We will continue with our discussions on compressible flows. We will now discuss on something known as stagnation properties. This term stagnation we have come across during our earlier topics that we have covered in fluid mechanics and one of the literal meanings is that the fluid is brought to rest at a point so that the velocity is 0. So, stagnation point is a point where the velocity of flow is 0, but that does not mean that it suffices the requirement of description of stagnation properties. So, we will now look into more deeply about some of the important properties which dictate the nature of the process by which the stagnation state is achieved. To do that we will refer to first an important thermodynamic property and when we are referring to a thermodynamic property we will be basically referring to the first law of thermodynamics to specify that. So, if we say that you have a control volume say some control volume which has some inlet I and some exit E. Let us say that there is some rate of heat transfer to the control volume say q dot cv and say some rate of work done by the control volume as w dot cv and let us say that the flow is steady and the state or the properties of fluid within the control volume is steady that means the properties within the control volume do not change with time. So, if these 2 conditions are simultaneously achieved then the corresponding form of the first law of thermodynamics is like this where h is the property enthalpy which is the internal energy plus pressure by the density. Now this particular form is also known as a steady flow energy equation just for common understanding. So, this is nothing but the first law of thermodynamics expressed for a flow process across a control volume when the flow is steady and the states within the control volume are also steady. Not only that there are certain more important assumptions what are the important assumptions all the properties at the inlet and the exit are uniform that means the velocity profiles are uniform the thermodynamic properties like enthalpy those are uniform. So, it is like approximately a one dimensional representation where uniform properties across the cross section for the inlet and the outlet. Now we are interested to apply this equation for compressible flows. So, when we apply this equation for compressible flows first of all if you have a system where you are not having any mechanism of extracting work from that. So, then this rate of work done will be 0 by the control volume. Then if what kind of process we are considering we are considering an adiabatic process. So, if it is an adiabatic process that means heat transfer across the control volume is 0. We are not committing whether it is reversible or irreversible. So, the reversibility or irreversibility features when we talk about the second law of thermodynamics when we discuss about that. But in the first law of thermodynamics it is just good enough to say whether it is adiabatic or not irreversible or irreversible does not feature here. Now, in most of the high speed gas flows the effects of the thermal effects and the kinetic energy effects are more important than the changes in potential energy. So, that is negligible and therefore you are left with h i plus u i square by 2 is equal to h e plus u e square by 2, okay. Now, let us say that we are thinking about 2 sections instead of i and e some generic section where the where the enthalpy this is specific enthalpy that is enthalpy per unit mass is h. The velocity is u this is at some section and when you go to some another section that section is a special section when the velocity is brought to 0. So, this is a section of stagnation. So, we are interested to see that what is the corresponding enthalpy there and let us say that the name of enthalpy at that stagnation section is h 0. Since it is a one dimensional treatment section and point are the same it is basically uniform. So, we can say from here that h plus u square by 2 is equal to h 0 because at the stagnation u equal to 0. So, this h 0 is known as stagnation enthalpy for an ideal gas it is known that dh equal to cp dt this is for an ideal gas where cp is a function of temperature in general. But when we talk about a perfect gas cp is a constant. So, if we say perfect gas this is a constant for perfect gas therefore, we may say h minus h 0 for a perfect gas is cp into t minus t 0 where t 0 is the temperature corresponding to this stagnation enthalpy this is known as stagnation temperature. Why we refer to the temperature? Because temperature is a directly measurable quantity from experiments. So, it is important that we refer to that. So, this is known as stagnation temperature. So, we can write cp into t minus t 0 plus u square by 2 equal to 0. Now, we can write cp in terms of r and gamma because just recall that cp minus cv is equal to r and cp by cv is equal to gamma. So, you can write cp into 1 minus 1 by gamma equal to r that means cp is equal to gamma r by gamma minus 1. So, we can write t 0 minus t in place of cp we write gamma r by gamma minus 1 is equal to u square by 2. u square by 2 is what? You can write u by c is equal to the Mach number say m. So, u square is equal to m square into c square. Now, what will be the expression for c will depend on the nature of the process. If it is an isentropic flow c square is gamma rt. So, this is equal to m square gamma rt for isentropic flow. See till now whenever we define this stagnation temperature. So, the stagnation temperature how it is defined? The stagnation temperature is defined from this equation as t 0 is equal to t plus u square by 2 cp right. This definition does not require the process to be reversible. So, if you want to find out that what is the stagnation temperature. In fact, this definition does not require any process because it is just an expression. So, if you know the temperature and velocity at a point and specific heat at a point you know the stagnation temperature at a point. So, stagnation temperature is defined at a point irrespective of what is I mean what kind of state is there at that point. If you want to physically achieve a stagnation temperature you have to bring the process to rest at a point in an adiabatic manner. It need not be reversible that is not necessary because the definition followed from the first law of thermodynamics by setting heat transfer equal to 0 without imposing any condition of reversible process. So, keep one thing in mind stagnation temperature just like any stagnation property is a property. So, it does not mean that at one point if it is not a stagnation point it will not have a stagnation temperature. It will have a stagnation temperature because it is just dependent on the local temperature velocity and cp. So, it is just like a combination of properties and therefore, it is a property. If you say that I want to physically achieve the property then you have to follow this kind of a process adiabatic process. Now, if you want to use this expression u square equal to m square into gamma RT that means you are now imposing the additional constraint that it is an isentropic process that means a reversible process. So, for an isentropic process this will be m square gamma RT by 2. So, from this what follows is so, gamma into R will cancel from both sides. So, you will get T0 by T is equal to 1 plus gamma minus 1 by 2 m square. So, this is the relationship between the stagnation temperature and the temperature at a point. What are the assumptions under which this is valid? It is an isentropic process that you have to keep in mind otherwise the more general expression is this one. Now, you may relate the stagnation just like stagnation temperature you may have a stagnation pressure and stagnation density. So, those properties also you may find out. So, for an isentropic flow for isentropic process you have PV to the power gamma equal to constant that means basically in terms of T and P you can write T2 by T1 is equal to P2 by P1 to the power gamma minus 1 by gamma. So, just like you have related the stagnation temperature similarly you can relate stagnation pressure P0 by P is equal to T0 by T to the power gamma by gamma minus 1 that means 1 plus gamma minus 1 by 2 m square to the power gamma by gamma minus 1. This P0 is stagnation pressure remember assumption again is isentropic flow. Now, so this considers compressibility. We have earlier seen a case where we used Bernoulli's equation to define a stagnation pressure and that was without consideration of any compressibility. So, we use just the Bernoulli's equation Bernoulli's equation means it is an incompressible flow assumption and the stagnation pressure. So, if you consider the incompressible limit P0 is equal to P plus half rho u square neglecting the potential energy effect. What are the assumptions? It is an incompressible flow. We use the Bernoulli's equation that means we implicitly assume that it is a frictionless flow. So, if you want to achieve physically this P0 you have to bring the fluid to rest in a reversible and adiabatic process that will mean that it is a frictionless process. If you want to achieve T0 physically you have to bring the fluid to rest in an adiabatic process it need not be reversible whereas to achieve P0 physically you have to bring it to rest by ensuring both that it is reversible as well as adiabatic. This is a very important distinction between like how you achieve physically a stagnation pressure and a stagnation temperature. So, now when you come to this incompressible flow so here you can write P0 by P for an ideal gas P by rho is RT. So, this is 1 plus half u square by RT. Remember that if it is an isentropic flow C square is gamma RT. So, this you can write 1 plus gamma by 2 u square by C square u square by C square is M square. So, this is an expression which is valid for incompressible flow. This is an expression that is valid for compressible flow. It may be interesting to see that in a certain approximate limit these 2 equations in certain approximation they agree with each other. To do that what we may do this is the more general expression. So, we may expand this in a binomial theorem just like 1 plus x to the power of n. So, if we expand that in a binomial theorem so P0 by P compressible. So, 1 plus x to the power n is like 1 plus nx plus n into n minus 1 by factorial 2 into x square plus let us just write another term n into n minus 1 into n minus 2 by factorial 3 into x cube. So, this is 1 plus gamma by 2 M square. So, you can see that up to the first term it is just like the incompressible flow expression. The remaining terms are the corrections because of the compressibility effect. So, what are the corrections? So, you can write may be the first 2 corrections. So, 1 is gamma minus. So, this is gamma by 8 M4 right then plus this is 2 plus gamma into gamma by 48 M to the power 6 like that sorry 2 minus gamma. So, what is this important implication say you are using a p-tort tube to measure the flow velocity at a point and you are negligent of the compressibility effect and you are using this expression for P0 by P because in a p-tort tube you may get the difference between stagnation and static pressure by connecting a manometer between the stagnation point and another point which is a point located upstream to that. So, when you get that expression that expression will require a correction and the leading order terms that will dictate the correction the first 2 leading order terms are like this. So, if it has to have a compressibility effect these extra terms for correction need to be invoked and we can see this these terms are higher powers of M. So, as M becomes smaller and smaller this becomes more and more irrelevant that means for low values of Mach number the compressibility effects are smaller and smaller that is quite intuitive ok. Next what we will consider next we will consider the similar thing that we have discussed till now may be isentropic flow to begin with but through a variable area duct till now we have not taken area as a variable parameter but now let us generalize the previous discussion somewhat and consider isentropic flow through a variable area duct. So, when we say a variable area duct maybe it is something like this maybe it is something like this we will not specify what it is but the area of cross section will vary. So, what are the basic equations that we may use here one is of course the continuity equation and we are all in all cases we are assuming that it is a one dimensional flow. So, rho into A into U that is a constant this is from the continuity equation then the fluid flow equation here remember we are talking about an isentropic flow. So, reversible and adiabatic. So, it is having no friction that means it is an inviscid flow. So, what will be the governing equation for that Euler equation one dimensional form of the Euler equation. So, Euler equation so that is what dp by rho plus U du equal to 0 that is the differential form of the Euler equation. Remember that in all cases of compressible flow that we are discussing we are neglecting the changes in potential energy the gravity effects are negligible as compared to the other effects. So, this is like the these are sort of like the fluid flow equation and the thermodynamic constant is the energy equation. So, energy equation is like h plus U square by 2 equal to constant but first of all we will not consider this energy equation as an important consideration but we will concentrate on these 2 equations and see what we get out of that. So, continuity equation rho into A into U equal to constant. So, what we will do is we will take log of both sides.  Say this is equation number 1 and say this is equation number 2. Now, if we want to relate these with the sonic speed see in equation number 1 there is d rho in equation number 2 there is dp. So, somehow if we find out dp d rho that will give c square. So, we can relate these behaviour with the sonic speed. So, we can so we write from 2 that dp is minus rho U du and or if you want to relate it with U square.  So, minus rho du by U why we have written in this form is because you have another form du by U in equation 1. So, the let us say this is 3 and from equation 1 you have d rho is equal to minus rho into dA by A plus du by U say this is equation 4. So, if you divide equation 2 by equation sorry equation 3 by equation 4 you get dp d rho into 1 by U square is equal to du by U divided by dA by A plus du by U. If you consider it as an isentropic flow d p d rho is c square. So, for an isentropic flow the left hand side is 1 by n square because m is U by c. So, from here you can write dA by A plus du by U is equal to m square du by U which means dA by A is equal to 1 minus or is equal to m square minus 1 into du by U. This is the relationship that governs the change in area with change in velocity and it is one of the very important physical relationships which we have to carefully study. So, if you write say dA by A. So, when you write dA by A we think about 2 possibilities. See I mean one of the possibilities is that along the direction of the flow the area is increasing or area is decreasing. So, this is an example with dA by A greater than 0. This is an example with dA by A less than 0 assuming that this to be the direction of flow. Now, if you consider m equal to 1 as a case. So, m equal to 1 if you consider then that will imply what dA by A equal to 0. That means if you want to achieve m equal to 1 m equal to 1 is called as a sonic condition. In an isentropic flow it must conform to dA by A equal to 0. dA by A equal to 0 if you look into it mathematically it may be either maximum area or minimum area right. Physically we will see that it will it will conform to the minimum area. So, if you consider a possibility of these 2 types say you consider this as a case. Let us say that you have the inlet flow with a particular Mach number whatever the Mach number at the inlet may be greater than 1 or may be less than 1. Now, we are interested to see the consequence. If you consider this particular geometry if you see that no matter wherever m equal to 1 is achieved we will see later on with a physical example that how m equal to 1 may be achieved. See just think this geometry. So, this particular geometry even if it is an incompressible flow you see what is your target. The target could be to increase the velocity that is why you reduce the area of cross section. So, these types of things where you have a variable cross sectional area with an intention of increasing the velocity and therefore the consequences reduction of pressure that is known as a nozzle. So, if you have a nozzle your target is to have an increase in velocity, but just this geometry does not ensure that it will be like that for a compressible flow. For an incompressible flow area reduction will imply that the velocity will increase. For a compressible flow if you think it like that it may be wrong because rho is also another factor. It is rho into a into v not just a into v. So, rho may vary in such a way that it might be that if area is increasing velocity is also increasing. So, it all depends on the Mach number at which the fluid is there. So, we will see later on that what is the physical implication of this minimum area when we discuss more about the nozzles the converging nozzle. This is called as the converging nozzle and the converging diverging nozzle, but look it in the other way. If m is not equal to 1 then can you have dA by A equal to 0? Definitely, if m is not equal to 1 then you may have dA by A equal to 0 if dU by U equal to 0 that means U is either a minimum or a maximum. So, from this we come to a very important conclusion that if for the time being we take that at the minimum area m equal to 1 is achieved that does not mean that at the minimum area m equal to 1 is always achieved. It means that if m equal to 1 is achieved somewhere it has to be a minimum area location, but the minimum area location will not always have m equal to 1. If it does not have m equal to 1 it will have either a minima in m or a maxima in m and we will see that how it is possible. To understand that what we will do is we will consider two different cases. One is m greater than 1 another is m less than 1. So, if you consider m greater than 1 you can see that if you have a reduction in A that means if dA by A is reducing then dU by U that is also reducing. That means if area decreases the velocity also decreases if the flow is supersonic. This is non-intuitive incompressible flow consideration will say if area increases the velocity will decrease. So, why it is happens? Roughly if you see that what you are keeping fixed rho into A into U. So, you are reducing A you are expecting U to increase, but with a reduction in A maybe there is such a high increase in density that there is actually a significant reduction in U to keep the product as constant. So, that is what is happening here physically. So, what we get out of this is when m greater than 1 that means if you have dA by A that is if area is reducing then the velocity is reducing therefore it is not acting like a nozzle. It looks like a nozzle, but it is acting like a diffuser. Diffuser is something where you want a decrease in velocity and an increase in pressure.  So, physically looking like a nozzle does not mean that it is a nozzle. One has to see what is the Mach number range in which it is operating. On the other hand if m is less than 1 you have dA by A will be if it decreases that will mean that dU by U is positive that means U increases. So, if so this situation we may intuitively think as physically analogous to an incompressible flow behaviour in a nozzle only if Mach number is less than 1 only if it is a subsonic flow. If it is a supersonic flow that is not the case. So, if it is a subsonic flow what happens if it is a subsonic flow so now think about such an arrangement. So, this is an arrangement where the area is reducing it comes to a minimum and then increases. So, in this kind of an arrangement if you see if you say if you plot so let us say that the arrangement is like this we plot the Mach number versus x for 2 cases assuming isentropic flow for 2 cases one is the entry Mach number greater than 1 another is entry Mach number less than 1. So, if the inlet Mach number is less than 1 say the inlet Mach number is less than 1. So, this is Mach number equal to 1 say inlet Mach number is half like this. So, as you go through the converging section the velocity will increase and therefore the Mach number will increase. So, the Mach number will increase and it will come to a maximum when dA by A is 0. So, it may not achieve 1 but it will come to a maximum and then it will fall and then it will fall because the area variation is different. On the other hand if the inlet Mach number is greater than 1 then the velocity will reduce in the converging section and therefore the Mach number will reduce it will come to a minimum therefore here and then will increase again. So, if the entry is supersonic the throat may have a minimum Mach number if the entry is subsonic the throat may have a maximum Mach number but these are limited by Mach number equal to 1. So, if it is supersonic it is remaining supersonic for all the locations it is coming only to a minimum here but that is still greater than 1. On the other hand if it is subsonic it is remaining subsonic everywhere at the throat it is coming to a maximum but still greater less than Mach number 1. So, from this we conclude a very important thing it is not necessary that at the throat this location of minimum area is called as the throat that at the location of the minimum area it is not necessary that we will always have Mach number equal to 1. But the converse is true if we have at some location the Mach number equal to 1 that must be at the throat. Again remember there are very important assumptions associated with it the assumption is it is an isentropic flow. So, if it is a flow with friction and flow with heat transfer then the location of this sonic point Mach number equal to 1 shifts it is no more at the throat it is at either the upstream or the downstream depending on the heat the heat transfer in the flow and friction in the flow. Now, it is also possible to write this expression of dA by A exclusively in terms of dM by M. So, let us try to do that because it will give an exclusive variation of or exclusive relationship between Mach number and the area. So, let us write say d so, we know that the Mach number is equal to the C into U. We are interested to express dU by U in some way in terms of dM by M. So, that we write dA by A explicitly in terms of dM by M sorry U equal to C into M right. Now, what you may do is you may take log of both sides and then differentiate see for all these cases by this time you have realized that there is a purpose in taking the log and differentiating because you are getting this type of expression dA by A dU by U like this by taking log and differentiating. There are other ways of getting it, but this is the easiest way of getting such forms. So, log of U equal to log of C plus log of M and then you differentiate. So, you will get dU by U is equal to dC by C plus dM by M. So, in an effort of expressing dU by U in terms of dM by M we have come up with a new unknown dC by C, but C may be expressed in terms of the temperature. So, let us give this equation some numbers. Let us say this is equation number 5 and say this is equation number 6. Now, we know that for an isentropic flow see we are writing all these equations for isentropic flow. So, C is equal to root over gamma RT for isentropic flow. So, again we take log. So, log C is equal to half log gamma plus half log R plus half log T that means dC by C is equal to half of dT by T. So, dC by C is half of dT by T therefore, you can write from 6 that dU by U is equal to half dT by T plus dM by M. Again another new unknown dT by T has appeared, but till now we have not used the energy equation that we may use. So, energy equation what it was? H plus U square by 2 equal to constant that was the energy equation. So, you have dH plus U dU equal to 0 and for a perfect gas this is Cp dT plus U dU equal to 0. In place of Cp we can write gamma R by gamma minus 1. If you want to write it in terms of dU by U just divide both the terms by U square and U square is equal to M square into gamma RT. So, this is M square gamma RT. So, gamma R gets cancelled. So, 1 by gamma minus 1 M square dT by T plus dU by U equal to 0. So, we have been successful in writing dT by T in terms of dU by U. So, from this we get dT by T is equal to minus of gamma minus 1 M square into dU by U. So, this is 9. So, if you combine 8 and 9 this is dU by U dT by T is written in terms of this half of the right hand side and so that will become 1 plus gamma minus 1 by 2 M square dU by U is equal to dM by M. So, that we may substitute in equation number 5 which is there to get dA by A is equal to M square minus 1 into M square minus 1 into M square minus 1 into 1 plus in place of dU by U we may write dM by M. So, from this equation we may get an explicit relationship between the area and the Mach number. So, if you know how area varies with x you can easily get how the Mach number varies with x. So, for a given geometry A as a function of x you will get an output as a Mach number as a function of x and from here you can clearly verify the statement that we have just made. So, if M is greater than 1 see the denominator is always positive because gamma is Cp by Cv Cp is greater than Cv always. So, this is positive M square is positive. So, denominator is positive. So, numerator is dictating the sign. So, if M is greater than 1 dA by A positive means dM by M positive and if M is less than 1 dA by A negative means dM by M positive. So, whatever statements we made in terms of dU by U similar logic holds for dM by M and hence these plots you can verify the natures of these plots. Now, the other consideration regarding these types of flows is the achievement of a sonic condition. So, we have given some emphasis on that and we have seen that if the sonic condition at all has to be achieved that is achieved at a location where dA by A is equal to 0. Although at dA by A equal to 0 sonic condition need not necessarily be achieved, but if it is achieved at all it is achieved there. Now, when the sonic condition is achieved these sonic states this is usually given by a quantity star in the description of the flow. So, this is just symbolic way of representing. So, if at a state sonic condition is achieved let us say the corresponding velocity is U.  These star quantities are important because these are some important reference quantities. Remember that there may be cases when no sonic condition is achieved at all look at these examples either the top curve or the bottom curve sonic condition is achieved nowhere in the flow.  For example, A star is what? A star is at a given condition what could be an area at which a sonic condition would have been achieved not that that area is physically there in the flow. So, for corresponding to each state there is a corresponding start quantity and if you see tables of properties of compressible flows these start properties are there. So, these are very important reference quantities not that these values have to exist in the particular flow condition but these are reference quantities with respect to which other quantities may be expressed. For example, if you have say a condition where this sonic state is achieved then you may write rho A v or rho A u is equal to rho star A star U star. So, this is a hypothetical condition if the sonic state is achieved it may be achieved in reality may not be achieved in reality but if it were achieved then still it should satisfy the mass conservation. So, you may write as A by A star as rho star by rho into U star by U. Remember that U is equal to m into square root of gamma RT right for an isentropic flow.  So, when you write star that means the Mach number at that state is 1. So, this may be written as rho star by rho into U star by U is root over T star by T into 1 by m right. How you can write T star by T? We may use the stagnation properties and we may use the reference with respect to the stagnation properties. Remember we had T 0 by T is equal to 1 plus gamma minus 1 by 2 m square we just now derive this. If it is a stagnation property remember that when it is an isentropic flow the stagnation property does not change. Why? For example, the stagnation temperature does not change for an isentropic flow. Why it does not change for an isentropic flow? See consider the energy equation h plus U square by 2 this is a constant and this is equal to h 0. So, whatever may be if h varies U also varies in such a way that sum of these is equal to a constant and therefore, h 0 is a constant h is like C p into T for a perfect gas and that is why T 0 remains a constant. In fact, it is not necessary that it has to be isentropic just for adiabatic flow T 0 is a constant because reversible condition is never used here. But when you use this relationship it uses the isentropic condition also because it uses p by rho to the power gamma equal to constant for the sonic speed derivation from which this expression comes. So, T 0 equal to constant that means you can write T 0 by T star as what? What is T 0 by T star? 1 plus gamma minus 1 by 2 that is gamma plus 1 by 2. So, you can write T star by T by dividing these two expressions. So, T star by T is 1 plus gamma minus 1 by 2 m square by gamma plus 1 by 2. Also, we know that T by rho to the power gamma minus 1 is equal to constant for an isentropic flow. So, you can write T by rho to the power gamma minus 1 is equal to T star by rho star to the power gamma minus 1. So, rho star by rho is equal to T star by T to the power 1 by gamma minus 1. So, a by a star. So, you have T star by T to the power 1 by gamma minus 1 into T star by T to the power half. So, T star by T to the power half plus gamma minus 1. So, half plus sorry 1 by gamma minus 1. So, gamma plus 1 by gamma minus 1. So, this is T star by T to the power of gamma plus 1 by gamma minus 1 1 by m. That means, you have a by a star sorry one half is there to the power gamma plus 1 by 2 into gamma minus 1 this into 1 by m right. So, what it tells is that given a value of m you can get one a by a star. Looking from the other angle given one a by a star you could have some value of m, but it is not a unique value of m. You could have multiple values of m that is very clear from this because it is an equation having multiple roots. So, it will have basically two acceptable values of m and if you look into the tables of properties of compressible flows usually these quantities are referenced. So, you have for each Mach number certain important properties are given. So, if you look into isentropic flow tables which in the next class we will look more carefully. So, if you have the isentropic flow important properties what are the important properties? So, for each Mach number you can have p by p0, t by t0, rho by rho 0 and a by a star. It is important to tabulate this because if you know the Mach number you can calculate all others, but if it is a reverse problem that is if you know a by a star calculate what is the Mach number all those multiple roots you may have to solve non-linear equations, but if you have a tabulated set of data you can just read from the table and that is why the compressible flow tables are there with every chapter every book in the chapters of compressible flows the corresponding there will be an appendix where these properties are there. So, these properties will relate everything with a reference star the reference is either the stagnation state or the sonic. Important thing is that the stagnation state is the same so long as it is isentropic flow. If the isentropic nature of the flow is disturbed then the stagnation property changes that means t0 is same so long as it is isentropic, but if the isentropic nature is changed it is if it is no more isentropic then the stagnation properties change and one of the important mechanisms that can create such abrupt change in stagnation property is a shock is the presence of a shock wave. So, in our next class we will see that how these properties get changed when you have an abrupt discontinuity in a compressible flow medium present in the form of a shock wave. So, that we will take up in the next class. Thank you.


Hi, welcome to my talk on super-efficient entropy accumulation. My name is Jie Xie. I'm a first-year PhD student in New York University Shanghai, and this is a joint work I did with Yvgeny Dodes, C.L. Guo, Noah Stevens, David DeWitts. Our work studies real-world random number generators. In 2019, Microsoft published the white paper of Windows 10's random number generation infrastructure. In their design, two steps are needed in order to get random bits. The first step is entropy accumulation. Multiple low-entropy sources are gathered together to form high-entropy states. Then, in the second step called randomness extraction, those high-entropy states are sent to a cryptographic hash function to generate random bits. In our work, we have modeled the entropy accumulation procedure of real-world random number generators and built the theoretical foundations for it. Prior to our work, entropy accumulation was often modeled by iterated harshing with that cryptographic hash function. However, this is not realistic in the context of real-world random number generators because many practical entropy sources, such as interrupted timings, come at a very rapid pace but with relatively low entropy, for example. So, running a cryptographic hash function every time we receive an input is too expensive to use. We would like to know what is the best way to design extremely fast and practical entropy accumulation procedures to accumulate entropy as fast as possible. To answer this question is helpful to see what is typically done in practice. Windows time implements the following rotate-dem-xor procedure. For example, in the 32-bit CPU, a register R of 32-bit LAM will be used to accumulate entropy. The entropy source X, such as an interrupted timing, is also a 32-bit string. To update the register R one needs to secretly rotate the bits of R by a fixed rotation number, 5, and then XOR the input X to the result. In total, there will be 32 entropy sources being accumulated into R. Similarly, in the 64-bit CPU, R receives 64 entropy sources and the rotation number is 19. While this design appears reasonable, it raises a lot of questions that I would like to answer. The first question is, can rotation indeed accumulate entropy? In other words, given about rotating the XOR procedure after receiving 32 or 64 samples, we really want to know whether the register R will converge to a high entropy state. If rotation works, then we want to know how Microsoft selected those mysterious rotation numbers alpha. In particular, are Microsoft's choice of rotation numbers 5 for the 32-bit CPU and 19 for the 64-bit CPU reasonable? Finally, is rotation really the best way for entropy accumulation? Can rotation be replaced by a better permutation? To start answering these questions, the first priority is to model input sources. According to the white paper, interrupted timings are the primary entropy sources of Windows time. So, as the first modeling assumption, we will assume interrupted timings are independent. While it might not be entirely accurate in practice, we believe that it somehow captures the feature of interrupted timings which don't appear fully adversarial. Second, to minimize the number of parameters and focus on the high-level picture, we will assume that the entropy of each independent sample is lower bounded by some parameter k. The key point is that our entropy accumulation procedure doesn't know the input source in advance. So, our goal is to find a rotation number alpha whose corresponding entropy accumulation procedure works to the best extent for all possible k. Finally, we will further restrict each sample to come from some family of distributions. In our paper, we have given a country example showing that the rotation of the XOR procedure is too simple to work for arbitrary distributions of entropy k. So, we must choose a proper family of distributions to both include most of the natural distributions and capture the feature of interrupted timings. Notice that the lower order bits of interrupted timings change more rapidly than the higher order bits. So, the intuitive requirement is that these distributions should have most of their entropy in the lower order bits. According to this, we can define a very wide class of distributions which we call two monotone. Two monotone distributions are unbeat distributions such that the probability mass function has at most one peak. This is a large class and it includes discrete gaucho distributions, discrete exponential distributions, and uniform distributions over the first k bits. These three natural distributions are often used to model interrupted timings. The simplest two-month distribution is the uniform distribution over the first k bits, where k-list significant bits are uniformly random and the remaining n-k bits are fixed. It's obvious to see that this distribution has most of its entropy in the lower order bits. Most surprisingly, our MinLama shows that any two-month distribution does in fact have most of its entropy in the lower order bits. To summarize, we will instantiate our family of distributions to be old monotone distributions on n-bits having entropy at least k, and we will allow arbitrary independent but not necessarily identical samples from the family. With entropy sources being modeled properly, now we are prepared to present our results. First of all, since any two-month distribution has most of its entropy in the lower order bits, we can use this property to show that any rotation on n-bits with rotation number alpha co-prime to n can accumulate nearly n-bits of entropy within n-steps. Although we typically think of rotation by one as the worst condenser, our result implies rotation by one can also condense two monotone distributions to linear entropy within n-steps. What's more, this result can immediately generalize to cyclical permutations so that any cyclical permutation can condense to linear entropy within n-steps. The first result justifies the use of rotation, but only if we are willing to wait n-steps. It fails to distinguish between different rotation numbers alpha. One rotation number alpha is one. Even if the input already has a very high entropy, we do need roughly n-steps in order to accumulate nearly n-bits of entropy. So if we wish to do better, we must somehow distinguish between different rotation numbers. To do this, we introduce a simple efficiently computable quantity which we call the covering number. Intuitively, covering number alpha k is the smallest number of samples needed for rotation by alpha to accumulate four entropy from the uniform distribution over the first k-bits. Equivalently, it's like covering a black segment of length n using a shorter red segment of length k. Every time the red segment is cyclically rotated by a constant alpha, the goal is to count how many times are needed for the red segment to cover the intel black segment. In our work, we show that the covering number is the right measurement of samples to accumulate nearly four entropy from any two-month distributions with entropy at least k. We justify this statement by both theoretical proofs and empirical data. To sum it up, our second result suggests comparing rotations according to their covering numbers. It effectively reduces a very difficult problem to a simple calculation. As we have discussed earlier, our rotation then XOR procedure doesn't know the input source in advance. Our goal is to find a rotation number alpha such that the covering number alpha k is relatively small for all possible k. We can use this theory to review Microsoft's choices on rotation numbers. In the next two slides, we will see the covering numbers of different rotations when the length of the register is 32 or 64. In terms of 32-bit CPU, we have selected four different rotation numbers, 5, 7, 9, and 13, and depicted their covering numbers versus k, the mean entropy of sources. The red lines represent the covering numbers of certain rotations while the black line and over k represent the optimal covering numbers. We can see that Microsoft's choice 5 is reasonable since it's very close to the optimal line but it's generally worse than 7. Similarly, in terms of 64-bit CPU, we have also selected four different rotation numbers, 15, 19, 23, and 27. We can see Microsoft's choice 19 performs reasonably well for all k. Our analysis of the covering number of rotations extends immediately to any thick-legged permutation. So can we find a better permutation to replace rotations? The answer is affirmative. We have constructed a permutation that we call bit-reversed rotation, TorN, where n is a power of 2. For example, when n is 8, we can write out the cycle notation of Tor8 in the following way. First, write down 0 to 7 in a cycle notation. Second, convert each integer into a binary string of length 3. Then, reverse the order of this binary strings and convert them back to integers. The resulting cycle is Tor8. Bit-reversed rotation has a very nice property. If k is a power of 2, then the covering number is n over k, which is optimal. So it has optimal covering numbers for all k, which is a power of 2 simultaneously. In this slide, we compare covering numbers of bit-reversed rotation against covering numbers of rotations used by Microsoft and the optimal value on over k. We see that bit-reversed rotation seems to perform at least as well as rotation and better in several regions. So we leave it to practitioners to determine whether implementing our new permutation would be favored in the context of their random number generators. Our study suggests that it seems to be the most natural choice from a theoretical perspective. Now let's move on to the proof session. In this part, I will present our proof techniques, our Milama, and a brief proof sketch to answer why rotation works. Suppose each sample is independently sampled from some two-month distributions of mi-entropy k. After receiving n-sept samples, we denote the distribution of the register as dA. Here, A is rotation by alpha. To see whether dA has linear entropy, we need to compute the mi-entropy of it. However, we can hardly compute the mi-entropy from the probability mass function because the convolutional form is invisible to compute. The Fourier coefficients arise naturally in our setting because they interact nicely with both convolution and linear transformations. So our goal becomes computing the sum of Fourier coefficients of dA. Since entropy sources are independent, each Fourier coefficient of the compound distribution dA can be decomposed into a product of multiple Fourier coefficients of two-month distributions. The Fourier coefficient of a two-month distribution has a very nice feature which is formalized by our Milama. Our Milama says that the absolute value of the Fourier coefficient of any two-month distribution at some vector w is small if the i-speed of w is 1 for some small index i. For example, if d is uniform over the first k bits, as long as the first k bits of w contain 1, its Fourier coefficient is 0. This formally captures the intuition that the lower-order bits of two-month distributions should have high entropy. So we instantiate our Milama by taking i to be 0. This means if the first bit of a vector is 1, then the absolute value of its Fourier coefficient is upper bounded by a small constant. For any vector w, we consider the set of n vectors generated by w and a transpose. We only need to count the number of these vectors whose first bit is 1, and then use the Milama to upper bound their Fourier coefficients. For remaining vectors, we'll use 1 to upper bound their Fourier coefficients. It turns out that if a is rotation by alpha and the alpha is co-prime to n, then the number of vectors among this set whose first bit is 1 is equal to the hammy weights of w. So we can take a summation over hammy weights and easily show the entropy of dA is linear. As a summary of our proof technique, if the first bit of w or the red dot in the illustration is 1, then the absolute value of its Fourier coefficient is upper bounded by 2 to minus k plus 1. Then repeatedly apply a transpose to w and check if the red dot is 1. After n steps, the register accumulates linear entropy. In this case, we use too many ones to upper bound a Fourier coefficient. Can we reduce the number of steps while still having strong condensing? The answer is affirmative. If the first k over 2 bits of w or the red segment in the illustration contain 1, then we instantiate our Milama and see the absolute value of its Fourier coefficient is upper bounded by 2 to minus k over 2. Then repeatedly apply a transpose to w and check if the red segment contains 1. If so, the absolute value of its Fourier coefficient is upper bounded by 2 to minus k over 2. Otherwise, upper bounded by 1. In this case, we only need to carry number alpha k over 2 steps for strong condensing from two monotone distributions. Unfortunately, in our proof, we lose a factor of 2 in k. In fact, we also show that roughly covering number alpha k steps is already enough for very strong condensing by empirical data in the paper. So we believe the factor of two loss is an artifact of the proof. If you reach the end of this talk, I just want to quickly recap what we have seen so far. We justified the use of rotation in Windows times random number generator and proved that the rotations satisfying some number theoretical condition can accumulate the linear entropy within a few steps. In addition, we justified Microsoft's choice of rotation numbers 5 and 19 and introduced the theory of contrary number. Finally, we suggested replacing rotations by b to reverse rotation in the real-world random number generators and gave some empirical data. This one closes my talk. Thanks for listening and bye-bye.


Another form of dating is a dating with sincere intentions for marriage. It's no joke. It's not a game. They're not playing. They're not going to have a fun time going out on a Friday night or a Saturday night to enjoy themselves. No. Number one, their sincere intentions for marriage. This is one. Two, they have the blessings and knowledge of their parents. The parents know that this young man and young woman are going out. They have knowledge and they have their blessings. Two, three, no one's dressed provocatively. No one has a lot of makeup on, heavy makeup or provocative clothing. A lot of skin showing. No. They're respected, dressed properly, good hijab for they go out to a public place. And when I say a public place, I don't mean a bar or a club. No. Somewhere that's respectful, somewhere where others are seeing them, watching them. They're not secluded. They're not sitting privately like an open cafe where people could see them and they sit and they discuss marriage, only marriage with sincere intentions of marriage. And this is another form of dating. Is this Haram who said, who said that this is Haram? That a young man goes out with another young woman with the permission of their parents, with the blessing of their parents, only with the intention of marriage, nothing provocative. They don't go to a place that is provocative and they only talk about plans of getting married to get to know one another for marriage. Who says this is Haram? Who says that there are Fetwas that say this is Haram and that they should not do this? In fact, if we read certain narrations, they say, they don't say that go out and date. But from these narrations, you can understand that if a young man and a young woman go out on this kind of date, if you want to call it a date, it's fine. For example, If a person comes to you and you're satisfied with their faith and their well, how do you get to know a person's faith and just by saying them at home or at a Majlis and that say you discover that person's faith and that person's Akhlaq, no, you have to get to know the person. You have to get to know them, whether at home or going on a date like this in the circumstances that I describe, and you get to know that person's Akhlaq. Are they angry? Do they have patience? Are they stuck up? Are they arrogant? Are they humble? Are they religious? You get to know them. You get to know their faith and their Akhlaq. From this sort of hadith, we discover that getting to know the person from a date like this is fine. Another hadith says, اختاروا لنطفكم فأن العرقات الساس choose wisely your children. How do you choose your children? By choosing the spouse? By choosing the right father? By choosing the right mother? Well, how do you choose the right mother and the right father? Just like just by looking at them or looking at a picture or from your mother telling you, no, by going out, by sitting without having pressure, getting to know them in an unprovoked matter without crossing the border lines, getting to know them. People discover that does this person make a good father or a good mother? There are other narrations that say to men, choose a smart wife. Choose a smart wife. How do you know she's smart? Don't you have to get to know her? Some narrations say choose a good looking wife. Yes, looks are important. No one tells you do not marry someone unattractive. No, in Islam, you should marry someone that is attractive. Attraction is a must. Yes, it doesn't have to be at the top of your priorities, but there should be attraction. How do you know these qualities? You have to get to know the person. So this form of date going to a place unprovokedly, being well-dressed, hijab is preserved, the blessings of the parents with the knowledge of the parents, the permission of the parents without going to a place that is secluded somewhere in public to discuss marriage and only marriage with sincere intentions of marriage, who says this is haram? However, you have to make sure that you don't cross the boundaries. You don't cross the limits. You don't cross the red lines. Salah ala Muhammad wa ala Muhammad. You know, this sort of date should be considered like an interview, like a job interview.  Have you ever been interrogated? The date should be like this. It should be a two-way interview. For example, you ask a lot of questions. You ask for a reference. Who knows you? Who says that you're a good person? Ask for a reference. Something like a letter of recommendation. Ask for a reference. You ask about that person's background and their history. What have you done? Have you been in previous relationships? Were you ever divorced? What happened? Why did you get a divorce? Ask. Such questions. What are your plans for the future? What would you like to do in the future? These are important questions and it's very important to ask the right questions and not silly questions. You know, I see a lot of young people when they're getting married, when they want to know the other person, they ask the silliest questions. What's your favorite movie? What's your favorite movie? Obviously, they're going to tell you Titanic. What's your favorite color?  You want to marry someone based upon what's their favorite color?   Of course they're going to tell you whatever you serve me and so on and so forth. These are silly questions. These are not the right questions to ask someone that you want to share the list of your life with. Ask the right questions. The questions that matter the most, right? Ask questions that will make it or break it, right? Ask hypothetical questions. Like for example, a young lady should ask the young man, you know, what would you do if I took off my hijab? Would you allow me to take off my hijab? Or would you divorce me? What is it that you do? Or the young man should ask a hypothetical question like, you know, what would you do if I changed my job and I started to own a liquor store? Or if I stopped praying? Or you know, these are the important questions to ask. And this is how you discover, does this person make a good father? Does this person make a good mother? It's a job interview. It's an interrogation.  We'll talk about Muhammad and Ali Muhammad.


We were over three-quarters of the way through the boys' hockey season, and if it wasn't fun already, things are starting to get really fun. Section 8-2A is no different. And tonight, we had a big section matchup between Bemidji and Rozo. The Rams knocked off the Jacks 3-2 back in December. Second period, no score. Rams with a great scoring chance. Bryant's toss cup feeds Alex Verbalt, but gets denied by Matt Fitzgerald at the net with the great save. Then the Jacks would take control from there. Alex misses the first shot, but then cleans up his own miss. Jacks go up one. Then later in the period on the power play, Chase Harchie drives the slap shot home to put the Jacks up two. They would add one more in the period. courtesy of Leo Spry, go up three-nothing after two. They would win tonight by a final of four to nothing. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


Good afternoon. On behalf of the McLean Center for Clinical and Medical Ethics and the University of Chicago Trauma Center, I welcome you to the 17th lecture in our 2017-2018 lecture series on ethical issues in violence, trauma, and trauma surgery. It is indeed my pleasure to introduce today's speaker, who is also a trauma surgeon and friend, Dr. Manta Swarub, who I met pretty much upon arrival to Chicago over 13 months ago. Dr. Swarub is an associate professor of surgery at Northwestern University, the Feinberg School of Medicine. He's also the program director of the Global Surgery Fellowship in the Division of Trauma and Critical Care at Northwestern and an attending surgeon at Northwestern Memorial Hospital. Dr. Swarub attended medical school at the University of Texas at Houston, where her mom still lives, and continued her training in general surgery at Washington Hospital Center in DC and at the University of South Florida. She then completed a critical care fellowship that brought her here to the City of Chicago at Northwestern and has been trapped in the orbit of Chicago ever since. She's a fellow of the American College of Surgeons as well as the International College of Surgeons and a founding member of the Board of Governors of the Academic College of Academic International Medicine. Dr. Swarub has won multiple procedures awards for her outstanding teaching and was also recently featured in Oprah O' Magazine. Dr. Swarub has developed the Northwestern Trauma and Surgical Initiative, an international program involving residents, medical students, and multidisciplinary fellows of which two are here, that aim to improve trauma surgical care in low and middle income countries throughout the world and in low income settings. More recently, she has also developed an important initiative on the South Side, the Chicago Trauma First Responders Course in collaboration with Ceasefire Chicago, which is an attempt to empower community providers and community members in the art of tourniquet and bleeding control. This course intended to teach community and layperson first responders simple skills to arrest bleeding with items found at the site of traumatic injury. You'll hear more about this and other initiatives largely around the concept of empowerment and ethical dilemma. Please join me in welcoming Dr. Swarub. Thank you guys so much. Thank you, Dr. Rogers, for that wonderful introduction. And I'd like to thank the McLean Center for Clinical Ethics for inviting me to give you all a talk on this series. My talk is actually on ethical dilemma of empowerment in the creation of a trauma care system. And although it may seem strange because how can there be a dilemma when you're trying to become stronger and more confident, especially in controlling one's life, how there's a dilemma in that. But there is, because with empowerment comes expectation. So I have no disclosures that are relevant to this presentation. But before we start, I want us to play a game.  Seriously. Your job is to get your arm down as many times as possible in 30 seconds. Ready? Go. All right. Good. So who got more than one? More than 10? Awesome. You guys got 55. So what was the key to this? What was key to success, someone? What was key to success, Dr. Siegler? Okay. And how about those of you who weren't able to get the other person's arm down? What was the issue there? All right. Well, in theory, if we work against one another, all right, then we're not going to achieve what we need to achieve. If we are working together, let's say Selwyn and I are playing this game, then we will have an optimum assessment of what our goals are and we'll both be able to achieve our goals. So this becomes important when we look at a box and a cone. All right. Let's say Selwyn is only able to look through P poll A. What do you guys think he's going to see? A triangle. Now let's say I'm only allowed to look through P poll B. I'm going to see a circle. Without the realization of what's being seen, we can't actually realize what's inside of the box, the actual object. If we don't take into consideration each other's perspective, we will never realize what is the truth. And so as we're planning any intervention, we must work together as a team. Otherwise, we all suffer. So to empower any one particular mouse may actually be very detrimental to all of the parties involved. And in our conversation today in ethics and trauma care, the ones who will suffer in this case would be our patients. So a brief journey. Here's an outline of our journey. A brief evaluation on the burden of trauma. Then we'll discuss empowerment and then how it relates to the global burden of trauma. First in first responders training and then in actual trauma systems development. And then how a bidirectional approach keeps us all out of the mousetrap. Before we actually evaluate the burden of trauma, I think it's important to delineate what's actually meant by trauma. So the word injury is oftentimes used in place of the word trauma. And injury is usually caused by something, some kind of massive force. Okay. And it can be intentional or unintentional. But when we think about what trauma actually is, it can include the above. It can include the actual injury to the self. But it also includes the mental health issues. And it is comprehensively involves trauma systems and care pre-hospital in hospital and after hospital. The trauma burden by definition is actually injury burden, right? Because we don't actually define what the mental health aspects of what we are looking at. So in 2013 globally, there were 4.8 million deaths of unintentional and intentional injury worldwide. And approximately 10% of the global burden of disease. What's interesting is that more than 90% of all of these injury related deaths occur in low and middle income countries. Now, I'm a very simple surgeon. So I like things delineated clearly, pictorially. So if you think about death from injury, it's almost 6 million people with another 30 million people disabled. Versus AIDS, malaria, and tuberculosis combined. And this is only going to get worse. If we look at years of life lost, okay, in the 1990s, this includes high income countries and low income countries. Road traffic incidents were only the ninth most common cause of death. And as industrialization has happened and the economies of low and middle income countries have improved, it's predicted that in 2020, road traffic incidences will be number three in the causes of death. So now what? How do we lessen this burden? How do we make this better for our patients? How do we improve outcomes and improve access to trauma care? Well, going back to our cube, we want to be able to see the comb. We want to be able to use the correct tools for the job by knowing all the different perspectives, by taking into account and gaining the buy-in from the screws, from the nails, from the hammer, and from the wrench. So how do we do this in a group, in a country? How do we make sure we're in sync with one another? Yes, the dilemma. So first, to engage in this conversation about the ethical dilemma, let's talk about empowerment. Empowerment for an individual refers to a process where an individual understands the process and results of an action and the ability to exert influence and control over that action. In a community, we strengthen experiences and proficiency. We strengthen the actual community framework and capacity. We remove barriers and we strengthen assets and resources. And with our goal in community empowerment, we are trying to reach equality and health promotion. But as you can see, strengthening individuals' communities is only a part of health promotion. So how do we achieve that? And ideal development can only happen when the interests of all of the stakeholders and beneficiaries align. So the screws, the wrenches, the hammers, the nails. And here is where we have a problem. How does one engage and assure that each stakeholder and beneficiary knows that the goals that we set will actually come to fruition? These aspirations are based upon ideals that are based upon mutual acquiescence. How can one promise an empowered community of better outcomes if they are involved in a road traffic incident without improving the environment or writing legislation to ensure that trauma care actually exists? As one develops ideas and thinks through how to develop and implement a trauma system to create a sustainable and contextualized solution, we must work from both directions. Our team at Northwestern Trauma Surgical Initiative realized the importance of working both ways up, from the top down and from the bottom up. Involving citizens in trauma management in a grassroots fashion encompasses the first two steps of empowerment. Developing this trauma system applies to the third and fourth. We propose a systemic way of approaching this dilemma from the bottom up via a first responders training course and from a top down by establishment of a trauma care system. And the synergistic benefit from this bi-directional approach reaches health equity, not equality. And this is a very important and definite difference that we need to be more precise. So our first intervention that we discuss is our first responders training. But first and foremost, will it actually even help to empower lay first responders? Is there a need for it? Is there a desire for it? So there's evidence that very simple things and empowering people at the lay first responder level can actually make a difference in people's lives. Even in complex medical systems, empowering lay people is very important. There is scant evidence that shows that advanced and costly approaches to emergency medical services actually improves outcomes. And in low and middle income countries, first responders may be the only or first tier of emergency responders in resource limited settings in high income countries, sorry. And when I say resource limited, I mean those who are disenfranchised, those who may not have a trauma center nearby, those who may due to economic variables be overburdened, and those communities that are indeed overburdened by high violent level of crime, or even communities that feel socially disempowered. And as per the Hartford consensus, which came out in September of 2015, it can be the difference between life and death. And they can turn bystanders into immediate responders, and we can prevent exsanguination. Having presence and participation of community members allows each individual to take on a role as both a provider and a beneficiary. In addition, the first responder can be a valuable resource and an active investigator in injury surveillance. As a person is in direct contact with those involved in the incident, first responders can provide and collect data in regards to prevention initiatives in the future. So involving community members in trauma care transforms passivity into active ownership of healthcare and allows the ability to control in a situation that is normally chaotic. Empowering individual members and eventually the community is a fundamental step in mobilizing society towards health equity. Empowering those at risk to participate in and care for and help save individual lives may actually keep them from taking a life. However, this approach alone cannot tackle the issue of trauma care, where the system has not even begun to catch up with what's actually going on. Without hospitals in the vicinity of a community or the modality of transportation to the hospital, the efforts of bystanders are hopeless. So we develop systems of care from the top down. And a trauma system we know consists of pre-hospital, hospital, and post-hospital care. And broken down further, there are even more arms that need to be developed. And extrapolating U.S. data for low and middle income countries, we know that in states that have trauma systems, there's actually a 9% less mortality rate compared to those without. We also know that the risk of death is significantly lower when patients are provided care in a trauma center. The value of a trauma center is cost effective, as resources are allocated based upon what is actually treated at the hospital. So combined with the recognition of trauma as a major burden in low and middle income countries and the success of utilizing trauma systems in high income countries, the World Health Organization and the International Association for the Surgery of Trauma and Surgical Intensive Care spearheaded the development of essential trauma care project. It was launched in 2004 and certain low and middle income countries such as India, Vietnam, Ghana, Sri Lanka, Botswana, and Mexico participated. The evaluations determined that basic resources and training were what was most critically needed at the level of the district or primary hospitals, which reached the highest volumes of trauma. Essential services are those that are high yield but low cost and which realistically could be assured to almost everyone in a given population. There is often a misperception that improvements in trauma care would be expensive and inappropriate in low and middle income countries. However, disease control priorities project has shown that several interventions that need to be promoted to improve trauma care are among the most cost effective in a healthcare armamentarium. So the goals, what were the goals of the essential trauma care? They were to identify and promote inexpensive ways of reinforcing trauma treatment worldwide. They wanted to work within the system of the actual low and middle income country and use all of the stakeholders at play because you can't implement a high income country system in LMICs. It doesn't work. It's very important to engage the stakeholders to train pre-hospital trauma providers and hospital based trauma providers and develop a trauma registry to evaluate how we make change. However, this too, this top down approach is not sustainable model by itself. Without proper trust of the community and buy-in into the system, the system is inoperable. So a bi-directional approach must be taken. And the things that we look at for a successful trauma system are systems based needs assessment to start off to evaluate the system and then coordination of all different branches. We then develop targeted corrective action and develop an appropriate model. The Northwestern trauma and surgical initiative aims to improve access to surgery and trauma care through education and research to low resource areas. NTSI implemented a trauma first responders training course in Chicago, first by performing a thorough needs assessment with focus groups and then we constantly elicit feedback and change the course as is needed. The course was founded in response to the high death toll that was seen from gun violence at Northwestern, even though there are six level one trauma centers in the Chicago city limits. Since its inception in January 2017, the instructors have trained more than 340 community members. The course focuses on pre-hospital care and pre-ambulance care in resource limited settings. Participants have shown that they actually feel more empowered even at six months after being given the course. And these efforts are not without saying that a trauma system does not need to be in place. And it's guided under that assumption that patients will eventually be transported to a level one trauma center where they will receive appropriate care. So NTSI also attempted the implementation of a trauma first responder course in Santa Cruz de la Sierra Bolivia with the same goal to reduce pre-hospital mortality. But it soon became evident that other than failing miserably, we had people who were very interested in becoming trauma informed and to receive training. But there wasn't any semblance of a trauma system to receive these potential patients. So even though tourniquet application may stabilize a bleeding patient at the scene, it won't save a patient's life eventually if there is no way to get to the hospital. Since then, we've redirected our efforts towards writing legislation to implement programmatic development that focuses on education. For example, ATLS, Advanced Trauma Life Support. The pass rate was almost 10%. It's about it. And we implemented a ATLS preparatory course which allowed our participants to actually improve the outcomes of passing the course and becoming ATLS certified. We're also working on a central dispatch system and an emergency medical technician training program that is to include first responders, chauffeurs, and emergency medical providers. There is no one size fits all approach in the trauma system development world in low and middle income countries. And this is even more important and more evident when you strain to put a high income country model into an LMIC. So in order to minimize the likelihood of a true ethical dilemma and a failure of a system, educational initiatives, public announcement of initiatives by all stakeholders should be ongoing. And there should be transparency in the work so as to build trust between parties and facilitate information transfer and assure the identification of the cone in the box. Thank you. Thank you for that expansive review both local and world, especially in Bolivia. And I want to explore a little bit more around the genesis of Bolivia and the pivot towards advocacy. Because in the space of advocacy, it's almost like in at least in medical school, I'm going to go from medical school perspective, it's something that gets beaten out of us. Some of us actually come with a strong advocacy bent and that somehow through all of the biomedical training that we do, we lose that. And I see some medical students in the room who may or may not agree. But if you can share a little bit about that transition realizing that you could transfer some of the knowledge around tourniquets and temporary hemorrhage control, but realizing that there was this big gap on the trauma system side. So as we started teaching in La Paz, it was a very interesting, that's the first place that we taught. And what we noticed was that there was no language that was spoken that was similar even amongst the hospital providers.  Because even I don't remember some of these things. Even when I take care of some trauma patients, I won't put a C collar on them. And I was a little bit devastated at that moment in time. But those things kind of build up in your mind about what is actually lacking. And it's not because people don't want to take care of people well. It's because they don't know. And not knowing is not, you know, is not their fault per say. Does that make sense? You know. And so as we empowered people, we noticed that, you know, the community was very receptive. But these patients would arrive to the hospital and they wouldn't have anybody to care for them. So in the Yungas jungle, it's an eight-hour roundtrip basically from the hospital, the nearest level one trauma center there. And these patients would come with their, you know, let's say they did get their pelvis is bound. What then? What would actually happen to them? So without actually, you know, stepping up the system and laying the foundation properly at the hospital level, we didn't feel that it would be appropriate to go into the community and start working there first. So that's how the, you know, the angle changed. We were lucky enough that we had contacts into the government.  This is his second year there. He was actually able to garner a seat in government. And so he created, he actually created a sector that deals just with trauma care.  And as we are, you know, getting to the point where we're going to start the paramedic school, the paramedic school is modular so that it can be, it can be, you know, simplified for a layperson as well as, you know, complex so that if physicians wanted to take the course, they could as well. I'm going to open up the floor at the stage. There are questions. Mention was made of ceasefire and project on the south side. Could you say something about that? Sure. So as we were developing the idea of having a course in the community, we knew that we would need strong community-based partners. Northwestern has had a relationship with ceasefire since 2009. And as we went forward and, you know, thinking about it, we thought that it would be an appropriate combination to work with ceasefire Chicago. And so what we've done is ceasefire has helped us with validity. So if I have a patient who comes in and tells me how exactly I should do an operation, that usually doesn't work out really well. So what ceasefire has done for us is actually allowed us to have some validity to access patients that we normally wouldn't be able to access. And so we've been able to be in communities that normally would never have the opportunity to either come to Northwestern and take the course or be, you know, around medical professionals that, you know, might be able to give them more access to healthcare.  Does that also apply to, like, the community? Like, when you empower people on a community level, like, what the expectations then look like for them? It's a great question. I think that it's really interesting to see, and so I'm going to refer back to some work that I did in Bangladesh. So there is a group called, or there is a group called Operation Smile, right? Op Smile. So Operation Smile has a group out of it called, there are the special courses in trauma care. And so we did first responder courses in Cambodia and in Bangladesh. And in Bangladesh, we partnered again with a community of young activists. So when we were teaching, we had to, you know, bridge this barrier that was, you know, in a very predominantly Muslim country, you know, men and women touching one another if there was an accident that happened. And in low and middle income countries, like, when I've been in India, my mother, like, will not let me go anywhere near an accident when it happens. Because of all of the different things that are, you know, you can be implicated in the accident itself. You can then be taken to the police station. There's so many different things. So as we broke that barrier, right? And, you know, since then, Critical Link has started in Bangladesh, which is a mobile application that, you know, takes care of the first responders that are in the area. And the community's expectations have increased because of that. Because now, if there is a incident that occurs, the community knows that there's a group of first responders out there who are notified based on location. So I think both ways there is expectation that occurs. I know you mentioned, like, men touching women and women touching men and, you know, whatever gender identified in certain places. I'm also wondering specifically because Chicago has so much gang violence and so much like segregation between different communities. How did you overcome that barrier? And also, how did you choose who would become a, like, first responder in Chicago? Was it self-selecting? Do you do it by geographic area? Great questions. So for me, it started off as a, this is a journey of passion, okay? So seeing my patients dying in my trauma bay made me focus on the community that is served by Northwestern. So that's how we started, okay? We talked to Ceasefire, first and foremost, after we did our focus groups with different communities throughout the South Side of Chicago, and then talked to them about who would be the most powerful to be play first responders, as well as during our focus groups we asked who would be interested in learning this kind of information. And what we found was that, you know, the violence interrupters were very interested. We're doing a big teaching in a couple of weeks with Ceasefire. We also found that, you know, people who go to the church and are in the community, not an active part of street organizations, but are affected by street organizations, wanted to learn this information. So a lot of times, the way that we run the courses, we have organizations that can contact us, churches, Ceasefire, et cetera, urban youth outreach, all sorts of different organizations that reach out to us to say, hey, can you do a training for us? And then we have open trainings, so social media, right? So we post them on Facebook, we tweet them out, and that's how people come and take the class itself. I'm sorry? Yes, sir. Urban youth outreach has in Inglewood. We've been teaching at six different schools. So we've taught at Dunbar Vocational School, at the Peace Center in Doulton. We've taught at Crane Medical Preparatory School. I've taught all the football players at Julian High School, which was very interesting class. And we've taught just community members who've been parts of different organizations. So we've taught also on the West Side. So the course has been taught in Spanish and in English, obviously in English, but also in Spanish. And we're actually creating a team so that we can target specifically to have more access to people who are Spanish-speaking only. Sure. So for the actual patient, there's the Good Samaritan law that protects the person. What is the law in regards to the first responder getting hurt? Well, there's no law specifically that addresses a first responder getting injured, but right. So no, if you're not a medical person and you're trying to help and do the best of your abilities and not actively trying to hurt somebody at the scene, there's no repercussions. Illinois has a really great Good Samaritan law. You've left people without any questions, although there's a follow-up question. I was just asking about the emotional impact of trauma and how much a physical injury can either be a physical injury or a long-term issue of PTSD. How do you train people in that? Sure. So it's not perfect, right? However, we do address emotions, self-emotions. You're, you know, being able to deal with your own emotions and also dealing with emotions at the scene and how you deal with conflict. Like by giving other people jobs, by calming the situation, using a calm voice, not, you know, escalating a situation. We also even address, you know, taking photography and how there's actually no need to take photography after an incident has happened. However, not to get into a verbal conflict again with an individual if that individual is trying to, you know, film the situation and doesn't put their phone away or doesn't do a job like calling 911 since they have their phone out. So we also, okay, so I also carry a phone that I give the phone number with a key chain to everybody so that if they use their skills, they can call me, right? And in addition to that, if they need to debrief about the situation, they can call me. And the third part of that is having resources. So Brightstar has just started having a hotline for mental health services a few times a week. And so I've given patient or I've given people that particular phone number because it's very jarring when you hear, you know, these stories that these kids tell you. So you mentioned a couple of religious organizations that have been helpful or sort of in the circuit with you. Have you run into any religious institutions, traditions that have been a hindrance to your work? Not as yet. Okay. I can't say, I can't say that in the future that I won't come across somebody religiously that would be a hindrance, but as of yet, no one has hindered the work we're trying to do.  So thank you. So like we're talking about training people at the point that violence has already occurred. So is there something apart of this process that you can use the experiences to kind of systematically go back and understand why the violence is happening and like not just in a, you know, oh, we started to understand it because we've been a part of this, but like, I don't know, not turning it into research, but just like some form of knowledge gaining that we're getting from the process. So we're going back and evaluating the people that we taught last year in the actual, you know, calendar year to evaluate how they've used and what violent situations they've actually seen, et cetera. But, you know, more to your question, I feel, you know, yeah, this has already happened now. Trauma has already happened. Violence has already happened. Whatever has already happened. The incident has happened. But these kids, we started a club, a true communities club, because we changed the name of the course. We call it trauma responders unify to empower communities. True communities is the name of the course now. And we started a club at one of the high schools called the True Communities Club. And these kids are advocates in their community. So it may, it's not trying to figure out why the violence has happened, but hearing their stories and then seeing their desire to be advocates into the community and advocating for their community, it'll be amazing to see how this process, where this process leads to. When we were teaching at the Peace Center in Dalton, one of the kids asked one of my fellows about becoming a neurosurgeon and just a simple like, you think I could actually do that? You know, having access to people who can show a different side of the world is a totally different experience for a lot of people. I'm fascinated by this model of community involvement, you know, really getting out there in the neighborhoods and involving lay people. And I wonder if you've thought at all about expanding that beyond trauma care. No, not yet. We've been working fairly vigorously and tirelessly in getting this training out there. And we've been partnering, we're just started conversations with some people who do psychologic, you know, the psychologic aspect of how to deal with trauma and bringing that training maybe to the teachers and to others. In Dalton, as far as we've expanded, we did a three-tiered type of system. So all of the teachers, we taught them the American College of Surgeons Stop the Bleed course. We then taught the curriculum of true communities, which includes making makeshift tourniquets and dealing with the airway over a five-day period. And then the third part and the fourth part of that is actually holding a session for community members where they learned how to place combat application tourniquets and make makeshift tourniquets.  And we created these makeshift kits. So that's as far as we've expanded so far outside of the actual teaching of community members. But we're working on it. If you have any ideas, let me know. Well, I was just thinking that there's so many other areas of medicine that could benefit from that.  To harness that for medical good would be amazing. There's actually an organization that teaches diabetes and hypertension management to high school students. And I believe the program or the, they're in 10 schools right now. I can't remember the name of the organization, but I could look it up for you and let you know. But there are people who are working on different aspects of it. So the example that you gave with the top down bottom up approach in Bolivia, I believe, and kind of strengthening the infrastructure of the trauma systems, I really liked. And I wondered how you think about that here in a place like Chicago where a top down approach might include things like advocating for gun violence prevention and changing the law or changing kind of policy and how you balance like how much to put it in that pot versus kind of a bottom up approach of teaching people how to respond to something once it's happened. Sure. So the only way that I know how to do things is by getting in it, right? So if you are trying to work on a top down approach or a bottom up approach, just do it and to actually be in it. So I think that part of what I've tried to do personally is get involved with the Illinois Department of Public Health and the Chicago Department of Public Health. And so as those connections are being made and joining committees and trying to be a part of the knowledge and community committee so that we can bring more awareness to this. And as well as advocating for gun, I mean for, not for gun violence, against gun violence and against gun laws. So I think that you know personally we definitely you know do that but I don't specifically you know and tell my students and residents to you know go to certain locations or it's I'll tell them if there's like we're holding a march on March 14th at Northwestern a walkout and so you know we'll tell everybody about that but I don't particularly put any pressure on anybody to attend such things. I wanted to thank you so much for coming the long distance of eight miles from Northwestern. I'm ensuring your perspectives and I look forward to ongoing partnerships and as we see how our joint work evolves. But thank you.