNS tumors are an important cause of mortality and mobility. Tying the diagnosis and treatment is therefore a necessity in case of brain tumors. Conventional MRI combined with perfusion MRI imaging provides useful information for diagnosis and treatment of brain tumors. Now, the perfusion refers to the delivery of blood at the level of capillaries. And it is measured in units of ML per 100 grams per minute. Perfusion parameters give direct insight about the tumor vascularization and proliferation, which is essential in evaluation of brain tumors, where more aggressive lesions typically display greater vascularity. Traditional imaging in MR requires bolus injection of contrast material through large-bore intravenous cannulas for the evaluation of blood flow to the brain tumors. This is an invasive method, hence has a limited use. Arteral spin labeling perfusion imaging is an evolving magnetic resonance imaging technique that measures cerebral blood flow without the use of an intravascular contrast agent. This technique provides a noninvasive way to evaluate cerebral blood flow by magnetically labeling the arterial blood protons before it flows into the area of interest. In this technique, two images are required, a control image and a labeled image. A control image is an image in which the blood water magnetization has not been inverted, and labeled image is an image in which there is inversion of the blood water magnetization. The signal difference between these two images is calculated, which is directly proportional to the amount of magnetization inversion delivered to the area of interest. Arteral spin labeling offers the most significant advantage over traditional contrast perfusion techniques, as it does not require a gadolinium-based tracer, that is, it is noninvasive. Hence, favorable for patients with renal dysfunction, for pediatric population, and for those required repeated follow-up scans. Methodology. The study, my study was conducted, a study was conducted in the Department of Radio Diagnosis in collaboration with the Department of Neurosurgery and Department of Pathology, VMMC, and Subdijang Hospital. It was an observational cross-sectional study, and it was conducted over a period of 18 months. For sample size calculation, formula for correlation analysis was used, and sample size turned out to be 33 by calculation. However, we included a total of 46 patients, participants of suspected brain tumors, and that was based on clinical history and previous imaging investigations, out of which 35 participants turned out to be brain tumor patients that satisfied our inclusion criteria, which we'll discuss later. MRI acquisition was carried out in a single session on 3-Tesla MR imaging machine with a 32-channel phased area head-neck spine coil. All cases of brain tumors referred from the Department of Neurosurgery in our hospital, that is Subdijang Hospital, were included in our study. Exclusion criteria included patients with one or other contraindications for MRI, like the patients with metallic clips, pacemakers, or patients having claustrophobia, patients with any patients with known malignancy other than brain tumor, with secondary metastasis in the brain, and patients of brain tumor with previous surgical interventions. Written informed consent was taken from each patient that fulfilled the inclusion criteria, and clinical history was noted from each patient, and findings were recorded of pre-designed performer. Patients underwent pseudo-continuous articles been labelling perfusion imaging on 3-Tesla MRI machine. MRI sequences, ASL perfusion imaging study was performed with whole brain extending from vertex to the base of skull. Images were obtained using background suppressed 3D stacked spiral FAC sequence. After performing conventional MRI sequences, that is T1, T2, and FLARE, 3D ASL was performed by use of pseudo-continuous labelling period of 1,500 milliseconds with post-labelling delay time ranging from 15-25 milliseconds to 2,000 milliseconds, depending on the age of the patient. The labelling plane was selected at the level of PONS medulla junction to avoid the curvature of peterous part of ICA and to select the end portion of ascending ICA. Slice thickness was taken as 4mm with no inter-slice cap. The tumor in its greatest dimension was made to coincide with the imaging plane by referring to conventional MRI sequences that is T1, T2, and FLARE. Post-processing, the ASL-colored maps were acquired and ROIs were placed in axial plane in the region with maximum perfusion. Non-overlapping regions of ROIs of size more than or equal to 5mm of equal size were visually placed on all the tumors on the axial ASL. And then their absolute and relative values of maximum and mean tumor blood flow was measured within the tumor. Relative TBF values were measured by taking the ratio between TBF and the CBF values, that is tumor blood flow and the cerebral blood flow values. Then these patients were followed up and tumor tissue biopsy sample of operated patients was sent to the Department of Pathology for histopathological analysis. Their microvascularity of the brain tumors were evaluated. The tissue sections were immunostained using a monoclonal mouse antibody directed against the CD34 antigen, which identifies vascular endothelial cells. Microvessals within the tumors were counted in three hot spots at both 10x and 40x magnification. And the mean of the three values of the vessel count was considered to be the microvessel density. Results, as we said before, but included 46 participants and out of which 35 turned out to be patients of brain tumors that satisfied our inclusion criteria and that could be considered a part of study. Out of these 35 patients, there were 19 cases of gliomas, including pylocytic astrocytoma, pleomorphic xanthastrocytoma, oligodendroglioma, diffused astrocytoma, anaplastic astrocytoma, glioblastoma and giant cell glioblastoma. 19 were gliomas, 11 were meningiomas, two schwannomas, two cleniform angiomas, and one was hemangioblastoma. In our study, most of the patients presented with complaints of headache, weakness of one side of the body, seizures, and blurring of vision in some cases. Correlation was a correlation between the mean tumor blood flow and the vessel count at 10x and 40x magnification was calculated using Spearman correlation coefficient and both of which came out to be positively correlated with p value of less than 0.001. Then correlation between maximum tumor blood flow and the vessel count at both 10x and 40x magnification also came out to be positively correlated with p value of less than 0.001. Now, there was a strong positive correlation between vessel count and mean TBF. TBF at vessel count seen at 10x magnification and mean TBF, and this correlation was statistically significant like we saw in the graph. And also, there was a moderate positive correlation between vessel count at 40x magnification and mean TBF. A very strong positive correlation between max TBF and vessel count at 10x magnification was seen and this correlation was statistically significant. A strong positive correlation between maximum TBF and vessel count at 40x magnification was seen and this correlation was also statistically significant. These are a few of the representative cases. In the first figure, the first figure was that of a patient which was diagnosed with Hemanju Blastuma, which showed a cystic lesion with solid components seen at left CP angle and it showed a very high vascularity. On ASIL color map, it showed the mean TBF value of 402 milliliters per minute per 100 grams and maximum TBF value of 578.3 milliliters per minute per 100 grams with relative TBF mean of 14.9 and relative TBF max of 38.7. It showed the Hemanju Blastuma showed a very high vascularity, also high in comparison to the meningomas or other high grade glermas. In figure two was a case of meningoma seen in the left frontal region and it showed on ASIL color map, mean TBF was 368 milliliters per minute per 100 grams, max TBF was 386 milliliters per minute per 100 grams, RTBF mean was 6.5 and RTBF max was 52.9. The third case was a case of meningoma arising from atria of the left glateral ventricle. The on ASIL color map, mean TBF was found out to be 127 milliliters per minute per 100 grams, max TBF was 143 milliliters per minute per 100 grams and RTBF mean was 4 and RTBF max was 35. The figure four was a case of atrial meningoma seen in the right posterior fossa region. It showed a low vascularity compared to the other meningomas. It's mean TBF was calculated to be 11.6 milliliters per minute per 100 gram, which is very less compared to the other meningomas and max TBF was calculated to be 15 ml per minute per 100 grams, RTBF mean was 0.4 and RTBF max was 37.5. On 1734 IHC staining, we got the pictures similar to given in this slide. Figure one shows CD34 staining slide with high microvessel proliferation. We can see the stained vessel, brown colored stained vessel walls in the first figure. And figure two shows a low microvessel proliferation. Discussion. The mean age of mean TBF obtained from our study, mean range was found out to be 133 plus minus 91.6. Max TBF was 160 plus minus 116. RTBF mean was four plus minus 2.8 and RTBF max was 39 plus minus 10.4. We used Spearman correlation that is a nonparametric test to study correlation between TBF and microvessel density in brain tumors. And the correlation between mean TBF and microvascular density at both 10x and 40x and maximum TBF and microvascular density at again both 10x and 40x was found to be statistically significant. A strong positive correlation was seen between mean TBF and microvascular density at 10x magnification. Moderate positive correlation between mean TBF and microvascular density at 40x magnification. A very strong positive correlation between max TBF and MVD at 10x magnification. And a strong positive correlation was seen between max TBF and MVD at 40x magnification. These findings were found to be in agreement with few studies which were conducted by T. Noguchi et al, Koizumi S et al, Kikuchi et al and Kimura et et al, which also show a positive correlation between mean TBF and max TBF with MVD, which is also known as the percentage vessel count. In our study, we also measured relative TBF values which were normalized to the CBF values that is the cerebral brain flow values. The mean range of the values of mean CBF was 33 plus minus nine and maximum CBF was 40 plus minus 11.2. CBF values were taken by placing ROI at cortical gray matter. For this, Steven images were used. Gray matter was taken as reference in concordance with few studies like those of Weber, MA et al, and Jutukonda, MR et al, which have mentioned that ASL underestimates white matter perfusion, thus favoring gray matter as the reference. Correlation between RTBF mean and vessel count at 10X and 40X and RTBF max and vessel count at 10X and 40X, which was also found to be statistically significant in our study showing a positive correlation between RTBF mean and vessel count at 10X and 40X. Moderate positive correlation was seen between RTBF max and vessel count at 10X and 40X. These were my references. Thank you. Thank you so much.