Now guys since we have talked about tangent let's take one question on finding the length of the tangent okay I'll take a very simple one find the length of the tangent find the length of the tangent drawn from the point 3, minus 4 to the circle 2x square 2y square minus 7x minus 9y minus 13 equal to 0 super simple problem I just want to test whether you are aware of that formula which I discussed with you a little while ago please four tangents how can there be a four tangents from an external point to one circle Nitya they can only be one they can only be two tangents from an external point to a circle I think you're getting confused with the common tangents common tangents to two non intersecting circles yeah I'm getting only two values of m right so two possible tangents are there so I got m value as 0 and minus 8 by 15 only so only two values so two tangents are possible so in this case guys if you recall the length of the tangent I had already discussed with you since many of you are traveling I'm sure you are not able to write is that the reason why you're not responding so length of the tangent is under root of s1 okay but remember when you're finding s1 first find your s out s is going to be not this but it is going to be x square plus y square minus 7 by 2x minus 9 by 2y minus 13 by 2 equal to 0 so s1 is when you substitute the point in this and when you do that you are going to end up you're going to end up getting 26 I guess let's let's simplify this so this is going to be 25 this is going to be minus 21 by 2 plus 36 by 2 which is 18 minus 13 by 2 okay so which is 25 plus 18 minus 34 by 2 which is 17 which is 26 so length of the tangent is going to be a root of 26 units next concept that we are going to talk about is the concept of pair of tangents concept of pair of tangents now to any circle from an external point let's say x1 y1 we already discussed that we can form a pair of tangents from this external point to this circle okay now the combined equation of these pair of tangents which you can draw from a point p on to this circle that is pt1 and pt2 the combined equation is given by the expression t square is equal to ss1 okay so let's say this equation of this circle is x square plus y square is equal to a square then what is t please be know please be aware of these following notations s is this s1 is this and t is going to be this t is going to be xx1 plus yy1 minus a square okay so the combined equation of the pair of tangents that you can draw from an external point to the circle is xx1 plus yy1 minus a square whole square is equal to ss1 this is ss1 okay now the question is how do we get this equation what is the proof for this okay so basically what I'm going to do is I'm going to take some arbitrary point let's say alpha beta on this tangent okay I'm going to take an arbitrary point alpha beta on this tangent now we know that if I know two points I can easily find the equation of a line by using the two point form right so y minus y1 is equal to slope times so this is going to be a slope times x minus x1 okay in other words if you simplify this you are going to get y times alpha minus x1 minus x times beta minus y1 and you're going to get minus alpha y1 plus beta x1 so it will be plus beta x1 minus alpha y1 equal to 0 okay now we know that the perpendicular distance of this point of this line from the center of the circle is going to be your radius of the circle right so I can say distance of distance of 0 comma 0 from 1 is going to be a units that's the radius of the circle so I can use the distance formula mod this by under root of coefficients of x square and y square this is going to be a okay square both the sides you will get b x1 minus sorry beta x1 minus alpha y1 square equal to a square times alpha minus x1 square beta minus y1 square okay now basically the equation of the pair of tangents is the locus of alpha and beta isn't it locus of alpha and beta is equal to the equation of pair of tangents this is something which you need to understand so it becomes a locus question once again okay so what I'll do here I'll replace my beta with y and alpha with x okay so when we do that you get y x1 minus x y1 square is equal to a square x minus x1 square y minus y1 square okay if you open the brackets I mean it's just a simplification process which you can do it at your end also if you open the brackets you get y square x1 square plus x square y1 square minus 2 x y x1 y1 equal to a square x square x1 square minus 2 x x1 y square y1 square minus 2 y y1 okay and if you further simplify it you end up getting y square take common from both the sides you'll get y square x1 square minus a square take x square also common you'll get y1 square minus a square okay minus a square x1 square plus y1 square equal to 2 x y x1 y1 minus 2 a square x x1 minus 2 a square y1 okay now just add just add x square x1 square y square y1 square plus a to the power 4 on both the sides okay if you do that y square will have x1 square plus y1 square minus a square common similarly x square will have x1 square plus y1 square minus a square common and not only that a square will have x1 square plus y1 square minus a square common equal to 0 oh sorry is equal to this side will have this side will have x x1 y y1 minus a square whole square and guys this is nothing but x square plus y square minus a squared times x1 square y1 square minus a square is equal to x x1 y y1 minus a square whole square so hence proved now the proof of this is not important the proof for this is not important but yes this result is very much important this result especially this one is very very important t square is equal to ss1 why it is important is because if you change your circle to let's say a general form of the equation of a circle you can still use this formula so let's say if your circle was if your circle equation was x square plus y square plus 2 gx plus 2 fy plus c equal to 0 then we can write the equation of pair of tangents pair of tangents can be written as t square t will be this this will be t okay t square will be equal to s this will be s s1 will be this okay so this is a universally used formula is irrespective of which type of circle you are dealing with okay but I would strongly discourage you to use this method you will say why then why did you teach it see there are there are easier ways to find this answer if you have been provided with the external point and the equation of a circle as you would recall the previous question that we did finding the equation of a tangent drawn from an external point 1 comma 4 that approach would be a much better approach to solve this kind of problem okay and that will actually give you the equation of a pair of tangents in separated form also okay let's see let's see a question where we can implement what I am what I am trying to say so first find out the pair of tangents find the equation of tangents from the point 3 comma 2 to the circle x square plus y square plus 4 x plus 6 y plus 8 equal to 0 plus 8 equal to 0 okay now again there are two ways you can use the formula which I gave you that is t square what is going to be t over here what is going to be t over here t is going to be x x 1 y y 1 plus g x plus x 1 plus f y plus y 1 plus c equal to 0 correct so x 1 is your 3 y 1 is your 2 so your t expression would be 3 x 2 y g will be 2 times x plus x 1 f will be 3 times y plus y 1 plus 8 okay you can further simplify this 3 x plus 2 x will give you 5 x 2 y plus 3 y will be 5 y and 5 6 plus 6 will be 12 12 plus 8 which will be 20 okay so you can write the equation as this square is equal to s this is your s that is the equation of the circle itself s 1 is when you substitute the point into this which is going to be 3 square 2 square 12 12 plus 8 which is going to be 9 plus 4 13 13 plus 13 plus 32 which is going to be 45 so you can take common 5 outside so which will be 25 times x plus y plus 4 whole square is equal to 45 times x square plus y square plus 4x plus 6 y plus 8 equal to 0 okay so cancel out a factor of 5 and this is 9 okay and open this you'll get x square plus y square plus 16 plus 2 x y plus 8 y plus 8x equal to 9x square 9 y square plus 36x plus 54 y plus 72 which on simplification will give you 4x square 4 y square if I am not wrong you will get minus 10 x y you will get minus 4x plus 14 y minus 8 equal to 0 okay whoo that was a big you know job to be done now the same thing gives me a equation of a pair of tangents this is the pair of tangents equation so I don't get the individual tangents from it I get a combined equation of a pair of tangents okay how do I separate those individual equations from it that's another task so for that all of you please listen to this carefully you drop the factor of 2 from everywhere so when you drop the factor of 2 from everywhere this is what you get okay how to break this into two lines that is what I'm going to discuss first focus on the second degree terms that is 2x square 2y square minus 5xy try to factorize it like this okay forget about the rest of the terms as of now so take 2x common x minus 2y take minus y common x minus 2y okay so it can be factorized as so it can be factorized as 2x minus y times x minus 2y okay now since other terms are also present it is very evident that there has to be some constants over here let me call it as p and q okay so what I'm trying to say is that when you multiply these two lines you end up getting this pair of straight lines pair of tangents is nothing but pair of straight lines okay now try to compare the coefficients of x so x coefficient will be 2q plus p correct and that will be equal to minus of 2 try to compare the coefficient of y y coefficient will be minus q minus 2p and this will be equal to 7 okay let's solve for p and q let's multiply this with 2 and add them you will get minus 3p is equal to 12 so p will come out to be minus 4 now if p is minus 4 we directly know that p into q will give you minus 4 correct so p into q is minus 4 so q will be 1 that means if I have to write this pair of tangents as two separate lines it would be 2x minus y minus 4 times x minus 2y plus 1 equal to 0 that means individually your tangent equations will be 2x minus y minus 4 equal to 0 and x minus 2y plus 1 equal to 0 but this I do not recommend using this method because of too much of work involved instead you could use the method which we discussed just before we took this problem okay so there is a circle okay and this circle is x square plus y square plus 4x plus 6y plus 8 equal to 0 okay that is it is a circle with center at minus 2 comma minus 3 and it has a radius of under root of g square plus f square minus c which is under root of 5 okay so guys what can we do over here is there any method to solve this problem okay so what I do now I will assume the tangent let the equation of the tangent be y minus 2 is equal to mx minus 3 so I'm assuming m to be the slope of the tangent and since it is passing through 3 comma 2 I can always assume the equation of a tangent to be this okay y minus 2 is m times x minus 3 which automatically gives me the equation as mx minus y plus 2 minus 3m equal to 0 okay now I can get the value of m from the fact that if I drop a perpendicular from the center of the circle it's going to be at a distance of it's going to be of length root 5 so I'm going to use the distance formula now that is m into minus 2 minus y mod divided by under root 1 plus m square is going to be root 5 okay so please simplify this and find the value of m from here it's a simple quadratic in m tell me the value of m so if you simplify this further you will get a mod of 5 minus 5m 5 minus 5m by under root of 1 plus m square this is equal to root 5 okay square both the sides if you square both the sides you get 25m minus 1 square is equal to 5 times m square plus 1 so you can cancel off the factor of 5 so 5m square minus 2m plus 1 is equal to m square plus 1 that gives you the equation as 4m square minus 10m plus 4 equal to 0 okay which is nothing but 2m square minus 5m plus 2 equal to 0 which you can factorize as 2m square minus m minus 4m plus 2 equal to 0 take m common and take minus 2 common so you get m minus 2 times 2m minus 1 which means m is 2 or m is half okay the moment you get this guys your job will be pretty easy because we have already written the equation of the two tangents what are they okay the equation of the tangent is going to be y minus y minus 2 is equal to m x minus 3 right so replace your m over here one by one so first put 2 when you put 2 you automatically get y minus 2 is equal to 2x minus 6 which means y minus 2x plus 4 equal to 0 is one of the tangents let's call it as t1 and when you put half when you put half you get 2y minus 4 equal to x minus 3 which means 2y minus x minus 1 equal to 0 let's say it's standard 2 so this work is much much much much easier as compared to what we had done in the previous scenario right in the previous scenario we had sat and found out the equation of pair of tangents and then we had split the two tangents from it


I wanted to start off by simply, could you explain to the audience, what is impact investment? Perfect, Poku.  Because when you buy a company, or buy a piece of a company, or we're not going to lend money to a company, this company can do something good for the world, or bad for the world. Really, we have companies that are producing fossil fuels.  So when you are investing in a company that's going bad for the world, okay, you can make money. But what is the cost for the planet and for the people of your investments? So impact investment is not a donation. It's a responsible investment in which you are going to have direct impact in something. So I'm going to give some examples. We have finance and smallholder farmers in the northeast of Brazil, poor people that plants cocoa and reforests. And in one year, the income of those guys increased around 38%. It's incredible. Because we are making money for us, we have a positive return. And also, we are helping the people to have a better life, and also to protect the nature and to reforest. So this is the impact investing. When you look at those other aspects of the investing, not just the graphs, which is important, okay, I'm going to make money, yes. But what's the cost for everyone? One thing that we see many times is that the companies and many investors privatize the profit and socialize the loss. If you are damaging the environmental, if you are creating some problems through climate change, then everyone's going to suffer and you're going to have the profit of it. How can we change it? So when we have an investor that looks in other ways, we can make the world better. You know, that's really good because I think being able to invest, make money but also have that fulfillment, we're self knowing that your money has been put to good use and impacted someone else's life. I think that's definitely the best way to go about things.


Can I now turn to you, Jacques, for a few thoughts, again, as I said, from an informed outsider, if you allow me to call you that way. Thank you, Mr Chairman. Thank you, Thierry, for the invitation, and just a caveat to state the fact that views expressed here are my own and not involving any organization with which I collaborate. Just a few excerpts from my daily medical literature review over the last few weeks. Two weeks ago, the FDA approved the most expensive drug ever, 3.5 million per patient to treat hemophilia B, a very rare disorder, which affects just a few patients. At the same time, almost at the same time in the wake of COP 27, 230 medical journals published an editorial calling for urgent action, urgent climate action in the interest of health care, pointing out the terrible increase in the burden of disease induced by global heating, mostly in poor countries. And the Lancet added a comment stating that many countries still provide societies to fossil energy, which are potentially higher than the health budget. So we see that governance may be improved. And finally, there was a flurry of articles criticizing health governance, culminating with very good article dating back to February this year by Jean-Pierre Zaniferry and the Bruegel team. And the title is explicit. It says health governance, a forensic analysis. So is governance really dead? I think it is not. I'm not going into the history of WHO creation back in 1948, the declaration of Altma Attab back in 1978, then Astana declaration in 2018, calling for the rollout of universal health coverage in line with sustainable development goals. But I do think that although WHO has been criticized mostly for political reasons, it did a good job with former pandemics. The globalization did a good job because it really took millions of people out of poverty and improved the health care system. So I think criticism is certainly in excess. Also, there are a number of levels for additional governance. The regulatory governance works very well. Agencies collaborate and we've seen how efficient they have been to approve new vaccines. There is a level of international governance which has an influence of health care and which is heavily criticized, which pertains to intellectual property and which has to do with sovereignty, with science, with scientific policy, with economic policy and certainly we'll have to address this in later panels, but I have no time today. And then we all know that all countries do try to have a governance of the health system with very varied means but which all resolve to cost containment. There are other angles of governance, moral or intellectual, scientific societies doing a very good job in their discipline to kind of disseminate good practice based on science. But by definition they have no mandate to propose to prioritize between various disciplines. Stock markets exercise a governance on health product and technology manufacturers, but they have an obvious bias which is shareholders' interests. And finally, we have philanthropic and humanitarian, humanitarian on the terrain, who too often have to establish a governance of their own because, I mean, they really have to do a triage between immediate cons. So how to improve the edifice? Well, my plea is that before thinking of structure we need to really agree on metrics because it's very difficult to measure health care. Actually, once you've gone out from mortality it's very difficult. Then I would really encourage institutions to agree on objectives and to submit those objectives to democratic criticism and debate because it always ends up in allocating two scarce resources and so the need for the population to accept this is very important. I would certainly advise to governance to relinquish the power in health care to health professionals because my 30 years experience actually with health care is that it's much easier to teach a doctor in economics or mathematics or management than to take a lay person, kind of an administrative or business person and teach them medicine. And very often the power in countries in terms of managing budgets is far too much in the hands of the administration and not enough in the hands of the physicians. And as mentioned, I'm not a physician, but I love the physicians. So my prescriptions in summary to kind of keep time in line. Once again, work on metrics, I mean really measuring health is a difficult issue and reinforce epidemiology. I think epidemiology is a science at the crossroad of mathematics and medicine and it's essential to really understand and propose the appropriate metrics. Educate the population. I think this was mentioned in the previous panel and because the choices are so difficult we need to educate the population. Turn the power to health professionals and finally I would definitely advocate for decentralization and turn the power in as much as possible to local players because they often know better than the people who are in the offices, in the central offices. Thank you for your attention. Thank you very much. Thank you, Jacques. So now I must confess I have a problem because we started this session 10, 15 minutes late and I'm told that we have to stick to the schedule and therefore we have no time unfortunately for discussion. Apologies because I was looking forward to a discussion. So with apologies, please let me just give a very short conclusion from what I've heard in the previous and in this session. One, the world is not better prepared today, December 2022 to face a new pandemic as compared or hardly better prepared than it was in 2020. Second, a number of processes have started. Many of these processes including the negotiation of a treaty, the negotiation of a new global health strategy in Europe, the negotiation of a political resolution and the UN General Assembly are slow, cumbersome as Anders said and yet as many of you have said including Lionel when it comes to some of the regional innovations, these processes are opening new encouraging perspectives. Third, there are two key issues in global health that we and preparedness, pandemic preparedness that we still not have clarity on. One is governance and the second is the financing and clearly the international financing facility as it called that was recently established is far from being where we would like it to be. And my last point is that I hope that as a public of the World Policy Conference you realize that health is not just anymore about health. Health is of course on the health agenda, but it is on the development agenda, it's on the global security agenda, it's on the economic agenda, it's on the social justice agenda and as we heard from Christian and the One Health issue is it's on the agenda of all of the interrelated crisis in which the world is currently confronted. So with that, please join me in thanking our panelists.


So, it's come to my attention that Akasan has discovered my contingency plans to take him out, if he were to turn Rogue well, Magnusite. Let's see what Akasan had to say. Oracle is that Tyrone Magnus, a.k.a. is explaining how to defeat me, Akasan. Akasan's reactions, I am Akasan, so let's see what the hell Tyrone's talking about. I saw his, I watched a little bit of his impression about doing Batman or whatever, but I decided to stop watching it, because I do Kevin Conroy impersonations as well, so I figured it probably would have been a good idea for Worlds to collide, the multiverse subspeed. It wasn't Kevin Conroy. It was my own impression of Batman. Spanning upon this idea of Batman explaining how to take out the Justice League, and now we have Batman explains how to defeat the four react- The react-tastic four, goddammit. How to defeat the re- Get it right! The four, including himself.   What? Stupid, I'm sure. Because we all know there's no way to really defeat me. Even if you pass my subscribers. Baa-ha! Move up, poke at you, James. Yeah? See what this is all about? It's about your destruction. This is Batman, security level, Omega, password, Delta Charlie-27-5-193. Where do you get these pictures? It's a new protocol. Off of Google!  That's right. That's right. That's bad. It's because of his innovation that the reactor community has come together and it's the same innovation that can make him a powerful adversary If he were to turn against us Shrack Samson of the Bible His dreadlocks seem to needle him to channel his power Cut them and he'll be powerless This himself, Ryan Wright, would be a very dangerous opponent worried to turn His homoerotic jokes, sighs, strength Swishly beard and amazing resemblance to Russin Trying to keep his current face Unbeatable opponent to bound But people like most strongmen His weak spot would most likely be This woman taking her hostage Which shortly emotionally distract him And neutralize him for good Along with his gay jokes I can remember no contingency Filed code need Crocodile Yeah Gator Martin was the first reactor I could notice of Before discovering the rest He has a strong subscriber base And a worthy sidekick known as Cooley Their friendship seems to be strong So taking Cooley as a hostage Would cripple him emotionally Also, because a reactor's main power Comes from being able to see what they are doing Distribute Gator's glasses To neutralize him for true power Face dog too I forgot he's got a little dog too Get you again and I'll talk to you Carbination While not a member of the Big Four Speaking in his own words Jokes is a good reactor Which is just one reason it would be Difficult to face in combat Should he turn against the Big Four It's not the thought that I relish But if it must be done The following strategy could be useful Because of his competitiveness If he could be convinced that he is fighting And he felt he could then theoretically be trapped In an unending cycle of combat Like he already knew it was coming That I've been a wonder woman Investigating the feasibility of neuro-virtual reality He knows, he's a fan He's thought comes A secondary form of neutralizing jinx Is to cut off his grape soda supply To most of his reactions These contingency claims are discovered In the wake of minding and capacitating Please understand This had to be done for each of us Which brings us to A fundamental contingency By all codename And more so Half rock Shut up A.K.A. The Black Viking A.K.A. The Black Kryptonian A.K.A. The Black Tiger A.K.A. The God that wields the Dark Milner A.K.A. The Jinx Savage A.K.A. The Mr. React Passage Is the God that will... And Maxito Brown The best way to disable his reacting abilities Would be to sexually distract him His head helps him pre-sensors Or as he affectionately calls them His magnetistas Are an excellent blind spot Slipping an anti-arretian agent Into his morning coffee With rendering him when they're useless Oh my god Filling his magnetistas with sexual fantasies In-between reactions With him sustaining a blow to his male ego In this way, he'll become withdrawn And then short himself Neutralized by his inability But right now, it's in the caption Think carefully before you do this Ha ha ha Think carefully, that's right Put the pen and paper down, A.K.A. Very well played Thank you If you want some backstory on that Highly recommend you go see the Ah, the comic was a little better But animated feature That was called Justice League Doom That's what Tyrone is kind of parroting off of And some of those Those tips were exactly what He was mentioning here The one with Jinx Was directly related to Wonder Woman Wonder Woman was Constantly in a state of battle And she was hallucinating Basically Green Lantern Basically That one was great He basically Thought that he was Blind and he couldn't see And it was through hypnotic suggestions He was blind and he couldn't see But He wasn't really But he couldn't use the ring after that Because there was some The worst one was Superman That was the date That was a messed up It was like an itchy kryptonite or something That was burning Superman from the inside I'll tell you You can pass it to the Green Lantern They can think he killed somebody Or so I can't remember Thank you And I'll cut it to your skull Again, it was Not an impression Of Kevin Conroy It was my own impression Of what Batman would sound Like if I voiced him That's it I didn't want to try to copy Kevin I just wanted to be my own Anyway Man sights Hope you liked the video If you enjoyed the reaction The reaction that just happened Press the like button share Subscribe If you didn't hit the like button share And subscribe One million subscribers


I would have known everyone. I feel really honored to stand here. And the subject of my presentation is the recombinant Dengue virus to NS5, an effective antigen for diagnosis of Dengue infections. Dengue virus belongs to flu-aware dial families and are classified into four immunologically distinct serotypes, can cause disease ranging from non-specific fever illness to classic Dengue fever, Dengue hemorrhagic fever and Dengue shock syndrome among the DHF and DSS are often fatal. And Dengue fever is endermic in tropic and sabotropic climates. There are nearly 390 million Dengue virus infections that occur annually and over the past decades, Dengue fever has separated from less than nine to currently about 128 in epidemic countries. Dengue virus is transmitted by female mosquitoes, mainly Egypti and ancient Alps pictures. All the serotypes can be transmitted from human to human. And the individuals infected by any one serotype will have life-long immunity against re-infection of the same serotype, but only partially protected from other serotypes. Infections with a different serotype are associated with a higher risk of severe complications such as DHF and DSS due to ADE infection. And the Dengue virus is also a prototype of other flu viruses. For example, the Zika virus, this homology raises the risk of cross-reactive immune responses and subsequent ADE infections in the case of secondary infections or immunization of the individuals. And the recent outbreak of Zika virus epidemics has raises a growing concern with both viruses. Around early 2016, the first Dengue vaccine has been marketed in several countries, but accumulating response indicates that this vaccine did not achieve the desired effect. And it should take conscious that this vaccine, this vaccine might cause ADE infection in populations. Here are some prevention and control strategies are proposed and practiced in Dengue endemic regions, but none of them achieve the effect. Dengue diagnosis is based on epidemic information, clinical symptoms and combined laboratory detections although there is no specific treatment. Early diagnosis is important for proper medical care to minimize mortality and for proper initiation of public healthy control measures. There are several approaches to establish laboratory diagnosis. And these are all different specificity and sensitivity. And require more than two detections, two detection indicators. Any single indicators is not enough to provide reliable and effective results. And there are some rapid diagnosis of antigen detection and antibody detection. Targeting NS1 are now commercially available, but these both of them require all the four stereotypes of recombined NS1. Why are we interested in NS file? Dengue virus NS file are highly conserved among stereotypes that have not been found to participate in the ADE phenomenon. Dengue single open reading framework includes a polyprotein precursor which is cleared by cellular and viral properties into structural and non-structural properties. NS1 and NS file appear almost at the same time. And NS file consists of two major functional domains. The N-terminal ion method transfer is domain and the C-terminal ion dependent ion polymericis domain. And the NS file IDRP domain plays a vital role in viral ion replications like other polymericis. Dengue virus I process an architecture that is conserved across different classes and families of polymericis. This structure mimics a half closed right hand with the three sub-domain termed the finger palm and thumb. NS file potential to be an anti-viral target and a biomarker of Dengue diagnosis. We constructed an IDRP domain expression placemates and NS file four length expression placemates. And expressed a purified 70 keto ketone fragment and the NS file a four length fragment in E. coli. And these two purified recombinant products reacted with the serial operations effected with Dengue virus in an ELISA with higher OD index with compared with control zero. And the recombinant Dengue virus two NS file showed strong reactivity for any of the four serotypes while the 70 keto fragment show strong reactive for Dengue virus two and four. And the Dengue virus two NS file might be an infective antigen for Dengue diagnosis and the 70 keto fragment also can be used for auxillian diagnosis. Thank you.


Thank you Dede. So I would like to thank the organizer for the invitation, especially I would like to thank Stefano for his hard work. So single backfield, I mean backfield with singularity, in fact I will concentrate on the singularity. Okay here is that this is a joint work with my student, Lu Songzhen. And this is a framework. So we can see the compact manifold without boundary and can see the differentiable backfields. Later on we were restricted to r equal to 1. And we'll use this small file to deload the flow generated by the backfield. And the compact file to deload the derivative of the backfield. We always use this symbol to adjust for, this is traditional. Okay, so we use this symbol to deload the backfield, that zero also the backfield. We call it the singularity of the backfield. Maybe somewhat called VIX point or REST point, but we will call it the singularity of the backfield. So we distinguish the periodic orbits and the singularity. That means, I assume, we don't think singularity as a periodic orbit. So it's a periodic orbit where we will request that it's not singular. Okay, so we can see the two most dynamics, two kinds of most. The first one is the stronger one. We can see the open and then subset of the whole dynamics. The second one is the weak, it's called generic. We can see the countable intersection of open and then subset. So with their properties is generic. That means it's satisfied for system in the countable intersection of open and then subset. So this is to a large part of the dynamic world. We will only consider R equal to 1 just because for R, for C1 case we have many powerful perturbation techniques. The first one is Frank's Lama and the closing Lama and the connecting Lama. So we will unconsider R equal to 1. If R is a little bigger than 1, it's stricter, larger than 1, then all these Lama maybe, at least in the strongest version of Frank's Lama is no longer satisfied. Even for the, for example, R equal to 1 plus epsilon, it will not satisfy. So it's a big problem for a larger than 1. But anyway, at the end of the talk, I have to borrow some idea from Patent Theory, so I have to assume R larger than 1, but in a very, very special case. Okay, so let me talk about what the system far away from host show, what I was talking about. So this is a revelation of most smell system. It's very, very simple. It's the first kind of system which is proved to be stretch stable. So the law is that the law on the set of the system consists of only finite, many critical, critical orbits. That critical orbits, that means finite, many singularity and the finite, many of periodic orbits, of course, is harmonic. And plus the transverse, transversality. That means a stable manifold of any critical points is transverse to any unstable manifold, to unstable of other. So we can see that this is a picture of a different model, not a picture of a, of a, of a theoretical orbit of laws, just for a fixed point of, of a different model. Since the transverse of, transverse orbit of a theoretical orbit, I mean the diagram is also easy to, to draw. So I just draw a very simple picture for the different morphism case. We assume it's a fixed point, a harmonic fixed point. So it's a harmonic point of, of the, of the fixed point if it's a transverse intersection of the, of the stable manifold of P and unstable manifold P. So we all know that back of Simeon, Simeon said that transverse harmonic orbit one needs to, one needs to horseshoe the existence of horseshoe. So what the so-called density, density conjecture, a kind of density conjecture punish, we call it the weak density conjecture. It claims that most system, and the system with horseshoe forms open dense subset of the whole, of the set of whole dynamics, whole, whole world. So, so this part is very, very simple. It's just the consist, so for the, the knowledge that just consists of finite many orbit. And this part we know since there the horseshoe is very, very complicated. I like this kind of statement very much. It's very simple and of course 1 plus 1 is equal to, it's also very simple. But this is not, it's the proof of, of such a, the statement is not far too far from trivial. So since, as I just said, the back of Simeon system, the back of Simeon theorem, the transverse harmonic orbit will imply the horseshoe. So in, in this talk they are always, they play the same role in, in the, in the following work. So there's a parallel, parallel density conjecture which needs a lot of need, much stronger than this one. So this is, so I, I was comparing with this, I call it strong density conjecture of palace. That, that is, that is a generic system far from homo, biification is hyperbolic. But I was not taught too much about these conjectures. I will not go on this. I just, I will come this, the best one, the weak density conjecture. But from the statement, homecoming biification means that the tangency or heterodimension cycle. Since, since both of these kinds of biification will lead to the existence of horseshoe. So this, the weak is, weak conjecture is real weak than the strong conjecture. So what about the progress of this density conjecture? Oh, let me, I will see more about this. I think palace state this conjecture for different morphism, canary in, in, in, in, in the paper in his paper. But I think that he did not state this conjecture for a fact field. But since it's a very, very close at least in the spirit of his density conjecture. So I also call this density conjecture even for fact fields. It's due to palace. But what the precise statement. And for this statement, this is also if you for palace state a similar conjecture for fact fields for the density conjecture. But in his statement, he, he can, he can see the homecoming biification of singularity. But now we un-consider the homecoming biification of the periodic orbit. This is a difference. I think this is an essential difference from his original, original statement. So in some, I, I strongly that the conjecture, this statement is stronger than his original one. Okay. So for, this is a program for different morphism, of course, just for recognize for different, for C1 dynamics. That means just for C1 dynamics. So this, in, in, in this famous paper, Pujols and Stambrano proved the strong density conjecture of palace. So as a consequence, of course, they proved the weak density conjecture. And with Boratia, when we proved the three-dimensional case for weak density conjecture, but for different morphism. At last, Kravizia finished this story for different morphism case. But how about for the flow case? For the, for the non-singular vectorials, I think they proved Arroyo and Vettric health. Proved the strong density conjecture. Oh, well, although they mentioned the singularity in their paper, but it's essentially for non-singular case in, in my opinion. And very, very recently I found a paper in the archive show and then gave a, gave a, in the paper, they, they follow the idea of Kravizia, use the central model path to the Pankalei, Pankalei map along the section of, of the flow case. So this is almost a parallel tool. Just use the same idea of for Kravizia. It's the idea of central model. So this, how about the singular case? For singular vectorials, previously, just one year, maybe two years, I'm not so sure. I go with Dawei Yang or we prove the weak density conjecture for three-dimensional flow. Three-dimensional is, in some sense, it's very similar to the case of two-dimensional morphism. So, and Dawei Yang, Kravizia with Dawei Yang, they launched the three-dimensional strong density conjecture for three-dimensional vectorials. But how about the high-dimensional case? So this is what I would like to talk about. But unfortunately, I did not, I did not, I could not get a very, very complete answer to the high-dimensional, just a partial result. So I have to introduce some technical things to, for the statement. So first, this is a so-called chain equivalence. So two-point chain equivalent means that for an epsilon, you can find an epsilon chain from X to Y and from Y to X. So we denote, see, are the set of chain equivalent set. That means X is equivalent to itself. And this race relation is a closed equivalence relation of the chain equivalent set. And the chain equivalent, the equivalent class under this equivalence relation is called, I will, I will call chain equivalent class or chain class or just simple class. So what I mean class means the chain equivalent class. So this is so, okay. The, the user way for, to, for proofing the weak density conjectures as follows. So we use this symbol to denote the set of MS, to denote the set of MOS, SMELL system and HHS, to denote the set of system with HOSCHU. So if, if a, so this is approved by contradiction. So I assume that weak density conjecture is not true. If, if the weak density is not true, then we can take a system outside the, the closure of a MOS SMELL, SMELL system and the system of HHSCHU. We can take a generic system. That means C1 generic system. And, and then we, we can find a long trivial chain class, sorry. This is repeated, sorry. We can find a long trivial chain class. Long trivial means it's not reduced to a periodic orbit. Long trivial. And then we can, there exists a long, long trivial, of course. Minimal set which is, sorry, this is contained in C. Where is partial hyperbolic splitting? And central is one dimension. And then to analyze the dynamics of center leaves, I'd like to get a contradiction. This is what the, the central model for, for, for, for Gravezial tells us. So now for my, for today my result is just for the partial answer to the step one. Not, it's a, nothing with step two. But for the, this is a, for the morphic case. But now we have a singularity. So the long trivial case for fact fields has a singularity. So what does a partial hyperbolic splitting look like? So let's have a picture. This is a famous Lorenzo tractor. But this is too difficult to analyze. So we will use the geometric model of Lorenzo, Lorenzo tractor. So this is, I think everybody, almost everybody know this picture. But I should emphasize something and I will come back to this picture later. So this is a tractor. A tractor looks like a boat. And this is like a, okay. So this is the main result. This is a rough statement, not so precise. So we take a C1 generative vector which is far from, which is far from most male system and hostile. So in something we assume that weak density conjecture is not, is not true. So we take, we can take such a kind of for a fact field. And then for any such kind of fact field, this fact field has a singularity such that the chain class contains, contains sigma is long trivial. The conclusion further, every singularity, then this chain class has a same index. The index here will mean the dimension of the stable bundle of, of sigma. So we always, we can always assume sigma is hyperbolic. That means, oh, okay. And every singularity is Lorenzo like, I will give it a definition later. And the chain class admits a partial hyperbolic split. So it's in the spirit of the step one. We put some partial hyperbolic split. I will, I will give a precise statement later for the partial hyperbolic split. Okay. First I will explain the so-called Lorenzo like. So give a single, a hyperbolic singularity when least the level of exponents of at sigma is lambda s to lambda t with multiplicity. So the set value of sigma is defined as the nearest to eigen value which is the, the, the largest negative neopelow explore pollens and the smallest positive neopelow explore. We take the sum of these two neopelow explore. So there's a symbol of the, the sign, the sign of the set menu is very important in the following. So we see the singularity is Lorenzo like if the set menu, set menu is not equal to zero. For example, assume is greater than zero. So the stable bundle of sigma can be split into the direct sum of two neopelow sub bundle such that the central bundle is, is one dimensional and of course this co-dimensional one with respect to the, to the stable bundle. And another condition is the way the strong, the strong statement of sigma intersect the chain class in at only one point, at only one point. This, let me have a look back to the, to the, to the geometric Lorenzo attractor. So this is a strong stable manifold. They will intersect attract only at this singularity. So we can like these two condition as the, of course a singularity satisfying these two condition Lorenzo like. It's like the singularity in the Lorenzo attractor. So, okay, more, this is more precise for the statement. The first one is, the first two are the same as previous. So if the set menu, this is for the passion habit splitting. So if the set menu is equal to the zero, then we get such kind of splitting. And then the bundle is, this is the strong stable bundle is one dimension less than the stable bundle of singularity. And this is a similarly if, if the set menu less than zero. So if, if the chain class contains a larger singularity which whose set value is, is the sign of the, the set value is different from the sign of the set menu of sigma, then we will get such kind of passion habit splitting. This, the center has two dimension, has two dimension. And I think this is the best at this, at this kind of passion habit splitting is the best we can, we can get. Since we have only one possible long, only, only one possible, possible zero depth of experience. I mean module as a flow direction. So this is the best passion habit splitting week. So this is what we can get. But it's not, it's still not so, so good. Since in, in, if we assume that it has two such kind of singularity, we can get such a kind of splitting. But if we consider only one singularity, what can we see? We, we don't know in, in general case, but in four dimensional case, we can, we can get more detailed statement for the result. But anyway the, the, the next result is not corollary of the theorem one. So I state the theorem two. The first two are the same. So we can see the, the index of the singularity. If the index, this is a four dimensional, four dimensional. So now, from now on we will concentrate on four dimensional case. I'll never talk about higher than four dimensional case. So if the singularity, the index of singularity is three, then it's, of course it's, it's well now that it's the upper of stable. The upper of stable, since the upper of stable is very important concept in the volume. So I forgot to give the, the definition. So we gave a compact set. It's a compact, I mean, very set. It's called the upper of stable. The upper of stable. If for any neighborhood U of lambda, there exists, there exists neighborhood V of lambda, V of lambda such that the positive orbit in V is contained in U for any T greater than zero. That means this is, this is an event set for any neighborhood U. You can find using, it's a small one. V such that every orbit in the, in the small neighborhood cannot go outside the, the big neighborhood. So always contained in this neighborhood. This is so-called the upper of stable. And this condition for C1 general case is, is equivalent to so-called quasi-attractive. It's equipped for C1 generic. Equivalent to quasi-attractive. That means you can find a, often, you can find a nest trapping region such that, for example, five, okay, nest trapping region. It's small and small and the intersect is lambda and five T, any say T greater than one. So it's a trapping region for the flow and it's smaller and smaller. So in C1 general case, they are equivalent. Okay. So let's come back. If the index sigma, the index of sigma is three, then that means the, the dimension of unstable manifold, unstable bound of sigma just one. So the unstable manifold is contained in the, in the chain class. Since the chain class is on trivial. So it's not stable. This is, and in this case, we get such kind of, such kind of splitting.  This is also two-dimensional. So this is the best, best partial publicity we, we can expect. So for the index one case, it's almost equivalent to the best one since you can see the, you just can see the back, the back, the, the reverse flow direction. And the set one is more interesting, later we'll, we'll, we'll spend some time on this case. For index two, index to assume the set minute greater than zero. Then according to the, the previous result, we'll get, we get such kind of splitting. But this is one-dimensional. The strong stable is one-dimensional. This is three-dimensional. But now we can prove it's volume expanding. Volume expanding means it has at least one, around zero, near proper exponents. So this, this is very important. And this is very interesting. This, this chain class could not be the upper stable. That means, of course, in this circumstance, this is not, there's such kind of, with unstable dimension, great, there's a so-called Lorentz-Nike tractor with unstable dimension, greater than one. But for all case, this chain class could not be the upper stable. So this is the same.  This is a real color, just a color of the proof. So for C1 generic field, if the back field has a singularity index two, if the chain class is the upper stable, that means the set value of sigma is greater than zero. And single-hybonic. Then, then the chain class contains theoretical orbits with complex eigenvalues. Should be complex. Of course, complex eigenvalues in the unstable bundle. So what's a single-hybonic? So following more like specific, we called a compact invariance set of the effect field, single-hybonic, if we can find invariant partial-hybonic splitting for the tangent flow, such that this one is uniform contracting, and this one is so-called sectional expanding. So for four dimension is just area expanding. If this is just two-dimension, that means it's area expanding. But if the dimension is higher than two, then it's, the condition is so-called sectional expanding. That means for any two-dimension subspace, the tangent flow restricts to the two-dimension space is uniformly area expanding. Okay. This is what I mean. The, the polarity of one ring, and then we are not constructed a tractor, a tractor, such kind of a tractor. So we, according to the current, the, the, the theoretical way, there exists a theoretical orbit in the tractor such that the, the, the unstable, unstable eigenvalues are complex. So let me say more about this kind of a tractor. So this is the, the three-dimension of Lorenzo tractor. It's very easy to construct a four-dimension Lorenzo tractor, just put a very, very strong contraction. Then, so you can increase, increase the dimension of the stable direction very, it's obvious, but it's not so easy to increase the, the, the the dimension of the unstable direction. This is what the contribution of this paper. They construct such kind of, kind of a tractor, but according to our corollary, there's some real restriction on the, on the, on the, on the periodic orbit. So, and also they, in fact, it's almost at the same time, more or less, and put yours, also write a lot of paper on, on the, such kind of a Lorenzo tractor. This expected if all this kind of for, attract, have homotonic tangency. Of course, the example tells, tells that they may, they may have low tangency, but, so, so we have four-dimension of case, we have such kind of a partially hyperbolic splitting. This is one-dimensional, this is three-dimensional. So we have low tangency with, with, of course, with respect to the, with respect to the, the periodic orbits. After some more perturbation, we have tangency with singularity. So we just talk about the tangency of, of, of the periodic orbit. But this is the finest dominated splitting. This is the finest dominated splitting. I mean, for the singular tractor. So it could not be split into fine, for example, C plus in your, your, it could not be split again. This is like, what the color tells us. Okay, let's, let's continue. So, let's, let's, let's, let's continue. So there's a related conjecture is, this is a very, very strong conjecture. The conjecture claims that every long trivial singular chain class contains periodic orbits. So it's a homoconing class. So if this, this is a very strong conjecture. If the, if this conjecture to the, it will imply the, the weight density conjecture for, for, for, weight density conjecture panacea. Of course, with the help of a central mode of convivial issue. So it's, since it will imply, if the chain class naturally contains periodic orbit, then it's a homoconing class, of course. And it will imply the existence of hot shoe and then, then imply the weight density conjecture. So this is a very, very strong conjecture. Of course it's open, even for three dimensional case. But in our, when we solve the, the weight density conjecture for three dimensional case, we solve the, we solve this problem under the, this kind of splitting, this kind of partial hyperbolic splitting. Here is one dimension, here is two dimensional. But for general case we don't know. This is for, for three dimensional. But for singular, I mean, this is a, for the polarity conjecture. So for singular hyperbolic case, if class, for gen, this is for, for any, if the class is the upper of stable, then the answer is yes. I mean, for the polarity conjecture. So for three dimensional, I think it's a result of, for, for less than the specific. And for general case, it's a result of, for Vienna and Jagangyang. It's, I learned this from a lecture at the IMPAR Internet, the web of IMPAR. And of course, Jagang told me. And they reproved this result very, almost at the same time, I think. And I will mention the method in the paper later. I think, okay, let me go fast. So this conjecture, of course, is even for the singular hyperbolic case, it's open for the set of class. For set of, set of means it's not as near plus stable. It's also not near plus stable for minus x. We don't know. So if, if you have such kind of a good splitting, for example, if you have a very, very good splitting, this is a one dimensional, one dimensional, two dimensional, and, of course, of a chain class. Even if you assume it's, for example, it's a very expanding, we don't know the answer. So it's, even if you, it sounds a single hyperbolic, it's, it's very, very close to hyperbolic. But in this case, we found that it's very different. So, okay, let's talk about, more about the proof. So this is, we'll use the so-called linear power flow. This is a tangent flow. So this is a normal bound of the, of the vector field. That means it's, the normal bound at x consists of vector field which is orthogonal to the vector, to the flow directing, to the vector, to the vector at x. So the linear power flow is that we can see any vector field which is orthogonal to the flow direction and can see the image of, its image on the tangent flow. Of course, the, the image usually is not orthogonal to the flow direction here and then we take the orthogonal projection to the normal bound. This is a so-called linear power flow. And, but, okay, this is a basic property for the linear, for the linear power flow. This theorem, this theorem has proved for different morphisms. But, but, I think it's, the idea is almost the same according to the Frank's number of flows. But the Frank's number of flows usually is not so easy to stay. To, to stay, of course, it's not so easy to perform. Anyway, we have such kind of Frank's number. So this is a, I translated from the different morphism case. You can, if here, h t means the set of vector field with a tangent associated to a periodic orbit, just associated to a periodic orbit. So I assume the vector field is far from tangency. Then, there is a neighborhood of the vector field and the uniform t greater than zero, such that for any hyperbolic periodic orbit of the, the small perturbation such that the period is greater than t, then we have such kind of domination over the periodic orbit. This is uniformly for all periodic orbit of the system and its small perturbation. So it's very strong, strong domination of a periodic orbit. Here it is, we can say that the hyperbolic splitting for the normal bundle, okay? We want to use this kind of domination. But now we have singularity. You know that the normal, the linear punga flow is not defined over on singularity. So if the, if the, if the sequence tends to the singularity, how to use this kind of information? How to use this kind of information? This, this is what we do for the extent, this is the aim of the extended linear punga flow. So it's not, it's defined, the linear punga flow is not defined on a long compact set, but it's had as a natural compactification. We call this compactification extended linear punga flow. So we, what's the, what's the compactification? So we can see that the projected bundle, that means that it consists of one dimensional subspace of the tangent bundle. And this is a grass, it's kind of a grass manifold. So we, you know, this is the projection, the boundary projection. So, and then we can see the pullback of the tangent bundle. So tangent bundle is over m. So we can pull back to a bundle over the projective bundle, the projective bundle. So the pullback is a subset of for the product space. So we can see that the, this is a one dimensional space L. And V is a vector field in, in the, in the tangent bundle. And the pullback means that they have the same base point. So we are seeing, this is the, the non-bundle of this pullback. We, we can see the sub-bundle of the pullback, such that the, the the vector field is a, is orthogonal to the base point. So this, and then you can, you can easily define the extended linear power flow over this large, large bundle. So just if you can see the flow direction at the, if the vector field, the non-zero vector will generalize a one-dimension subspace. So it can, can be naturally embedded in this flow. This is what we call extended linear power flow. And now if we discuss dominated around a singularity, we will always use the extended linear power flow. This is very, I think I'm too slow. So first we will approach so-called Lorentz like this way. This is a very simple observation. This is a three dimensional diagram. But from this diagram you, you, you can find, this is the, the compact vacation at a singularity. So this is at, at the tangent bundle, at the tangent space at singularity. And then I think I have no time to explain on this. Okay. Just escape it. The second one, you can see the homogeneity of singularity. We just, if, if you have two kind, if you have two singularity with different, with different index, this is the index two and this is index one, then you're just connected to a loop, to a heteroclinic loop by, by connecting them. It's possible anyway. And then you choose two, two orbit arc here and here.  And then by choice, by a proper choice of the, the length of the orbit, this orbit arc and this orbit arc, you can, you can give the contradiction. Of course it's not so easy to, I will escape it. Okay. And last, we want, we just gave some idea to prove that if the index is, this index of sigma is two, it's not Leopold stable. So I assume on the count, on the count you assume it's Leopold stable, we'll get contradiction. So we should, we'll prove this is impossible. So I assume it's Leopold stable, then every singularity is also indexed, since we already prove it's the homogenous. And the sedimentary is greater than zero. Since the stable, unstable manifold of, it's contained in the chain class, so it should be greater than zero. If less than zero, we'll get contradiction immediately. The local star property is, that means you can find a neighborhood of the vector field such that any periodic orbit contain the small neighborhood of the chain class. And for any small perturbation, it's harmonic. So I try to prove this. This, if you all have proved this, then you can use some previous result to show it's a single harmonica. And since it's a Leopold stable, single harmonica means the existence of a periodic orbit. So we'll get contradiction. Okay. I have no time to mention the result, the favorite result of the Latian tunnels. Okay. Nice. So if it's not, if the star property is not satisfied, and then you always have a 2-1 domination, of course, first you'll have a 1-2 domination. But if it's not, if the local star property is not satisfied, you'll find another domination.  You can find such a kind of set. This set, according to this property, it's not the whole set. It's not the whole chain class. And then you'll get such a kind of splitting. You can prove that every round-travel environment supported and the chain class should be supported on the small set. And then you'll get the splitting over this whole chain class, such kind of the CO boundary is bottoming spending. And then, of course, we have some, something like machine and entropy. I just give you a half a look at it, and I think I'll stop here. Thank you very much.


However, I've now spoken so many times here that I'm rather afraid of repeating myself because I have, like most people, only a very limited repertoire of ideas. But I console myself with the possibility that if I have forgotten what I said before, you almost certainly will have done so. Well, I do remember, I think, that I pointed out before that practically everyone is interested in murder. I think I took a straw poll. I asked people to put up their hands if they found murder a boring subject. And, of course, nobody thought that murder was a boring subject. And I think I also mentioned that the literature of most countries would have been very much poorer if no murder had ever been committed, and if murder was not part of the spectrum of human conduct. Well, murder, of course, is the subject of an entire genre of fiction. Indeed, any large bookshop will have a section devoted to crime novels, and by crime, of course, is meant murder because no one really is interested in petty pilfering. And there's no crime that approaches murder for interest. But in most bookshops, the section devoted to murder is almost certainly one of the largest and probably larger than that devoted to the history of the world. Now, the evolution of crime novels, by which I mean, of course, murder novels, over time, and that are produced in the same country, may tell us something significant about the evolution of the society of those countries. Of course, fiction is fiction, and we should not make the elementary mistake of supposing that because many of Dostoevsky's characters spent an inordinate amount of time discussing philosophy, that philosophical discussion was the principal activity in the Russian Empire during his lifetime. Nevertheless, no student of Russian history could or would dismiss Dostoevsky's novels altogether as evidence. And I think the same might be said of crime novels, though, of course, we shouldn't expect them to be of Dostoevsky in depth or levels of merit. Although, of course, murder was by no means unimportant in Dostoevsky's work. Well, I'm just going to compare an early crime novel by Agatha Christie, the murder of Roger Ackroyd, published in 1926, with Saints of the Shadow Bible by Ian Rankin, published 87 years later in 2013. Both authors are immensely popular. Indeed, it is often said that Agatha Christie has sold almost as many copies of her books as have been sold of the Bible, which actually attests to her much greater popularity than the Bible, given the Bible's considerable start in time. And I should imagine also that Ian Rankin very considerably outranks the Bible in sales. Well, the first and overwhelmingly most important thing that one notices in making the comparison is the totally different social atmosphere described by the two authors. Agatha Christie, of course, tends to be rural and Ian Rankin is absolutely urban, but the difference is not simply that of the urban rural divide, nor is the difference attributable to the fact that Christie is writing about England and Rankin is writing about Scotland, because the differences between England and Scotland, not withstanding the Scots nationalists who rely on what Freud called the narcissism of small differences, they are very similar. The social degradation in Scotland is absolutely the same as the social degradation in England. Well, Christie in general describes a cosy, stable, superficially almost timeless, upper middle class and aristocratic world into which murder intrudes in a most unlikely fashion. And thanks to the investigations of her amateur detectives, Cule Poirot and Miss Marple, this temporarily disarranged world, the world disarranged by murder, is restored to what seems almost like the natural order of peace and tranquility, and so we are relieved. And in fact, so well-ordered is that world that it has occurred to me that actually Poirot and Marple must be themselves serial killers, because no other hypothesis explains why wherever they go, murder soon follows. By contrast, Ian Rankin describes a gritty, violent and generally degraded social reality in which murder is only to be expected and which there is no good order to restore. So when the murderer is found, you just know that there's going to be another murder very soon. His city is Edinburgh, which is a good deal less violent than the other large Scottish city, Glasgow. And I remember some time ago, in the days when it was still quite well-ordered, it's actually 50 years ago now, when I lodged with a friend in a rather grand Edinburgh house, there was Calvin's Institutes of the Christian Religion in the bookshelves, and we breakfasted on a boiled egg, and I mean one boiled egg between two. And to ask for more was regarded by the landlady as a sign of habitual riotous living, or at least as having been spoiled as a child. But Rankin's Edinburgh is certainly not that of this persliped Calvinist propriety, which hardly exists anymore, but that of a city in which the rich are vulgarly hedonistic and the poor are in pursuit of the most brutish pleasures, but the only difference really between them is one has more, the rich have more money than the poor. Now of course Mrs. Christie has been accused of, or at least been described as, having described a world that never really existed. She is a fabulous writer of what in effect are fairy stories, a kind of Hans Christian Andersen of detection. And insofar as murder is, and has always been a sordid affair, this is probably true. We find her stories delightful precisely because we think they are so unrealistic and because in the last analysis they are therefore unthreatening. They lull us rather than call us to think sociologically or criminologically. Good is good and evil is evil. The world and human conduct has moral meaning. Ian Rankin by contrast is a social realist. His is a world of drug taking, thugs, bent policemen, violence, disabused lawyers who use corrupt methods, corrupt businessmen, a world in which success is obtained only by the most dubious methods. There is a moral ambiguity and complete relativism. There's nothing of the fairy story in his books. They are if anything hyper realistic, confronting us with the most sordid aspects of modern existence, which are many and seem almost to be the only aspects that there are. Now, Poirot Christie's amateur detective in the murder of Roger Ackroyd, as I'm sure you all know, I don't need to tell you this, is a fastidious little Belgian dandy who finds even a speck of dust on his sleeve of his impeccable suit highly disturbing and who lives very neatly among well-chosen antique furniture. Rebus, Rankin's professional detective, is slovenly, of course, because almost everyone is slovenly. A heavy drinker, a chain smoker, Poirot smokes, but of course discriminating the only fine cheroots and not the kind that Rebus smokes. And Rebus lives in an untidy flat that he barely keeps clean. Rebus chews gum and drops it on the ground when he has finished with it. And like a quarter of British smokers, he does not consider that cigarette ends our litter. Or if he does, he doesn't mind just spreading it. Something that is inconceivable that either Poirot or Miss Marple would do. Poirot is an epicure while Rebus subsists on a diet of unhealthy British proletarian fast food. And there are parts of Glasgow, incidentally, where the life expectancy is barely of Soviet length. Where Poirot may play subtle tricks, Rebus bends the law when he does not actually break it. In Christie, the British police may be stolid and rather stupid, but they are honourable. In Rankin, they are shrewd, unscrupulous, brutal, and almost always verging on the corrupt. In Christie, the local head of the police, called the Chief Constable in England, is public spirited of high social class. He is usually a retired senior officer in the army who consorts with aristocrats and upper middle class. While in Rankin, he is a successful careerist aparachic, much more concerned with preserving his position by means of public relations and politicking than with catching criminals and protecting the public order. How far does the difference in character and atmosphere of the two authors reflect real social difference and change? Both writers are often witty and humorous, and there is irony in both of them. But the irony is of a very different kind. In Christie, it tends to be feline in Rankin, it's reflective of a savage existence. Here, for example, is the narrator of the murder of Roger Ackroyd who turns out to be the perpetrator describing his sister, the spinster Caroline, with whom he lives. Caroline can do any amount of finding out about what goes on in the village by sitting placidly at home.  When she goes out, it is not to gather information but to spread it. At that, too, she is amazingly expert. Here is one of Rankin's character, a policewoman described at home. She was stretched out along her own sofa, a cookery program on TV, and a microwave meal on a tray on her lap. This is an observation, incidentally, rather of the kind that Michel Werbeck makes in his novels. This absurd situation where someone is watching a cookery program and eating a disgusting, prepared meal. In Christie's world, it's inconceivable that anyone should use foul language. In Rankin's, it's inconceivable that anyone should not do so. And this is actually a true reflection of the language of my country now. Christie's world is, as I've said, one of settled social hierarchy. Give or take some social climbers. Rankin's is at least, in theory, a meritocracy that is more just and open to all. But despite the superior justice that we associate with meritocracy, in which people rise or, of course, sink, we usually forget the sinking part of it, to their deserved level, nothing can disguise the fact that Christie's world is infinitely more attractive than Rankin's with its crudity and vulgarity. There is absolutely nothing whatever that is attractive in Rankin's world. In Rankin's world, intimate personal relations are almost impossible. Divorces the norm, that is, if people get married in the first place. Illegitimate birth is rampant. It's accepted both morally and as a kind of fact of nature. Whereas in Christie, divorce is spoken of as something almost unthinkable. And an illegitimate child would be the social catastrophe of social catastrophes. Not coincidentally, I would say, that Rabus is continually playing the horrible British popular music of the 1970s and 80s whenever he can. His tastes never progressing beyond the adolescent. And we are, incidentally, entering the first age of the geriatric adolescent, or the adolescent geriatric, whichever way you want to put it. One can't really imagine Poirot or Miss Marple sitting down to listen to the productions of a musical group called Spooky Tooth. But Rabus listens to this kind of thing as much as he can, all the time at home or in his car. And silence, with which everyone in Christie's world would have been familiar, is anathema to him, as it is actually in reality to many people nowadays. In Christie's world, even the evil characters maintain the outer social proprieties in beautiful surroundings. Not for nothing did Miss Marple once remark that there is a great deal of evil in an English village.  Cramped offices, meaningless bureaucratic tasks, unmade beds, alcoholic fumes, traffic jams, cigarette smoke, the constant beat of this terrible music. One has difficulty remembering that it is Rankin's world that is several times more economically prosperous than Christie's, as measured by economic output per head. In Saints of the Shadow Bible, one of the minor characters called Kennedy is a thug now dead, and Rankin describes him. He was a housebreaker, that's the Scots word for burglar, who always carried a knife with him on jobs, scaring the daylights out of anyone who happened to find him in their home. And the elderly and frail were a specialty. Sheltered housing was never quite sheltered enough from one of Kennedy's nocturnal visits. He would often follow his victims home from the post office on pension day. In those days, pensions were paid to people in post offices, and he would then kill them. Now, in the days, Kennedy was actually killed by the police in this book, and it was covered up with the help of a crooked forensic pathologist. So in Rankin, even the forensic pathologists are crooked. And this is, with the possible exception of forensic pathologists, all that Rankin here describes is absolutely realistic. I had many patients when I was practicing who had suffered precisely these kinds of crimes. Indeed, it was so normal that the attitude towards it by the police is revelatory in itself. In another part of Saints of the Shadow Bible, a man appears to have been murdered in the course of a break-in in his house. One of the detectives investigating the crime says, looks like a house breaking gone badly wrong. This, in fact, is precisely what the British police spokesman say to the press after someone is murdered in the course of a burglary. Though just as Have a Nice Day has been transmuted into Have a Great Day, so they now say that the burglary went tragically wrong rather than badly wrong. In other words, the police are now so impotent that they accept that there are burglaries that go happily right. The burglar breaks in, doesn't do too much damage to property, escapes with whatever he wants, and no one is hurt. And these, of course, are the burglaries that the police don't have to investigate. Their function in such a burglary is merely to give the victim a crime number so that he can claim his insurance. There are no similar crimes of this kind of crude brutality or sordid kind in Christie. Not merely because she was writing about a different social class or because she was writing a fairy story. In fact, she was in many respects a very shrewd and realistic observer of the human condition and human psychology. And I'll give you one example. This is from the murder of Roger Ackroyd, where the narrator and perpetrator of the crime says, it is odd how when you have a secret belief of your own which you do not wish to acknowledge, the voicing of it by someone else will rouse you to a fury of denial. I burst immediately into indignant speech. And this surely, this is a very shrewd observation of human character, I think, and explains some of the extraordinary vehemence of so much modern discourse about public affairs where the most evident realities are denied with absolute fury. Christie was very shrewd, for example, about the value of the practice of medicine in her days. The narrator and perpetrator, as I might have mentioned, of the book is a doctor. And one of the characters in the book, a Miss Russell, an unmarried woman in those days, was still unashamedly miss rather than moose, goes to him with a painful knee. Miss Russell's account of vague pains was so unconvincing that with a woman of lesser integrity, I should have suspected a trumped-up tale. Well, thank you very much, sir, for this bottle of liniment, doctor, she said. Not that I believe it will do the least good. I didn't think it would either, but I protested as duty-browned. Now, it's been estimated that at about the time when the murder of Roger Ackroyd was written, that a visit to the doctor was about, had changed from more likely to do you harm to doing you, having as good a chance of doing you good as of doing you harm. So Mrs. Christie had a very, very shrewd appreciation of the value of medicine in those days, which was, apart from giving people comfort, almost nil. And she was much more shrewd about it than the vast majority of doctors or the population in general. The reason no such crimes as those described by Rankin do not appear in Christie is not because she was writing fairy stories about the upper and middle classes, but because they didn't happen in the lower echelons of society in which she was writing. If we take the case of interpersonal violence of murderous proportions, it is easy to work out that it is probably now 20 to 50 times as common in Rankin's Britain as it was in Christie's. The homicide rate has actually only doubled, but it has been estimated that such are the advances in medical and surgical treatment that if we were to use the same techniques as we used in 1960, up to five times more people would die of violence than new. Moreover, great advances had already been made by 1960 by comparison with 1926, so that it is clear that many of the people who died of violence in 1926 would not have died had they been treated with modern methods. This ratio of murderous violence, comparing 1926 with 2013, when the two books I have considered were published, is equal by the rise of other kinds of crime, for example street robbery. There were more crimes of such robbery in one London borough in 2000 in a single month than in the whole of Great Britain in 1925, in a year in 1925. And in my childhood I experienced the tail end of the historically short period when Britain was a well-ordered society, well-ordered in the sense that people obeyed the law to a very large extent. As a child of 10 or 11, for example, I could wander the streets of London without anyone supposing that I was either neglected or abused. In other words, the comparative gentility of Christie's crime stories is accounted for, not merely because she was writing fairy stories, but because in the world in which she wrote, such gentility actually did exist, though she was shrewd enough to recognize also that it was breaking down slightly. In Rankin's world, no such gentility exists, and social class differences, as I've said, boil down more and more to the possession of money or the absence of money, with tastes and conduct otherwise coalescing into a very unrefined way of behaving. In Christie, it's the traditional vices linked to greed and lust, to money, sex power, that lead people to commit murder, and they continue to operate in Rankin's world, of course, but there's an added layer of sociological explanation. Crime is no longer merely the result of individual human decision, but of social conditions, and it's my belief, though you'll be pleased to know I don't have the time to go further into it, that sociological, criminological, and psychological modes of thought actually conduce to an increase in crime by putting a kind of intellectual screen between people's thoughts and their own actions. So crime novels, whether they intend to do so or not, tell us something about the era in which they were written, and I therefore grant you intellectual absolution for reading them if you feel you need such absolution. Thank you very much.


Hey everyone, this is Arvind, I'm working as a SDF just-pay, just-pay is a new basic start-up which has started here in 2012 and we were mainly focused on payment systems in India. Yeah, sorry for my voice, I had a bad throat today. Yeah, we have been doing payments from last 10 to 12 years and most of our strikes are mainly in functional programming. We use Haskell and PureScript at a very high scale. So over the years, using PureScript and implementing a very huge data code base, we have faced some issues while using compiler. So then we evaluated some of the ways to make the compiler better and I'm going to share some of our thoughts and what are the changes we did and what are the changes we're planning to do and how can we merge this to upstream PureScript compiler. Yeah, if you have any queries, I'm happy to take one the talk or we can meet in the hangout after the session. Yeah, this talk is mainly about PureScript compiler in cases of incremental. So before even going further, I'll just give you some of the metrics. I just based one of the code base, not considering all the code bases and I considered one of the main code base that we use which handles around 5 million transactions per day. So the metrics are like, we have like almost 2.5 lakhs lines of code and every time a developer does ability to take more than 10 minutes and we have on an average 100 devs working on the project on a day, on an average. So this is the agenda all the way. So earlier it used to be like this, like when we say PULP compiler PULP build, it used to take like, you can just go out and grab a lunch and come back. So your PULP build will be ready. So now with the incremental changes we did, now it's like if you do a PULP build, maybe you can get a chance to go and grab snacks. The next thing was like the future that we're planning and some of the ideas that on the implementation were like, you just do PULP build and no more, like you're not going anywhere.  I guess. So considering main use cases, when we are working on any project, some of the major use cases would be like adding a new functionality that would be considered as adding new functions in functional programming language. And second thing would be changing some values. Maybe you want to try building out with different values in UI or different incremental variables or some constants you want to switch to. And something else would be like, you want to do some debugging. So you want to add some logs, maybe comment out some logs, sorry, comment out some code to make sure that which part of code is taking more time or per analysis or even understanding where the work was introduced. So considering these use cases, like this is one of the main code ways that I was talking about. So ideally, first-time compilation takes around 4,365 seconds. And let's say I made a small change, which is nothing, but I have updated my default version from one to two. And then my compilation time took around almost the same. It's like I'm compiling every time to almost 37 minutes or around that time, 37, 98 seconds. So ideally, the thought was like, why don't we are making these kind of changes? Why does it have to do the compilation like how it does for the first time? From this pain point and from this thought, we have started working on the optimizing compiler. So you can even see how the CPU was behaving. I mean, it's taking all the cores and memory is also high. And that's the reason why I said, like when you do pulp build, you just go and grab a lunch. So it's going to take a while. Another interesting thing that we observed was like, when I even don't make a change, sometimes some of the IDs make this crazy auto save, even though we don't change anything, or you might have commented the line and uncommented the same line, or you might have removed the extra lines and all. That's what I considered as no change in the code. Even then, the compiler took almost the same time, like no more of an intelligent system which says that, hey, man, you didn't really change any code. I'm not going to compile the code versus, hey, I have seen some of the file has been changed, the modified time has been changed. I'll just literally recompile everything. See, okay, now I'm going to talk a little about a principle thought of mine and mostly that we followed Jaspe. So one of the principle thought is like we always try to attack any problem with 80-20. So the main idea itself is that can we find that 20% of effort that can be solving 80% of the use cases. And see, this is one of the main reasons why this compiler was, we kind of found only few places where we really need help or it takes most of the time from developers. So those are the main problems that we focused on and those are the main problems we solved with more or less a 20% effort. To be honest, it's not like we have considered all the scenarios and it's going to be like so good at all the scenarios, but we have considered most of the scenarios that developers use and which were added also in the use cases part and in all those cases we have put 20% of effort, minimal changes that you can do to the compiler to get the maximum of the benefit. And this is one of the way we work at Jaspe. We will always try to find any 80-20 and try to, if you see the metrics here, it's like you can solve it, 99% of the problem with just 24% of your effort. So this is something always we try to find out and solve the problem more or less very fast away. See, this is the first thought that triggered to me when we were actually trying to understand why the compilers are taking time. The very first thought that triggered to us was why do I have to compile when my function signature was not even changing? See, even before coming to this point, we were asking questions like what do we mean by compilation? So what are we really saying when we say compilation? Is it doing a type in friends? Is it generation of whatever the back end we support, JavaScript, Python, PHP, anything? Is it what exactly do we say? Who is taking how much of time? And in that we have noticed that when the function signature was not changing, ideally you don't have to do the type in friends for all the dependencies, right? There's one of our first thoughts and we tried to evaluate that using some of the changes. So if you observe, we read the modules, like we have a module, which have a function called add five, and I'm trying to import that module in another module called y. And when I have made change in module x, saying that I just issued the x plus y with y plus x, and then we have realized that module y shouldn't be recompiled ideally. If you don't want the module y to be recompiled because the type in friends are no more required, right? Because add five is always an end to end and module by using add five won't have any issues. Yeah, I mean, these are some of the metrics that I like after making this one change where when a function signatures was not changed, we don't want to recompile all the dependencies. With that one change, we could able to bring down numbers like on the left, which are very high at the second and all, and we bought them down to 10 seconds. In the same way, when there is no change in the code, maybe you moved the lines, maybe you commented and uncommented the same line, then and all, these numbers are again, the numbers on the right side are more or less using a stop board. So because there is no time come and I could do in a watch mode. But yeah, these are more or less the numbers that we that we were able to achieve now with a very simple change that I explained in the previous slide. I'll just give you some of the implementation details what we actually did. So to solve this problem, what we said was when we are actually parsing and when we're actually trying to build a particular file, we actually build a hash map which will have a function name and the function signature. So every time you make a change and you try to compile, we again build this name and function signature hash map and we make sure that nothing has changed. Let's say for particular functions, function signature has changed. That's when we will say, okay, go and recompile, like I can't give any advantage. But let's say for any particular function, the functions type signature has not changed, then we can simply say that, hey man, see you compile yourself, but don't expect or don't tell your dependencies to compile them. So that's how we majorly solve the problem. See one of the main concern, to be honest, till now is the CPU and the memory which which we started working on. We kind of figured out a couple of ways to make these changes and try to use less CPU or memory, but it's still in our implementation. So I can't really give out numbers as of now, but to be honest, it's right now good enough to heat up the laptop. So this is still a concern from the compiler that we are using. See we did a release. So people can find this release in NPM packages under the name hyperfine pure script. But as of now, we released only for the four versions which are mainly used at just pay. So we have very old code base that even still using 0.11. So we have only these four versions, but we're planning to add for 0.15 or the latest versions also. And we hope like before any new releases, we will try to bring these changes into upstream. If anyone is interested, they can get these old versions, which I mean, I can't help it if someone is using 0.15 as of now. But if you have any code base using these versions, you can try out the compiler using the NPM package. Or if not, you can visit just base GitHub. It's a pure folk of pure script repo and we made changes on top of that. So so ideally you can even observe what kind of changes we did and maybe some more suggestions like like any any suggestions regarding the changes that we did and the way we did. Also any people have any other thoughts regarding the use case versus this 8020s that we can do early and try to come up, try to achieve some higher numbers or higher advantages where we are happy to hear and there was also a post on this post regarding this and we are happy to like interact with folks and we are happy to speak with more folks to get more inputs regarding this compiler and see if there are any more changes that we can or if there are any issues that are being faced with people or more or less in that way. So as I mentioned, until now this is one of the main changes we did and we were able to achieve the numbers that I shown ago. But there are other thoughts which we were evaluating and also started working on it and they seem like giving even more benefit and also helping out in many more use cases. One of them is to build a function level dependency. So if you observe like in the previous explanation what we did was like we said if a particular function signature doesn't change then only you don't recompile. But if a function signature change we will simply say go and recompile the dependencies. But ideally let's say a module imported a function and that function is not being used or it being used but it's really not changing the function signature of the current module. So example could be let's say we have a x-module and a y-module. x-module have an add-fi function and y-module imported that add-fi function and somehow we changed the add-fi function type signature. So ideally we say go and recompile y and we don't reapply the same logic on the y and we simply say recompile all the dependencies. I mean the better way could be you consider y now and since add-fi signature has changed you again look at all the functions of y and see if the functions of y functions of y's add signatures has changed or not. If not I don't recompile all the dependencies but recompile only if y-file function signatures are changed. So this is something we were evaluating and looks like most of our use cases are like this. So even though some of the util function type signatures have changed I don't need to compile till the main mostly because the util functions type signature or the function whose signature has changed is mainly being used by more or less only few modules and we want to compile only them and then we re-evaluate the same logic and on the change in modules evaluate whether those functions the functions in those modules type signatures has changed or not. Yeah I'm taking a question so sort of ask like what about the inline functions? This is one thing that we observed when there are these inline optimizations the ideally we have to recompile and generate the JavaScript code but as we noticed like most of our code is not doing any inline optimizations so that's one of the main reason that we were able to use this compiler but yeah this is this is really a this is really a right question where if any inline optimizations were done by the compiler we can't really avoid recompiling the dependency modules. Yeah see this is something we were evaluating and trying to solve the problem in the more general way not just not just like saying that oh see in just a minute we were not getting any inline function so we'll just use this compiler but we were trying to look at we're actually evaluating the JavaScript compiler we're seeing is there any way we can actually disable the inline while we are doing the while we're using this compiler and maybe the final pull build maybe or the release build right you we can add a flag saying that it's a release build and then we'll just remove the optimizations and we'll simply say hey just go and compile everything and generate the proper output so yeah it's a it's a it's a genuine question and this is something we have evaluated and and and it's a known issue but but as of now and since we're using this compiler for a very time as of now we didn't see any issue or or any bug that that got introduced because of the inline inline concerns yeah yeah back to the functional level dependency graph we just don't want to yeah we don't want to go with the file level but we want to go at the function level and and build the graph and only the function signature change we build the modules which are dependent on the function not not like okay I imported this file so I'll simply go and recompile that file other than this like there is another thought which is for first time compilation but but this is mostly I'm not sure like how well it is useful for a general audience but but considering a company like us where we have around hundreds to 120 days work on average every day and and make new features make new releases we thought we can actually use something like IPFS and maybe share the output folder across us such that our first time compilation also won't take much time because it's always like this right like when the code is ending up in a mid bucket it's being pushed by one of my friends or one of my colleagues so ideally if I could just like I didn't if I could just create a tar file of the output folder and get it into my laptop I can use it so we thought like maybe why not IPFS and the piers to compiler itself can using the git permit hash it can look at the IPFS network and if the output module is fine output module it found it can just bring it down if not it can it can do a simple compilation as it does right now so again as I mentioned I'm not sure like is this really useful for the general audience but but if you're a company and you have like a good enough number of people and you make changes most of the time and you see a lot of new branches and new features that you always do I would say this is something that we are yeah this is something that can be majorly useful because like as I as I shown it on the screens earlier the first time compilation is something is still a problem and it takes around yeah it takes like huge amount of time of devs and which is not like which is which is one of the major hindrance that we're still facing facing but we were seeing if IPFS can be evaluated and and maybe maybe add the commit level based output output bringing into the system by using IPFS network is something we were looking at but we are not completely sure okay yeah see other than this like majorly just maybe we work on functional programming and and we build products of five we build products of payments at the scale of India and most of our stacks are running in Haskell and PeerScript and even Rescript so we were one of the major company who uses types and who who gets the functional programming to the scale of India and into the production directly and as I mentioned about the 80-20 this is one of the things that we always like are trying to figure out any 80-20s in doing the task see as if you observe even the piers to compiler it's not like we have considered all the all the scenarios and we have come up with a complete 100% working compiler but it tends to solve 80% of the problems and it helps a lot of our developers right now in-house and and they could able to make releases faster they could able to push code faster otherwise like it usually takes an hour or two for for any person to like make a change if there is any bug found it takes around two hours for our developers to make a change maybe maybe add more logs go through the code the compilation again you make some more changes compilation again you make some more changes find out about come up with a solution and push it to production it takes around a two to three hours on an average but but it kind of dropped into less than five minutes because because because of the use cases that we usually have but but there are scenarios as I mentioned if we have to change the function signature or adding a new functionality or or updating the dependency graph or is it a first and compilation we are still at we're still at a issue level where we have to decompile from the first and it does take a lot of time and and as the code base increases at the as the code increases we kind of see we kind of seeing this compilation is actually going exponential not just linear because earlier when we have very less number of files or less number of modules it used to be like very linear not increasing or not taking much time it kind of went from five to twenty very very fast way because because we are just like working we are just adding more features more features and suddenly we just went to this 30 minutes 40 minutes compilation time and that's become a high endurance for us uh yeah I mean true I'll kind of have a bad throat so if if if you have like if if something was not clear maybe you can ask questions so I can I'm happy to help but sorry for my voice I I'll just add a back throat today so thank you Arvind