Hello everybody, I'm Daniele Buono and this is a seminar on the work we did to improve the security of QEMU by using control flow integrity. Now, I was the main developer of this project. I also got a lot of help and support from my team at IBM, so I would like to thank them and also thank the QEMU community for the big help in upstreaming this work, especially Paulo Bonzini. So, I will start with a bit of action now on why we want control flow integrity in QEMU, then I will explain how it can be implemented in general and what we need to do in QEMU. Finally, we discussed the status of the patch you submitted, what we accomplished in this feature and talk a bit about future work in this area. So, the main problem that we have is that QEMU, like any other program, is subject to bugs. This is a table that shows the vulnerability trend over the years. As you can see, we keep finding bugs in QEMU although at a slower pace than in the past. However, we as cloud providers, we are mostly interested in integrity attacks, because with those, an attacker can gain access to the provider infrastructure or even worse, to data in the end of other clients. Now, the main two ways an attacker can use to cause an integrity attack is by using drop gadgets or indirect function called hijacking. For drop gadgets, the idea is that you can use a buffer overflow on the stack to break a new chain of return pointers. By chaining small pieces of code ending in a return, an attacker can force QEMU to do practically anything it wants. The second type of attack can also be used with a heap buffer overflow and the idea here is to find a data structure with a function pointer and change this pointer to whatever the attacker wants. Now, this attack is very effective in C++ because of virtual functions, but also in SQL that rely heavily on callbacks. And generally, what an attacker does in this case is to call a function in libc that translates in a system call, like a map to allocate new memory or and protect to change permissions on memory pages or event system to just execute another program. Okay, so we know that QEMU has vulnerabilities, but how effective are they in causing an integrity attack? Usually, we rate a vulnerability using the CVSS score. And now if you look QEMU data from 2017, 41% of vulnerabilities are rated medium or higher, but only 4% is rated higher critical. So one may think that only a small number of vulnerabilities can do a lot of damage. However, the CVSS score may be misleading sometimes. Let's take for example the CV over here. It's rated at 6.5 and it's supposed to cause partial integrity attacks. Well, it turns out that there is an attack demonstration that shows out by ejecting the QEMU timer system. This vulnerability could be used to execute any program on the host. And there is a similar attack that has been demonstrated with another CV that only has a score of 4.6. And then in some cases, multiple vulnerabilities can be stacked to increase the damage. Here, for example, we have a vulnerability with a score of 5 that can only be used to disclose information. However, when paired with another CV with a score of 4.6, we can create an integrity attack. For example, an attack could be constructed where we use and protect to mark a page of the guest as executable on the host and then be able to run our own code on the host. There is an example on a FRACT magazine that shows how we can actually execute a shell on the host that can be controlled by the guest. So if you ask us, we would say that just to be safe, any buffer overflow, no matter what the CVSS score is, should be considered as possible integrity attack that can compromise the host. Now, stacked buffer overflows can also be used to create a rope attack, but statistically only 5% of the CVS in QEMU are stacked based overflows. On the other hand, we have up to 31% of them that are buffer overflows, and therefore, we think that CVIs should be able to stop integrity attacks for about one third of the total vulnerabilities on QEMU. So it's clear that QEMU, as any other program, is subject to bugs, and some of these could be used to cause an integrity attack. So how can we make sure that these bugs do not affect our infrastructure? Well, the most obvious option is to remove bugs once they're found. It is, however, as the problem that we can only fix known bugs, and also updating QEMU generally requires stopping the run in the end, which hurts availability for a cloud provider. Another longer-term solution that is currently advocated by some is to completely avoid bugs by using safe languages like Rust. These, however, would only affect some type of bugs, and this is impractical for a project like QEMU that has more than 2.5 million lines of codes. So the only way it would be totally right, which is being pursued by other projects like Cloud Advisor. A third option, which is what we are proposing here with controversial integrity, consists in reducing the effectiveness or the damage of bugs. This has actually been done in the past for a long time with techniques like SecComp, C Linux, C Groups, etc. The idea here is to encapsulate a process and only allow operations that the process may do in normal cases. And the problem here, however, is that QEMU has several different behaviors, so these filters end up being too loose in most cases. Here we think that control-flowing integrity, or CFI, has better chances to stop unwanted behaviors and actually act earlier than other techniques. In our opinion, Google is the golden standard for CFI and other security features when we talk about CNC++ code, and this is because of their large production projects, Chromium and Android. The approach they decided to follow is to automate security features by adding them to Clang and LLBM. So now, thanks to Google, Clang has backward and forwarded CFI, hardened memory allocators, and even strong undefined behavior checks. And since these are in the compiler, it could be used for other projects like QEMU with limited work. But before we go into the implementation details, let's see what type of protections we could use. Let's start with the stack. The common way to protect the stack is by using a shadow stack. The idea here is to have a second stack where we store only copies of the return pointers. And then, before executing a rat instruction, we make sure that both stacks have the same return address. Now, this can be easily implemented both in software and hardware. However, software versions, especially on X86, are not very safe, because there is a rest condition that would allow a second thread to invalidate the return check. On top of that, there are also performance degradations because of the added operations that need to be performed of every function calls. A hardware version of shadow stack could solve most of these issues. For example, the Intel CT avoids the rest condition by introducing a special call and rat instructions that work atomically on the shadow stack. So given that only special instructions access the shadow stack, we could also make it read only for normal load and store operations. An interesting alternative to the shadow stack is safe stack. The basic idea of a RAP attack is to use a buffer overflow to overwrite a return pointer. Safe stack protects the return pointer by storing them on a safe stack that cannot be accessed by buffer overflows. And this is done by moving all the structures that can actually cause a buffer overflow in a second stack that we call unsafe. And keep return pointers and fixed length variables on the normal stack that we can now call safe. Now in this case, even if there is a buffer overflow the return pointers are not accessible because they are in a different memory area. So I would say that safe stack is safer than software-based shadow stacks because it doesn't have the issue of rest conditions. It also had very limited performance effects because it basically doesn't add instructions. We only need an additional register to store the pointer to the unsafe stack. It does, however, change the position of variables in the stack. So if you have a highly optimized stack it could cause some performance degradation. So overall, I would say that safe stack is more comparable to hardware-based shadow stack both in terms of safety and performance. It should be said that a hardware-based shadow stack could protect the shadow stack from normal store operations while safe stack doesn't. But a change in the safe stack could only be possible with arbitrary writes which also open to other types of attacks. So drop attacks is not really a problem. The main concern there. In terms of performance, hardware shadow stacks still has more complex instructions in place of call and write. So we think that in some cases safe stack could actually outperform the hardware-based activity. and could outperform the hardware-based implementation of shadow stacks. Okay, so let's talk about adding safe stack to QEMO. In theory, we should just add a flag and we'd be done. Unfortunately, QEMO makes heavy user coroutines. And now, since every coroutine must have its own Nintendo stack we have a problem here. We can't just create a new safe stack. We also need to create a second unsafe stack for each coroutine. And we also have to make sure that we update both when we do a coroutine switch. Now, coroutines in QEMO is either view context or signal stack to create the new stacks and both of them are not supported by safe stack. So we had to update the implementation in QEMO to manually allocate and update the pointers to the second unsafe stack when a new coroutine is created. However, after that QEMO uses a long jump which are already supported by safe stack to switch between coroutines. So this is all for stack protection. Let's focus now on how to protect function pointers. Here, the common approach is to use forward add control flowing tag. The idea, simplistically, is to check that the function pointed is a correct or allowed function. The main problem is how to define allowed functions. In theory, we could use a call exact match. However, this is not feasible, so we have to use approximations. And the two most common approximations are to either consider every function in the binary as allowed and this is what Intel CT or Microsoft CFG do or to consider as allowed only the functions with the correct signature. This is what Clang is using in their I call protection and what Microsoft will be using with XFG in the future. Now, how can you do that? For signature base checks, Clang uses a order jump table. The idea here is to create a jump table for every function in the binary and order the table by function tie. Now, a function pointer would be allowed only if it points to an address in the correct interval. Another option used in some cases by Clang and by XFG is to compute the hash of the signature and store it at the beginning of each function. So before performing the jump, we need signature hash of the function and we make sure it's the correct one. Now, if you want to only make sure that we're pointing to a function any function, you can add a special instruction or some data at the beginning of each function. And this is what Intel CT does. Now, in terms of protection, obviously a signature checking is much more powerful and allows you to explain in more detail how Clang I call works. If you look at the example on the right, we have the real functions f12f6 in the bottom half of the memory. The upper half stores the order jump table. As you can see, the order is different because it's based on a signature. Addresses 0 to 3 store functions that take an integer and a character pointer as an argument while addresses 4 and 5 store functions. The key here is that the compiler will replace any function pointer with a pointer to the corresponding function in the jump table. Then, before executing the call, you will check that the address of the pointer is in the correct address window of the jump table. If that happens, this is considered a valid jump. Otherwise, the program is terminated with an exception. Now, before we try and apply the callback function, we have to use the callback function that takes a star and the callback type is a charge style or a void style. Now, the general answer is that yes, QMOOT does respect function signatures, but sometimes it is a bit permissive with pointers that are used. Specifically, there are cases where a callback type will be a different pointer type compared to the callback function itself. So, for example, you may have a callback function. Luckily, Clang has an option to do pointer generalization, and this way we can consider all pointers equal. There are still a few sensitive points where a function won't have a corresponding enter in the jump table. This happens mostly in two cases. One is when the function has been generated with just in-time compilation because it did not exist at compile time. Or if we're using a callback function, it does not add to these calls and therefore does not add them to the jump tables. In particular, for QMOOT we have issues in the following things. TCG, when we call a translation block, in TCI when we interpret instructions, all the callbacks for plugins, modules in general, and the signal end railing QMOOT. Now, for all these cases, except for modules, we can disable CFI checks on the QMOOT. We cannot do this with modules because in these cases, the changes and the disabled areas would be too extensive and pervasive in QMOOT. This would actually become an issue in terms of security because we are disabling checks in a lot of function calls. For now, we just decided to not support modules. We actually also have an interesting bonus side effect from this work because to combine it, it langues to use link time optimizations. This actually required us to test and then support in QMOOT for LTO. Now, to be fair, most of the work was already done by Mason, but still we now have this as another feature of QMOOT. Now, let's talk for a minute about the stages of the patches. So, both save stack and CFI I call are supported upstream. The main case is for GitLab. But unfortunately, some of these have to be executed only manually because of the significant burden of LTO in terms of compilation and memory. So, basically what happens is that the shared GitLab runners are not powerful enough to allow wide testing of LTO in the daily CI CD. So, both features can be used today already. There are only two main caveats. Basically, we need to use Clang to compile QMOOT and this is a bit of a problem because most distributions are still using GCC for it. And the other big problem is that we cannot use modules and CFI at the same time. Now, this is actually becoming a pain point for the future because some distributions like REL are moving towards a modular build. So, they would have to decide if they want to support modular builds in the short term. They're going to do modular builds only. So, now that the patches are included upstream, we can ask ourselves, what did we accomplish? Well, if you look at the CBs, a total of 35% of them are buffer overflows. So, we can say that by using control flow integrity, we are mitigating about 1 third of the vulnerabilities and making integrity attacks much more rare. On top of that, we can also support CFI. Now, for the future, the main thing left to do is to include support for shared libraries and this is mostly important for modules. The problem I said before is that the jump tables are completed on the binary, so they have no information on external libraries, even if the libraries itself were compiled with CFI. Now, client does have a solution to, if your local CFI check fails, instead of just terminating the probe like we do now, we check if the address was in a shared library and if it is, we perform additional checks. Now, in this case, if the external library was instrumented with CFI, there is a method to check the signature against the jump table of the external library. However, if the external library was not instrumented, the code would not be protected at all to make this protection effective. We would need to instrument the system-wide BPC and we don't want to do that yet. So, we probably suggest to change to LLDM so that we can fail CFI if the external library was non-instrumented. Another big issue is that cross the SOCFI does not support pointer generalization. So, if we want to make this work with QEMU, we would have to change QEMU and other places where pointer generalization is required. Finally, cross the SOCFI is still experimental and does not work very well with DL Open. And the only way to effectively fix this is to change the BPC or the DL to properly support cross the SOCFI. So, there is a lot of work required here, but we still think that it's possible to do. This is the presentation. Thank you for following.


Hey, Psych2Goers! Welcome back to another video. What, exactly, is emotional pain? Well, it's a broad term that could apply to a wide array of painful emotional experiences. Emotional pain is just as serious as physical pain, and it should be taken seriously. It molds the way we respond and interact with the world in good and bad ways. Becoming aware of your emotions and reactions to stress and pain can be beneficial in maintaining and improving your mental health. So, here are 10 signs you're dealing with emotional pain. 1. You have excessive altruism. Are you used to having your personal needs ignored, and so you only know how to put others first? While altruism is an admirable trait that can improve the quality of life for others, it can also lead to self-neglect. Excessive altruism can be motivated by psychological scars and be indicative of the desire to also receive help and affection. 2. You micromanage. Do you have a tendency to control every part of a situation, every small detail? While micromanaging is often seen as a personality trait, it can also mean that you have a need for control and have difficulty trusting others. There was likely a time where you felt out of control of your environment, and you micromanaged to compensate for that. So, it's important to address the root of your trust issues. 3. You isolate yourself. Humans are social creatures who need interpersonal contact to learn and grow. However, emotional pain often springs from relational conflict or trauma. As a result, isolation can become a coping strategy that creates a perceived sense of safety. Without social contact or support, you can become your own worst enemy. Isolating yourself can intensify unhealthy thinking patterns which are challenging to break free from. 4.  Perfectionism is a common cognitive distortion that can lead to having unrealistic standards. Those with emotional pain may receive their self-worth from trying to be perfect, which is a heavy burden to carry as it can lead to excessive people pleasing and overachievement. 5. You ruminate about your problems. Rumination happens when you replay a situation in your mind over and over again. While it can be helpful for problem solving, analyzing a situation or emotion beyond what you can control can be damaging. Those who fall into thought patterns of rumination are also more likely to face issues with depression and anxiety. 6. You form toxic relationships. Are you in a toxic relationship right now? If you constantly form toxic relationships with others, it could be a sign of emotional pain. Being a victim of abuse can lead to a vicious cycle of toxic patterns and behaviors in relationships. Whether you're an abuser or a victim of abuse in a relationship, emotional wounds often drive the cycle of toxic and abusive relationships. 7. You constantly rush or worry.  Being in a constant state of busyness or panic is often a sign of internal pain. Unhealthy work-life balance or even workaholism can be accompanied by low self-esteem and fears of failure. 8. You experience physical pain. Do you experience stress or pain in the body that you can't explain? Sometization is when emotional distress manifests in physical symptoms. While feeling your muscles tense up when you're stressed is a light example of somatization, some trauma and pain can be suppressed in the body to the extent that you suffer from chronic health concerns such as headaches or nausea. 9. You're only attracted to depressing music. While listening to music can be a powerful way to alleviate stress, being attracted to only sad and depressing music can actually reflect your internal state. Sad music can be an addictive coping strategy that may fuel feelings of despair rather than distract you from it. 10. You have angry outbursts or frequent mood swings. Anger is a normal reaction to being hurt or betrayed. However, when you accumulate emotional pain throughout your life, any situation that goes differently from what you expect can trigger emotional flashbacks. Along with anger, you may also experience shame, doubt, fear and guilt in response to emotional distress. These crippling emotions can feel angry outbursts or mood swings. Do you relate to any of these signs? Let us know in the comments below. If you found this video helpful, be sure to like and share this video with those who might benefit from it. Don't forget to subscribe to Psych2Go for more videos and the references and studies used in this video are added in the description below. Thanks for watching and we'll see you in the next video.


keynote speaker, Professor Marilyn Thoreau is from the University of Technology in Sydney, specifically the Centre for Midwifery, Child and Family Health. She teaches undergrad and post-grad Midwifery students and supervises students undertaking the honours, masters and PhDs and she's published in over a hundred journals, book chapters, edited books, particularly an amazing book called Birth Territory and Midwifery Guardianship. Marilyn's been a Midwifery clinician, academic and researcher for three decades working in Australia, New Zealand and in Denmark. Her PhD was one of the earliest randomized control trials of continuity of midwifery care conducted in Australia and now it's part of the Cochrane Systematic Review on Midwifery-led models of care, demonstrating conclusively that midwives and babies benefit if they have opportunities to get to know their midwife caregivers. And for the past five years Marilyn's research has focused on the impact of the birth environment on the neurophysiology of laboring and birthing women and on their supporters and care providers and this is the topic of this morning's presentation. So join me in welcoming Marilyn. Thank you Marilyn. Thank you Deb and happy international day of the midwife to midwives everywhere. Can you hear me alright is the first question? Looks like it's happening. Good. Thank you. I feel very privileged to be part of this amazing community of midwives to make a difference in the lives of millions of women and their families every day. I'm sitting here on the land of the Gadigal people of the Eora Nation. So you can see we're spread across Australia far and wide as well as the rest of the world. I'm very pleased to be part of the virtual conference to share some of the ideas we've been exploring for the past five years around how the space in which women give birth and where midwives work might influence what happens and in particular to explore the prevailing emotion of fear that many of us feel about birth and I want to explore a little bit about where does that feeling come from? How does the space that we are working in make a difference to that feeling and what can we do about it using the concept of design? I've got multiple things happening here in front of me and I'm trying to get the technology to work properly so forgive me if I'm coming about here a bit to do that. Okay so what we're going to do is fundamentally explore three questions. First of all I want you to consider the spaces in which you work be that at home or in birth centres or in hospitals and here are the questions is the space in which you work a sanctuary or what we might call a surveillance space and just what does that mean? Does the space in which you work create feelings of trust and safety or feelings of insecurity mistrust and fear in you and in the women for whom you care and finally just what do we mean by that and what can we do about designing out this concept, this idea, this feeling of fear. One of the people who's had something to say about design was Steve Jopes who's the co-founder of the Apple company. He said this, most people's vocabulary design means the veneer it's interior decorating just the fabric of the curtains or sofa in fact nothing could be further from the meaning of design. Design is not just what something looks like and feels like although they are critical. The most important thing is that design is how it works. I'm going to come back to that again. First of all I want to take you on a small journey of the imagination.  You've been allocated a room so you open the door and you walk in. I want you to focus on the thoughts that might be appearing in your mind. Focus on how this space is making you feel what might be happening as you move around the room and look at what's in there. Now the spaces in which you work of course might be very differently set up with more or less of what that room contains. It might look like any of these rooms. What messages or images do these rooms bring to mind? What's common for them all? Many years ago a group of us put together what we called the safe satisfying birth hypothetical model to see if we could pull together what was understood at that time about that the elements that made up an environment a space in which a woman could experience a safe and satisfying birth. A lot of it was based on the work of an architect that we'd met many years before called Bianca Lappori and in order to design spaces that she thought would best meet the needs of women in labour she followed women at home. See what it was like in environments where women weren't constrained by what was around them but in their own environment and what she discovered was that at home women seldom give birth in the bedroom but more often in their sitting room where they select an empty and protected area never exposing themselves at the centre of the scene. The birth room to house women in hospitals is clearly a bedroom and it's not the cozy private nest that women create at home but a stage on which the woman becomes a spectacle under constant surveillance and control. So the place of birth matters and here's a list of the kinds of places where birth occurs at home free-standing birth centres alongside birth centres and in hospitals either tertiary secondary or indeed primary hospitals and the UK place of birth study which was published in 2011 in the British Medical Journal looked at maternal and perinatal outcomes by planned place of birth for healthy women with low risk pregnancies. It's called the birth place in England it's a national prospective cohort study and they produced reams and reams of wonderful data revealing that where the women birthed made a difference to the kinds of outcomes they had and the kinds of interventions they experienced during labour and birth. I'm not going to show you the reams of tables what I want to show you is the way a journalist from the BBC reconstructed some of that material to show you very clearly why he came up with the conclusion that home birth might be the best option for many babies. What James Gallagher did was to extract the data from those tables to reproduce this table divided by home free-standing with unit alongside unit and obstetric unit to demonstrate what was the experience of mothers and babies. These data are rates per 1,000 babies or 1,000 mothers going into labour so for similarly risk women serious medical problems in their babies occurred at the same rate from home to hospital with a slightly lower rate in alongside midwifery units but normal vaginal birth occurred more per thousand births at home of course than it did in the obstetric unit. Physiology was less at home compared to the obstetric unit so there in birth was far less for women who started their labour at home compared to those in the obstetric unit and instrumental births have a similar pattern so clearly intervention rates alter depending on how complex the unit is and home is where you experience the least amount of intervention for the same rate of wellness in babies so I think his conclusion looked pretty reasonable on the basis of that data. The place of birth matters just why what is it about those different places of birth that might be making a difference to the outcomes so let's explore just a couple of those places home birth center and hospital and this woman is experiencing birth at home and every home is entirely different in terms of its physical layout and construction the aesthetics the temperature the smells the sounds the light the colors the people who are with you your culture and of course the element of fear at home during the course of labour women can move freely from one space to another moving from laying down on a bed if they want with other people if they want they can be making food in a very domestic part being part of the domestic and intimate daily life or they can retreat into into themselves through immersion in a bath or pool in order to focus inwardly there are many ways at home that the woman can be in that space this is a birth center the this is one of the woman who took part in our a particular piece of research where we followed women during labor and birth in various locations it's the middle of the night so the photographs are quite dark because the soft subdued lighting there are mats on the floor where the woman's mother has made her a nest to rest in the sister is sitting by her on the couch asleep almost because it's the middle of the night at one stage the mother got up off the floor and said she needed to lean against the wall the mattress happened to be leaning against the wall itself so she leaned against it I was interested to find that this is clearly a movement that other women make during labor because on the Royal College of Midwives normal birth campaign website there are illustrations to suggest the kinds of movements activities that might be possible for women and I found they similarly had drawn a picture of a woman standing and leaning against the wall but this woman in the birth center who ultimately had a straightforward normal birth there was no sense of fear she labored for 15 hours she resisted any suggestions of interventions to speed up her labor or to receive analgesia so in the birth center she achieved the same kind of outcome as the woman at the home birth these are another three women from our research very generous people who agreed to have us in their filming them during the labor so they could see how they interacted with this with the space and with the people they shared the space with they all experienced the vaginal birth with healthy babies and how different or how similar are their birth spaces to each other and how are these spaces different from those of the birth center or home think about how does the hospital space enable the woman to be herself to move as she wishes and to do what she wants and what is the pervasive sense of safety security or fear in this kind of a space what's common and how do they differ and I've made a list of some of the commonalities and the differences in all of these spaces they certainly look and smell different and in their level of familiarity and homeliness they may differ on which women can access which locations what models of care are on offer what are the levels of surveillance or sanctuary and we're going to explain that a little more they differ on how autonomous are the clinicians who work with them what access is there to drugs or interventions or more complex levels of care they differ on what are the cultures of care who has the power in that place and then there are unknown unknowns that we don't even know about yet that they may differ on so basically how do we make sense of this and here we go how can we make sense of this the place of birth is quite complex and all of these characteristics may interact in known and unknown ways so there are three questions that we need to consider what is it about the place of birth that makes a difference if we can find out what it is can we design more of it is it simply the physical nature of it remember Steve Job said it's not just what it looks like and feels like there's something about how it works that is the key element how it works is clearly influenced by what it looks like and feels like and what this in what this implies what you are meant to do in this room and in hospitals we mostly work in rooms that are to a larger or a lesser extent versions of this kind of a space it's probably fairly easy to see that this kind of space might make possible different feelings and therefore different kinds of birth outcomes it's a beautiful new birth centre in Toronto in Canada very few of us will ever have the possibility to rebuild our hospitals to look like this so let's explore some theoretical ideas that might provide some principles we could use in our existing unit to design what we have to work differently Kathleen Faye developed this idea of places for birth as either surveillance rooms or sanctuaries and I'm sure you don't need to which kinds of rooms might be preferred by women and why the ideas of surveillance and sanctuary are also multifaceted and complex ideas and it's not as clearly differentiated as you might imagine for instance is this woman also experiencing surveillance or sanctuary I met a wonderful person called Marie Stengland many years ago and Marie is a linguist a social linguist and she worked in the area of semiotics or what are the meanings of objects and spaces and Marie produced this concept of binding that I think helps us understand even more about what we mean by a surveillance space or a sanctuary where women might feel safe and secure or unsafe and afraid the concept of binding talks about the way spaces close in on us or open up around us spaces that close in around us in a particular way feel comfortable make us feel secure and are the basis of what is a sanctum spaces that are too close too tight around us or who or which are much too open with too little enclosure actually make us feel quite insecure and these are the characteristics of surveillance spaces have a look a little more what Marie's theory suggests to us is the reason why many women want to gravitate towards a birthfall or bath during labor if you think about it in terms of okay we're just taking a minute to try and fix the the problem here we won't be in a moment if my microphones back on again now can you hear me did yeah we all seem to lose sound then so we'll just get your screen back to where you're up to and carry on Marilyn maybe a minute just taking a minute to get the PowerPoint back up to where I was you might be able to take this opportunity to stand up almost there okay while we're working on getting the presentation back okay might take a minute we're just having to search for the slides perhaps I see in the comments Marilyn people were really enamored with the idea of the sanctuary or surveillance and I see that you're just starting to unpack that now which is fascinating yeah I mean certainly thinking about women in Australian hospitals in particular all want to be able to have access to order immersion during labor and indeed often end up giving birth in the bath to the point where in New South Wales the state that I'm located in the government has made a mandate that every birth unit must provide women with the opportunity for water immersion during labor which is pretty unusual and Marie Stingland's concepts of binding kind of give us an understanding of why that might be there we are so we're back to why a woman might want to get into a bath or indeed stand under a shower and basically when we and we have with Robin Maude in New Zealand I interviewed numbers of women about why they got into the bath during labor basically what they said was well it's a place where no one else can touch me it's a private space it's an enclosed space where I feel much more secure and safe so this idea of binding gives us an idea why women might want to get into the bath or indeed stand under a shower because they know that other people aren't going to get under there with them and get wet they're certainly not going to get in the bath with them all although obviously partners sometimes do at the woman's invitation so using this idea of bonding suggests or suggests why this might be important for women I want you to look at this space and think about in terms of the bindness or unboundness of this space it's a newly renovated birth unit previously the unit that they were in had no outside windows and the spaces were quite enclosed and cave-like how would women feel in this space and where does it fit on the the bound or unbound spectrum and I think you'll agree with me it's beautiful from an architectural point of view wouldn't you love to be sitting there having a lunch looking out at that wonderful view but for a woman in labor this space is experienced as incredibly unbound and an unbound space feels unsafe so what's happening in practice is the blinds are kept closed the entire time and the woman is not gazing out at the view because she feels exposed and vulnerable and under surveillance in this kind of space about two bound spaces again in interviewing women and women for instance who are connected to a CTG machine and many of them for the entire length of their labor and most of our units can't afford to have telemetry monitoring so the woman is strapped to the machine and therefore marooned on her bed or in a chair unable to move and she certainly feels trapped and potentially too bound and this idea of not being able to move freely evokes feelings of insecurity and fear and apprehension so again thinking about how do we design out fear in our spaces how many women are we keeping attached to CTG monitors so Marie's theory about binding came up with the kind of idea that makes a sanctum is one that is optimally bound and optimally unbound because again there are times during labor where there's an ebb and flow where the woman wants to interact differently with people where she wants to move or be or lay or stand or sit or talk and so we have to be able to think about how the design spaces that can accommodate this ebb and flow one of the places that I'm aware of is in fact in Denmark and in this space the designers have thought very carefully about how do you accommodate the ebb and flow of labor or they may have it done it accidentally but this is what's happened this unit is certainly not at a beach what you're looking at is a projection of a beach on the walls plain white walls of this birth unit and it's done by a very simple piece of equipment that's located on the ceiling it's a little projector and on the table you can see a small little computer screen or iPad screen and the woman and the family in the space can actually dial up what kind of an environment they would like to be in an open unbound space like this one or at a different time in a labor she might want to feel that she's in a more bound enclosing and secure kind of space and in fact I can imagine you could put in all sorts of images that might be even more personal for the woman in the room that would make her feel secure and bound or at times when she wanted to be open and engaged with other people you could have an image of a much more open vista this equipment is not expensive I've been in my local Apple shop and I can purchase the projector to do this for around two hundred dollars so at least in the developed world where we are relatively affluent we could all afford to do this kind of thing in our Birkin challenges of course we need to have walls which are plain and unobstructed by other sorts of equipment and paraphernalia in the space so let's have a look more carefully at what's happening at a neurophysiological level the limbic system there that little yellow kind of horseshoe shape in the middle of the brain on the right is hardwired to translate emotions to keep us safe and surveillance activates very core of this limbic system the amygdala it stimulates the release of all sorts of neuro hormones that have to do with flight fight and freeze but in particular adrenaline and those of you you know me know I bang on about this stuff all the time that we need to know what's going on neurophysiologically with women in labor not just would be a uterus because if a woman is afraid fearful stressed feels like she's under constant surveillance and her amygdala activates this process she will produce adrenaline in particular but also nor adrenaline which has a slightly different effect let's focus on adrenaline adrenaline when it increases it disrupts the production of oxytocin and it interferes with the rhythmic contractions of the uterus either making them irregular or making them slow down to the point where uterine inertia is diagnosed on the other hand increases in adrenaline divert blood away from the trunk of the body into the muscles of the arms and the legs for fast running away or fighting and into the brain for thinking about how to get out of this fearful situation so in fact it constricts the blood vessels to the abdomen decreases uterine blood flow which then decreases potential perfusion and fetal oxygenation leading to fetal distress so whilst we haven't done experiments on women to actually see that this happens they have been experiments done on animals and it can demo we can demonstrate in laboring primates in particular you can induce both uterine inertia and fetal distress by making the animal feel afraid so what can we do if we can't change that space as many of us can't we can actually use the human body to simulate that experience because the very first sense of shelter we might have is that of being in your mother's arms so that we can make spaces that are comforting or protective in that same way by being in someone's arms and again the Royal College of Midwives normal birth campaign website has wonderful cartoon illustrations which show exactly how you can make bound spaces for women in places where you can't modify the environment and here are just some of them these enveloping arms help the woman to feel that she's in a bound secure safe space and you can do it in all sorts of ways with the woman sitting on the birth ball with the woman squatting in between her partner's knees she can get into the bathtub and it doesn't have to be a deep immersion pool although that's ideal but in this even in this kind of a little space the woman is not going to be having anybody else getting in there with her so she may get that sense of security and a private space for these kinds of places even using inanimate objects like the chair which the woman woman can in billop also gives her a sense of being bound and more secure so there's much more that we can talk about but we don't have time today these are just a small snippet of the kind of ideas that we've been exploring about how do you optimize birth physiology basically we need an optimal birth environment that might be optimally bound for women but we also need relationship-based care because the two together help initiate the amazing neurophysiological calm and connect system that ensures that the woman has optimal oxytocin to help her lay the progress it lowers her blood pressure her heart rate increases her pain threshold and normal birth is more likely if a woman has straightforward normal birth then she is more her baby is more likely to have its own neurophysiological system initiated in an optimal way there are many many studies that I could talk about we've also looked at the impact of these kinds of places on midwives themselves and Athena Hammond is one person who's produced several papers in this area and this paper is also from Deb Davis and Caroline Homer recently looking at how does place a birth impact on the flights what Athena has concluded is that the current design of many hospital birth rooms challenges the provision of effective midwifery practice and changes the design and the aesthetics of birth rooms may engender safer more comfortable and more effective midwifery practice because if midwives are working in environments where their brain is affected it shuts down their prefrontal cortex and makes their amygdala fire up so that they are fearful and in the fight fly for freeze moment I think we might call it a day there that's the end of my presentation thank you and I'm very happy to receive question what a lovely joyous family photo to finish on there Marilyn thank you so much we'll open the floor to question so if you can raise your hand if you want to ask a question and we can give you the mic alternatively you can type it in in the chat box we did have one question just while people are getting ready to put their hands up Marilyn from somebody in the chat box I think it was rain from Western Australia and it might have been the Danish birth room and we wanted to know the name of the equipment he might have been referring to the projection or the room itself the projection equipment I think if you just go into any one of these techno shops it's it's it's a projector that can project it has a little projection apparatus that has four outlets so it will do 360 degree projection they're very simple pieces of machinery I don't know exactly what their name of them Rita thank you and I think the the images that were projected were specifically made for that purpose from memory yes yeah I think they are scenes of a forest in Denmark seems of a beach somewhere in Denmark and they have other amazing things that were going so and they also had the sound of the lapping water and I think the one that they particularly have was purchased from the Phillips company and it costs many many many thousands of dollars but I discovered it is possible to set it up in a much less sophisticated way and a much less expensive way thank you I'm just scrolling down does anybody want to take the mic and ask a question or make a comment I can see Eva Wilding made a question what study was it that showed the security of home birth there is a paper by Bianca Lepore and it's called trying to think of it now it's in a journal called about children's spaces I've lost I've lost it now did I can't think of what it's called but you'll find it referred to in our paper on safe satisfying birth so have a look there and you'll find the paper oh yeah so someone's also mentioned making an allergy with newborns and how they need that close nesting kind of approach rather than something unbounded yeah absolutely you certainly wouldn't leave a newborn laying out in the open and watch what it was doing you want to cuddle them close and help them feel secure in that bound way so absolutely the same sense I think what I really appreciate a Marilyn was that you you drew on some great new theoretical insights I love the idea of the bounded and the unbounded but you brought it down to a level of practice so there's great practice tips really for people how they can kind of understand this theory and what they can do I mean any sort of environment because not everybody can have a home birth and many women are birthing in hospitals which are environments that we can't change immediately but you gave us some great ideas for what we can do just to help women feel more secure in in the worst of environments really yeah and one of the challenges is that in Australia I know for sure and it happens in most developed countries that many many millions of dollars are being spent every year on renovating or rebuilding birth units and unless midwives get to talk to architects and designers who are part of the teams putting these together then they will build or renovate birth units like the illustration I showed you of the one with the blue couch and the blue bed and all the beautiful windows in it it looks great if its purpose is other than for women during labor and birth you have to help them understand what it is that women during labor and birth knee in order to make the room work so designers about how it works not just what it looks like or feels like in Australia there are several units that are using these design principles and have used them to establish their birth units debut work in some in Canberra I do yes we've got a beautiful birth center in Canberra and that is really a sanctuary I think but I was going to comment as well when people are asking about the redevelopment and involving other people that it's really hard work to get the midwifery perspective and some of this theory and understanding through isn't it to architects and the powers that be when a new hospital or a new unit is being developed I don't know if you want to comment on that I think you had a lot of experience with that. Yeah it is challenging and certainly all of these possibilities are filtered through budgets ultimately but if we can get some principles in the mind of the people who are designing them then they will interpret them in various ways but if the principles are strong and hopefully that you know these ideas of binding will be embraced within the principles. Next week I'm about to start work with in New South Wales the part of the health department that writes the health facility guidelines for how you build amongst other things like birth units in hospitals and we have been consulted in years past and parts of our work is included in them but now there's a whole redevelopment of these facility guidelines about to happen. These facility guidelines influence what happens in the building of all maternity facilities in Australia and in New Zealand as well depending on which companies get to build them and often they're Australian related companies that are building all over the Australasia region. I also work with a private architecture firm on their health facility guidelines and they build facilities throughout Southeast Asia, parts of America and India and their health facility guidelines pretty much match what is done in the New South Wales health guidelines so that's one way of trying to influence what happens. Hopefully we've put in an abstract at ICM for actually running a workshop for midwives in what do you need to know to sit at the table in order to influence the design of the birth unit in your place. So hopefully our abstract might get accepted and we can run a workshop. Thank you. Tracy, the issue of smells which I think is really important and the role of essential oils. Yep, absolutely critical.  And I spoke just yesterday to a group of new midwives, new student midwives first year about to start their clinical placements and they've walked into these units and they say wow it smells like disinfectant and kind of the metallic smell of blood is in the air and it's terrifying for them. So yep, aromatherapy is a critical part of setting the environment. Thank you. And maybe just the last point a good one to finish on was Anna was asking how she can follow your work Marilyn. Certainly through our publications Anna and if you just Google my name I'm somewhere in some people's papers but we're hopefully going to be able to write a new book that pulls all of this together because it's a critical topic we have to get it right. We can't be wasting money on rebuilding units that aren't fit for purpose and the purpose is helping women to have a straightforward normal birth and we keep building units that look like modified operating theatres with material all around them that women are very well aware is going to be used on them and in them. So it's quite a frightening prospect. So hopefully in the future a book but certainly in our publications currently. Thank you Marilyn. Okay I'll bring it to a close right on time. I want to thank you Marilyn for years and years of dedicated work and the most fascinating work particularly in this area it's just given midwifery and so much. So thank you for that and thank you for sharing it so generously as you very often do with this audience and more. So join me everybody in thanking Marilyn. You can do a virtual, there's a virtual clap happening. Thank you. Thank you everybody and happy international midwifery day. You too. You too. Thank you. Okay everybody just bear with us now we'll be doing a changeover. We have about ten minutes to get ourselves set up so it's time to stretch your legs. Just delivered me a coffee into my office which I'm going for you.


A famous pair of Harvard studies, which involved so many people over so long a time, they've by now chalked up millions of person years of data, found that the consumption of anthocyanin-rich foods, foods containing those bright-colored plant pigments, was associated with a lower risk of developing type 2 diabetes over time, particularly blueberries, just two or three servings a week, associated with a 23% lower risk. In my daily dozen, I recommend berries every day. Why, though? What do berries have to do with diabetes? Well, type 2 diabetes is caused by insulin resistance, and interventional studies evidently clearly show that dietary berries can ameliorate insulin resistance. Yeah, but that was in diabetic mice. What about in men and women? Those consuming lots of anthocyanin-rich foods like berries didn't just have less inflammation, but significantly lower insulin resistance. Okay, but by how much? By as much as you would get walking like an hour a day, seven days a week. Wow, how many berries were they eating? That was for 35 milligrams of anthocyanins a day. So like a cup of strawberries or cherries, a half cup of raspberries or just a quarter cup of blackberries or even just a few spoonfuls of blueberries. But that was just a snapshot-in-time cross-sectional study. What we need are interventional trials where you give people blueberries in a double-blind or randomized and placebo-controlled clinical trial to truly put them to the test. Okay, here you go, so they could fake people out with a placebo if they used powdered blueberries. The equivalent of about two cups of fresh blueberries worth in a smoothie and got a significant improvement in insulin sensitivity. Two cups is a lot, though. Any benefits for just a typical half cup serving? This study demonstrated a significant reduction in post-prandial oxidation, meaning all the free radicals created when you eat some sugary breakfasts like cornflakes. Here's the antioxidant capacity of your bloodstream, taking a nosedive two hours afterwards as your body tries to cope, but eat it with a half cup of blueberries and you start out higher and stay higher after the meal. Note they also tried just adding a quarter cup of blueberries and that was clearly not enough, so we should strive for a full serving. The reason we care about free radicals, though, is that they can damage our DNA. Can a single portion of blueberries really improve protection against DNA damage? A single portion of blueberries can improve protection against DNA damage. They drew blood from people before and after they ate some frozen blueberries and exposed their white blood cells to free radicals in the form of hydrogen peroxide, and blueberries significantly reduced the DNA damage done within a single hour after berry consumption. However, the protective effect was transient and our DNA vulnerability returned within two hours. So we want to be eating super healthy foods like berries at every meal. In conclusion, one portion of blueberries can improve our cellular resistance to DNA damage, thus supporting the importance of consuming healthy plant foods regularly.


Ok, so let's start as always with this real chamber picture. I hope you remember it. End of course. So we have here, this is chi 1, this is chi 3, this is chi 2, so these are the kernels. We have here the size plus plus minus minus plus, minus plus plus, minus plus minus. Then you can finish. Ok, so this corresponds to the sign of the first direction of the Lyapunov exponent along the first direction, the second direction and the third direction. So we keep with two matrices A, with this row from C square, SL3C. We have these three Lyapunov exponents. We have the splitting E1 plus E2 plus E3. And the first, the chi 1 is the Lyapunov exponent along the first direction, the chi 2 along the second direction, the chi 3. This Lyapunov exponent along the third direction. So that's the picture we need. So we know, so we have our alpha from C square into different morphisms of C3. So we are going to assume infinity different morphisms. We are going to use the DRC infinity. C1 plus epsilon is enough, but you need to modify the technique. If you want C1 plus epsilon, you want to use this technique. You will need CR with probably R equals to 10, or maybe a little bit more than 10, maybe 200. Some finite R. So we were able to take a finite in the subgroup gamma of C square and try to build H from T3 to T3. H equals alpha n equals to rho n equals H for every n in gamma. H was Heller continuous, and the image of H was also Heller continuous. So it's a homeo. And moreover, we had explicit formulas for the H. And you can look at the proof, and you can see a little bit more. So some u of x, the alpha n, we were able to lift it to our n. So this was rho n x plus some function phi n of x. These are the periodic functions. And we gave explicit formulas for the H, but let me write them there with some more care. So we can write ux as u1x plus u2x plus u3x. Know that R3 splits at the sum of three sub-stories. So I can take this u of x and split it as the sum of three vectors, one on each space. And the same I can do with this phi n. And write it as phi n1 of x plus phi n2 of x by n. If you remember what we did when we show the existence of this H tilde, you can see that if phi i of n is positive, let's write the exact formula so that I don't make a mistake, this is negative. Then I of x is minus sum from k equals to 0 to infinity e to the chi i n times k and i on alpha k times n. Pause with the second. This is positive. This should be negative here. Pause alpha minus n. Okay, so you have this number is negative, so this is an exponential conversion sequence and this is a bounded function. So this series is conversion by the wire stress n test. And in the case the chi i n is positive, then you have a similar formula. Oops, x equals to sum from k equals to 0 to infinity. Oops, there is a factor in front. e to the minus chi i n times the sum from k equals to 0 up to infinity of minus chi i n k i n i alpha k n. Okay, now you may complain in principle. There are too many indices here. Okay, so the point is when we made the proof, we picked this n naught here and we did all this computation with this n naught. Okay, so the n was equals to n naught. But now I can look exactly the same with any n. So this expression makes sense for whatever n. So in principle these UIs will depend on the n, but I proved before that the h was the same independent of the n. Okay, so I have these expressions independent of the n. Okay, so these very same functions Ui have a lot of way of being written for each value of n I can write it in this way. This will be very important, improving smoothness of the guy. Did you can see just from solving this equation, you can just, it's a matter of rewriting this equation, you can see that you have formula U1 prime from which one is deduced very easily which says that the Ui of x is minus some from k equals to 0 to n minus 1. So it's essentially the same formula, but I'm only adding up to n minus 1. Chi i n times k by n i on alpha minus k n plus compose alpha minus n of x plus e to the n chi i n times the Ui compose alpha minus. So we have this. So this is, okay, where? Here? Yes. Minus k times n. And yes, so these two guys together is minus k plus 1 times n, I agree, so you could put them together. But I want to make them separate because there is some kind of symmetry here.  And then this is some dirt that I don't want to see. So this formula is exactly the same as this formula, but only treated n times. And then if I take n to infinity, this goes to the total sum, and this guy is killed because once I know Ui exists, this guy is bounded, and I have some exponential conversion term here. So this will get any bounded terms. So you have C0 conversions of these partial sums to the total sum. And there is a counterpart to prime. I will not write it, but it's essentially the same counterpart because you have here. In the case, the guy i n are positive because if the guy n is positive, then here this goes to infinity, so you cannot say much. You want to use the other formula. Okay, so we have this formula, and these are crucial formulas to prove smoothness. Let me see if I'm forgetting anything or that's all I wanted. Okay, that's all I needed. So let's try to prove smoothness. I will make my first attempt. Probably I will fail, but then I will introduce more here, Ian. Hopefully we will succeed. So I have this explicit formula, say here. Okay, so I told you yesterday that I happily could move along any place here and the guy will be an ossef. Okay, I will have stables and I will have contraction along these stables for whatever n I choose there. Let's see if I take even the very n naught. What could I do? So I want to have, say, there the... I will try to prove smoothness of the u1, smoothness of u1. So the u1 here is the first direction. So here the first direction is contracting, so I'm using the first formula. So I want to prove smoothness of this and if you have a series, if you want to prove smoothness, what you do is you take derivatives. Okay, you take derivative of these terms. If these terms, the derivative of these terms are summable, then you are in good shape. Okay, we just take derivative then. Derivative of ui is... will be more specific of how I'm taking derivative soon, but let me just write it down. This is just a number. Then I'm taking derivative of phi and i, pose alpha minus k, and compose alpha minus k. And, okay, here is my first step. So this guy is independent of the k and is smooth, so I can't forget about this guy when I'm going to do my computation. Okay, so let me not add it. It's very painful to have this guy. That's what we have. So I have some exponential convergent guy here and then I have the derivative of this piece. Now some chain rule is in order, so you can do derivative of phi and i, compose alpha minus k, and times the derivative of alpha minus k. So that's what this guy is. So if I'm taking first derivative, that's what it is. Okay, this is just a function composed with homomorphism, which is what the difference is, which is onto, so the c0 norm of this is bounded. So this is not a problem. But now I have the norm also of these guys. Okay, now these are matrices and the norm of these matrices are growing to infinity. And indeed you can be a little bit more specific. I could take a vector here in the unstable direction. Okay, if I take n in that cone, if I take the vector in the unstable direction, then this is exponential conversion. I'm in a very good shape, but we will see in a second that this is useless. So I would have been able to prove it faster before. So the interesting case is that I take vectors along this stable direction and when I take the vector in the stable direction, this grows exponentially. This is the hyperbolic condition that will tell me that this will grow exponentially. Now I have an exponential decay, an exponential grow, and the problem is that most likely this guy will win to that guy. And if you take higher order derivative, indeed, what you can do, so you can use just more fancy general formulas, and so the Fadi-Brino formulas and essentially what you get is a bound like this, but then you will have a power k here. Okay, so that's what you're paying, but it's even worse because you have exponentially increasing to the power k, so it's k times this exponentiality against only this term, but maybe k is not a good quantifier. And this is the degree of infercibility. Then I have here this guy, and I have to kill this guy. So this is not working, so how you fix it? How you fix it is you fix it in the following way. First of all, I want... Yes, that's what I want to do for higher smoothness, exactly, but this is not working because the bound I can get here will explode, so I cannot really control this at all. So then what should I do? What I will do is I will, first of all, try to fix a little bit this expansion that is appearing here. Try saying, okay, I don't want really to use the formula I used because this is really bad what is happening there. Okay? So what I want to use is the second formula. I want to use this formula because if I use this formula, forget about this very bad guy in principle because I'm... the end is still down here, so it's not up there, so I am down there. So this guy is bad now, so I'm using the second formula in the wrong case, but this guy is very nice because when I do this very same argument I did there, so I will have instead of the minus here, let me write this down what we'll do with the second formula. So the ui the second formula will be the guy i n so this minus guy here, I forgot the minus sign here, but that doesn't matter, and then I have the sum from k equals 0 to infinity e to the minus guy i n times k, and then I have derivative pi n i negative compose alpha k n now I do the same argument there and this I can bound by the norm of partial n of pi compose alpha n pi and then the second guy I have to bound is this d alpha k times n then I want to see what happens along stable directions along unstable will not be a problem I will tell you later how to do and I will need to control this bound and now this is beautiful because if I'm taking positive iterates this has exponential decay and this exponential decay essentially will win to this other guy also this one has to be careful this will not be 100% true because I don't know how much faster, I don't know this exponential and I don't know really how much faster this is so I have to work a little bit more even to say that but at least it's a little bit more hopeful than that the big problem is that even if I can take say imagine I take higher derivative then the point is I can play a little bit and in case this I don't have a function to take derivative to begin with if chi i n is negative this doesn't make sense this is not a function so what you do and that's essentially the idea of fissure, cullinan but here it's not a function, it's true but this is a distribution so as a distribution it makes sense one has to prove it and then if it is a distribution you can take derivative of a distribution and if you eventually show that taking enough derivative you get a nice function then you can say something so that's the claim that's the rema u1 take n to be chosen carefully c is this cone chosen carefully write it, this is formula 2 then formula 2 defines ui of x i, i, e for any function psi p the integral of ui times psi is equal to the sum from k is equal to 0 up to infinity of the minus i, i, n there is an e to the minus i, i, n also here there is a k here integral of pi, n, i composed alpha n alpha k, n times psi so this is yes, for some expression to be chosen carefully I didn't tell you exactly what does it mean I will tell you later I don't have even a function to differentiate yes, that's why I don't have I could take formal derivative of this I could do that and I will have a serious but even if I do that which is what is written there still not obvious that this exponential contraction here will win to this exponential expansion there it is not, no it is not it is not so this will not win to that because yes absolutely you have to make very careful things but even if you were in the best of the cases the only thing you may hope is that this number is exactly the same as this number so in the best of the cases you will have balance so this will not explode but it will not go to 0 it will be used yes so I still need to control this so the point is that what I can show essentially here is that this guy doesn't grow exponentially but not too exponentially so super exponential it at most grows only exponential with some explicit balance on the exponential I will have now this will be enough first of all to get this statement and the next statement which is much stronger because this time I can get it without this discussion but the next statement I will need this discussion to get it but you only discuss things in the distributional sense so I need to modify a little bit all my statements here to make it work but I think that's where everything comes from so the way you realize that this is the right thing to do is by looking at this term so if you want to get conversions in the distributional sense of this series you need to know something about what you are summing now what is this let me just translate this in a very crude way so your say your alpha n of x so your alpha n is a function f phi n i is just a function phi which is a sinfinity function your psi is also a sinfinity function so what is this is the integral of phi composed with fk times psi let's say instead of dx I put a d mu now maybe you start realizing what is this term if I take out the integral of phi times the integral of psi so this is the decay of correlations for these two functions I may be very lucky and have that this is less than e sum tau times k minus tau times k is norm of phi curler norm of psi I may be lucky enough to have exponential decay of correlation for curler continuous function and also systems used to have that ok so I only need to do it with respect to the right measure and constants of course will not kill my problems up there I will not have problems with the constants ok so that's why you hope to have some conversions and observe that when you want to say that this happens in the distributional sense it means that I need to have conversions of this series but I need to have bound on the c r norm of psi for some r and here I am getting respect to the curler norm it's a distribution but it's not even of very high level let's state let's discuss a little bit this issue for the one that exists the measure mu equals to some cell function eta x x where eta is in infinity and mu is alpha n invariant we have an absolutely continuous invariant measure for this moreover h star mu is hard measure I'm sorry measures go from push back the measures you don't pull them forward or you pull them back you define a measure there also it's ok it's hard to measure on this you take the h which maps on your t3 with the proaction you have here the 3 with your alpha action you take the measure mu here and it's sent into the most natural invariant measure there which is hard measure this in non-trivial statement is a consequence essentially of Lipschik theorem or Katokkonenko or more so the best form is a consequence here but it's not that hard to prove in this context you have to play some homological equations it's not really that hard in this context so that's the first thing to do so I have this measure this dx and I have this eta which is fixed so this statement will tell me that it's not harm if I put the measure mu here instead of this measure dx when I'm discussing this monic analysis that's the first statement second statement by Gorodnik and Spachier but in this in this framework has an understandable proof in the general framework the proof well of course there are at least two persons that can understand and more has a referee and one can understand it but use heavy machinery so you use green tau tuition results but in this setting of the torus it's really some Fourier business which is quite understandable so it says the following which is this decay of correlation so of course you will say it's decay of correlation for the nose of map so this is a very old subject let me just be careful on the statement so given theta which is the Heller exponent there exists tau positive the row action is given here so these guys depends on the row action but only on the row action did you know less than that but it doesn't matter now such that if phi theta psi is also in c theta and that's it then the integral of phi that composes alpha and times psi x, alpha not rho so it's for the linear action this is minus the integral of phi the x times the integral of psi dx smaller than or equal to some constant yeah there is a constant here positive e to the minus tau norm of n times now it needs epsilon more space norm of phi c theta norm of psi so the decay is uniform for all the elements of the actions so that's the key business and since the con sugan c h is Heller continuous I can take this decay of correlation exactly the very same with the same exponent tau there maybe a modified theta here 2 decay for the alpha action and this is exactly what I needed here exactly what I need there and as I told of course there appear the integral of phi and the integral of psi but this is not really big deal but this is not a problem this decay when you change the alpha instead of the rho is exactly the proof of this level yes and I guess I get the conversions so here you have to do the following things so when you go to the proof assume first the integral of psi is 0 and then this thing here is exactly the same as this so this guy decays exponentially but also with bounds of the norm of psi c theta indeed let me just put it here what I know is that ui but it was continued to begin with so what I'm going to write here is useless but it's important this is c theta star that's the proof that this guy is in c theta star of course the fact that ui is in c theta star is back so I know that ui is Heller and Heller will be in its dual c theta this is not fun what is important here is that this formula holds in the distributional sense okay and indeed rather than using exactly this sum you can use this formula here and get it even faster but let me not enter into this now comes the second lemma which is even more important this heavily so the key point here is being able to use the wrong formula okay so that's the key issue oh yeah maybe I should say something more probably that's why this is complaining yes I'm sorry yes so here I have some clear bound tau this is more than tau I have tau mod of n k this decay now I need to win to this guy here which is positive so that's this beaches in California so the proof of lemma 1 is just the following there exists n indeed for every eta positive there exists n such that I want two statements one is chi i n is negative that's just because the guy belongs here but it's larger than it minus eta that's times n and this is just essentially irrationality of this guy that's one thing and then I will need other more things but let me skip until the next step where I need to prove the next lemma but once I have this then I can choose really this n so that this is in absolute value much smaller than the tau I am winning and the tau is fixed independent of the n second lemma positive n derivative along the s direction of ui this is n derivative along ws direction belongs to c theta so there exists theta so I am taking nth order derivative but only for vectors along the stable direction for this guy I have and I know they are all always in the same distribution space of the same degree c theta so this that happened here is not only true just for the ui which was used it's also true for the derivative and I don't need to move the theta and that's the crucial business because of course from here you will get that dn ui is in c n plus theta star so this is almost a triviality okay but you can do it without modifying the theta the prove is a little bit more complicated and I just realized I have only 5 minutes but follows exactly the same spirit here okay and there is one very important step that I'm not putting here but it's it's what I said so it's this guy now since I'm getting very to the boundary of my n of my c this guy now is not anymore exponentially contracting well it's exponentially contracting but I don't have good control on how fast it is but at least I can play this eta business and create some control so I have a counterpart of this eta for the non-linear action also which comes in the same flavor as what we did yesterday when we show that all the elements here were an awesome so once you know that for every measure the Lyapunov exponent has disbound it's true uniformly and then you play exactly the same game here and for all Lyapunov exponents you will have a bound like this and then you will have this type of bound uniformly for the non-linear just by playing the Lyapunov exponent so you need this type of bound to play this let me not enter into this because if not I will need today, tomorrow and another week just to prove lemma 2 but that's the the philosophy of lemma 2 is essentially you have some plus some interpolation techniques where you bound what you can bound in c theta star and then the rest you allow to go to c and plus theta star and then you do the rest ok so that's what you get the next lemma putting this plus this together so it says that if action w from t3 r is theta so it's a further continuous function and the partial derivative of order s of these w functions are in c theta star for every n so exactly what I'm having here so this partial derivative makes sense in distributional sense and as distributions belong there then there exist alpha positive which is little bit smaller than theta so theta as you wish but it's a little bit smaller such that this dns w belongs to c alpha these partial derivatives are actually functions and are further functions so this is just an interpolation technique so it's a very standard fact in harmonic analysis if you have a function you bound the c r norm and you bound the c l norm you can bound all norms in between ok and that's what you are doing here ok so you have that the very high derivatives are bounded here so this has some implication on how this w norm and then I can bound all the other guys in between so this interpolation plus all of embedding is just some very basic harmonic analysis so it's the only subtly that you have to work a little bit harder is that everything here is subordinated to the stable direction not to the total space so then you have to do some harmonic analysis subordinated to the stable direction but that's doable, that's not really it's not even painful it's nice ok good so I have now that my function u i is differentiable along the stable direction let's analyze u i along the stable direction so I have the same way I split the u i I could split the h tilde as h tilde 1 plus h tilde 2 plus h tilde 3 ok and I know that h will take the stable manifold of n naught of a point x into the stable of the linear guy which will be h of x plus the stable space of n naught which is nothing but h of x, there is tilde here everywhere plus the stable space which is the e1 plus the e2 direction so we take this stable manifold onto this translated space now what is this translated space so here I have say the e1, e2 e3 so I have my h tilde x and I have this now I have the unstable manifold correctly I have my unstable manifold of this point x so these are curves and this is just a plane now this plane is mapped into this plane this line is mapped into this line through the point x so it should be into this line ok now this line by definition so you have the counterpart here so h tilde of the unstable manifold n naught of x is h tilde x plus the third space which is the unstable manifold for this n naught so this the fact that the image of this manifold is this line means that this first coordinate is not moving and this second coordinate is not moving ok so what I get is that h1 tilde restricted to the unstable manifold of this point x is constant it has to be constant it cannot move it's a constant function it's constant h1 of x ok the only variable that moves is the third guy so the first is constant the second coordinate the third is moving well constant function is moved now u1 is h tilde minus the projection of the first coordinate projection is moved so u1 is moved as well along the unstable and then there is to finish a theorem of Schurme h1 minus the projection of the first coordinate so h because h tilde is x plus u so h tilde 1 is projection of the first coordinate plus u1 ok so it's the natural projection from r3 into this e1 coordinate so if this is constant and this is constant and this is smooth this is smooth it's just this statement so Schurme theorem if w from t3 is h tilde and this here we need continuous let me formulate the way I want to use it have dns w in c alpha and dnu w in c alpha for every opposite fly for every n then w is same thing ok so he has much more statement like that it's smooth ok then we have to go to u2 and to u3 now let me just comment one very important thing we needed this eta here and to get this eta it means that I have to take dn very close to this line where the chi1 is very close to 0 I needed to be able to take this this point here ok and that's why I was able to handle the e1 direction and handle the e2 direction by taking the guy here but I cannot handle the e3 direction because to handle the e3 direction I need to make this chi3 of n very close to 0 so to handle the 3rd direction I need to shamp this wall and approach here but to do that I will need to know that the guy is here not an awesome and that's the next thing to do cross the wall and get an awesome guy there and once I get an awesome guy there then I'm done that's what we are going to do tomorrow


Sometimes parents are demanding something from their children and the children cannot provide. The issue is they don't understand.


Babes Wajimo and Mampintja mourn the passing of a loved one. Mampintja and Babes ask that the nation includes them in their prayers as they mourn the passing of a loved one. Shimura took Instagram not so long ago to reveal that they have laid his brother to rest. His fans have taken to the comment section to show him and his family support. The couple is also dealing with the fallout between Shimura's mother and Babes' mother in law. Babes all started when they apparently never invited her to their wedding. That alone was deemed culturally wrong by Zama who said certain rituals had to be done from her side to grant her blessings.


Hi, I'm Darlene from GoDaddy's How-To, and I'm Emma from The Journey, and today we're going to talk about managing your customer loyalty program. And these programs can be the lifeblood of repeat customers, and they essentially reward customers for returning often to your business. And back in the day, it was all about punch cards, right? I know I had one for my favorite sandwich shop, but now these loyalty programs have become more sophisticated and essential for your business. And if you currently don't offer a loyalty program, this might be the opportunity to start one and communicate those customer rewards out in your marketing efforts. It's all about building loyalty and customer attention. Did you know that a 5% increase in customer attention could increase your profitability by 25% to 95%? That's a huge return, and it costs five times more to win a new customer than retain an existing one. Yeah, so here are some ideas for retaining those customers and keeping them happy. Number one, giveaways. People love free stuff. So think about something your customers would love to have. Could be a free slice of pizza. I know I would love that. All the pizza or a piece of merch, like with your logo on it. And you could send it to influencers on social media to create buzz around the giveaway. And this is a great way to bring customers to you and your services. Another idea is to offer your customers VIP level rewards. These are often special perks for spending levels for customers. An example here is Mac Cosmetics, which has a Mac Lovers program. And as you can see, they give customers more perks for higher spending levels each year. This gives customers an extra incentive to be loyal to their brand. So another loyalty program idea is offering points for purchase. And this allows your customers to gain points related to every purchase in exchange for free goods or services once you've gained enough points. And this is the closest program to that old sandwich club card I was talking about or a coffee punch card. Ten punches and you get a free cup of coffee. I love that. You buy enough of something and you get something free. That's all it is. Now Starbucks has been doing this for a long time with their Starbucks rewards. And as you can see, they have a lot of ways to keep their customers engaged with their brand. They have an app birthday rewards games. They're doing it right. But the rewards don't last forever. And there's a six month window on the point expiration. So again, creating an incentive for customers to purchase often before their points expire. So that brings up a good question for businesses that have loyalty programs. What do you do when customers can't come into your store during a crisis like we're seeing with COVID-19? Yeah, and that's exactly what Starbucks did. They communicated out to their reward members that they would be extending the expiration limits to cover reward benefits while their stores were closed. So consider extending those benefits to your customers. So when they return, you'll have lots of happy customers ready to spend money and earn more rewards. And if you're a business that is open during this time, but maybe in a limited capacity like a restaurant, you might want to consider offering a discount on rewards. So if a free coffee normally costs a customer 100 points to redeem, maybe you bump it down to 50 for the next 30 days or offer double points this month, which is essentially the same thing. Try both campaigns and experiment to see which one gets more traction. While businesses might be slow, this is a great opportunity to build customer loyalty by offering them an incentive to buy from you. Oh, I actually have a good example of that, Darlene, of the limited capacity. I noticed here in San Diego, there's really popular car wash, Soapy Joes, and a way that they are limiting the capacity is that they're only allowing their members to come in through the hours of 9 a.m. till 5 p.m. at all of their locations. And remember, I know we've said this 100 times already, but communicate with your customers and it doesn't have to be overkill. Just an email or tweet once or twice a week, letting them know that we got you covered.  Well, that's all for today. Check out some other videos and resources GoDaddy has put out there for small business owners and entrepreneurs. And if you need help, you can always call our customer service member and speak to one of our guides. Until next time, stay safe and stay healthy.