My name is Dr. Ahmada Ombran. I am a staff cardiologist in the Department of Anesthesia and Pain Management, Toronto General Hospital, UHN University of Toronto. And this is a lecture about echocardiographic assessment of prosthetic valves. This lecture is for cardiac anesthesia fellows. In this lecture, I'm going to use a couple of guidelines by American Society of Echo and Society of Cardiac Anesthesia. The first guideline was published in 2009. Recommendation for evaluation of prosthetic valves is echocardiography and Doppler ultrasound. This is a little bit old guideline for assessment of prosthetic valves, but nothing changed compared to that time. And this is a 2020 guideline again by American Society of Echo and Society of Cardiovascular Anesthesia. This is a guideline for the use of chances of facial echocardiography to assist with surgical decision-making in the operating room. This is mainly a guideline about the decision-making in the OR. And the last guideline, that's a 2020 guideline, American College of Cardiology and American Heart Association guideline for the management of patients with valve or heart disease. The first valve replacement surgery was done in 1962. That was after the time that cardiopulmonary bypass pump was invented. That was 1952. Approximately 90,000 valve substitutes are now implanted in the U.S., so in Canada it would be about 9000, and 280,000 worldwide each year. Despite the market improvement in prosthetic valve design and surgical procedures over the past decades, valve replacement does not provide a definite cure to the patient. Instead, native valve disease is traded for prosthetic valve disease. So we are changing one disease to another disease. Outcome of patients undergoing valve replacement is affected by prosthetic valve hemodynamics, durability, and thrombogenicity. Many of the prosthesis-related complications can be prevented or their impact minimized through optimal prosthesis selection in the individual patient and careful medical management follow-up after the implantation. Ecocardiography plays a major role in follow-up of these patients. The type of prosthetic heart valves we have several times type of the valves, and I'm talking about most of the valves that we are using in North America. The biologic valve can be extended. It's a porcine xenograft, pericardial xenograft, a stentless valve, porcine xenograft, pericardial xenograft, a homograft or allograft, autograft, and percutonous valves that are coming and coming. Mechanical valve, biliflet valve that is more common, single-tilted disc valve that was popular in 1980 and after. Now we don't use it usually. And caged ball valve or a started valve valve, that was probably the first successful mechanical valve that was invented. We have to talk about a couple of terminology. Stented valves, when we say stented valves, consist of a radiopec or radionucent base ring or a stent frame covered by a suture cuff from which three stent posts or struts rise to support the valve. A stentless valve used back on close or porcine aortic root as support instead of a stent. Stentless valves provide increased effective orifice area and lower transvalver gradient compared to the stented valves, but their durability is in question. This is an example of the stented valve or magna valve for example. This is swing ring and this is the strut of the valve that supports the leaflet. And the swing ring by the suture will be sued to the annulus of the patient. This is an example of Toronto stentless valve or SPV that was manufactured by St. Jude and this valve was invented by David in Toronto. It was a popular valve in 1990 to almost 2000, but in a long-term run was clear that after seven years or eight years the valve deteriorated now is out of the market. And this is another stentless valve. This is not the valve, it's a root actually, it's a porcine root or freestyle root that is made by Metronik and rarely these days again we use it. When we talk about the xenograft, a tissue graft or organ transplant from a donor of a different species.  Allograft or homograft, a tissue graft from a donor of the same species as the recipient but not genetically identical. Aortic homograft and pulmonary homograft from human cadaver are used for aortic and pulmonary root replacement in cardiac surgery and they still are in use. Autograft, a graft of tissue from one point to another of the same individual's body. In ROS operation for example, pulmonic valve or autograft is taken and replaced the diseased aortic valve of the same person so that is called valve switch or ROS operation. Porcidic valve sizes. Porcidic valve sizes are stated by manufacturer companies are based on outer dimension of the porcidic valves or materials. Porcidic valve size are expressed by odd number like 21, 26, 25 or porcidic ring size, dachron tube, homograft and percutaneous valves are expressed by even number like size 26, 28, 30. These are some of the valves like a ball cage valve or started valve. There is a ball inside the cage. There was a disc and cage as well that is disappeared for a short time. This is a metronic hall tilting disc valve and this is buccially valve. Buccially valve there was a problem in terms of the anchor of the valve and the disc that was broken sometimes but otherwise it was a good valve sometimes. There are mechanical double disc valve. These are the common valve that we are using these days. St. Jude mechanical valve is very popular. Carbon medics mechanical valve and annex valve. Anex valve for aortic and mitral are a different design especially for aortic position. If we use annex mechanical valve we don't use high dose of comedy or we can use other substitutes. Bibocidic porcidic valves, Hancock 2-bibocidic valve that is made by a metronic company. Hancock was first implanted in 1982 by David in Toronto and is very popular valve in our center. Metronic mosaic valve is a porcine valve is a bioprosy valve. This metronic mosaic valve by a one very big methanol study is the best valve for mitral valve replacement. Epic valve in the mitral position has a short strut and if you are worried about the LVUT obstruction after mitral valve replacement because this is short profile we can use it for mitral valve replacement in a patient that there is a risk of LVUT obstruction. Bibocidic bovine pericardial valves again the famous one is Carpentia valve, different type of Carpentia valve. Magna, Magnaese this is a very popular valve in Europe and even in also America. Metronic Avalos valve is a pericardium is made by a metronic company and we use it in our center here. Surin mitral flow was a very good valve sometimes like 5-10 years ago but disappeared from the market because was deteriorating quickly after 2-3 years. Senju trifecta valve again it was a pericardial valve and now is out of the market. So these two valve mitral flow and trifecta are out of the market. These two valve Magna and Avalos we are using now. Socialless Bibocidic valves this is like a competitor for Tavi valves. They don't need sutures so implantation is very fast especially in high risk patient that you want to classical on time be lower less you can use it. It's a self expandable valve first valve is called Perseval made by Surin company doesn't need any suture is a self expandable. It's approved in Europe is not approved in North America. Avalos intuitive valve that's a balloon expandable and need only 3 sutures and metronics 3F enable valve that was popular 5-6 years ago but now is out of the market. One of the problem is this valve is very long and because of the effect of pressure recovery when we do a Doppler gradient across this valve we might overestimate the valve gradient. For example if we call it valve gradient peak 40 or 50 in reality is less than that maybe 30. Percutanus valves or Tavi or Taver valves this is made by metronic companies called core valve and this is by Edward companies called Edward sapien valve and now the generation 3 or sapien series in the market and this is a melodic valve made mainly for pulmonic valve replacement. Aortic and pulmonary homograph these are homographed so these are taken from the cadaver human being aortic homographed is a tube and pulmonary homographed pulmonographed. Now we use it for during the ROS operation for reconstruction of the RVOT aortic homographed is not available very well and rarely we use it. What about anaeroplasty ring there are many rings available now in the market the most famous one is a carpentry ring that is a physio 1 and physio 2 these are rigid or semi-rigid ring. Cosgore of ring is a half a ring and again is a semi-rigid you can call it Cosgore of ring or band is only posterior and this is for tricuspid and this is a simply the band this band was invented by David now is manufactured by metronic company and is not a ring is just a band for anaeroplasty of the mitral and tricuspid. And in our center for mitral valve repair and tricuspid valve repair this is mostly used. There are some other way of repairing the valve like a mitral clip or tricuspid valve clip that is again for a special group of the MR and TR and we should talk about this in a separate lecture. What about criteria to selection the valve so for patient above age 65 we use bioprostic valve so doesn't matter is a mitral aortic position 65 is a cutoff in North America to use the bioprostic valve and 50 is the cutoff for mechanical valve. So below 50 we should put mechanical valve for aorta and for mitral position and above 65 for short bioprostic valve. Between 50 and 65 we make a decision based on the individual and is a shared decision even for all type of valve the decision and preference of the patient is very important. So in a patient above 65 age it is better to use bioprostic valve for aortic and below as I said and in a patient below age 50 who prefer a bioprostic AVR and have appropriate anatomy replacement of the aortic valve by a pulmonic autograph or ROS procedure may be considered. Is it to me and it should be done at the comprehensive valve center or center of excellence for valve replacement like our center and we have many cases now for ROS operation. In European guideline ROS operation is not there also the ROS operation came from UK from Mr. ROS but now is not part of the guideline in European guideline. So this is the algorithm for valve replacement and selection of the valve. What about complications of prosthetic valves? Patient prosthesis mismatch is one of the complications. Geometric mismatch like when we move the pulmonic valve to the aortic position they should match together if it's not matching because of geometric mismatch. The heat sense of the valve is one of the complications usually early the heat sense is because of the technical problem late the heat sense is because of the endocarditis. Primary failure of the valve is sometimes the valve will fail quickly even less than one year especially bioprostic valve. Thrombosis and thrombogenicity it depends on the patient to the host as well. Panus formation usually panus is developed in a long run like more than five years but sometimes you see the panus formation in aortic or mitral very sooner like two or three years we had the case last week for this. Panus in aortic position is more than mitral position. Soda and ariesom formation endocarditis and hemolysis all of this can happen in a patient that had a valve replacement. So for panus especially I want to emphasize that in aortic valve is more than mitral valve. What the generation of the valve in mitral position is more than aorta. Patient prosthesis mismatch what does mean? Patient prosthesis mismatch is present when the effective orifice area of the inserted prosthetic valve is too small in relation to body size. Its main hemodynamic consequences is to generate higher than expected patient's gradients so normally function in prosthetic valve so gradients high but the function of the valve is good. Parameters used to characterize patient prosthesis mismatch is effective orifice area indexed to the patient's body surface area. Patient prosthesis mismatch is considered to be hemodynamically insignificant if the index valve area is more than 0.85 centimeter square per meter square. It's moderate if it's between 85 and 65 and it's severe if it's less than 0.65 centimeter per meter square that is for aortic position. Prevalence of severe patient prosthesis mismatch is about 2 to 11 percent. In aortic position again is more common and in mitral position is less common because in aortic position surgeon has to put the valve in the size of the annulus. In mitral position usually mitral annulus is dilated if somebody has MR so there is not much limitation. This is an example of a patient has a mechanical mitral aortic valve and developed panacea formation and this valve one is extracted. This is a panacea so in aortic position the panacea will develop both sides but more in LVUT side. In mitral position panacea will develop in LA side. So the evaluation of prosthetic aortic valve. Doppler echocardiographic evaluation of prosthetic aortic valve this is based on the guideline of American study of echo that was published in 2009. So Doppler echocardiography of the valve we should measure the peak velocity and the gradient. Main gradient we should look at the contour of the jet velocity and acceleration time and we should use Doppler velocity index. This Doppler velocity index for aortic position used to be called a dimension less index so we call it Doppler velocity index. Effective orifice area, presence, location and severity of the regurgitation and we should look at the chambers as well like LV size function and hypertrophy. This is an example of a normal aortic valve Doppler and obstructed aortic valve Doppler. In normal aortic valve Doppler we see the mean gradient is 22 millimeter mercury Doppler velocity index is 0.4 that is okay and acceleration time is 75 millisecond. Acceleration time is the beginning of the aortic click to the peak of the aortic Doppler. Overall this Doppler of the normal aortic valve doesn't matter is a bio or mechanical is a triangular shape. It means fast going down and this phase triangular. In obstructed valve this Doppler is parabolic is not triangular is a parabolic shape. So acceleration time increased and ejection time increased. So acceleration time in this case is 180 millisecond and mean gradient is 80 millimeter mercury and Doppler velocity index is 0.18 and I will show you the numbers that is normal. So that's a way to calculate the acceleration time and the ratio of acceleration time the direction time that I will show you later. This is how to measure the LVUT to measure the aortic annulus diameter to be used for continuity equation. So we can use the annulus diameter dimension just below the valve at the junction of the valve and the tissue of the symptom or anterior micro leaflet. The Doppler velocity index it means the velocity of the LVUT to the velocity of the jet of the across the aortic valve. So this velocity to this velocity this is not dependent to any other measurement. So it's a very simple one and we call it Doppler velocity index. This is a phenomenon is called pressure recovery. So I would like to talk about this a little bit. What does mean pressure recovery? Look at this tube. This is the LVUT and this is the aorta and here is the valve as a matter of biopsy valve or mechanical valve. So when the flow is here the velocity is not high. Okay. But the pressure is high. When it reached to the close the valve the velocity increase but pressure will drop. So because the pressure and velocity they have an inverse relation. Then after the valve when the flow goes gradually the velocity will decrease and pressure will increase. That's the reason that we call it pressure recovery. It means pressure will recover. Pressure here is very low here recover to the baseline. So it's called pressure recovery. So when we measure the gradient by the Doppler we are measuring the gradient just at the across the valve just here. When we are measuring the gradient by catheter we are measuring gradient between here and here. So the pressure difference between LV and this point by catheter for sure is less than a gradient or pressure difference that we measure at this point. So always Doppler measurement of the gradient is more than cat measurement of the gradient. That is because of the pressure recovery. This pressure recovery happens more if the aorta is narrow and happens less if the aorta is dilated. So if you have a dilated aorta pressure recovery is not happening too much. So it means the cat gradient and Doppler gradient are very similar to each other. But if you have a narrow aorta because of the pressure recovery the Doppler gradient is more than cat gradient. So assume somebody had a aortic valve replacement and replacement of the ACD aorta. If the ACD aorta replacement the Dachron is less than 30 millimeter or 3 centimeter that pressure recovery happens and overestimation of the gradient by Doppler will happen. That is the reason that any time we have a bental operation mechanical valve and Doppler tube when we measure the gradient by Doppler we might overestimate it. So you have to be careful. Sometimes you might get a very high gradient and surgeon might put a catheter here and catheter aorta and say oh there is no gradient. So both of us we are right. We are measuring the gradient at the level of the valve and they are measuring the gradient between LV and the far away from the valve in ACD aorta. This phenomenon of pressure recovery happens when we have a mechanical valve as well but it is more than bioplastic valve because the orifice at the middle has a higher velocity. So we have a higher velocity we have a more pressure recovery. So when we measure the mean gradient peak gradient across the mechanical valve if our cursor line is crossing at the middle orifice or central orifice we might overestimate the gradient. That is the reason that we should put the cursor in a different area and take an average of this gradient. The Doppler parameter of porosity or the valve function in mechanical and extended biopolastic valve if the velocity is less than 3 m per second that is normal more than 4 is civilian stenotic. Mean gradient less than 20 is normal more than 35 is significantly stenotic. Doppler velocity index less than 0.30 is more than 0.30 is normal less than 0.25 is civilian stenotic. Effective orifice area is centimeter squared more than 1.2 is normal less than 0.8 is civilian stenotic in adult patient. Contour of the jet velocity through the prosthetic valve triangular is normal rounded symmetrical or parabolic is abnormal. Acceleration time less than 80 millisecond is normal more than 100 millisecond is significantly obstructed so 80 and 100. Now look at this algorithm sometimes the gradient is high but the valve function is normal. So if we have a velocity more than 3 m per second across the orthic valve doesn't matter by transverse or by T. We take the Doppler velocity index more than 30, 25 to 30 and less than 0.25. If the Doppler velocity is more than 3 and Doppler velocity index is more than 0.30 we look at the jet contour. If the jet contour is parabolic and is more than 100 probably the valve is stenotic. If it's less than 100 valve is not stenotic but the gradient is high because his patient process mismatch or high cardiac output stay. If the Doppler velocity index is less than 0.25 again if it's a parabolic the valve is stenotic. If it's not parabolic is a triangular shape. Acceleration time is less than 100 it means the LVUT velocity is not proper. It means the LVUT velocity sample volume for LVUT is not in right place so it is far away from the valve. For evaluation of severity of prostatic orthic valve regurgitation this is all criteria is very similar to the assessment of regurgitation in native valve and I'm not going to repeat it. Evaluation of prostatic mitral valve. Prostatic mitral valve in terms of regurgitation in transtallocic the mitral regurgitation if the valve is mechanical it might be covered by mechanical valve shadow so we might not see the regurgitation in LVUT. That's the reason that T is better and we'll show it. So again what's the criteria to see the mitral valve is stenotic. We look at the evave velocity of the mitral inflow. If the evave velocity is more than 1.9 like in this case is 2.2. If the VTI in this case is 42 and mean gradient is 7 millimeter mercury so this valve is like the stenotic. So then we go for LVUT VTI and we use this ratio. So the VTI of prostatic valve to the VTI of aortic valve if it's more than 2.2 that make mitral valve is stenotic and I will show you in next slide. So parameter that we use for prostatic valve dysfunction in the mitral position pick early velocity as I said more than 1.9 is abnormal. Mean gradient we have to look at the heart rate as well. Pressure half time we can use it for prostatic mitral valve not for valve area just the number of the pressure half time is important. Doppler velocity index ratio of the Doppler VTI of prostatic valve to the LVUT effective or if it's area we can measure it. Residence location and severity of recogitation and other chamber LV size and function LA size, RV size and pulmonary artery pressure are important. These are two example of the two valve is a normal prostatic mitral valve evave velocity is 1.1 if it's less than 1.9 I said is normal. Mean gradient is 4 usually mean gradient less than 5 or 6 is normal. Pressure half time is 123 so pressure half time less than 120 is totally normal. This valve is stenotic evave velocity is 2.5 is very high mean gradient is 15 very high pressure half time is high. So this valve is stenotic this valve is normal. So this is the criteria to assessment of prostatic mitral valve stenosis. Evave velocity less than 1.9 is normal more than 2.5 is very abnormal. Mean gradient 5 and 10 ratio less than 2.2 is normal more than 2.5 is very abnormal. Effective or if it's area more than 2 is normal less than 1 is very abnormal. Pressure half time 130 not 120 I said 130 is normal and more than 200 is very abnormal. So these are the number that for assessment of prostatic mitral valve stenosis you should measure it. For regurgitation is very similar to the stenosis. Again we use the evave velocity the ratio of the VTI mean gradient TR velocity. If somebody has a mitral regurgitation TR velocity goes up and the stroke volume calculated by Doppler and by 2D. There are big difference and systolic flow conversions might be seen. Echocytography and Doppler credibility of prostatic MR using findings from TTE and TE. This is the whole criteria that you can read it. And these are the one that we should remember always the area of the MR to the area of the LA. Flow conversions and the shape of the mitral inflow. Evaluation of prostatic pulmonic valves again is very similar to uortic valve. So peak velocity and peak gradient is important. Mean gradient Doppler velocity index effective or if it's area presence location and severity of regurgitation. Some of these criteria are not very validated. Related cardiac chamber or V size function and hypertrophy. So the one that we use mainly is the peak gradient and mean gradient. Finding suspicious for prostatic valve stenosis. Casp-oliphate sickening. Narrowing of forward flow. Peak velocity more than 3 meter. In a prostatic valve and more than 2 meter in homograph. Increase in peak velocity on serial studies that's very important. Impaired every function. So the peak velocity is the most important one in assessment of prostatic pulmonic valve dysfunction. For pulmonic regurgitation again the criteria are a little bit similar to the uortic regurgitation. But some number are different. And like pressure halftime for example less than 200 millisecond in AI severe. In pulmonic regurgitation less than 100 is severe. Tri-cast width valve again is very similar to the mitral valve. Peak early velocity is important. Mean gradient and pressure halftime and the ratio. This is an example of the case with prostatic tri-cast width valve stenosis. You can see the turbulence here and you can see the mean gradient is high. So the peak velocity more than 1.7 meter per second is abnormal for tri-cast width valve. Prostatic valve mean gradient more than 6 is compatible with severe TS. Pressure halftime more than 230 millisecond is compatible with significant stenosis. And effective orifice area and the ratio are not very validate. So these three are important. For tri-cast width regurgitation again all of you know it. The jet area it is the most important part that we use it. And venal contractor. So jet area, venal contractor. What about the guideline of T guideline in the OR interrupt T guideline? A couple of issues almost we reviewed all of this. But for aortic valve replacement for example in the OR assessment of prostatic valve in the aortic position. We should identification of the swing ring and evaluation of the proper functioning of the valve leaflet. It's important exclusion of presence of pathologic regurgitation, intra or paravvalor. And establishment of the hemodynamic profile of the newly implanted valve. Evaluation of prostatic valves in the aortic position includes several view at the midisophageal trans-gastic view. The entire circumference of the swing ring should be visualized in short axis view. And the measured gradient of an aortic valve prosthesis depends on the ventricular contractility, loading condition and type and size and location of the prosthesis. Immediately following implantation, the prosthetic valve should be evaluated for pathologic regurgitation. Intravvalor regurgitation is a common finding in normally functioning bioprostatic valve 10% of time. And it's often seen as a small central or commercial AI, especially pericardial valves that we see every day in the OR. Mechanical valves have a specific pattern of washing jet that minimize blood stasis in the hinge mechanism, preventing thrombosis formation. These washing jets are seen within the swing ring, occur early during valve closure and are of short duration and length. Simultaneous multiplying imaging permits easier identification and characterization of these jets. Regurgitating jet features that may suggest more than mild regurgitation include wide jet origin, multiple jet, jet path that is visible around the stand or swing ring and a visible proximal flow convergence. These are all criteria shows that the regurgitation is significant. The ACE guideline does not recommend the use of jet lengths or jet area for prosthetic valve to assess the degree of regurgitation. Values of quantitative indices that may indicate significant valve obstruction include the peak aortic prosthesis less than more than 3 meter. It's abnormal in the presence of an elevated acceleration time more than 100 and low Doppler velocity index less than 0.27 is abnormal and acceleration time to ejection time more than 0.4 is also consistent with prosthetic valve obstruction. This is mainly in the American study guideline. It did not come in 2020 guideline. As patient prosthesis mismatch can lead to diminished LVM mass regression and poor long-term outcome after the aortic valve replacement, the effective orifice area of the newly implanted prosthetic valve should be calculated using the continuity equation. The effective orifice area should be compared with other Doppler parameters for concordance and reasons for discordance. Mitral valve replacement assessment of prosthetic valve in the mitral position by 2D and 3D. The interop environment provides unique challenges for the assessment of prosthetic valve due to possible acute and frequent changes in hemodynamic. A prosthetic valve in the mitral position should be inspected for adequate functioning of the mechanical disc or bioprosthetic leaflets and the presence of intra or paraviral leak. Adequate motion of the prosthetic valve disc can be examined after removal of the aortic cross clamp. Excaution of prosthetic valve disc leaflet may be limited by interposition of subvalver tissue or in the presence of low flow across the valve in a partially filled LV. Comprehensive evaluation of prosthetic valve should be performed after complete separation from bypass. The entire sewing ring of the mitral prosthesis should be imaged at the mid-isovusional level by sweeping the multiplane angle from 0 to 180 degrees. Off-axis view sometimes is needed. Color flow Doppler should be used to locate abnormal intra and paraprosthetic flow. The normal washing jets of mechanical prosthetic valve should be identified and differentiate from pathological regurgitation. By providing a fast view of the mitral valve, 3D echocardiography with or without color can evaluate the location and characteristic of the paravavular regurgitation. E-Mobile leaflets in the presence of adequate loading condition and moderate or severe paraviral leak should trigger surgical intervention while the management of a mild paraviral leak is controversial and can be left from the war. The decision for immediate correction requires a team approach within imaging. Cardiac anesthesia and the cardiac surgeon should be tailored to each patient and critical situation and the weight against the risk of prolonged surgery if the LV function is not good. Ormonic valve replacement. Again, we should check it for PS and PR. And for tracheal, the same. We should check the gradient and any paraviral leak. So now I'm going to show you a couple of case examples. Very short. This is a patient that had a mechanical mitral valve replacement. As you see, the two discs are anti-anatomic because anatomic anterior disc should open this but still should this. So this anti-anatomic position of the mechanical mitral valve. This valve has a small paraviral leak as the arrow is showing. And when you do 3D, you see it. Always try to get the 3D of the mitral valve. It's a little bit aortic valve that you can say from where the leak is coming. Early paraviral leak is common and if it's less than mild, we just leave it. This is another case with aortic valve replacement by a plastic valve. You see a leak here. When you see a leak also is mild, but you have to say from where it's coming. You put the X-plane. You see the leak is inside the swing ring and is mild and lifted. So this is seen mainly in pericardial valve. And this paper shows that the paraviral leak or cough leak in magna valve is about 2% of all valves. And we see it more in our center here. This is another patient that has a leak like this. In the war, we said, okay, this is a mild leak. We can leave it. We left it. And it was a transvalvular. And next week the leak increased. And main reason for increase was this calcification. Because the valve was sitting in the calcification. After a couple of days, the calcification will be absorbed a little bit and leak will be more. So this week increased and we had to bring the patient back to the war. So always be careful. If the leak is more than mild in the war, we should not accept. This was a case that we had to do a re-do it the week after. This is another case that had an aortic valve replacement one year ago and now has a severe part of our leak. So this is really severe. And this patient had to re-do AVR and no leak anymore. This is another case under a bio AVR with root enlargement. You see there's a turbulence here. We should not have it and we have a leak. This leak is more than mild. Two jets. So we should not accept it. But sometimes the surgeon are pushing us to accept it in the war. The gradient was high. This patient came to ICU. The degree of the AR increased. And we took the patient back in three days to the war. And what the surgeon expected, they saw the patch that they put it for root enlargement was interfering with the function of the valve and valve was leaking. This is another patient had a mild valve repair, not replacement. But the Doppler gradient, you see these two shadows. I showed many of you in the war that we take only the dense shadow. That might have a repair or replacement. And this is one of the paper that shows that these two shadows mainly because of the effect of the Doppler. That we call it Doppler effect. And we should always take the dense shadow. This is a patient that had a bio positive mild valve. That was a small like a part of our leak here. But this patient came the year after. And it was not part of our leak. It was actually the circumflex. It was damaged. They had to coil the circumflex. And this is the reason. So if the patient has a right left dominant, the chance of damage to the circumflex is more than right dominant. Because especially this area, the circumflex is very close to the discommission and appendage is here. So during the appendage closure or during the valve repair and replacement, damage to circumflex might happen. It's not very common, but it can happen. And this is a paper. So this is the end of the talk. Thank you very much. And I will answer the question when we see each other in the class.


Welcome back to our lecture series math 4230 abstract Algebra 2 for students at Southern Utah University. As usual, I'll be your professor today, Dr. Hansh missile nine. In lecture 31, we are going to talk about the idea of a polynomial code. We'll define exactly what a polynomial code is in the next video. In this video, we're going to find the related notion of a cyclic code. So imagine we have an N by N linear code. We say that that code is cyclic. If you take a arbitrary code word, so let's say we have the code word a 1, a 2, a 3, all the way up to a N. Of course, these code words we can identify as vectors in the vector space Z2N. So we have N bits of those N bits of course are encoding M bits of information, but there's some check bits that have been inserted, right? Of course. So we say that a code is cyclic if every cyclical permutation of a code word is still a code word. So in particular, if you take the code word a 1, a 2, up to a N, if the cyclic permutation a N, a 1, a 2, a 3, up to a N minus 1, notice what we did here is we took the very last one, we moved it to the front and bumped everyone down. So basically, everyone moves down. A 1 goes to a 2, a 2 goes to a 3. I should be more specific here. A 1 goes to the 2 spot, a 2 goes to the 3 spot, a 3 goes to the 4 spot all the way down. So a N takes over the, a N minus 1 takes over the Nth position and then a N will come to the front and take over the first position. So that's what we mean by a cyclic permutation of a code word. So the code, we say the linear code is cyclic if every code word is cyclically permutable into another code word. Every cyclic permutation of a code word is still a code word. In other words, the cyclic group ZN naturally acts on the set Z2N by this cyclic permutation, right? We can identify ZN very naturally as a subgroup of SN where we're thinking of ZN here is generated by the permutation 1, 2, 3 all the way up to N, like so. And so this N cycle clearly belongs to ZN. The cyclic subgroup generated by that will be isomorphic to ZN. We're making that identification right now, that permutation action. And so we say that a linear code is a cyclic code if it is in fact a ZN set, that is the group ZN acts on the set here. So notice what we've done here is we've reviewed these ideas of algebraic coding theory. These aren't just arbitrary messages. There's algebraic structure to it. We introduced the idea of in math 4230 to be precise. We introduced the idea of a group code and a linear code by adding a group structure to these sets because after all, Z2N has a group structure. But there's not just a group structure with respect to addition. There's not just a vector space structure with regard to skill and multiplication. There's also very naturally a group action on Z2N. So in particular, if you take the whole set Z2N, ZN acts on Z2N by this permutation action. And so if a code is of course a linear code, so it's a subspace, but if it's a subspace for which this cyclic permutation action is closed upon, that is we have a ZN subset, then we call that a cyclic code. So we're looking for those vector spaces of Z2N, which already gives it some algebraic structure. We're looking for vector spaces that have this additional group action to it as well. Because the more algebraic structure you put on these codes, it seems the stronger they become. So consider the following 6 by 3 matrices. We'll call them G1 and G2. G2 is a little invisible right now. We'll scroll down in just a moment. But G3 is this 6 by 3 matrix. This is our generating code. So in particular, since this is a 6 by 3 matrix, what's going to happen is you can times this by a 3 vector. So you have A2, A3 right there, arbitrary 3 vector. And as there are six rows here, it'll turn three vectors into six vectors. And so because our matrix is 6 by 3, our generating matrix is 6 by 3, that tells us this will produce a 6, 3 linear code. And the basic situation is the following. If you take this matrix and you times it by 0, you're going to get 0. Every matrix times 0 gives you 0. If you take, and we don't have to go through all of these here, but if you take like 0, 0, 1 as your vector, you're just going to grab the third column of the matrix. So you're going to get 0, 0, 1 dash to 0, 0, 1. I'm just adding the dashes so that it's easier to read these codes here. Of course, if you times it by 0, 1, 0, you're going to grab the second column here. So 0, 1, 0, 0, 1, 0. If we do this one, I'll give you the first column. This, if you times it by 0, 1, 1, that'll be the sum of the last two columns. So you get 0, 1, 1, 0, 1, 1. You'll notice, of course, that the scheme is much more, much more simple than that. This encoding process is just you take your word and then you repeat it twice. So this is just the double, double the message. You send it twice. 1, 0, 0. We send it as 1, 0, 0, dash 1, 0, 0. 1, 1, 0. You'll be able to be concoated as 1, 1, 0, 1, 1, 0. Okay? So that's what this code is doing. But I want you to be aware that this code is, in fact, a cyclic code. So notice what happens here. If you take the 0 vector, now, because every bit is the exact same, every cyclic permutation of the 0 vector gives you back the 0 vector. This element is fixed by all cyclic permutations. Okay. This is also true for the vector 1, 1, 1, 1. The all 1s vector, all 0 vectors, these will be fixed by all permutations in particular, the cyclic permutations, like so. Now consider this one right here. 001 dashes 001. If we were to permute it cyclically, that is, everyone goes to the right by one step, right? What that's going to do is that's going to turn you into the vector 1, 0, 0, 1, 0, 0, right? Because looking at this vector here, there's just a two 1s. Let's keep track of where they are. This one's going to go to the front, like we see right here. And then this one's going to go to the other side of the dash, which we see here. So this vector, when you permute it once, you get this one. Now, if you permute it again, that's going to produce this vector right here, because this one will go over, this one will go over. That's exactly that vector right there. And then this vector, if we cyclically permuted once, this one goes over, this one goes over, and we get back to where we started here. So there is this three cycle here, I'm going to do this in yellow. We get this one, this one, and this one. These three vectors are an orbit of that cyclic permutation. Now let's consider, notice these were of course, all the vectors of weight two. They had two ones in them. What if we look at the vectors of weight four here, we get 011 dashes 011. Let's pay attention to the zeros this time, where they go. These zeros will go to the left. So this should be in the middle now. Oh, that's exactly this vector right here. You end up with 101101. If we permute the zeros again, this zero go to the right, this zero goes to the right. That produces exactly this one right here. One zero, excuse me, one, one zero, one, one zero. And then of course, if you permute this one more time, you'll go back to where we started with this right here. So these green vectors I've now highlighted represent a cyclic orbit of the Z in action on the Z six action on this set. Then of course, like I said, the zero vector is by itself. The all ones vector is also by itself. And so we see here that in fact, all all eight of these vectors are in fact, cyclically permuted into each other. This does in fact give us a cyclic code. Let's come down to look at a second matrix, look at this one here, G two. This time, your matrix looks like the first column is 111100. Then the next column is 011110. And then lastly, 001111. Do I say the right number ones there? But you'll notice that, you know, when you look at the matrix, you do see some like cyclic behavior, right? Look, you look at these zeros, you kind of cyclically permuted the columns there. So you got a zero here, zero here, do it one more time, you get that. So I mean, like, hey, you look at the matrix, I've cyclically permuted the columns, does that produce a cyclic code? Well, clearly, like I said, the all zeros, the all one vectors, if it's even present, the zero vector definitely will be but the all one vector isn't present in this code. If you look at the all zero vector, it's always fixed. So no big deal there. Let's look at this word right here, this code word, it has a weight of two, it can only cyclically permute into another vector of weight two. Where are they on the list here? Well, if we move the ones over, so you're going to get, if you move the ones over, this one moves to the right, and this one moves over here, so we should have 101000. Okay, so you want a 101, here's a 101, but that's not all zeros. And then you scan, scan, scan, scan, scan. There's no other one who has a 101 in it in the first three bits. So it turns out that this vector right here, cannot be cyclically permuted into another one, it's it's cyclic permutation is not included. So this first code we looked at was in fact, cyclic, this one here is not a cyclic code. Even though like I said, there is some type of like cyclic permutation happening on the columns here, but the resultant code isn't going to work. Okay, now when you look at these codes, I do want you to note sort of the following situation here. When you look at these codes from before, what was the minimum weight of these words? This first one, our minimum weight was two. So that's going to be the minimum distance of this code. Now since two factors of decomposes has one plus one, we see that this code is a one error, one error detection, no level of correction. So it's a very, very simple cyclic code, but it is cyclic with one level of error detection. This one right here, G two, if we look at the minimum, the minimum weight, this one also had a minimum weight of one. So that tells us we're going to have one level of detection, no level of correction on this code. But again, the first one's cyclic, the second one's not. So even though the the minimum distance turned out to be the same, so the level of detection and correction appears to be the same, you can have a code that is cyclic and one that's not. Does that cyclic component add us an extra level here? And the answer is going to be yes. And so while these codes do have very, very low level of detection correction here, let me kind of emphasize why you might be interested in a cyclic code in the first place. Because when you have errors, it's not like it happens randomly. It happens chaotically, which is not the same thing. Chaos wall may be difficult to predict. It's not truly random. There is a reason behind it. Like if we have two, two communication devices that are trying to connect with one another, and this one sends a message to the other one. Well, if there's an error, there's some type of noise in that happens, maybe some type of like electrical burst in the system affected the transmission, that burst happened at a moment. And so the bits that were sent during the burst are the ones that are likely going to be affected. And so I guess what I'm trying to say here is that if a message has errors, the errors are typically going to be clustered together. It's not like they are truly randomly distributed out equally, equally likely. The distribution of errors is probably not equally likely as we predicted before, they're probably close together. And so if you found one error, those elements next to it have a much higher probability of being erroneous as opposed to ones that are farther away from it. And so one of the advantage of a cyclic permutation is that if you have like a transposition that is like a two, two bits next to each other got switched around, or if there's a cluster of errors together, the cyclic code has a better opportunity of detecting that and correcting that as opposed to just an arbitrary linear code, which is having the assumption that all errors are all bits are equally likely to be erroneous, as opposed to the cyclic one that's like, oh, the errors come in clusters likely. And so there is a strength to be in a cyclic code that we will talk about of course later on in this lecture series.


Hello. I am the storyteller. And today we will talk about Barcelona. Barcelona's cultural roots go back 2,000 years. Since the arrival of democracy, the Catalan language has been promoted, both by recovering works from the past and by stimulating the creation of new works. Barcelona is designated as a world-class city by the Globalization and World Cities Study Group and Network. It has also been part of the UNESCO Creative Cities Network as a city of literature since 2015. Barcelona has many venues for live music and theater, including the world-renowned Grand Teatre del Liceu Opera House, the Teatre Nacional de Catalunya, the Teatre Lire and the Palau de la Musica Catalana Concert Hall. Barcelona also is home to the Barcelona Symphony and Catalonia National Orchestra, the largest symphonic orchestra in Catalonia. In 1999, the OBC inaugurated its new venue in the brand-new auditorium. It performs around 75 concerts per season and its current director is AGOA. It is home to the Barcelona Guitar Orchestra, directed by Sergio Vicente. The major thoroughfare of La Rambla is home to mime artists and street performers. Yearly, two major pop music festivals take place in the city, the Sonar Festival and the Primavera Sound Festival. The city also has a thriving alternative music scene, with groups such as the Pinkertones receiving international attention. El Periódico de Catalunya, Louisiana, Vanguardia and ARA are Barcelona's three major daily newspapers while Sport and El Mundo Deportivo are the city's two major sports daily newspapers, published by the same companies. The city is also served by a number of smaller publications such as ARA and El Panavuí, by nationwide newspapers with special Barcelona editions like El País and El Mundo, and by several free newspapers like 20 Minutos and K. Barcelona's oldest and main online newspaper VilaWeb is also the oldest one in Europe. Several major FM stations include Catalunya Radio, RAC One, RAC 105 and Cadena Serre. Barcelona also has a local TV stations, VTV, owned by City Council. The headquarters of Televisio de Catalunya, Catalonia's public network, are located in Sant Joan d'Espi, in Barcelona's metropolitan area. Barcelona is also home to numerous social centers and illegal squats that effectively form a shadow society mainly made up of the unemployed, immigrants, dropouts, anarchists, anti-authoritarians and autonomists. Peter Gelderloos estimates that there are around 200 squatted buildings and 40 social centers across the city with thousands of inhabitants, making it one of the largest squatter movements in the world. He notes that they pirate electricity, internet and water allowing them to live on less than one euro a day. He argues that these squats embrace an anarcho-communist and anti-work philosophy, often freely fixing up new houses, cleaning, patching roofs, installing windows, toilets, showers, lights and kitchens. In the wake of austerity, the squats have provided a number of social services to the surrounding residents, including bicycle repair workshops, carpentry workshops, self-defense classes, free libraries, community gardens, free meals, computer labs, language classes, theater groups, free medical care and legal support services. The squats help elderly residents avoid eviction and organize various protests throughout Barcelona. Notable squats include convis and conmostu. Police have repeatedly tried to shut down the squatter's movement with waves of evictions and raids, but the movement is still going strong.


So good morning everybody, how's everybody doing? Let's get a little applause going for Dr. Bob Murphy. You know, I would like to say that I personally have really enjoyed this lecture. I consider it one of the more important and engaging lectures of the week because I'm actually quite proud of the fact that the Mises Institute is a place where we can at least consider or explore or maybe even advocate the concept of a truly stateless society, one where even supposedly public goods were national defense, so-called, where streets and roads and police even and judicial services are provided privately. And of course, this is a necessary topic in that sense. But nonetheless, I think it's one that's important and one that we need to consider seriously. So I'm glad that you all made it to this plenary. But earlier in the week, I mentioned that the relationships that people have made over the years and the connections are as important as the ideas themselves because that's how ideas are transmitted through actual human beings. And so we would be remiss if we did not mention that our great friend and senior fellow Dr. Bob Murphy recently wed his girlfriend, Kellyanne. And we just wanted to congratulate him. We have a set of matching his and her towels from Kmart or anything like that. But we just wanted to congratulate them. And we wanted to say how pleased we are for them and that, on behalf of the Miseson student, everyone here, how much we love them and care for them and wish them many, many happy years. So congratulations, Bob. Thank you so much, Jeff and everybody. I'm pretty sure that that's a copy of human action in there. But it was a pleasure to be here. Thanks for showing up, everybody. And as Jeff said, this is a fun one. Let me just clarify. So I'm going to be going over lots of different topics in this one pretty quickly, breezing through. However, the issue of military defense, that's such a thorny issue in that there's so many conceptual hurdles there that that's going to be, if you're interested in that, I'll be covering that tomorrow in a separate lecture. Last housekeeping notice, as far as private law, like police and judicial services, the single lecture you want to go to for that, it's called the Market for Security that I've given at previous Mises use. And so that's the one you want to look up for that as well. So without further ado, let's jump into this talk. So just to set the stage for this, I like to open with this quote. I'll read it for those in the back. For if the bulk of the public were really convinced of the illegitimacy of the state, if it were convinced that the state is nothing more nor less than a bandit gang writ large, then the state would soon collapse to take on no more status or breadth of existence than another mafia gang. Hence the necessity of the state's employment of ideologists and hence the necessity of the state's age-old alliance with the court intellectuals who weave the apologia for state rule, okay? And so that's kind of the context and partly what I guess our mission is for those of us who lecture at Mises University is just educational to show people once you see things in this fashion, it's pretty obvious what the conclusion would be. And I believe it or not, some people might recognize this quote, but it actually comes from Christina Romer. If you, yeah, well, she was younger, she was pretty, guys, come on. It's Murray Rothbard, give me a break. All right, and see, if you believe me for even half a second there, that's the problem, okay?  You gotta think for yourself. Well, you should trust no one, all right. It's your fault the state still exists, okay. All right, and so I'm gonna obviously jump into specifics here, but let me just also, in terms of the general outline, whenever you encounter a problem, like it's because the typical pattern is that there's some difficult social issue, you know, people are being harmed or their prosperity is being shackled by some thing going on. And then unfortunately, most people immediately rush to, oh, well, the state can do something about it, right? And that's the first thing that people go to. But what I want you just to remind you of is that if everyone knows that a certain voluntary arrangement would, quote, lead to disaster in some area, then that means there's a huge opportunity for an entrepreneur to come in and fix it, okay?  It's like there's this market failure and everybody on the planet can totally see what the problem is and knows the obvious fix except the people who would make billions of dollars from doing it. They're assumed to not know how to fix it and they're just gonna see, oh, well, it's free market, can't do anything about it. In particular, the way this manifests itself when it comes to economic models of what's called market failure is that they have a very narrow set of strategies, let's say, to use that technical jargon that the firm can engage in. So just to give a simple example of what I mean, something, there was this problem that economists deal with where what if marginal cost doesn't begin rising at some point? Certain applications like air travel, things like that where once you're gonna build a plane and have two seats available, then to add more and more passengers, the marginal cost of the airline is pretty low. And yet if the airline merely charged every customer what it costs to just add one more person to the flight, well, then it doesn't work out, right? The airline would be losing money if they charged every customer the marginal cost of the flight. And yet they also couldn't charge the first customer the full cost, that sort of thing that the first person can't be ended up paying a million dollars to fly somewhere but yet to add the 37th passenger that's a pretty low marginal cost and yet every ticket can't cost that. So if you're familiar with mainstream economics, you know that under ideal conditions, the market is optimal or you reach a Pareto optimum when price equals marginal cost. And if it doesn't, oh, there's monopoly power and blah, blah, blah. All right, so that's just one example of the kind of thing I mean where when you try to apply conventional economic tools that real life situations, it sometimes pops out but the market's stuck and can't fix itself when obviously there's other pricing strategies. Another example would be something like wholesale clubs like BJ's or Sam's club, if you guys are familiar with that where you buy things large bulk purchases and they charge you a much lower unit cost than you'd get elsewhere. So they're not literally charging you the marginal cost to them in terms of the accounting but it's much closer to that and so how does that model work as they charge a large fee for you to be in the club to have the right to come into the store in the first place and then you also pay unit prices for the stuff you buy. So that's just one example of how they partly solve this problem of oh, what if marginal costs are really low for large ranges of output? We can't reach the optimum. You could say, oh, well instead of just charging a unit price to everybody who buys products, maybe you charge a membership fee and that's how you somewhat separate. So you're charging for that consumer surplus if you know that term. Okay, so that's just some examples of what I'm talking about where they sort of arbitrarily fix what it is that private business is allowed to do or charge based on and then they conclude up, see that's gonna lead to a market failure and then they have the government come in and it has much more tools than its disposal. Okay, so let's talk a little bit about money. I think they probably covered a lot of this in the earlier lecture that you saw in this but it's okay if there's some repetition here. So is Carl Manger, the founder of the Austrian school explained money emerged on the market and this was a tour de force of his explanation where he walks through and shows, for example, that the so-called state theory of money doesn't really make sense. It really doesn't work to say, okay, well there was a time at which humans didn't have money and then there's a time later when clearly they do have money. It's not a natural thing, right? It's not like trees. So clearly money somehow is related to human activity and so the natural conclusion most people would have is there must have been some wise king or philosopher somewhere in the past that invented money and then maybe could Joel people or persuaded them or used force to get the community to start using it and then the benefits were made manifest and there you go and that's where money comes from. And so Manger had several arguments to show that that really doesn't work. So one thing is we don't have a record of such a person. You would think if some wise king thousands of years ago invented money that might have been recorded but there is no such record of someone inventing money. Also it's just the inherent implausibility of it that if you hadn't seen money in operation if someone tried to explain it to you, it sounds dumb, right? If you think about it, imagine some king saying, okay, right now you guys are trading horses for eggs, let's say, and it makes sense why you're doing that because you use the horse for transportation and you guys eat the eggs so you can see why you would do that. But how about, here's these shells that nobody really cares about one way or the other. What if instead you sold the horse for these shells and then someone said, why would I do that? I don't want the shells. Don't worry, because this person with the eggs will also accept the shells.  Trust me, if we all act stupidly in unison it will all, right? It's sort of like a frat initiation ritual. But, so that's, you see how that, if you were trying to explain to someone who had never seen it before, it sounds crazy. And so, Menger just goes through and he shows these problems. Even if you solve that problem, let's say the king did convince everybody in the realm, okay, from now on, every time you want to trade something, first sell it for these things that you really don't care about one way or the other, but don't worry because somebody else in turn will do likewise and reciprocate. Even if you could get everyone to agree to do that, or maybe they did it because you're saying, or chop your head off if I catch anyone selling against things besides these shells that the king's holding up, how would you lock in the purchasing power, right? It's not enough just to say the person selling your horses, now you gotta do it against these shells. You don't know how much is one's shell worth. You know, how many horses, or how many shells should one horse fetch in order to answer that you would need to know, well, I kinda wanted to actually go get eggs and so I need to know how many, you know, these shells, how many eggs do they command in the marketplace before I know if I wanna sell my horse for shells. And so you see the problem is really difficult once you start seriously considering it. So Manger came up with a theory for the origin of money that solved all those problems or that was impervious to those objections. So real quickly, he said that, okay, even in a, I'm paraphrasing obviously, but even in a state of barter where there's no money, there's no even what's called a medium of exchange, still different goods would have different degrees of salability or marketability or liquidity if you know those terms. So like eggs, there's more of a market for eggs. More people would be willing to accept an egg on any given day than people who are in the market for like a fancy telescope. Okay, so a telescope's very valuable. If you found the right buyer, you could get a lot for it, but most people on any given day are not looking to acquire a brand new telescope. So the idea is if you're going into town with a telescope that you're trying to unload, you're in a worse marketing position than someone going into town with two dozen eggs. All right, and so let's say the person with the telescope ultimately wants to get horses, the chance of you finding someone with a horse who also wants a telescope that day are pretty low. And so what you'd be willing to do is anybody who wants a telescope and has a good that's more marketable than telescopes are, you might consider that as a stepping stone, as an intermediate transaction to get rid of the telescope and get something like maybe a bunch of chickens that are closer that you know is more marketable, that you're more likely to find someone with the thing you want who is accepting chickens that day, okay? So that's the process that seems pretty straightforward. And yet if everyone's doing that, just think about the implications. So that means the goods that initially had a wider market just because of natural preferences. Now the range of people who would accept it is enhanced from that first round of just thinking through, oh wait a minute, I would not only be willing to accept the stuff I directly want to use, but something that's more marketable than the thing I'm starting out with, okay? So the goods that were initially the most marketable, their advantage gets amplified. And so Manger just said that process you can imagine would continue as people see other people doing that. Now the things that were more acceptable like eggs, let's say are even more acceptable, even people who are vegan might still accept eggs because oh, I know a lot of people like these things. So that's what would happen, but it's more than just the acceptability. Obviously eggs wouldn't be very useful as a medium of exchange because they're so fragile, they don't last very long, even if you attended them properly, you can't cut them in half very easily, something costs half an egg, that's awkward, right? And so that's why with that process in mind, things like gold and silver ultimately arose as the market's choice of money because of their property. So it's not that gold is money because it's easily divisible per se, that's not the definition, but the fact that gold is very easily divisible and so on, it's durable, it's homogeneous in terms of its quality, that an ounce of gold is an ounce of gold, unlike diamonds, sorry, so that's why diamonds don't really work well as money because to say something costs a kilogram worth of diamonds, it depends how big the stones are, right? It's not that they're interchangeable, whereas with gold and silver, the weight, as long as it's a specified quality, purity of the metal, the weight's really the only information you need to know in terms of saying how valuable is this pile of commodity, all right? So that's how Menger explained that process and so notice at no point in that explanation did it involve someone seeing the big picture and realizing, oh, if our whole community could switch over to using money, it would be a lot better. Nobody had to realize that. They each individually were just acting in their immediate self-interest and yet, so they're being rational. They weren't just randomly trading stuff. Each transaction made sense on its own terms, but the whole thing taken together led to the emergence of money, all right? So that's Menger's explanation for the origin of money and so that's how you could explain how a community might start accepting gold or silver as the money and quoting prices in it, but then there's also the emergence of coinage and so here too, that's something that historically the private sector handled. So George Selgen actually was just a while ago now gave a great talk here at the Mises Institute just giving the history of private coinage, all right? So again, that's something that a lot of people will just assume, oh, the state must have been in charge that no, private companies first, private mints first did this and then the state came in and took it over and shoved them out of the industry. But originally, so again, what's the function of coinage? So they're using gold already and I've explained how that could have happened and then the issue is though, all right, if you go into a store and you just have a pile of chunks of yellow metal, that's cumbersome, that's hard to effect a transaction, especially if it's a big one, because then the merchant has to have special equipment to test to make sure that it really is gold and there's various things you can do and so you don't wanna have all the merchants being part-time chemists in your town that slows down trade. So the function of coinage is to just somewhat ensure the authenticity and to show what this thing is, right? And so the private mince function is it takes raw gold and silver as it were and stamps them into coinage. They have like the ridges around the circumference so that the reason for that in case you don't know is because otherwise you could like shave off the edges of it and so the coin slightly shrinks and you get little shavings of gold or silver. So that's the function of having those notched edges so that it'd be obvious if someone tampered with the coin. All sorts of things like that that signify the authenticity so you know this is an ounce of gold. That's what the, so the private mince are not creating money. That's important to realize. All they're doing is taking the money which is gold or silver, whatever it is, and just stamping it into a very recognizable form so that people can more comfortably trade it. Okay, what about banking? All right, so here too, for those who saw my lecture on the Rothbardians versus the Free Bankers, this is somewhat redundant but here I just wanna reiterate there's distinct functions of banking. You have demand accounts, like checking accounts and you also have time deposits or like savings accounts, things where there's genuine loans occurring. So those are distinct functions but as far as just right now thinking about checking account balances, just what's the reason for doing that? Well it's for security and also just convenience. So people are walking around town, they have gold coins and I'm saying the next level, the next evolution layer on top of this just to enhance transactions would be commercial checking services.  Okay, so there again it's pretty straightforward and we have both theory and history to show how this can emerge in the absence of the state and in fact central banks in practice they do the opposite of what the public thinks. All right, so the standard story of that the public hears as to why do we need a so-called central bank is to say oh well we go look at history that when we had unregulated private Wildcat banks they would just start up, they would issue notes that were claims on gold or silver and then the public wouldn't know any different and so they'd accept all these different notes from fly-by-night organizations, there'd be wild currency movements, there'd be depressions, financial panics and so the point of having a central bank was to ensure the integrity of the money and also to smooth out the business cycle. All right, so both of those claims are just empirically demonstrably false, right? That obviously the soundness of the money if by that we mean the purchasing power of it clearly has steadily declined with the advent of modern central banking and even using conventional measures the business cycle was worse with the Fed than before the Fed and what's funny is the way sometimes apologists for the Fed try to compare and show the relative stability they'll start in the post-war era, right? They'll assume that oh yeah what we mean by the Federal Reserve era is 1946 onward. You see how that's a convenient omission, right? And sort of like the Great Depression's a mulligan. Just say okay yeah well they were just getting you know getting their ducks in a row but now that you know they started a new job, okay they learn where the water cooler is, okay. Now no more depressions go. And then after the financial crisis hit which by all measures was the second worst crisis to hit in US history it was not to then say geez that's kind of awkward that the first and second worst crises to hit occurred when the central bank was allegedly smoothing out the volatile free market business cycle. No instead they were just, how did they spin that? They said well look it the financial crisis in 2008, 2009 was not as bad as the Great Depression so good thing we had the Fed there, right? And so because they're saying, think about it how perverse that is. They're saying good thing the Fed was there because otherwise the economy might have gotten as bad as before when the Fed was also there. All right so it's a not juxtaposition but in any event also even just on its own terms again some of this is redundant so I'll try to speed it up here but the point of central banking one of the functions that they'll say not critics putting words in their mouth but them probably declaring is the central banks a lender of last resort. And so if you endorse Mises's theory of what causes the boom bus cycle you don't want private banks getting the go ahead to go ahead and expand credit and don't worry if you get caught with your pants down the central bank will come in and provide liquidity. No that gives banks the incentive and the motivation to do what causes the business cycle. Okay another one, who would build the roads? All right so here as with a lot of this stuff the early turnpikes in fact were privately financed at least in the United States and only later did the government get involved and some of this stuff was funny like I've seen Alex Tabarak and some co-author or some co-editors I'm gonna forget their names has a book I think it's called The Voluntary City and they have an essay in there I forget who the author is on private roads and they have some examples to show like how did they finance them? So merchants in a town would realize oh if we pay and get the funding for a turnpike to come through here that will boost business. So some of the big merchants would all hit each other up and say let's kick in and do this and there's some examples that they have in the essay of like the fundraising letter as it were where some of the merchants are sort of shaming the other ones along the lines it would be unfortunate if the community learned that you're not willing to contribute to this product so they're not threatening them with anything besides just telling the truth to people but the idea being a shaming campaign to get some of these big merchants to kick in. So again just showing that's not something that's conventionally available in a mainstream mathematical model of the economy where oh you build a road and then you charge service unit prices for the use of the road and you know all right. So also in this realm sometimes people will say oh well gee everything would be discoordinated and you know maybe as you went from one neighborhood to the other all of a sudden red stop lights would mean go and all that sort of thing and you know there's nobody in charge of the English language right and it's not that stop you know STOP means go in some states and not in others. You see what I'm saying like everybody they have standards and things like that even in terms of like screwdrivers fitting screws. You ever think about that? Like there's not a government agency in charge of saying make sure that the screwdriver head fits into the screw. That's something that businesses have figured out standards all right.  But what you do want though is you do want experimentation. So it's wrong to think that oh only if one agency is in charge of all the roads that we're gonna have public safety maximize. That's incorrect. You want there to be some experimentation because maybe right now the way people make roads is inadequate. And so the best thing I can do to get you to see that is when you get a chance go to YouTube and look up Hans Monderman. All right you can see the spelling here. And so he was a road engineer and there's this amazing video. So his the background on this guy his view is when you're building a road if you have to put up a sign that gives information to the drivers then that's an admission of failure. That's showing that your road is not properly designed if you have to sort of cheat and give exposition to the drivers in terms of signage. And so he wants to design roads that by their very nature keep drivers alert and minimize accidents. And so there was one where he designed this traffic circle. So when you're driving and you approach the traffic circle it's very disorienting. But that's good because you don't want the drivers fiddling with the radio or texting. You want them looking at the road and whoa what's going on with your immediate instinct when you're approaching this traffic circle is you slowed out. And he's saying that's what you want people to do. And so he had this great demonstration. There's a camera crew doing a story on his road designs. And so he approaches this real busy intersection or traffic circle I should say.  So he died but I think we should applaud. No, he was fine. So. So what? All right, but what happened though is so it was risky like cars were honking at him and swearing at him but they didn't hit him because the point was he knew that the road he had designed it in such a way that when you're driving that thing is a magnet for your eyes. Like you can't be looking away because it's so disorienting. And his point was that's what you want. You don't want drivers getting lulled into how like American drivers are on the interstate where you kind of, you know, doze out. I mean, it's, I have heard a radio host one time say he watches movies on interstates. Like he puts the laptop and the footwell of his car for real. And you know, it sounds nutty but you can kind of see how someone might do that.  But the point being that's not what you want people to do. At least if occasionally there is cross traffic because then it lulls people into a, you know, they doze off. All right. So that's that's the idea. So we don't really know what the optimal road design is. And I think sometimes people fall into the trap of assuming the way the government does it is correct and how would a bunch of private businesses mimic exactly what the government's outcome is? No, we don't want the government outcome. The government outcomes bad. There's not only are there more potholes than there should be. Like that's pretty a standard critique of all these roads are terrible and that's true. But it's also the design. And so like intersections where that are referred to as death traps, OK, that there's intersections where a lot of people die every year and in a market where the roads were privately owned. I think the company would have much more incentive to deal with that and to figure out why is it that people keep getting in deadly accidents at this intersection and they would do something about it. It's not that the government road engineers want everybody to die. I'm not saying that, but I'm saying the incentives in place in the how the system responds to that sort of information, if you will, and counteract it or deals with it. It's much more sluggish when it's a government monopoly that it's not that the mayor is going to not be reelected because one intersection has a lot of fatalities because first of all, the people in that town or that community don't view it as a government failure. They view it as, oh, wow, that guy shouldn't have been running the red light. Or, gee, that person shouldn't have been drinking before he got behind the wheel. They don't blame the design of the roads. All right.  And Walter's point is that if a private business had that kind of record under its belt, there would be congressional investigations. There'd be all sorts of regulation into this crazy industry where it's profits over people and they don't care about consumer safety, but since it's the government designing it, people just assume, well, that's the way the world is because everyone knows the government has to run the roads. Also, this isn't so much a big deal in smaller towns, but when it comes to large cities, there are systematic, predictable traffic jams, at least twice a day. In the morning, Russian people are going to work, and then so-called rush hour when they're going home. And depending on the city, I mean, it might be that many of the roads are just unusable for all practical purposes for four hours a day. When you just know it's going to be a parking lot, would be the ironic phrase people would use to show how slowly you move through. And so that right there, that's not just up. That's a feature of roads and that's how modern life works. No, that's government-owned roads. A traffic jam, just think about it, it's a shortage. It's showing that the quantity demanded of the available roads surface per unit time or however you want to quantify what the good is or the services is the quantity demand that exceeds the quantity supplied at that particular moment. And that's why you get a jam-packed full of people trying to squeeze in there. And so if the roads were privately owned, the immediate change would be they would raise the prices at least for those hours or those times of operation and that would speed up the flow. But then because there's open entry, if this were a private free society where all the real estate's privately owned, then if you're seeing these abnormally high profits from the people who own the few bridges and roads and so forth, they would build more. Okay, so it's in the long run, all that would be returned to the consumer and things would be cheaper, but the immediate short-term necessity, if every morning there's way too many people trying to use a bridge or a road to get downtown to go to work, the immediate thing that has to happen is the price of that shoots way up. And that's like a signal, if you will, to say, hey, build more roads. Other things too here, it's not, I mean, the stuff I'm talking about is real plain vanilla economist stuff, but it's also more sinister in terms of if you view the state, not as a bunch of well-meaning but bumbling folks who don't understand Econ 101, if instead you view the state as a gang of thieves writ large, well then you really don't want the roads in the hands of that institution, right? And you see examples of the stuff. So Bridgegate, in case you don't know what that is, so Chris Christie, when he was governor in his administration, there was a scandal and some of his operatives allegedly, or I think maybe they might have admitted it now, shut down a certain bridge lane of traffic just to cause traffic jams, to cause problems for the governor's political enemies. All right, and the scandal was that somebody, I think was sick in an ambulance and couldn't get across it because there was this big traffic jam that they deliberately caused just for political reasons, okay? And so that's the kind of thing we're talking about where normally when you're debating the merits of government versus private ownership of the roads, most people don't say, oh, and a reason you wouldn't want to have a governor have any influence is in case he's mad at someone else, he might have his lieutenants intentionally cause a traffic jam, just to spike that person, right? That you wouldn't even think of something like that and yet that really did happen.  And I mean, it might take months, if ever, to get your money back where you have to prove you're not guilty of something, right? Again, the reason that's such an issue is because the government's control of the roads. If it were privately owned and the owners of the roads could set their rules, obviously it wouldn't be good for business to become well known.  If any company had that policy, everybody would stop using that particular company's roads. All right, and so you can see how that sort of thing would be minimized if you had competition among the roads. And the last thing I got here is involuntary blood draws. Again, agents of the state have checkpoints, they pull people over and there's cases where the police will have a medic or somebody there and say, okay, take some of this guy's blood because we think he's been drinking too much and the person refuses, doesn't consent to it, says, no, I want a lawyer, I'm not doing this. And it's an awkward situation where like the medical personnel are being ordered by the police, and I know some people that just told the police, no, we're not doing it. We don't want to take their blood, go ahead. But this patient is not consenting to this medical procedure, so I'm not doing it. So I'm just saying this kind of thing comes up and again, why is that even an issue? It's because the government controls the roads right now and that's a choke point for a lot of transportation. Okay, so continuing in this vein of transportation, imagine if airplanes or movie theaters ran their businesses the way that buses and subways work, it would look like that. All right, and so again, if you haven't been in a big city, this might not really ring true to you, but for those of you who have been in like you try to take the subway home from work at 5.30 p.m. in a major city, and it's like people really crush in to take up every available square centimeter of a surface area in the place, okay? And so that's, again, if a movie comes out, a blockbuster movie and it's all sold out, once you get into the theater, you have a nice comfortable seat. It's not that the movie theater sells five times as many tickets and so people are sitting on your lap and are scrunched into the theater and you can't even see, and yet that's how so-called public transportation works. Okay, so again, just look at the different incentives and just think through why is that? So again, it's not an issue of all, well, the demand's too high and that's why there's crunching in the subways, because when there's a blockbuster movie that comes out, the demand is high also, or if people wanna fly somewhere, you might get on the plane and say, wow, they sold every seat. This is a popular flight and you're grumbling that you're sitting in between two people and maybe their arms around your armrest, but that's night and day compared to what happens in so-called public transportation. All right, free and compulsory schooling. Government schools are a euphemism for prison in some communities and that's not funny. It's a tragedy, but in all seriousness, I mean just compelling children to go to school and again, some people say, oh, this is a conspiracy theory. I like Tom Woods's analogy on this one. He said, imagine like if Walmart ran the schools or people sent their kids to a school that was run by Walmart and they spent a lot of time in the history classes just holding up pictures of the founders of Walmart and the inner family and the major shareholders and look at how great their accomplishments were. And then in 1994, we had this initiative with our paper bags and you can imagine, how people would derive this, oh, give me a bit of self propaganda, yet when kids learn about the founding fathers and the wonders of America and then Abraham Lincoln did this and FDR did that in government schools, that's just, yeah, that's our history, right? And so that's also too, again, I'm speaking more to an American audience here, so I apologize for those who are from other countries, but from the US perspective, it's like Americans understand and believe that government schools indoctrinate children in every country except the United States. This is the one area where, no, no, they're getting me unvarnished truth. Okay, and so, and there's more and more people realize that homeschooling and other non-traditional approaches outperform typical establishment ones, you can look at test scores and stuff like that. Okay, also on this, just imagine, it's hard for me to get regular people to agree that way too many people are going and getting undergrad degrees, and that's what I think that it's partly just a cultural thing where not everyone thinks, oh, you have to go to college or else you're wasting your life. And also there's obviously all sorts of government subsidies involved that help perpetuate that outcome.  Imagine if that were the trend, you could see, most people say, yeah, that would be crazy because what would happen? It would cost a lot of money. There'd be a huge opportunity cost in the sense of people missing out on five, six more years of their potential work career by staying in school that much longer and also in order for this to be possible, getting a PhD in all these fields, they're gonna have way more degrees granted now. The standards would have to come down. It couldn't possibly be that just by spending more money, a bunch of people can get PhDs in physics or chemistry, or the standards would have to drop, all right? So that you can see how that wouldn't be good there. So I'm saying, all right, you think just right now we're at the optimum level of formal education being received and obviously I think not. Okay, safety regulation. Every time there's a crisis, foodborne illness or a plane crash, people will say, thank goodness we had the government agency that was in charge of not letting that happen, right? And I'm not putting words in their mouth. There was a plane crash when I was younger, it was a big deal. The company was called Value Jet at the time. They rebranded themselves after and I think it was in the Florida Everglade and they crashed and it was a big thing and someone wrote an op-ed that we ran in my local newspaper that was saying civil libertarians might complain about government funding but after a plane crash, the rest of us are glad that the FAA has its people working overtime. And so that's fine, but again, just think through what would have to happen for them to be upset with the FAA, right? Because there was a bad plane crash and the investigations found that it wasn't like it was just a freak thing. It was that the safety inspectors weren't following the protocols that they were supposed to. All right, and so again, that was chalked up to, yep, that's the free market for you when the FAA's inspectors don't do what they're supposed to do and there's a plane crash. There it goes, laissez-faire, right? So it's just this weird thing. So maybe it is true that others inadequate funding, but the point is what could possibly happen to show you that the FAA is doing a bad job and we should consider an alternative approach besides the fact that a plane still crashes on the FAA's watch. All right, so how could you get rid of that? You could have private insurance, right? So what if private insurance companies, what if when you bought a plane ticket, part of what you were buying was an indemnification clause saying if the plane crashes due to things besides acts of God, then the insurance company owes the estate of the people who die in the crash a million dollars or whatever. So if that were the case, then the private insurance company's on the hook and they're not gonna agree to that unless they know that the plane is following adequate safety protocols. So the insurance company then might send out inspectors to check to make sure that the safety logs are up to date. They might give random sobriety or drug tests to the pilots just to make sure that the pilots aren't showing up drunk, that kind of stuff. So a lot of what the government conceivably could do in terms of regulation, you can see private watchdog groups doing that as well. And again, the big difference is the incentive structure. If some private agency, some insurance company's vouching for an airline and it's not doing a good job policing the pilots or the maintenance crew and there's a crash, I mean, the victims are the people who die in the crash obviously, but also the insurance company now is gonna be out several millions of dollars, okay? So they have an incentive to not find themselves in that position. Whereas again, perversely, if there's a big plane crash, the people running the FAA can get more money from Congress because they can say we're understaffed, we need a bigger budget. It's true, maybe the higher ups might have to resign just to remove the scandal, but the institution itself does not suffer when it doesn't do its job. It actually perversely gets more money. Okay, there's a similar thing with the FDA. I'll be real quick on this point. It's standard for a free market economist to complain about the FDA and say, that's the Food and Drug Administration to say they have these unreasonably high levels of proof to jump through all these regulatory hoops to show, if you wanna bring a new drug to market, you have to do all these tests and show clinical trials to show such and such. And so drugs that could be helping people are held off the market unnecessarily long. It raises the prices. By some estimates, it costs more than a billion dollars, billion with a B to bring a new drug to market. And so you can see in that environment why there's only these blockbuster drugs that cater to something that's pretty popular as opposed to real niche products. And it just makes things really expensive. But they also commit the opposite error where the FDA will approve something that really is dangerous in a meaningful sense, because everything isn't, there's no such thing as a safe drug, all right? But the point when I say dangerous, I mean in the colloquial sense that if people knew the full risks, they wouldn't be taking it. And yet that gets approved and go look up the Vioxx scandal if you want and you'll see like how there was an insider who was saying that the FDA was, they approved it and they shouldn't have and then it takes a while for them to admit their mistake. And it sort of gives its blessing on something that it probably shouldn't have done so. Okay, what about vaccinations? This one to me is real simple, even though this is a hot topic now. So remember, everything's privately owned in a free society. And so every institution, every property owner can set the rules he or she wants. So like someone running a private school, if they want to, they can have the policy and say to the parents, hey, if you send your kid here, you got to agree to these particular schedule of vaccinations as put out by the local pediatrics group, blah, blah, blah. And if not, just take your business elsewhere. That's, they had the right to do that. And if some schools want to have a more open policy, they can do that. And so you let the market decide. So it's not that we need to come up with what's the libertarian answer to the vaccination question. It's just you leave it open and let institutions decide. What's funny here is I participated in a debate on this is that in some areas, you know, the case, like when it comes to contagious diseases and things, a lot of times, you know, you can see why there'd be a prima facie case for coercion to be involved to set up a quarantine. And then, you know, it's tricky to come up with, well, how would a free society handle that? But when it comes to just stuff like standard childhood vaccinations there, I mean, it is odd that prima facie, if a bunch of parents all do the right thing and vaccinate their kids, those kids should be somewhat protected from the unvaccinated kid, right? And so it's ironic that the people whose own kids receive the vaccination are often the ones really concerned about an unvaccinated kid playing with their kids when it's like I thought the vaccine was supposed to keep your kids safe, right? So there's that element. Now, what the response is, just to make sure you know it, the response from the people who think there should be coercion involved and the state has a role in forcing everyone to get vaccinated is they'll say, okay, well, there has to be this thing called herd immunity. And if a sufficient fraction of the population is vaccinated, then, you know, the disease or whatever can't get a foothold. But if we have too many that are unvaccinated and at any given time, several people have to be unvaccinated because there are certain medical conditions you might have or really young children who aren't yet ready to be vaccinated or would be dangerous if they took the vaccine. So that's fine, but then notice now, we're not saying the vaccine is safe or dangerous. The people who are pro-coercive vaccination are admitting there are some people in the population who can't get vaccinated because it would be dangerous for them. And so now you're just disagreeing with parents over where the line is to be drawn. You're saying, no, no, we think it's safe for your kid and the parent of that kid's saying, no, I don't. And that's what the argument's over. And so in general, the idea that we're gonna overrule what parents think is safe to put in their kid's bodies. I mean, that's pretty horrifying, I think. Okay, I got about two minutes here. Let me solve the immigration question in two minutes. You guys ready? Hang on. All right. So as it was something like prayer in school, there's no good answer here. Okay, that the people on both sides make compelling points. So when you're in a status framework, arguing over what the powerful, you know, institutional people running the state should do, everything's gonna be bad because it's involving the state, okay? What I would say, though, is there's also, though, no such thing as a right to freely travel, which sometimes people talk about, and that's if you think about, no, in other settings, that doesn't make sense. You can't just, the right to go anywhere you want. People own things. So let me just show you what the first best solution looks like and then you can try to figure out how to apply it in a status setting. But in a free society, private landowners set whatever policies they want. So when it comes to something like the US-Mexican border, think of it like this, okay, where you see all the different landowners who all conveniently have very short first names and it worked out well. Okay, so last thing here, you guys ready for this? So I'm saying people could set whatever policies they want and so some of them might be, what about Pam? What if Pam's crazy and she just lets, you know, Al-Qaeda throw parties in her backyard and they just come and go, is they please? Ready, watch how the free society would deal with somebody like Pan who's letting these people cross the Mexican border too quickly. Boom, you see how that works? Okay, so you need to get outside of the mentality of just thinking, oh, crossing this one line between Mexico and the US, if each parcel of land is privately held, it would be this sort of situation. So if somebody had really liberal policies, well their neighbors could then have more stricter ones and that would contain the problem if there really is a problem, okay? So again, that's the first best solution that you can quibble about, okay, what do we do in the current environment? Okay, that's my time, thanks everybody.


This is what all the parts and pieces of my prosthetic leg are called and how some of them work. At the bottom, we've got the foot shell. Pretty self-explanatory, this looks like a foot. Unfortunately, it does wear out pretty quickly so I'll get holes in the toes from time to time. Next is the actual prosthetic ankle itself. These move all different kinds of ways. I've got a couple different ones, but there are a lot of brands and a lot of styles you can choose from. This part is the socket and it's what my residual limb or nubbin actually inserts into. So this is what is around my leg all day, giving me the stability to be able to walk. Right underneath the socket is this valve. This is what actually allows air in and out so my prosthetic can suction to me properly. Moving on up, we have the sleeve. This is the external part that connects my prosthetic leg to me. It is sticky on the inside. I'll show you why in just a second. Now this is the liner. It is what is in contact with my skin all day, every day. If you turn it on over the interiors, that same kind of sticky substance that the sleeve is. This allows them to stick together, basically form that suction and allow me to walk. There are variations on all of these and every prosthetic leg is a little bit different, but this is what I use and what some of the parts are called.


My poem is called, When I look up at the stars. When I look up at the stars, I thank God for giving me my son. When I look up at the stars, I imagine a family, me, my son, and his father. I know that's all in my imagination though, but I generally want to know what having a family feels like.   But I honestly rather raise my son alone than with a father that doesn't try. When I look up at the stars, I see the different and old path of my life that I no longer will follow. There was a dark street of insecurity. My eyes were blinded by love. It was like being in a car that was driving by itself and couldn't be stopped. No one heard me yelling, help me, save me. I used to think drugs would make me feel better about myself. I remember waking up and feeling like I couldn't change my life. I couldn't change the life I was living. Feeling lonely like love didn't exist. My family and friends telling me to leave him. Then there's this street of sunlight, the path I have chosen to live forever. My son changing my life for the better. Walking with my son in my arms, kissing his chubby cheeks, feeling so confident love is here. And life is worth living just by becoming and choosing to actually be a mother so successful in all the duties I have accomplished. When I look up at the stars, I realize how being a single mom has made me so strong. It's incredible. All the people who criticize me don't matter because I am a mother.  I love him so much. I may not have a complete family, but I love my son with the love of a father, a mother, and a best friend. All that love together just for one person and that person is Elias. I never do anything for my precious baby boy. I hope he looks back on his life and realizes how much his mother loved him. I want to feel loved one day, but I look up at the stars and sigh. Sometimes I wish I had all the money in the world to buy us a better house. But at the end of the day, money doesn't make me happy. Elias does. That's all that matters to me. Elias, I love you with all my heart. Mommy.