Welcome to Fuzzing NASA Core Flight System Software. My name is Ronald Broberg. I work for Lockheed Martin. I've been there for 25 years. I work in LMSpace, started my career there back again. I've been a software engineer. I work test and integration, network security engineer, cybersecurity engineer. My, one of my first tasks was working on programming for the Space Defense Operations Center, Spadok at NORAD. And in the recent years, I've been involved in more site, more active cyber security type of work, including a red team engagement at Cape Canaveral. And that's what brought me into testing of satellite software. So what is the NASA Core Flight System Software? Brief intro. This is the Solar Parker probe, the magnetospheric multi-scale satellite, and the lunar reconnaissance orbit. These satellites plus maybe a dozen more recent or current satellites all run core flight system software. It's real flight worthy software as being flown in missions today around the sun, the earth and the moon. And so it is certainly of interest from a cyber testing perspective. The core flight system software from NASA's own description is reusable software framework composed of a set of reusable software applications. They stress this reusability for good reason, having to do with time, schedule and money. There are three key aspects related to the architecture. It has a dynamic runtime, a layered software design and a component-based design. All of these are meant to decrease the time to develop and test flight software for individual NASA missions by emphasizing this reusability core. And here's an architectural view from NASA documentation. If you focus on the blue ring, that's the software bus over which these modules communicate with each other. If you focus on the lower right-hand corner, you can see the software bus time services, executive services, event services and table service modules. Those are the core of the core flight system software. But the open source release also includes many of these others components and includes two what they call lab applications designed for test and development but not for a mission deployment. And that's the command ingest and the telemetry output by which commands can be injected from the outside into the software bus and to data flow from the software bus to outside clients. There's also, for instance, in order to make a complete mission set of software, you'll need guidance, navigation and control and that's what's being represented here but in the purple in the center. And there are some file system management components as well, some of which are in the release that's available open sourced. If you look in the upper left, excuse me, upper right-hand corner, the space wire 1553 bus and instrument manager, these things would be specific to it but particular satellite and are not included in the open source release. Another view of the core flight system is this application stack view again, adapted from NASA. The items in gray are those that would be required to be developed specifically for a new mission and wouldn't be shared necessarily between missions depending on the payloads that you have perhaps. The items in blue are the reusability components. So you can see that there's quite a bit that's already provided to help us start a new mission off with their software development. In the lower layer here, the OSI abstraction API, this provides the portability to the core flight system software. You can run this on Linux x86 on Raspberry Pi arms, power PCs, there's real-time operating system versions. So a multitude of different platforms this either is running or can be easily ported to. The NASA core flight system software and what attracted my attention originally is open source software. It's been open source since at least 2011. Don't know it's been on GitHub that long but you can find it at github.com slash NASA slash CFS. There are two major releases, the Akela release and the Buddhist release. These aren't just left in stasis, they've been updated over time to try to keep them current. And in addition, there's of course the main development branch. You can note in the upper left-hand corner that they have a very active GitHub repo with updates occurring almost weekly, if not even more frequently. Now that we have an introduction to the core flight system software, the question arises, how do we go about testing it? A common testing approach of course is fuzzing, which fuzzes the user input into any particular application. In this case, the user input is via telecommand on the command ingest module or application, which is listening on UDP port one, two, three, four. Note that the command ingest module itself is not multi-threaded, although the CFS application overall is. When fuzzer is fine that there's a network interface, they often go to replacing that with a file system interface. Prini provides the capability of doing that pretty easily for TCP, but doesn't have UDP interfaces as part of its core package. So that would be additional software we'd have to write in order to build out that direction. Another option is to build the file system interface directly into the application in USA use AFL. This is a great approach because it'll give you coverage, but the CFS executable is multi-threaded with the high dependency on shared library applications and table spaces that I found difficult to configure with AFL. So I chose to use a pure network fuzzing tool called Fuzzatron, which natively supports both UDP and TCP. It uses Redomsa for blind fuzzing. That is, you provided a set of inputs and it will just start randomizing based on those. Or it can use BLAB for protocol aware fuzzing. In that case, you have to build a protocol definition file first and it will start fuzzing the individual components of that protocol. I did occasionally see it crash early on start. The Fuzzatron issue, there's an issue for this in the Fuzzatron GitHub repository. Deterministic mutations completed, but that wasn't really much of a problem because I was running this manually. It was simple enough to just restart and go. You might need to pay attention to this if you build an automated framework. An issue I did have though is that Fuzzatron sends tens of thousands of packets per second. That was way faster than the core flight system software processed. To resolve that, I had to slow Fuzzatron. I took the code a little bit to add a timer and I had to speed up the core flight system. There is a time out there where it was, I believe it was 500 milliseconds to process a particular packet before it would process the next one. So I reduced that to like 50 milliseconds. In the end, I was able to get a sustained 800 packets per second for test. The CCSDS packets that we're processing have a primary header composed of packet identification, packet sequence control and packet data length. It also has an optional secondary header that can be included as part of the data field. Some of the NASA software, core flight system software indicated the secondary header was actually a mandatory field, but I did not find that to be true in the open source release. As you can see here in the middle, there are a couple of packets that have been broke down to their binary format. And we can see the application ID. We can see the sequential counter. We can see the packet length, but we don't see a secondary header here. So read the code or in this case, read the packet. In order to begin the blind fuzzing using Redamso, we have to feed it a core group of inputs instead of inputs. And in order to collect those, you can use the ground system application that's included as part of the open source release, which has both the telecommand component and the telemetry component. The telemetry receives from the core flight system on one, two, three, five. It sends to the flight system the telecommands on one, two, three, four. So we set up a TCP dump. We send one packet using this application. We save that packet off, reset TCP dump, send another one. Using this, I collected 24 or so different packets from different modules that I could use to begin the fuzzing. Walking through the methodology here, yes, you can start the core flight system application named core CPU one, name of the executable. You start the packet capture. You run fuzzetron until it detects the seg fault of the executable under test.   It's worth noting that it's not the last in the file. There's a slight delay between when fuzzetron sends its packets and when it can detect the seg fault of the executable under test. That delay means that you're gonna find that packet. Several dozen, maybe even a hundred or two packets up from the bottom, probably not quite that much, but several dozen. So once you have carved out your kill packet, of course you need to save it. So a brief demo of this process. We're going to start the executable that we wanna fuzz the core flight system here. That stop flywheel is a good indication that you've reached the complete bus initialization. Then you run the demo. You can see here that the TCP dump is being launched. It's gonna save its PCAP file and that out directory. There's a little bit of logic here to find the process identification, the PID for the core CPU.  We've got our set of packets in that command directory. We're running on local host port one, two, three, four. And there's the PID that we're watching. We're not gonna run to the point of seg fault here. It can take a hundred thousand or a million or so cases before you get that far.  So we're gonna restart the core flight system software. You can see it's ready now. We're gonna go up and take a look at the packet we're about to send. You can see here that I've collected a couple dozen kill packets. And when we look in it, if you look at those last eight words there, you'll see in little indian 800, that's the application ID and 57AA, again little indian reversed. And I believe that's about 31K bytes. That's a declared length of this. Even though you can see the data, here's those trailing zeros as much smaller. When we launch the kill packet, we're going to see our seg fault. So verify that indeed we've sent the kill. Note that it's transmitted eight bytes. So this is an eight byte packet we sent, even though, I'm sorry, the length of that was probably 22K. So we found a collection of UDV packets that can seg fault the core flight system when sent to the command ingest application. But what's actually causing that? We need to do a root cause analysis in order to see that. A couple of tools that we can do as part of that analysis is to examine the core dump, to examine the UDV packets themselves, to look at the code and do maybe some dynamic analysis in the debugger. We'll take a quick tour through those. This is a snapshot of a part of the core dump. And we can see here that frame four, the CI lab command ingest, main function is entered and then moves to the read up link. That's where the UDV packet is actually being read into the application. Once it gets that data, it calls a CFE function, the software bus send message function. And that in turn calls the send message full after which we see the core dump. Using a more robust version of the core flight system software, if we send the packet, we can see here we have the 800 application ID, but most importantly, the declared length in the packet, 22K bytes, is not the same as the bytes received or in this case labeled expected bytes. This mismatch is the core problem, the root of our problem. We can look at the read up link and here we can see that where we're going to receive data from a socket and the amount of data received is actually going to record it in the status. That's the number of bytes received. In this case that we were just showing that would be eight. We checked to make sure the status is larger than the minimum number of bytes needed for the command header and it is. And we checked that it is below and less than the CI lab max ingest. It is. No, that is not the declared length. That is the length as received. So then we call the send message function in the CFP. When we get there, part of the processing is to determine the length or the size of the buffer. And to do that, it hands off the message pointer to this subroutine and get total message length, which in turn reads the CCSDS packet length. So that's the declared length. So our actual buffer was built on received bytes, but we're about to prepare a buffer based on the declared length. So we go back into the send message and we can see this little bit of logic here. If it's a zero copy, we are not going to pull a buffer from the pool, but if it's not zero copy, we do so. Asking for a buffer the size of the declared length. Then once again, if this is not zero copy, we're going to do a mem copy, where we're going to copy the declared length from the message pointer into this buffer. This message pointer though is a buffer that was only built for eight bytes in our example. So we can also try looking at a debug version of this. We're going to run GDB here in a moment, but before that, we're going to set up the core CPU software. And this is the more robust version. And then we're going to send a, this one's a slightly different packet to that. And we can see once again, there's our application ID, there's our declared length and our received length. 31K for declared, 14 for received, which matches the 14 bytes that UDP replay tells us we sent. We can take a quick look into this packet to see what we've actually delivered. And from here, you can see that little end in 800. We can see the 4079, which matches the 31K of, and again, that'd be 7940. And that matches the 31K of length. The, we're now we're going to run the vulnerable version and we're going to run that in the debugger. Once we get that started, we can note, as I stated earlier, this is a multi-threaded app. So we can see that different threads have been launched.  We do a back trace. And you can see this looks very similar to the core dump we looked at earlier. We note that our function of interest is going to be in frame one. We pull back to frame one and there's the mem copy that kills us, complete with the different variables declared there. So we look at the total message size, see it 31K bytes. We can see the message pointer. This is where it's going to copy data from. And if we take a quick peek at that, we'll see that if we look at those first 14 bytes, I believe it was, we'll see here the 800 app ID, again, a little in the order there. And then we'll see the 4079, which I skipped over, that's the length. And there's the payload data that we recognize from the packet itself. So there indeed is our packet in memory and CFS. But we didn't copy this 14 bytes, we copied 31,000 bytes, which is going to be about 7,700 of these words here. So first thing we notice that we quickly overrun the memory dedicated to the CI lab application. We're into a bunch of other stuff. And now we're into other people's stuff. There's C libraries here as well as lots of other application libraries and tablespace app main processing. And so lots of stuff for us to stomp all over and pull into other parts of the application. But it's going to get even slightly worse as we try to copy the whole buffer over. We're going to completely overrun the memory that's been provided for this application, for these modules. So no surprise in that we have a sec fault. Just very briefly, you'll recall that the length of the copy comes from the CCSDS packet header. The amount that should be copied is determined by the UDP packet length. This misalignment of buffers is what leads to the sec fault. And though we only briefly looked at it, there is a zero copy approach that partially mitigates this or at least bypasses it. That's completely implemented by April, 2021. But it doesn't really take care of the input validation. Well, the memory copy has been made safer. The input validation isn't being properly performed. And interestingly in the CI lab, there is code that does exactly that. It compares the received bytes to the declared bytes to determine if they're the same. And it's using a different part of the CI lab processing right now as of late 2020. But hasn't been used in that read up link function to verify that what's been received is actually valid. So work to be done there. So now that we understand what the root cause of these kill packets is and what the problems are in the core flight system, where do we take it from there? Well, we can certainly do much better job of fuzzing. There are protocol aware types of fuzzers. At the very least, we can break the header from the data, the payload data and we can exhaustively fuzz each component of the header. In turn, we can exhaustively fuzz a certain length of payload depending on your test rig. And we can build out test cases to make sure we reach the edge of what can be ingested by a particular module such as command ingest. Also, the command ingest is not the only thing available for fuzzing. Each of these modules has an interface of the software bus where it sends data and receives data. So we can fuzz each of these modules individually. In addition, there's these file system management components. The core flight system stores applications as shared library objects and table space there as well. So there's a place that we have the ability to do manipulation of data input. So there's a lot more fuzzing left to do in the core flight system.  And at that time, they were comfortable with that. That was not a security problem. After I've done, completed my root cause analysis due to other priorities that wasn't until this summer, I reach back to them and they verify that their stance hasn't changed on this. First and most importantly is that the command ingest app is just not flight software. And that's kind of obvious. It's an ethernet UDP interface. And that's not what's gonna be deployed on a satellite. In addition, the core flight software as seen on open source is not exactly the same software that is flown. While there's a lot of reuse, it's also customized per mission. So just because we find a particular vulnerability in the open source software, doesn't mean that it's reflected in the mission software. And on top of that, this was only against the Buddhist release. So the current development releases of core flight system don't even have this vulnerability because they use that zero copy approach for memory management of the messages. So the object of this wasn't just to find or particularly to find holes in the core flight system. It was to use the core flight system software to develop test approaches that we could then bring into other environments for testing a flight software. The space domain is quickly changing and a lot of the assumptions around security and satellites are changing and the test approaches are gonna have to become more comprehensive and more rigorous. And the core flight system offers us an open source application to develop some of those approaches, prove them out before we try to find time, space in a resource constrained environments for testing. Even this simple example that I walked through here, we needed to understand the system under test well enough to do the tuning that was required and to flow through the root cause analysis. We also need to understand the limits of the test rigs we do that we use. In this case, you saw that I had to go in and modify the timing that we were using for the packets. So these aren't necessarily plug and play. Again, emphasizing that we can develop these methodologies using open source software such as the core flight system in order to test the flight software that's not necessarily so. I appreciate your attention through this and we'll be happy to take questions. Thank you very much.


Okay, good morning everyone. It's really delightful to be here. I'll tell you why. I was supposed to be at the first hands-on school that took place in India in 2008. I was a post-doc at Los Alamos back then. Harry knows this painful story. I did not get security clearance to travel to my own home country to participate as an instructor at that first hands-on school. So I'm truly delighted to be here finally. It took what, six years? Eight years? I'm not good at math, as you can see. So I'm sorry I missed the first week. I had to be in Leo for the stativist meeting, but better late than never as they say. The title of my talk is Hydro in Parentheses, Dynamics of a Self-Propeled Camphor Boat at the Air-Water Interface. And this work was primarily done by Dr. Satish Akela and Dr. Dheeraj Kasing. They are post-docs in my group. They did all the experiments. I'm the fellow who gets to stand in one corner of the lab and clap and encourage them and get to give the talks. It's very unfair because I'm not the expert on this problem. Satish and Dheeraj are, they should be giving this talk. We received a lot of theoretical guidance from Ravi Singh, who was then a student. Now a doctor, he works at Google Labs now, doing a different kind of science, and Professor Shreyas Mandre, who is a very dear friend and a close collaborator at Brown University. So, just so you know the faces and we are not headless personalities, that is me and that is Satish, who is currently somewhere in a queue on campus. And I want to start off by giving you a brief introduction of what we do in my group. So our group's research interests lie in both fundamental and applied, experimental, non-linear and non-equilibrium physics. This comes from a shortcoming of one of my own limitations. When I was a student like you, I was very limited by my imagination.  I don't study stuff I cannot see. So that pretty much limits me to classical stuff. But there is a rich spectrum of problems still waiting to be understood in classical, non-linear and non-equilibrium physics. And the specific focus of our research group currently is in interfacial fluid dynamics involving flowing soap films. And what I will discuss today with you and we will do experiments together the rest of this week on camphor boards. We also study amorphous solids, particle rafts, hydrophobic particles that sit at the air-water interfaces and behave like solids, aggregates and granular media. In the last four years I have gotten into biomechanics, particularly these days we are busy studying the evolution, stability and energetics of the human foot. So you will find that I wear these funny looking shoes because I am running an experiment on myself for the past three years. And finally, just to keep my sanity, I keep a problem to myself. I do not collaborate with anybody on it. And I work on, nowadays I work on fluctuations in wind and solar photovoltaics because we have only one planet to live in and we have to care about it, it matters. So if you are interested in any of these other topics, please feel free to catch me at any free time, coffee break, lunch, dinner and chat with me. And I also want to spend a minute introducing my campus. You can see we also have a beautiful beach and you are all welcome there. And we are a brand new graduate university, international graduate university situated in Japan, which means English is our language of communication. 50% of students, research staff and faculty have to be non-Japanese. So we are a very international place.  I am one of the founding faculty and we are adding seven faculty every year. We are about 50 faculty right now and we are expanding. So we want to double our faculty size to 100 by 2023 and eventually reach 300 faculty. We only have a PhD program. So if some of you are looking at applying for PhD abroad and you are interested in interdisciplinary sciences, then please do take a look. Also, since we are expanding fast, we are also constantly looking for post-doctoral researchers and technical staff. So in the intermediate term, you again have opportunities and once you are ready to apply for faculty jobs, again take a look at us because we are hiring seven faculty every year. So you should be looking at us constantly. So outline for the next one hour. I am going to keep this talk very simple and approachable, which means first I will describe what is the phenomenon we are going to work on experimentally this week. And I will explain the phenomenon without the mathematics. Mathematics is a language which condenses the idea in minimal information, but with minimal symbols, but rich in information. But the same can be explained in a descriptive manner as experimentalists especially first learn by just staring at the phenomenon. We can into it from observing. And this is a very old phenomenon. The first recorded experiment was in 1686, but it still has modern relevance. So why should we care about this experiment today and I will explain that also. Then we will go into designing the experiment briefly. Most of the details will be in the lab and then imagine analysis. What quantities do we measure? And finally the results. What are the different modes of this motion of the cell propellant particle? And then understanding the modes of this origin. As I mentioned the emphasis will be on physical intuition rather than the mathematics. The experiments you will be performing together with us have not been published yet. So these are not hot of the press. They are still baking in the oven. So you are going to be working on stuff that I am still thinking about. I will point out unsolved problems along the way each worthy of investigation. Some of them are worthy of becoming PhD problems. So if you are looking for a PhD project you will have plenty of opportunities. And if you are interested please come look me up, talk to me. I am happy to share all the literature and all details I know. And I have no expectation of collaboration because I am a vegetarian so I cannot say I have other fish to fry. I have other grass to eat. But if you are interested please let me know. I also noticed a poster yesterday from Zanjan Syed Mola'i. So this is very closely related to your poster. So what is the phenomenon we want to look at? What you are looking at is a Petri dish sitting on a light tablet like a TV monitor or a computer screen filled with water, distilled water or mineral water. And you see this black dot over there. That is the camphor boat. I will explain what a camphor boat is shortly. It is floating on the surface of water and it just moves by itself. So that is the phenomenon we are interested in. Stuff particles etc when floating on the surface of water it is natural for them to move when the water is itself moving. Here the water is not moving it is static and yet this particle is moving by itself. And this is not the only motion it shows. It can show some other type of behavior also. It will remain static for a long time and suddenly jump to a new position. So it is not just one phenomenon. There are different facets, different varieties of this motion. So this is the phenomenon we want to study. This is not a new phenomenon. As I list here, it was first reported to my knowledge in the year 1686 by Dr. Haydia. I do not know who he or she is. And you can see from 1686 it goes down to 1869 when it was finally understood.  You see some of the most illustrious names in the Annals of Science listed there. Sir Benjamin Franklin who was an American statesman and a very famous scientist. Alessandro Volta after whom the unit for electrical potential differences named Volts. Lichtenberg of the Lichtenberg figures. Giovanni Battista Venturi of the Venturi effect in fluid dynamics. Jean-Baptiste Biot of the Biot-Sabbat Law. And Charles Tomlinson you may not have heard of but he was a fellow of the Royal Society. Finally it was explained by Fandaman Sprucher and later immediately after Lord Rayleigh himself worked on this when he was researching the effect of surface tension. So as I said this problem occupied some brilliant minds over nearly two centuries and many in science had to. I can tell you a story about how did people decide on the fixed points of thermometry 0 degrees and 100 degrees Celsius. It took a Royal Society commission of 35 people about 15 years to decide that even Newton made a mistake there. So there is a story behind every effect that we study in the textbooks and it helps to learn what were the difficulties they faced. Because it's not just us who face difficulty when we do science. They faced it too. It's a very human process. And if you are interested in the historical introduction I suggest you look at this paper. If you would like a copy I am happy to post it on Google drives to all the literature that I am citing here. I have copies I can share it with you through Google drive together with this presentation. And this one I do not have because it's in French which is all Greek and Latin to me French is Greek to me. So that I do not have but I have an English translation that was provided by Charles Tomlinson later. So the effect that you saw the video of the basic mechanism starts with this concept of surface tension. So what is surface tension? I took this image from this website because it does a good job of explaining the phenomenon. In a liquid we have molecules that are all packed in some disordered configuration and they are all interacting through atomic or molecular bonds. They could be covalent. They could be ionic or something else. But the point is when a molecule is in the bulk of the liquid it sees neighbors in all directions. But when a molecule comes to the surface half of the neighbors are missing on the other side the other phase. So the bonds that you see in red along the surface they lead to higher energy. As a result the surface behaves like a stretched membrane with surface tension which opposes the distortion. It wants to minimize the surface because being at the surface is not a very happy state for these molecules. So they cannot avoid it so they will try to minimize the exposure to the surface. Which is why bubbles like soap bubbles etc take up very perfect spherical shape because it's the minimal surface. Now at the surface since we have only half the neighbors it increases the energy at the surface and therefore the forces are acting on the molecules. It forces the liquids to adjust shape to expose the smallest possible area. The symbol I will use for surface tension is gamma. Its units are energy per unit area so milli joules per meter squared or force per length milli newtons per meter. Now the surface tension is what we call an equilibrium construct that means everything is more or less static on average. But things can change when you take stuff out of equilibrium so I will explain what it means to take stuff out of equilibrium. If I take a drop of water on a surface leave it on a surface forever assuming there is no evaporation it will just retain its shape. There may be molecules moving about within that but on average over the observational time scale it remains static. But suppose we consider a different situation this situation which I clicked yesterday morning in Venice as I was waiting to board my train. This gentleman is making soap bubbles that is a very non-equilibrium process. And that soap bubble look at it it is fluctuating so its surface area is changing constantly. So that is the non-equilibrium construct. So what happens you have surface tension on the y axis and the concentration of something on the x axis. What is that something that something is a surfactant molecule or an amphifile.  And hydrophobic tail which heads water so it will stick out of water.  So when I introduce so soap is made of amphifiles. So if I introduce very small quantity of soap maybe I have a very few number of molecules sitting at the surface. I keep increasing the amount of soap I add to the surface of water say a beaker of water. It keeps increasing at some point the whole surface is crowded with these molecules. If I introduce more of these molecules they cannot sit on the surface anymore. But they do not like going into the bulk because the tails hate water. So what they do is they form these ordered structures we call micelles. The micelles the hydrophilic head sticking out into the water and hydrophilic tails sticking in so that they do not meet the water molecules. So now suppose I have a soap film. So I have a soap film and it has these hydrophilic at both the surfaces of the soap film I have these amphifilic molecules sticking out. So the head is sticking into the soap film and the tails are sticking out. Now suppose I suddenly stretch this soap film I have created fresh surface new surface. But that means that I have suddenly decreased the number of if I keep the number of amphifile molecules fixed there are fewer amphifile molecules per unit area. So if I divide the total number of molecules by the area if I increase the area the concentration has gone down.  So the amphifiles introduced at the surface change the surface tension right. So when I stretch the soap film during that stretching the surface tension has is changing because the number of molecules is kept constant but the area is changing. And it takes some time for the molecules to come to the surface and again bring the surface tension back to normal. So when I had dilute concentration of these molecules I had some high surface tension which was close to that of water. As I kept increasing the number of molecules on the surface it came down and then this is called the critical micellar concentration or CMC point. There basically any excess molecules I add will go into the bulk and form these ordered structures ok. So now if I am past this CMC point the critical micellar concentration point and now I stretch the soap film the micelles will come up and they will again bring the surface tension back to this point. So it may go ok. So that stretching and the time it takes for the molecules from the bulk to come up to the surface is a non-equilibrium process that is what you see here. He is creating the soap bubble he is dipped to filaments in soap solution and then he is using the wind air he is basically pulling it like this and it creates a bubble. But while this bubble is not spherical it is fluctuating with the air currents and so its surface is constantly changing as a result it is always in a non-equilibrium condition ok. So again to recap it when the soap film is stretched the anaphylic molecules from bulk come to the surface to occupy the newly available area. But during stretching the molecules are at the surface are not evenly spread then surface tension is not the same everywhere it is the surface tension varies with the location. So if I take a gradient which is basically this the partial derivative of the surface tension with the distance it will show me some characteristic change. That is a force technically it is a stress but for our purposes we will think of it as a force and it is called a Marangoni force. And this Marangoni force is at the heart of the self propulsion of camphor boat ok. So what happens in the case of the camphor boat? Let us say I introduce this red disc which is the camphor particle at the air water interface. The camphor is a waxy hydrocarbon it is what we call a van der Waals solid van der Waals forces are much more weaker than covalent bonds or ionic bonds. So the camphor particles can easily break if with the hand most hydrocarbons are like that. So those of you who are from India know what camphor is very well because it is regularly used in the temples.  What these materials do is they undergo what is called sublimation at room temperature because their atomic or molecular bonds are so weak. The fluctuations in temperature are enough to knock one atom or molecule out from the solid. So this solid can go directly from this material can go directly from the solid to the gas phase it does not melt into a liquid ok. So when I introduce a camphor disc on the air water interface the camphor molecules are moving into turning into gas and they spread along the surface. So these are not amphiphilic molecules they are just camphor molecules their camphor is not the surfactant it is it does not have this amphiphilic structure. But when it spreads along the surface it reduces the surface tension locally ok. So the camphor will spread out like this radially outwards uniformly and it will reduce the surface tension. So there is a gradient in that means the concentration of camphor molecules is changing as I go from the center of the camphor particle out towards the edge of this petri dish ok. So there is a gradient that means there is a force. In fact the force is same along all directions so it is like taking this bottle of water tying ropes to it and each one of us pulls but we pull with the same amount of force. So the bottle will not move anywhere but suppose one of you is stronger than the other and pulls with slightly higher force then the bottle will tilt towards that person. So fluctuations in the air will or air currents will lead to fluctuations in the evaporation and that breaks the symmetry. And the camphor disk will slightly move to one direction and that will amplify and that changes the spreading of camphor into this comet shape. When it turns into this comet shape it just starts moving by itself and we will see this we can visualize it ok. So that is the basic mechanism and it took 200 years to come to this point. So you have the camphor disk and basically the gradients in front so the force in front is different from the force in the back as a result the camphor moves along a particular direction. So if you look at it from the side this is the top view from side view you have the camphor disk and you have this camphor material that is oozing out onto the surface. And it has a longer tail on the back than it has in the front it is moving in this direction. So and stuff gets from out from the camphor molecules get out from the disk onto the surface and then they have to eventually evaporate or dissolve. If we are using camphor it will evaporate if you use camphoric acid which is what we will use because it is more stable it will dissolve ok. So it will get out. So there is a flux an influx of the camphor molecules from the tablet onto the surface and out flux either through dissolution or evaporation from the surface and this moves ok. So any questions at this point please feel free to ask questions.  That is what I was told when I was a post-doc by my advisor. So no questions you understand everything then I do not have to talk anymore ok. So let us now the cute photographs are over now we will get into movies. I come from India Bollywood is a big industry we love movies right. So let us visualize this mechanism what I am going to show here let me first explain the mechanics. So I take this is not a camphor board that is moving about I take a tablet we stick a needle to it. So it goes and touches the surface and it stays put and because it makes it easy to visualize we have a camera. So you have a light tablet you have a petri dish over it with water and then with a needle the camphor pellet comes down onto the surface and we have a camera above and we are imaging at a high speed and we have seeded the water with tiny glass spheres which are neutrally buoyant. So they just go around in the fluid all over the place but sometimes they come to the surface when they come to the surface they are swept away by the camphor molecules that is how it looks. So it is a real effect. So you see that the camphor is getting out so the particles are here you see that the particles seem to be moving in slightly that is basically because they are coming from below the dish and once they come to the surface they are quickly expelled and here they are not moving that is where the camphor has evaporated. Here we used camphoric acid so it has dissolved. So there is an out flux of camphor from here and it spreads and then it dissolves ok. You can look at it from the side so yes 50 microns plus or minus 10 microns these are yes. These are hollow glass spheres it is a very excellent question. Glass is more dense than water so it will sediment right. So he is asked trying to bluff me because how come how can glass particles come to the surface. So these are hollow glass spheres filled with the gas so that they can control the density. So the density is slightly higher than water it is 1.03 ok. Here we are looking at the same effect but from side. So I have a laser sheet that goes through the it cuts through the petri dish that is the camphor boat you see over there. This is basically a mirror effect that you will you will notice what it is. But basically these speckles you see are the glass particles and this the camphor is spreading along this direction ok. So let us look at it. So ignore this above part that is basically a mirror effect at the interface. But the point is the camphor does not spread out of from the disk from the tablet onto the surface in isolation. As it is spreading it is pushing it is trying to drag the fluid with it.  So there is convection in the fluid below. So if I were to take a long exposure of this video and watch it you will see two huge vortices over here ok. So we had taken this video for an experimental imaging technique that we call particle imaging velocimetry. Unfortunately so who knows Yogi Berra here not the Americans who knows Yogi Berra. Yogi Berra if you do not know you should know he is my favorite baseball commentator and he had one of the finest one-liners. So the one that is relevant here he says theory and practice are the same in theory. In practice they are different. So theoretically speaking this particle imaging velocity technique should have given us what we had hoped to measure. But in practice we could not do it. So we had to go to other methods which we pulled out the data that we wanted to but it is still an excellent way to visualize and qualitatively understand what is happening. Now what you realize because most of the dynamics is at the interface right and there is this mirror effect which we can get rid of. But the dynamics is actually limited to a one millimeter layer which we call the boundary layer in hydrodynamics. If I want to image one millimeter with this it is a little difficult but we can do it with another technique. Anyway so the point to note here why what is the take home message from this video. We learned that the camphor particle does not behave like that in isolation. If I were to leave the camphor disc on this table it will not move around by itself. It is moving in response to the forces it is setting up on the water surface. And in the process it is disturbing the water which acts back on the camphor particle. So that is why I put hydrodynamics because up until now people studied the dynamics of camphor goods. But what is the effect of the water below? What happens is the merengoni force that I talk spoke of or the merengoni stress is trying to move the particle. There are viscous forces in the water trying to hold it back. So there is a balance that must come.  Now why should you sit here and listen to me for one hour? It is good I am glad that you are sitting here and listening to me but I have to give some reasons. And why should you continue to maintain interest in it? This is a very old system as I pointed out but it continues to maintain relevance in important unsolved problems in basic and applied science even today. It is a very simple system with which to study these questions. In statistical physics how many of you have heard of active matter? All of you. So for those who have not when we study basic statistical mechanics let us assume this is a jar containing neon atoms. I pick neon because it is a monatomic gas it is an inert gas it does not react. Life is simple. Let us say it is sitting at room temperature 25 degrees Celsius. The atoms are moving about in this jar randomly in response to thermal fluctuations which are set by the room temperature. Now that is the kinetic energy. So when we study basic statistical mechanics of such a system the energy is set at the scale of the container that is the scale. But suppose I look at a bunch of these scamper boards where the energy is not at the scale of the Petri dish it is at the scale of the disk which is 3 millimeters or I could make it 1 millimeter or 500 microns. Then and if I throw a bunch of them and they behave and they interact with each other the statistical mechanics that went into describing the neon atoms is not the same as the one I should use for this because the energy is at the microscopic level not at the container scale. So that changes the physics. So active matter is basically an area of research that has started in the last 10 years and is currently in progress we do not have all the answers yet. If you are interested you have a simple system with which to explore those questions experimentally. Hydrodynamics I say viscous merengoni propulsion. So you have this particle it is moving about on the surface due to surface tension gradients or the merengoni force and there is viscosity acting. Look at when this paper was published Eric Lauga and Davis 2012 not more than 3, 4 years ago but you will notice that this towards the end of the talk I will give you a question. But you notice that this paper came out just 3 or 4 years ago so very recently. So these questions are still relevant. In biology chemo mechanical transduction molecular motors they do not work as the regular heat engines. You do not have a Watson's engine sorry not Watts James Watts steam engine somewhere in my body that does all the work. There are chemo mechanical transducers and the camphor board system is one such example. In materials autonomous motion and self assembly and in soft matter physics. So these are all active questions the experimental requirements are very minimal. So as I said you have a light source you can take a computer monitor with a blank power point screen and you are ready. On top of that you place a Petri dish with distilled water deionized water or this will do mineral water. All you need is a clean surface at 72 Newtons per meter surface tension for water. A camera webcam will do logistic webcam as I learned from Harry. And he also pointed out the virtual dub software which is open source to image. I have done it with smartphones also they are more commonly available these days. And as I said you do not need camphor or camphoric acid. If you use mothballs at home you can use that also the same effect he will see. Matlab for image analysis or if you are old fashioned like me I use image magic with C++ because I hate paying money for software. I am just cheap. So that is all you need. And the quantity you measure is basically the position of the camphor disc. So this is one of the experimental images that Satish took. You see this white circle over here. The white circle is basically a zone beyond which so the red part of the trajectory we are discarding. Why because I told you the camphor is leaching out of the disc onto the surface. It goes up to a certain distance. So if I have a 3 millimeter camphor disc it goes can go up to 3 centimeters. So the effect of the boundary of the Petri dish the wall of the Petri dish on the camphor particle we wanted to get rid of that. Like a free electron we wanted to study what is the hydrodynamics of a free camphor board. So we all our analysis was limited to this region. So all the only the blue parts of the trajectory sorry. Now when you take those positions and you pull out the speed of your camphor board something funny pops out. On the top plot you are looking at the average speed as a function of time in hours. So it starts off at t equals 0 and goes for about 6 hours. So Satish is a very patient gentleman. He sat in the lab for 6 hours and took this recording. I am on the other hand as you will find out this week I am a very impatient man. I want everything done yesterday. I am such a reasonable fellow. So what you notice is the average speed of the camphor board starts off at about 4 centimeters per second. And constantly decreases it changes slope it goes down. But so it is what is happening is the tablet only has a finite amount of camphor in it. It does not have infinite quantities. So with time the amount of camphor that is coming on to the surface is decreasing. As a result the surface tension gradient that I mentioned which is basically the force that is driving the particle is decreasing. As a result this is never in what we call a steady state over long periods of time. It is slowly decreasing its average speed is slowly decreasing. But as it is decreasing if I look at say 8 seconds worth of data in this region I will notice oscillations in the speed. But in this region if I look at say 8 seconds or 16 seconds it is a constant speed. But here for about 1 the camphor speed is 0 on average for long intervals. But at regular intervals it will suddenly jump with spikes. So mode 1 we call harmonic because it is almost sinusoidal. So this is the average speed this is the average speed but this is the instantaneous speed. So here since it is sinusoidal like we call it the harmonic mode of motion. Here it is a steady state motion and here we call relaxation oscillation. I will explain why we call it the relaxation oscillation towards the very end. We will not get into the mathematics of it but I will point you to the literature there. Any questions? Everybody is with me so far? So I told you about early on at the very beginning I showed you these beautiful pictures of Satish where he draws this comet. These are not real experimental systems and this is my illustration which is much more crude compared to what Satish made. The point is this is not some imagination in our mind you can actually visualize it in the experiment itself. So what we did was we now we use a different kind of glass particles again before you pop the question I will answer it. These glass particles are naturally buoyant they have a specific gravity of 0.25 that means the ratio of density of the glass particles to the density of water. So they are only one quarter as dense as water so they naturally float on the surface. So let us say you use talcum powder or Johnson's baby powder it will work you do not need fancy particles they will float. Decorate your surface with these particles and put this camphor particle and you will notice that the camphor boat when it moves it will create a whole particle free zone. This particle free zone is where the camphor molecules are spreading out. So it gives you a clear way of visualizing what is not clearly visible with just the camphor particle going around in the water. But by using these particles you are able to see something else something more. So in the first mode the harmonic mode you will see this long electrical shape. So this dark gray region is the particle rich region and this light gray region is the particle free region where the camphor is sitting. As the disk is moving so this disk is moving towards the top left corner it is leaving a trail behind it. And you notice that so sorry so this black plot is the speed. If I get the area of the particle free region which is basically telling me something about how much of camphor there is. Remember I told you that you do not have infinite amount of camphor right. So with time the amount of camphor on the surface is decreasing. So this gives me a measure of how much camphor there is on the surface at each instant of time. And from that I can plot the area of the camphor which also oscillates together with the speed. So the camphor concentration is oscillating. In the steady state we picked a region where there were some slight changes. But you will notice that this is between 4 and 4.5 cm per second but this is between 2.4 and 2.6 so there is only 0.2 cm per second. And then when you look at this relaxation oscillation regime this part of the plot is taken from the point when the camphor particle was just sitting stationary. I will show you the movies also. It is just sitting stationary and slowly the camphor is spreading and it pushes the glass particles out of its way. It increases to a certain size and then suddenly jumps to a new place ok. So we have another way of visualizing. So the second measurement is using the decoration of the surface with these hollow glass particles to pull out an estimate of the area of influence of the camphor. So here are the movies. See the oscillations. You do not see the oscillations in this you actually pull out do the image analysis you will pull it out. Satish actually highlighted the camphor free area the hole with in green in fluorescent green but that is how it basically looks ok. But in the steady motion you if you compare this you have a large comet in steady motion the area of that comet has decreased ok. And once we move to the relaxation oscillations the particle is sitting static. But slowly the hole is increasing in size and suddenly it will jump and then it goes to a new position and then it grows again slowly ok. So clearly the amount of camphor is playing a role but the amount of camphor is controlling the force or the surface tension difference. So the next thing that Satish immediately hypothesized was well this is because of the surface tension difference.  I am going to do this slightly differently I am going to change the surface tension of water by introducing some material like soap for instance. Here he used a material called sodium dodehyde sulfate SDS. And by providing meter dosage he did not have to wait for 6 hours to get to mode 3 he got it in the first 2 minutes. So here you have this pure water with camphor the same case you get the harmonic the sinusoidal oscillations. And then he changed the water surface tension from 72 dynes per centimeter to 68 dynes per centimeter and immediately it went steady state. When he changed it to 65 dynes so reduced it further it went to relaxation oscillations. So the Marangoni force is directly related to the surface tension difference and since the board speed depends on Marangoni force we have one more quantity. This and now we are getting into the relaxation oscillations for that you need some two competing time scales. So one is the time it is taken for the camphor to leach onto the surface the second is coming from the amount of time the camphor board spends at a given location. Why because if the camphor board is moving it may not be leaving giving enough time for the camphor to get dumped at that position in space. So when that means that the board speed also must matter so there is a coupling between these two. And this coupling is a source of the non-linear oscillations especially in the third mode which we see more pronounced the relaxation oscillations. This can be expressed as a pair of coupled ordinary differential equations and it links to the this camphor board system to the system of non-linear oscillator in the theory of self sustained oscillations. So this was first studied in the mid to late 1800s goes with singing arcs by Blondel in France and Henri Poincaré later Balthasar van der Poel the van der Poel oscillator. So is a very rich and work by Soviet mathematicians Andronov is a very rich theory. I am not getting into the equations what I want to do is lead questions. So I told you about active matter I showed you the effect for a single camphor board which is the experiment we will do for the rest of the week.  I told you about viscous Marangoni propulsion. In fact the data that I showed you does not fall in the viscous regime it falls into what we call the inertial regime. So if you are interested you have a paper to write that goes beyond what Eric Lager did called inertial Marangoni propulsion. Can the boards be exploited for self assembly if so how I do not know I do not work in self assembly I do not know much about. But if you have ideas you can pursue it similarly for mechanical chemo mechanical transduction and actuation. Then there is this result I told you I take the camphor board fixed to a needle and introduce it in surface. So at t equals 0 there is a transient there is some time where the camphor must spread. That initial spreading will occur like that before it reaches steady state. If we plot the rim of this the spreading rim as a function of distance from the center which is what you did for your poster. It goes as some function of time for surfactant simple surfactants like soap etc. This should go as time to the power three fourths for volatile surfactants like toluene or kerosene it will go as t to the one half time to the one half. Camphor is not a surfactant it is but it is behaving showing sign of some behave like a volatile surfactant. So I am showing you a log log scale plot for camphoric acid camphor methanol chloroform they all go as time to the one half. Experimentally this is known but there is no theory for it. So if you are interested there is a PhD problem waiting there ok. Why does camphor behave like a surfactant we know it is not a surfactant. There is something peculiar about it that is why it took these very brilliant scientists 200 years to figure this out. They just so happened that they went and stuck their heads in a very peculiar material. There is something peculiar and I do not understand it completely. So I showed you this video the steady flux of camphor is set up on the surface. When there is the steady flux this velocity as a function of radial distance. So I will call this velocity u of r goes as some power law r to the power x where x is a fraction. There are two theoretical predictions that exist. If the dissolution of camphoric acid into water is as dominant as the spreading of camphor on the water. Then theory says it should go as the radial velocity should go as r to the minus. If the dissolution is negligible that is if it has an affinity for the surface u of r should go as r to the minus three fifth ok. Minus two thirds is minus 0.67 minus three fifth is minus 0.6. It is a bit difficult experimentally to settle between these two values. It is challenging but not impossible. So these are the data we used glycerol water mixtures because we were interested in looking at the effect of viscosity. But you will notice this solid line is minus three fifth this is minus two thirds. But there is a more brutal test for settling this and here is the only equation I am going to show. Suppose you have a quantity radial velocity so u is a function of r. It goes as some constant times r to the power x. If I take the logarithm on both sides log u of r I will get sum of log a plus x times log r. And if I take its log derivative the partial derivative this is the a has no dependence on the radial coordinate. So this will cancel out. So we are only left with this right. So the partial of log r with log r is one so x will come out as a constant. So this is the most convincing test of a power law exponent and derivative is inherently noisy measurement. So it is more brutal. When we do that I am plotting the log derivative sorry. I am plotting the log derivative as a function of distance radial distance for camphoric acid and methanol. This is for camphoric acid this is for methanol minus 0.6 here. All the data is sitting close to minus 0.67. So it is minus two thirds is minus 0.667. So you notice this is varying between minus 0.64 and minus 0.7. So this should be minus 0.667 if you. So there is a way to experimentally determine this settle this. Camphor is not behaving like other materials that spread that are non-suffactant materials that spread on the surface of water. It behaves in a peculiar way. There is something about its physical chemistry that I do not understand. If you can I would be very interested in learning from you ok. So let me stop there.


So you know there's going to be a lot of a lot of things going on but we've just got to focus on the end goal which is the process of doing the best race possible, potentially a lifetime best, potentially world records we're talking so yeah I mean you can't let anything affect you in sport and yeah we're just going to go with that mindset hopefully. If I came away with you know more than one goal, well goal firstly you know I never want to take it for granted, I know what the competition is like internationally but I want to solidify my position and the 100 breaststroke and then we'll focus on the relays and how we can you know obviously solidify and you know capture that goal hopefully on the mix and the medi relay. I think we've got some amazing opportunities ahead of us but really as an individual athlete I've got to focus on my individual performance and that will hopefully give me the outcome that I want.


Ladies and gentlemen please welcome to the stage Jeff Brooks chief marketing officer of Casper. Hello hello how is everybody yeah well rested see what I did there you get your 8.4 so housekeeping matters first contrary to the queries of about three people now this is not a pajama top someone sent out an email saying that if you own a piece of linen this would be the appropriate venue for it Kate's closed okay enough about that so that was awesome by the way Alex is great and it's such an honor to be here thank you at week and brand week and in the company of some great brands among them Casper I'm Casper CMO I've been working with the business for about a year and a half half of that time on the agency side running their agency and then for the past nine months in house as their CMO and it's been quite a journey and I'm gonna tell you a little bit about it today and hopefully one or two things will stick with you beyond this conference first of all how many of you have Casper's in this room it's pretty good that's about in line with West Coast consumption that's not bad fascinating right so for a company that's just over four years old that started with one mattress one distribution channel one geography today we have over 10 product categories with hundreds of SKUs we have owned an operated retail fleet of 20 stores and growing in the US and Canada we have wholesale distribution with partners like Amazon Target Nordstrom and we ship to seven countries around the world so pretty pretty awesome and the press since the theme of this conference and presentation is disruption the press has been talking about disruption to from the beginning but what I love about it is that the things that we're doing are clearly getting picked up as time passes right so the beginning was all about disrupting an old category and bed in a box and you know upending traditional mattress it's moved to establishing really like a sleep as a lifestyle and what the mindset around that is and most recently taking on brick-and-mortar and bringing that same spirit of design thinking customer centricity innovation into the physical world so it's been pretty awesome and and when you when you do stuff like that consumers tend to reward you I'm gonna just read you one or two of these because I'm going somewhere with this my Casper mattress these are all in the last year and most of them in the last few months my Casper mattress is so comfortable I didn't get to feel the earthquake I have to say that hand on my heart my mattress is the most comfortable mattress I ever slept on currently going to bed around 8 p.m. just to spend more time on it I may not even get up on Christmas Day right like this is the stuff that comes in every every single day somebody tried to tell me their mattress was more comfortable than my Casper hashtag fake snooze that was a good one that was a good one right and so why what why is the business taking off like this why is Casper still a darling of the press four and a half years later and why are consumers anthropomorphizing this mattress as though it's a member of their family my conviction to you my thesis for you today would be that as we think about challenger brands that a lot of times we get caught when we think about innovation on the hamster wheel innovation and that is a cautionary tale where you get stuck in the commodity trap just because the pace of change is simply too fast to keep up if you're chasing what I call dash ER marketing better marketing right so your product has to be better on some level your service has to be better on some level your value proposition has to be better on some level or else you don't have a business but different differentiation is the thing that actually in my mind creates sustainable long-term advantage it's easier to defend and it actually is where the core of your value proposition sits and that's what we're going to talk about a little bit for the next I can't possibly seven minutes seven minutes really oh man I gotta go so Casper started you guys all know based on an observation in a category that hadn't been changed in 150 years right which was that a few players controlled supply and distribution and the the experience of buying a mattress kind of sucked you went into a big store clearing house of mattresses all over the floor commission salesperson hovering over you with his clipboard trying to get you in that bed and out the door and Casper revolutionized that so the idea of sort of putting people first in the DTC model was core to Casper fortunately for me and all of us the founders of the company realized that they had to very early on go beyond just what I would call a business model sense of disruption into disruption in a more experiential way and a lot of times when we talk about digital transformation or disruption we tend to think about technology and business model a lot of what I'm going to show you today is not that it's about thinking about disruption where every single interaction you have with a prospect or customer is a brand touch point thinking about building a world a visual world for your brand and your products that is so differentiated that it can't be copied right that's what this company did four and a half years ago that we still push out in the world today this whimsical approachable playful sort of aesthetic that drives a lot of what we do same with the tone of voice so from the top of the page to the bottom this is from four years ago to two weeks ago and I won't read these because in the spirit of time and keeping moving but you're starting to see that there's there's a playfulness and inviting nature to the way that we talk about this that really resonates with people you spend a third of your life in your bedroom or with your mattress and so for us to be able to make that more approachable is really really compelling I love that one by the way a copywriter deserves a bonus for that your mattress will always be there for you through the good times in the bedtime so we like our puns at Casper you know there's a couple more coming your way don't worry but it's really important this is fascinating to me so if that tone of voice and visual kind of world is what we would call marketing the one to many we spend as much time maybe more and what I'll call the one to one so we have a dedicated in-house group of people who do nothing but DM with customers and prospects every single day if you guys could read the the library of stuff that I'm fortunate enough to read daily or nightly it's it's a blessing this woman on the left her Instagram handle is Vagablogger she for 135 days straight including today has been publishing stories on Instagram of her DMs with Casper we are now in the part of the relationship where we are planning a trip together we're going somewhere tropical she decided and we told her that it was a great thing we'll bring our humidity fighting duvet this is the kind of stuff that happens on a daily basis someone said hook that duvet up with a cake and I promise I'll buy it we asked him what his favorite kind was we sent it with a go-to-bed message on it he sent us back the purchase receipt for the duvet okay this is the kind of stuff that really really matters if you think again about what is this category that has basically treated customers like numbers and receipts and how do you get to them on a human level so they want to participate in your brand why is different greater than better because this is the stuff that truly creates lasting value Casper has gotten into the world of physical retail so we have as I mentioned just over 20 stores now in the US and Canada and there's some very deliberate things that we've done here the first is that we don't have commissioned sales people so all of our sleep specialists and store associates are salaried employees who go through slurps sleep certification and brand value training just like any other employee would and critically on the right side you know we did a lot of consumer research and we found out guess what people don't like to try beds and lie on beds that they're going to spend a lot of money on a time with in a giant open environment so we created these done right like but we did it we created these modular beautiful little homes that sit in our stores could the stores be more productive from a dollar per square foot standpoint if we shoved more mattresses all over the place maybe but our conversion rates are super high the stores are more productive than we thought and in fact this business model has been so successful that we can't keep up with demand because now you have to book your time in the stores in 10 minute intervals to try all the beds even when we go into wholesale where we lose a little bit of control with our brand one of the things that we're really keen on is making sure even in those co-branded environments that we have privacy screens simple little things that keep and remind consumers that we understand them from tracking along with them on their shopping journeys we understand where they want to be in the space they want to be in when they're trying this kind of product we also pull consumers into our product development and i know a lot of companies talk about that a lot of them don't do it so Casper Labs has existed since the beginning of Casper it's an r&d facility in san francisco where most of our product design is done through co-creation with our best customers so they receive an incentive oftentimes to come help us ideate do shop alongs beta test products take new products home it's unbelievable some of our greatest innovations have come through there we've created videos for product design and development where we interact with them it's really really important and again for a category that really just thinks and drives its product development and pipeline by what you know it's going to create the most money for them versus what do consumers really want what are the unmet needs that was a big unlock for us now i'll have you know that some of our customers are non-humans you know Casper was one of the uh Casper was the first company to create a dog bed in this category number have copied it since but what did we do to launch our dog bed recently we created what we called a dog fluenser steak dinner so we went out and found uh the most i guess you know the the dogs with the most social cred on the interwebs and invited them all to a steak dinner um where they could try the bed and and nausea and enjoy themselves a little bit a lot of press wrote about it every a list dog you know is that this is insanely posh event right but even that notion of customer centricity down to the four-legged kind i think is pretty cool that drives a lot of what we do um and look part of Casper's belief from the beginning was that it's really healthy to get the conversation of sleep outside of the bedroom okay so for three and a half years now we have had what we call our nap tours where we go around the country with these beautifully outfitted uh you know vans and trucks and we go to places where we think people really need sleep so these are not places where if you're hung over and you just want to crash for two hours it's not that i mean maybe it wasn't the very early days and we were like a dot com brand doing all that but now it's about more purpose driven giving people who need rest that chance to rest it's also obviously a great commercial opportunity for us to get people trialing our products and then buying them online but it's not just at the pavement level it's at 30 000 feet so about a year 15 months ago we became american airlines uh preferred sleep partner so we outfit their planes now um uh with Casper products ranging from pillows and duvets and mattress toppers to other types of things and i think that's another way where again it's healthy to bring these the conversation of sleep outside of the bedroom and most recently guys i'm at zero is it okay if i go on for about three minutes yeah okay um most recently about four months ago um we opened an experiential uh space in manhattan called the dreamery and the dreamy is a place where you can come in and buy a nap now why did we do that because we believe that in this day and age especially for the under slept which is most of you it's one of our largest you know consumer profiles or segments you're all the under slept in case you didn't know that um not being it's actually really healthy too long a nap is not healthy but if you take a nap for about 30 35 minutes and if you've done this you know it re-energizes you it's powerful we have nap pods in all of our offices it is not uncommon at Casper to walk around and see employees drooling at 2 30 in the afternoon and other people passing by as if nothing was going on we have totally normalized the idea within our company that when you are tired it is okay to put your head down and snooze out for a little bit but for a long time i think we've been fighting some cultural headwinds right the the CEO of Netflix saying HBO is not i'm sorry if you're here by the way HBO is not my enemy sleep is i'll sleep when i die i think we've turned a corner thanks to ariana and a lot of other people and Jeff Bezos who are publishing you know you're noticing that people who are well rested are actually you know perform better in the world and they're happier and there's data from every single scientific study that says that sleep is as critical to our happiness our health our moods our stability our relationships our mortality as exercise or wellness um so for the last two or three minutes what i want to talk to you about is what we have our sites set on next from a disruption standpoint and that is disrupting this stigma that still exists in large part that it's okay it's okay to not sleep and that you'll make it up on the weekends or to come into work with four and a half or five and a half hours of sleep it's not okay in fact let me tell you something i'm going to show some startling numbers for those of you that haven't seen this yet the world health organization has basically declared a sleep loss epidemic in industrialized countries i'm not going to go through all these stats you can read them 1.2 million missed work days a year 25 percent of fatal traffic accidents are sleep related and guess what if you don't buy into that stuff and you want to put your commercial hat on 2 percent of our country's gdp is is affected in terms of loss productivity from insomnia or fatigue okay this is a big big deal not just in the us but around the world and here's the thing we all know it so we've just conducted some research and we asked thousands of people this is us only you know how much do you think each of the following contributes to your physical health and your mental well being and the amount of sleep i get in both cases trumped god i can't use that word beat the amount of exercise i get each day or how healthy i eat so the reality of sleep is indeed a third pillar of wellness it's the third pillar of wellness and we have a really big job to do to cement that you know sleep's position in that conversation because it has huge huge impact on everything else there's uh you know i mean if you want to just google it and check it out there's plenty of stuff you can read about it i feel like we've turned a corner now in our culture and this is a part that really excites me about casper um we'll continue to make new products we'll continue to do fun stuff with animals we'll continue to do world-class marketing but i think if you're gonna you know be having me back in two or three years the thing i'm really hoping that we're talking about and what i'd ask for all of your help in you all you know believe in exercise and fitness you all don't sleep enough or the majority of you don't you all have companies that have wellness programs that invest in initiatives for exercise and for diet get sleep on the radar talk to us talk to other people but we believe that a well-rested world is a better world and uh and with that sorry had to do it thank you


Hello everyone, this is Alice Gao. In this video, I'm going to discuss two questions in lecture 5 on slides 27 and 28. The correct answer to question 1 is B. As the temperature decreases, the probability of moving to a worse neighbor decreases. The correct answer to question number 2 is B as well, as the cost difference delta C increases, the probability of moving to a worse neighbor decreases. The intuition for both answers are similar. Moving to a worse neighbor is a risky move. As the temperature decreases, we want to take fewer risks. Therefore, it makes sense to decrease the probability of moving to a worse neighbor. Similarly, as the neighbor becomes worse, it becomes riskier to move to the neighbor. After all, our goal is to minimize the cost of the current state. Therefore, it makes sense to decrease the probability of moving to the neighbor. Let me solve the first question mathematically. The cost difference delta C is positive and the temperature T is positive. Therefore, the fraction delta C divided by T is positive. As T decreases, the fraction increases. Then the exponent, which is the negative of the fraction, becomes more negative and decreases. Therefore, the probability decreases since the exponential function is increasing. You can also solve this by trying some numbers. Let's fix delta C to be 10. If T decreases from 100 to 10, then the probability also decreases from 0.9 to 0.36. Similarly, we can also solve question 2 mathematically. Delta C is positive, T is positive. Therefore, the fraction delta C divided by T is positive. If we increase delta C, then the fraction delta C divided by T increases. The exponent, which is the negative of the fraction, decreases. So the probability decreases because the exponential function is an increasing function. We can also solve this by trying some numbers. Let's fix the temperature to be 10. Then if we change delta C from 10 to 100, then the probability decreases from 0.36 to 0.00045. Here's the takeaway from these two questions. Moving to a worse neighbor is a risky move. It is a type of exploration. Therefore, as the temperature decreases and as the neighbor becomes worse, we want to explore less. So we want this probability to decrease. That's everything for this video. Thank you for watching and I will see you in another video. Bye for now.