So Good afternoon to everybody. Thanks for coming. My name is David Inglis. I'm with Bloomberg television. I'll be your moderator for Today's session. I guess let's first start. Let me first introduce our panelists for today. Mr. Boody gunadis a deacon CEO of Bank Mandiri in Indonesia Mr. Jose Isidro Lito Camacho vice chairman for Asia Pacific Credit, Swiss Mr. Chani in president and CEO a Kleda Bank Cambodia Miss Chetna Sinha social entrepreneur founder man Deshi Bank and president on man Vicas so magic Sancha India and right beside me Excuse me right beside me. Mr. Jaspal Binder, of course group executive director and CEO Standard Chartered Asia and Mr. Matthew driver president Southeast Asia Mastercard Thank you for joining us. Now, maybe just to go through how things will flow We'll be having a discussion here up front and a bit later on perhaps towards the end I will be opening and up the floor to questions just in case of course You may have some lingering thoughts on what's going on right now now our topic for today is financial Inclusion or I guess in layman's terms, how do we reach out to the unbanked of Asia? How do we include them in the circle? I mean certainly it does It's very apt that we're talking about this right now given that we're in the Philippines or in Southeast Asia You do have rapid growth, but at the same time, of course alleviating poverty and reaching out to the poor Will certainly be very important if all of these economies will I Guess be able to sustain any sort of sustainable Economic momentum and development going ahead. So in short the key question we try to answer is what changes to? Financial products have we seen how do we use technology to reach the unbanked in this region? So I guess to start off me seen how let me start with you I guess for our audience and for the panelists as well. Can you give us an idea? Who is the client? Who are we trying to help here? so Mandeshi Bank actually started with a little bit of challenge because most of our women were non-literate and Banking license were rejected because how can a central bank issue a license to Whose promoting members are totally non-literate? So they are non-literate, but the interesting part was that women told officers that Tell us to calculate the interest of any principal amount if we fail don't issue the license but tell your officers to do it without calculator and That's how the debate started and 14 years back. We've got the license. So these are the clients But the interesting part is that these women don't only treat very smart in business and most of them are street vendors are sheep and goat raiders dairy who are in dairy and For such clients what products do we have? There was no precedent and in fact I remember that when we started a banking with these women I was actually fired by them because we had a very Fancy our product for women saving product having a boxes with a photo of Mickey Mouse and they and we were waiting that women Will come because of that attraction and women said that whose crazy idea is this? We are not going to come to the bank. We don't have time to come there So the first lesson was to have these clients was that if they are not coming bank will go to them That was first second thing how what product because we felt that maybe that these women require loans so we start with loans, but they said we want to save and Interesting is that we are not going you come to our doorstep We want to do savings and we want to do daily savings So we had to design a product in such a way that doorstep banking Daily savings and if they are taking loans women said that we want to repay daily So it was a challenging that how do you design and at the same time I After the first firing, I didn't have an I couldn't dare to explain them and think of Educating them because they were so clear and they did not require a financial literacy education because they said Doorstep banking daily savings daily repayment. How do you do that? And with that challenge actually in 2001? We were the first bank to design this electronic passbook for these women Which does not only just give a saving opportunity saving repaying and Also pensions so it's very interesting. I'm just like would like to end that these clients They don't have time they do they want a simple solutions and how do you do that? So try to bring everything together make their life easy listen to them and they come out with a very different solutions which you just have to cope up and So we had a smart cut for these women who are and I'm really surprised that when we started this product within eight days 7000 women and they pay 50 rupees for these cards So it's not that everything they require or they are asking for free No, but the one thing is very clear that you should bank should try to ease their problem and provide an opportunity of saving pension insurance Credit and they are ready to do banking if it comes to their doorstep with their terms So these that's how the Mandishi Bank operates and I'm proud to tell you that today around 210,000 such women are banking with Mandishi in two states of India Maharashtra and Karnataka Yeah, because I before I guess I move on I'd also want to ask that just we better understand that the persons or the people We're trying to help do they actually have money to save don't they live day-to-day So this is very interesting question. We generally think that Poor people do not have a surplus and so they do not save but I would like to say that there is no relation of surplus and saving Everybody wants to save why they want to save they want their children to go to school and they want to spend They want to repair their house and so they want to plan in fact Mandishi Bank started with this that one women came forward and she said that not a single bank is opening my saving account I want to save and our question was simple. She's not asking loan She's not asking grant and she's not asking subsidy and I I also had the same question I told her that how can you save and why do you want to save do you have a money to save? She said that before monsoon.  Maybe you can expand on that Yeah, clearly You know the starting hypothesis is that half the world's adult population is unbanked so it's a very large number three billion of people who are unbanked and On the one hand, there are lots of conduits in terms of mobile technology enabled channels to be able to reach these unbanked people but The starting point is that to cover the last mile there needs to be an awareness and education and understanding at the receiving level of how to be comfortable doing it and I think the whole challenge of making that segment aware the unbanked segment aware of the benefits of financial saving Exactly as was said by Gita that there is a huge latent requirement, but how does it sort of become Known to them. How do they become aware and the second point is that they are very intimidated They are intimidated by the institution. They're intimidated by the documentation They are intimidated by technology So this whole thing about providing convenience at the doorstep is a big big part of the whole move. So I would say that financial literacy has to be a very big part of the process to Make financial inclusion possible Whose responsibility is that? Is that the responsibility of the bank? Is it the government? Is it does it fall in the arms of NGOs? I think if we all believe that financial inclusion Has its benefits, which I believe it does because if you bring three billion people or whatever fraction of three billion people into the system and you give them financial independence you not only Create a good thing for them, but you create a new market. You create a new opportunity for Whether it's for an FMCG company or it's for the payments company or it's for a mobile telco as it is for commercial banks So clearly it is in everyone's interest who stands to gain. I think the government stands to gain the most Because what we take for granted is that cash is a no-cost option Whereas any other form of payment technology enabled Is expensive but actually cash is a very expensive proposition. It's fully subsidized by the government So the government has the most to save by moving away from cash into Either a card payment or a mobile payment or whatever electronic system of payment Nobody has ever estimated but I can tell you because in Hong Kong we print the currency We store the currency we know as a bank that it is a very expensive proposition to be printing currency And to be having to store it secure it transport it it is a big thing But it's a big thing even for the FMCG companies when they collect at their sales counters cash It's a big thing for the merchants so cash management has this cost and rather than sort of Subsidizing the electronic or the technology enabled payments. We actually charge more for the technology Enabled payments. So we are creating a disincentive rather than creating an incentive And I think that's a gap that the government and all the other beneficiaries have to Take into account Thank you I guess we'll go back to the topic of technology and expound on that a bit later on how we actually deliver this in low-cost Protecting profits and also making things affordable Matthew Mastercard has a few initiatives in terms of Financial education financial literacy. I believe if I'm not mistaken me and Mar Partnership in Myanmar. Can you expound in that and what is it achieved? Well, I think the Just a point on on the back of just Biles pointing and cash is a fall at a word and I think that the challenges How do we Get past that and I think the the work that we've done in Myanmar We're working in the Delta region there with Mercy Corps is about working with the villagers Engaging at the community level to ensure that we're making them aware of the benefits of inventory management Planning for a rainy day, which obviously comes with the monsoon season ensuring that they have the the basic tools to understand the benefits of money management and they're targeting essentially farmers and rural female entrepreneurs who are running a small store within the village and what we're looking to do now is Take that and essentially expand it and work with mobile operators to distribute that training So we're trying to leverage the The experience we have on the ground and now use the new technology to distribute that training on to the mobile device But you must first own a mobile device. I would imagine sure free that to be in my roots. It's it's early stage But across the rest of Southeast Asia Virtually every adult right not quite has a has a mobile phone, but the bank penetration is significantly lower So mobile really is the key way to go whether or not that's virtually via a E-money solution or whether it's a companion prepaid card Associated with that account that really empowers that individual to use the payment network Chani if I can bring you into the conversation here because you're for McLeod that That's a very good model to copy across the region. Maybe you could perhaps tell us about how you started how you first obtained a Special and then a full banking license Okay, so thank you David. So Bank in fact the full name of my my bank start Association of Cambodian local economic development agencies. That's the long name So we call a Cambodian call a CELIDA and foreigner call a CELIDA we start as an NGO for small and micro enterprise development and then in 1998 it became a break even That's the time when we work on the transformation from NGO microfinance to To bang so we start with the paid up capital four million US dollars in in 2000 So obtain license as a specialized bank as a specialized bank We can only do one like it can provide loan or can provide payment services or can collect domestic deposit so this under the regulation then and and in 2003 it is the three year later after we became a specialized bank for the paid up capital of four millions So we triple our paid up capital to 13 million so that we can become commercial bank We want to provide all range of a financial product and services to all segment of the community because as a specialized bank there is a limited services and then 2003 we become we obtain license as a commercial bank like the other bank but we have done more than the traditional bank because we services low segment that is micro small and medium enterprise and Currently the bank have I think have a coverage nationwide over 251 branch and offices across the country and then we Expand to law in 2008 as a commercial bank. We expand to Myanmar obtain license as a microfinance in 2013 last year, so we are now in three country Cambodia Myanmar and Laos So I see that it possible because of the flexibility of the regulation But now the regulation alone we cannot we cannot do like that We cannot there will be the boundary between the NGO and licensed microfinance institution because in Cambodia they Conduct the reform on banking law and finance institution in 1999 which allow NGO transform from NGO to license microfinance institution So one is the we call conducive law and regulation, but but allow such a transformation Yeah, and then secondly the the size of the paid up capital So when the central bank national bank Cambodia allow they set the Like the paid up capital just 70,000 US dollar for microfinance to establish a licensed microfinance institution It means they encourage more because you know those institutions because were an NGO before so it no tax They pay no tax they they provide loan but subsidized some subsidized some at commercial but no tax So but when the regulation Develop they allow transformation. So not just from NGO to license microfinance institution, but Company you know private individual can also establish the licensed microfinance institution too No, bring them to the legal system framework. They pay tax. They charge at commercial rate They open more access. No, I mean because if they were remain as an NGO They rely on the donor fund. They they cannot implement their business plan properly Then when they obtain license as a microfinance, they can Can access to commercial fund to finance their loan growth? So my bank again, we don't start as a microfinance We start as a bank like I said in 2000 obtain license as a specialized bank Small-paid up capital of four million and then we see that a great opportunity, you know two things on One on one hand we can continue to Service I mean a low segment at the same time we continue to serve them we grow what we grow together And then we also make profit. We can be profitable. We can achieve a social objective and commercial objective at the same time by by the end of April last month our paid up capital is 225 million US dollars and total asset around 2.6 billion US dollars So again as in the role of the regulation is very important open access to finance Inclusive finance can can achieve without we cannot achieve without the flexibility of the regulation I don't want to talk about flexibility in by Violate the international rule and regulation as in line with the Internet international regulation Secondly on the the product diversification diversification product is very important if As a bank when the customer come to us and said oh, no, we cannot provide small loan I think this is we we close the access to finance for them already But if they say that any kind any types of loan any size of loan you can have access and then form of documentation like it simplify based on I mean based on the nature of the People in the countryside which they don't have their document properly, but we can live with that so the role of product diversification and then certainly the network I heard that some of our Frances talk about the the the electronic infrastructure I think electronic infrastructure and physical infrastructure play a very important role for opening access to finance also if the customer can if They can have access to finance during the office hours or during the office closer or on the public holiday I think electronic is is one of the better means for them Via ATM machine via point of sale and also telephone telephone bank we have Established the telephone telephone bank call is it a unity which open access For customer across the across the country. I think those are the three main thing that we Like a V exercise experience so far so the regulation which we talk to the central bank and secondly the product diversification We listen to the customer and we we add one product after another I forget to mention when we start We only provide micro business loan and small business loan, right? But little by little we add because the customer explain to the customer need that the customer Request to us and then we develop according to their need and then the branch and offices and the electronic infrastructure So that they can have access on the 24 hours basis. Okay. Now, it's a very different story for credit Swiss little It didn't start as an NGO. I would imagine credit Swiss But you're also playing you also have very big initiatives in this space. Can you tell us about that? Yes? Thank you David. As you mentioned in a credit, which is a global Financial institution, so it's much difficult more difficult for us to go to the ground and and do microfinance lending as such So what we do is we focus on what you know, we can do using the resources and competences that we have in the bank First let me just say that Microfinance is one of the one of three pillars in our CSR globally And within that we really focus on capacity building This is where we can use our competences. We work with partner institutions people like Finca actually on the women's the world women's banking And so on providing, you know grants providing technical advice We do other related activities For example using our product skills We look at innovations how to scale up the capacity of microfinance institutions might be a listing of a successful microfinance Company that I think we've done in Mexico and India. It might be setting up a An impact investment fund that would provide equity capital to small enterprises that would otherwise not be available to them it might involve refinancing of portfolios of Microfinance institutions so that again they can scale up and do and do a lot more We also try to encourage our employees particularly young employees to volunteer and get involved and we do have a program that Allows us using our partner institutions to deploy young bankers Globally, it might be an investment banker in London in a flying to India and spending six months working with the microfinance institution and helping them on risk management and IT and other Functions, you know where he's or her technical skills can be deployed we through we also have a credits with research Institute And through that Institute, you know, we do research and we do publications around microfinance, you know Like impact investing again a way out to promote and propagate, you know the concept We also in fact are a partner of the world economic forum There is an initiative within Wef on financial inclusion. So we We are members of the steering committee with one of my colleagues and even at the working level So our focus in credits, which is really how we can we're very committed to the sector But we are not able to work at the lowest level So we try to capacity build and empower enable Expandability of successful microfinancing institutions to do more and to do better Now perhaps a bank that's near the ground But if I could also bring you into the conversation because your back actually operates in a country with 17,000 islands if I'm not mistaken That's a key challenge To reach the unbanked Yes, financial inclusion is topic for the poor about the poor so looking at the number of audience in this room I realized that this region has become extremely rich But you know I used to work for a bank Dutch bang the Dutch enter Indonesia 350 years ago and Since they came until now we only have 50 million Indonesian have an account Have a bank account and we are already GDP ranked number 15 in the world So you can imagine if you can increase that from 50 million to 100 million or money enter the banking system can be used to lend Increase the velocity of money GDP of country will increase drastically. Maybe we'll join the g-10 t member or if you can increase from 50 million to 200 million Then maybe the next Indonesian president will not be invited to attend a g-20 meetings But instead he will be invited to attend g-8 countries meetings because our GDP will grow faster Now the problem is if it took us 350 years to penetrate 50 million Indonesians Based on simple calculation. We might need 1400 years, you know to penetrate 250 million Indonesian to have a bank account For your information a lot of Indonesian now have a much better access to cigarettes rather than to open the bank accounts Our smoking inclusion is much higher much better than our So Then then then the issue is how we can accelerate the penetrations of financial inclusions I have my colleague a CEO of Indonesian telecommunication company talk to him When did the telecommunication industry enter Indonesia? He said when the dust came 250 years ago and we only have 30 million house phone and office phone But he mentioned in 1994 they introduced a new technology called mobile phone and in 20 years 220 million Indonesian have access To telecommunication inclusion providing basic telecommunication services such as talking and texting And that is without zero government subsidy So in 20 years the telecommunication industry successfully penetrated more than 220 million Indonesians for telecommunication inclusion Basic telecommunication services zero government subsidy Financial inclusion our government has subsidized trillions and trillions and trillions and only 50 million Yet you already number a rank number 15 So now the challenge for for Indonesian is how can we accelerate? piggybacking on the success of the other industry to increase the penetration faster and cheaper You mentioned cost does it and anyone can can please if I could get your opinion so that This penetration also mean do we still stick with that model of putting up branches where the clients are? Because typically as you mentioned just how They're intimidated by all these documents people are used to walking into a brick-and-mortar Perhaps if that's the first step that they have to do before we actually get Them bank accounts and then we can work with mobile phones. Do we still need the branches where they are? we invited we invited Michael Joseph the head of MPSR three times in Indonesia and I asked Michael Joseph Michael Joseph how many branches do you need to penetrate MPSR in Kenya? He said 20,000 Michael Joseph you came to Indonesia three times What is your guest estimate? he estimate 200,000 booty and then I do my checking I talked to my Unilever coca-cola proctor and gamble because those products have access to 200 million donations How many outlets shops do you have and their answer will be the same around 300,000 to 400,000 Cigarettes company mobile operator company that have access successfully to 220 million nation They need 200,000 300,000 outlets Until now all banking system in Indonesia you add all of those branches only 20,000 So that is exactly what we need But we can't build 200,000 branches because 350 years we only be able to build 20 So then we have to do something the branches banking model the agent banking model to make sure that we can accelerate You know the penetrations of the branches This is something that I've been lobbying to the center bank governor to give us some leniency in in in term of of Licensing opening branches. You know what actually I feel that There is a problem of financial inclusion on supply side how? Government policy makers and mainstream banking sector particularly which are government owned they look financial inclusion as opening accounts And then they keep complaining that these accounts are not active It's a zero balance and then it has a such a poor vision Zero balance account. I mean I was when this whole concept comes with financial inclusion and zero balance account Which means that you are Going to the clients who are not going to do banking But if you see if you talk to a rural women or Unbanked who want to do banking They want to create a wealth by being a part of the bank It's not just inclusion. It's creating the wealth And how do they create as you mentioned in Cambodia that you have a diversification of product? So you provide a loan for a goats for buffalos Sometimes for education of the children. This is the wealth they create by banking So I think the whole idea is also inclusion inclusion But also the main issue is that how do you create? Why cell phone in India? More than 80 percent of the household all over India have cell phone. Why it's because it's helping them in so many different ways They don't have to travel so much So same if we think banking in that way Then the one thing is that branchless banking doorstep banking banking with Not much hassle as you mentioned that you know if you require To open account kyc norm so many papers. No, it is not possible. How do you make it very simple? Very easy with one idea. It is possible and So I feel that there is a need not only just to change the talk about inclusion but also need to Think as a wealth creation for poor people because they are thinking that way And I just would like to end with that that just if if there is any Proper research done What are the people doing with the money which they get from the bank? And I'm sure I mean we did a impact assessment of our client and it wasn't it was spent so wisely I mean why I say that because we did the research with the household and we saw when men they save They would say that we want to buy three wheelers that two wheelers. That's why we save Women They would say that I was I save because I want to buy a buffalo or I want it's something to do with You know, which will give her a multiple income and I come last which is like most wisest thing I have seen is that you talk to young girls also are savings And I was thinking maybe the young girls are saving for marriage But no they said we are saving for our higher education So you see this rural population see the aspiration They want to save go to the bank for the higher education also So I think the whole mentality needs to be changed and with technology everything can be possible I mean Monday. She has the deshi girls bank within the and with by designing this product for young girls I'm very proud to say that within three months We had 12,000 young girls saving for higher education and see the Investment in this human capital what results we are we can have I mean what wealth we are creating So I just I mean That we have to change the mentality and I guess let's let's also revisit this before we move on What is what's the most popular product because people think about Microfinancing as credit is is that what people need or do they need savings first? For me financial inclusion means financial transactions financial saving financial credit and a financial Insurance and that has to come that particular order So people need to be able to do transactions before they can save Then people need to be able to save before they borrow So our whole initiative is started with transaction first and then saving and then credit And insurance a lot of government make a mistake They think that if we give you a credit then every everything will be solved We have seen that trillions and trillions of us dollar has been spent It is it is more of popularity contest rather than you know a real financial inclusion initiatives He told you anything? Yes Obviously, I'm not going to be talking about credit swiss But I just want to share a personal experience Having heard the presentation and then actually seeing the institution and you know Pabu these in Pabu this country. This is btpn. I don't know how many people have heard of btpn But it in my mind is one of the most successful commercial models of what financial inclusion is all about Because their business is all about lending to the poor and borrowing from the rich And it's very very simple and and I think it's because of the point that you made about cost Right. I mean to be sustainable And to be scalable it has to be cost effective and that's exactly what they've done They only have two customers. They only have micro entrepreneurs and pensioners And I had the opportunity to visit some of their branches in Indonesia. I was floored I had to rethink my ideas of what a bank looks like because they don't look like banks They look like more like community centers Unintimidating, you know where a poor person a market vendor would not be intimidated to enter a bank door You know where you've got marble floors, you know marble tile counters uniform guards and uniform count Tellers, you know, this looks like a community center, which is very welcoming And and it's it's very simple. They really Looked at how to simplify the process of lending So it can be done as cheaply as possible It's I thought of it as the you know the fast food of banking Um, I was so inspired that I I actually thought that geez I could do this in the Philippines And with permission from credit swiss I'm actually working on a project in the Philippines working with a couple of banks to see if we can replicate Perhaps not as big a model as btpn, but at least as successful as successful as they are I mean just to give you an idea of how commercially successful it is It's a business that five or six years ago Private equity fund TPG invested 400 million dollars to buy the pension bank Today's market cap is four billion dollars and they're helping the poor They're helping millions and millions of the poor. They have about a thousand branches in Jakarta. They're all Located around market public markets I visited one of their pension Business branches, you see old people. They have a medical center They have community activities around pension payment dates It's just mind-boggling. You just have to Re throw away all of your banking concepts And and think of how you can concentrate on what The targeted Clients really need and what would make them comfortable to deal and be included in the financial world Inspiring Matthew, I'd like to bring in as well because mastercard you have You're trying to put into place very innovative payment solutions. We talk about transactions These people transact multiple times a day In in in your experience and from what you're doing. Can you tell us a little bit more about how I guess we're trying to drive Innovation in in this space. You know, I think that the points have been made about you've got to change the business model that exists today I think you have to reinvent and you have to look at the The situation that's relevant to that consumer group. So when we talk about It doesn't matter if we're talking about training or inclusion You're celebrating when you're repaying alone, right? Typically at the bank you're not really celebrating when they pay you off the the money, right? So I think that how are you creating the right incentives that come with the structure also just innovating with Electronic payments is going to be critical. But I do think it's a combination of all those things That's the point that's been made about regulation about branch banking about having you a reasonably coordinated agent banking Regulation that enables the banks to reach out In a in a way that's lower cost. It's about integrating Technology to ensure that you're lowering the delivery or the manufacturing cost for that product It's about engaging at the community level our success in South Africa is all about your really engaging at the Ultimate village or community level whereby that gives you the ability to expose those clients to The technology and the card and they can feel it and they can Understand it. I think all those things are are really critical And then you have to educate and work with them and to to celebrate their success and engage with the communities You're working in so it's a multi-dimensional Solution if you like and Jaspal Is from I guess the perspective of a bank and the implications of how you operate Is is there a trade-off between reaching the poor? And microfinance for example and profitability I mean, certainly we do have to rethink certain different types of models of trying to reach these people and now we have the technology to do it Do you have to make certain types of investments to put that infrastructure in place to make it profitable and sustainable? I think the issue is really We have to answer two questions. Is there sufficient capacity? to be able to Make financial inclusion possible And secondly, is there sufficient willingness? by the players to be able to extend I think we can we can never answer the capacity question till we have addressed the willingness And with all respect to everybody on the dais, I have to say there is a lot of room in terms of willingness because we have this very Popular notion that when we talk about financial inclusion, we're talking about the poorest person 17,000 islands away there is a lot of unbanked population in urban cities in Manila in Jakarta in Hong Kong in Singapore in London in Bombay Everywhere there is a lot of and I'm talking millions of people. I'm not talking 10 20 30,000 people here There are millions of people who are unbanked. We just don't have as an institution sufficient incentive And I think it's a combination of incentive from a profitability point as you point, but it's also from a regulatory point I think As capital is going to continue to be raised You know, you're going to your appetite is going to reduce to the most profitable sectors So even before you can figure out how profitable financial inclusion is you're not Experiencing that whole space sufficiently So I think there's a lot of room for a combination of the commercial institutions and the regulators to come up with where there has to be far more In the normal flow incentive To get this done rather than You know, somebody sort of do it as a very special act or a very special institution as Mrs. Sinha has But I think we have to just make it very possible in the normal course Then profitability is not that relevant because there are lots of products and segments we do With are either loss leaders or are not really profitable on their own But they bring in a relationship and the relationship is profitable And I think we haven't got to that stage yet And Chani can if I could also bring in to the point and before I open it up for I'd like to ask you Did you get help from the government in Cambodia? No No in in terms of regulation We have them subsidies incentives. No, no subsidy. It's truly commercial But we do have the government in terms of regulatory development We sit in the government committee Because in Cambodia the government established the gpsf the government private sector forum I'm the co-chair of a working group on banking and finance But we can give comment to the government in terms of what kind of regulation which Impact on on on the bank and on finance or institution When we see that it It blocks us for growing we make recommendation to the national bank of Cambodia Yeah, so we don't we we don't we don't have any subsidized from the government Does anybody want to say something I was going to say the government governments can lead I think the the whole point is that the models have to be sustainable in and of themselves Because otherwise you're always going to be you're limited by CSR Now you have to be able to build a self-sustaining ecosystem But I do think that governments and a lot of their programs have the ability to kickstart the process Whether it's by saying I want to be able to Electronify the benefits that I want to put together. I want to think about how I can use electronic Identity or national identity programs and combine that with payment potentially to create Use incentives for people to want to come and make themselves available and then What would happen would be the savings that are made available to the government those savings can be realized to Build the infrastructure and I think those models are there It's just probably a combination of things that happen That that need to put it together because I think the key thing is getting some impetus Getting the use cases there getting the benchmark that you can look at and then people then think about the idea and that's why We've had success in South Africa and that's why we're now moving that to Nigeria That's why we're looking to have those conversations in Southeast Asia as well for the the same reason that there is a role for government railetry And in terms of you know creating an impetus to make things happen I certainly when David if I may just pick up on One aspect of government and where government can play a role and it's really on the regulatory side I think as more and more models for Lending to the poor or or doing you know financial transactions with the poor It's very important that the regulators understand that this is not quite conventional banking And some of the prudential standards limits, you know requirements that are required when you lend to a you know S&P 500 company may not quite apply to a you know a sidewalk food vendor because You know in the Philippines for example, and I would have to test the center You know Banco Central when I make the application But if if one of the requirements to establish a lending Relationship is to require a BIR or a tax return You know as I walk food vendor may not understand what we're asking for and therefore it defeats the purpose from the very beginning So I think it's very important for regulators if they truly want to promote financial inclusion And and microfinance lending and so on it's really to understand the needs And the profile of the clients just like the way the bank has to and and the regulators have that important role as well So that they can provide the the right regulatory framework for a different type of financial activity I do think that those Examples do work I think Pakistan for example I think it's got a tiered and proportionate KYC Procedure which means that okay my the proof that I have for this transaction needs to be lower because I'm only sending you 100 rupees Right, but if I want to make a much more significant transaction Actually, I'm sorry, but I need to know much more about you and who you're sending the transaction to so I think the models are there It's a question of you making sure that we're we're sharing the best practice in Encouraging the dialogue the system accommodates these models And perhaps for those who are not aware Lita is the former finance minister of where we are right now Okay at this point we have A few minutes for some questions if someone would like to ask yes, ma'am, please Can you please introduce yourself and maybe I'd also Hi, I'm Lizelle. I'm a global shaper from Davao city. It's in Mindanao the south of the Philippines And we're talking about inclusion. We are talking about the unbanked. I want to give first a context There are a lot of communities and people who are whose income is not enough So I appreciate very much Earlier, you know, you're talking about the culture of saving But what's actually happening in my area in our community in Mindanao, we have a culture of loan So if you have a problem, the only thing that can augment it is a loan because your income is not enough the other the other culture is I have this idea of if I don't see my money, I am not confident. I'm not secure So I have to physically see the bills and count it for me to be Really secure that I have something to spend So what financial transaction is left? It's the sending of the money in and out of the area Now in the Philippines, we have a chain of pawn shops lending institutions And so now these are enabled to send money in and out of the area So I don't need to go to a bank. I just need to go to a pawn shop fill up a form Send my physical cash to my kid in the city who's studying And then there's a question of again saving So if my income is not enough to augment my need how I have no other income left to save So this is this is a context. This is a situation So now my question is are we talking to these people and if we are what's the message that we are sending? Are they part of the inclusion that that we are trying to you know achieve? Is there anyone in particular you'd like to Um, I would very much be be very interested to hear the opinion of someone from the Philippines Specifically, I guess I could be Or myself, but I can't answer. I'm the moderator so I think for Financial inclusion, I think we need to make a distinction You know that the situation you describe where an individual does not earn enough for his or her basic needs Or his family or her family's needs Microfinance is not going to help that Right, that's the job of government and that's what they do through cash transfers and other subsidies What financial inclusion can do is enable that person to enhance upgrade improve His or her earning earning capacity so that at some point they will be able to fulfill all the basic needs of the family Or the individual and I think that's the role for you know People around this this stage and in many of you, you know who are involved in you know Microfinance and other related activities. It's how to empower The poor who otherwise may not have that access To financing to capital to to financial transactions that would allow that person To be gainfully employed or doing a business so that he or she can provide for for the basic needs It is not about You know filling the gap of the you know the shortfall between earnings and basic requirements That is not sustainable that happens with gifts with grants with government subsidies not with you know Microfinance or other related activities Please sir Hi, my name is Aldi. I run a mobile financial services company in Indonesia. My question is to miss sinha and mr Chani So you both managed to scale very disruptive business model.  How did the mainstream banks and incumbents react? Did they start a partner with you? Did they try to crush you or did they simply let you be? And in hindsight, how do you think they should have reacted? Thank you Very interesting question Actually mandishi bank started with no outside fund no grants nothing it was mobilization of Share capital because it's a cooperative bank and then mobilization of deposits and lending When you go through this model which I now I think at that time I used to think like why can't we take a grant and you know have a big institution But now I realize that helped us to create a very good mid business model one and a very solid product diversification, so it's actually When you start such institution It takes time to scale and I personally also have Sometimes ambiguity about the scale like having a single product of joint liability groups Save group of five and scale all over the country you can do it But the question also is that what is the quality of impact do you have? It's very easy to have a single product and scale all over but that doesn't mean that It's solving the mission or the purpose What I think is that when you it's a scaling off at both the level like when you are banking with those people You want to see a qualitative impact on that that their income increases And that's why people also are banking with you because they want to create a wealth So are we creating it if we want to do that then you have to also have a broader broaden your Products and so you scale not only just vertical, but you scale horizontally that is one Second in spite of saying that if you want to bring down the cost you need to scale And that has to be there whenever you are doing business and so for that there are various I mean with mandishi what we had to do is that to see that our cost is not increasing Cost of like administration cost and how do you do that? So majority of our agent who are doing banking They are on commission basis So that helps to keep the cost low, but also helps to scale And while scaling then what do you see is that how much how many people one person is going to serve? So it's very interesting that by with using of technology and everything Our agent first they what they see is that is it possible for us to reach at least 75 people? If not, we are not going to use the technology and it's very important because these people are Are the forerunners of the bank. So for scaling you have to provide a very different delivery mechanism as far as Banking to unbanked is concerned because those people are not going to come to the bank You have to reach them and how do you reach you have to reach in such a way that you have a scale And you also manage the cost both the things you have to and there is an incentive So there so how did we scale is that our Field agent had an incentive because they get a commission for the additional client That is one with the technology so that you have a proper monitoring system And you also control fraud that is second and third to keep the cost down so that you have a enough margin Because I also feel by end of the day very important thing is that how much profit you are making yearly And how much reserves you are creating for the bank and these things are also important So it's a very I mean it's a very balancing approach and very tough Operating but your delivery mechanism has to be very important for scaling up and if you Otherwise like my micro finance institution in India had a lot of problem with the scale If you are scaling and ending up into a multi or depth or a multi loan then also it is a problem So I think you have to think on all those issues and and in scaling and profit is important finally with the quality Jenny Thank you for the question. So in in in my case when we we start as an NGOs the fund To your early on question that the fund is a grant from the UNDP 600,000 US dollar and then the UN Advised that 600,000 provide loan to 1,400 customer. So And then the interest rate is it They call subsidize them, but in fact it's not subsidize because it's 10 percent flat 10 percent flat And you see when we have a small team we cannot we cannot this we cannot disperse 600,000 to 1,400 so and then later on When we obtain license as a bank, I mean our staff got trained properly We have the system in place. We have The network bill I don't think we can This can provide loan or more to a customer Not just loan I mean loan and finance services to to the customer. So again like if In terms of scope and scale no like the the small size when you you offer and also the large scale when you provide so I I can see that when we were NGO we we run on the subsidized based on the donor funding support But when we became commercial bank, I mean the professionality of the staff and also the understanding Well understanding of the customer as in these two combinations and with the support of the local authority We can provide a finance service loan and without Almost non-performing loan almost zero at this afternoon I I listened to the speaker of the president of indonesia He mentioned that non-performing loan in indonesia four percent four percent In in in khyberriak in my bank our non-performing loan is less than one percent for 10 year or this year 11 less than one percent So if we are four percent we we we get we get lost We we we lost no so less than one percent so Again, no like do do less and then we get lost and we do more and then in terms of light scale as in Yeah, profitability will be from that. I don't know if I respond to the right question, but Yeah, and this one and then second Related to the customer so when we when we Subsidize by the the donor And then when we obtain license as a bank as in these two different things from the government perspective the government see that we Contribute to the their budget in terms of tax a paid because when we obtain license We pay tax when we were NGO we didn't pay tax and then we we reach a small number of customer like I said Even we set the target, but we cannot achieve but when we pay tax We set the incentive base for per branch for per grade officer, you know And then we can measure The effectiveness of the individual product line so that we can achieve more in the in light scale Okay, maybe just to end I think just why you want to see something very quickly just very quickly I can speak for India and I think Institutions which are either specialized microfinance or special institutions like missus in us are actually very welcome To the larger commercial banks because we can use them as an intermediate to get to people We would have never got to otherwise So actually there is really no conflict and to the lizards question earlier my response is that I understand that there's only transaction Possibility and there's no saving and borrowing capacity yet But even there if you substitute the pawn shop with the mobile phone transfer It should be easier. It should be in theory cheaper and it definitely is more secure So I think there's room even in that scenario in mind allow to sort of bring in A little bit more into inclusion at a cheaper cost Yeah, thank you. Just well, I guess I mean that's all we have time for we could spend pretty much all night Really talking about this topic and really how better to deliver these services But I think that's one thing that's fairly clear Is that the models are there there are success stories out there I think the challenge right now is certainly just Bringing that model and trying to adapt it based on I guess the needs of different localities Challenge really now is for the government really to make Itself accommodative For those models to thrive and sustain themselves because I mean, let's not kid ourselves if there's no profit It's not going to be there Not next month. I mean perhaps next month, but I guess in the next few years Now on that note, I'd like to thank our panelists for all their time And I'd like to thank you all for coming. Thank you very much


To je pravda, da me prejsem Giovanni Bellettini, sej member z UCTP, in zelo se pravda o vsej konturstv, in rekonstručenih soličnih vsej. Čakaj. Čakaj. Čakaj. Čakaj. Čakaj. Čakaj. Čakaj. SehemST, n endurancekla mi mi, obs valovAH nWelcome H externallime masnice. Čakaj 80 dal crawlingovo, dar sem se pogledTw svaril! ČakajAl mi? Čakaj. Čakaj. Čakaj. Čakaj, ... toward the tales will be writtenin this book three years ago. It was published by Springer with three co authors of mine, three colleagues. Ok. So let me explain the initial motivation. The motivation is the motivation from applied mathematics if you want, Or also from how the human brain tries to reconstruct a shape, a three-dimensional solid object, starting from a draw on the plane. So for instance here, in this plane, you see in this plane, there is a casp, presence of a casp here. And this casp comes as a projection locally of this fold, of this surface here, b-dimensional surface in three dimensions. Also this here, another projection. So the problem is, if I draw a sort of graph in one plane, suitable plane, why the human brain reconstruct almost immediately and very often a three-dimensional, uniquely essentially a three-dimensional solid object? Why is it the case and what's happening? So I will focus on the projection of a contour, say, on a graph in the plane, and then I will try to reconstruct the solid object, the scene. It is called the three-dimensional scene. Possible applications, as usually in the reconstruction of images, come from images from satellites or medical images, computer vision, image segmentation, and so on. I am not at the moment, I will not discuss really these applications. This is a talk focused on mathematics. One of the motivations that we had is the following interesting example. So you have this two-dimensional draw. And how is it possible that most of us, depending also on how far we are from this picture, but most of us are sort of reconstructing some triangle here, which is not there, but it is, in some sense, our brain automatically imagine a triangle here. So and the problem is still open here. Try to find a variational model, some energy to minimize, which is capable to reconstruct the minimizer of which could be, say, something which contains this triangle. This is a quite difficult problem in calculus of variation, I have to say. This is, these are one of the many examples of Kanica several years ago. Concerning these kind of problems, our starting point were an article by Nitzberg and David Manford in the 90. And almost immediately, three years later, it appeared a book on this, a book on computer science. And again, you have given a given grade level. Like this is a grade level. You can imagine a function, which is, say, one here. Corresponding to the black part, or to the gray part, and zero corresponding to the white part. In any case, you have given this grade level. And you want to find an action, functional, and energy to minimize, to be minimized, and energy defined on some sort of plane curves. And the minimizer of which should be the correct object that you imagine to, your brain is imagining. This is very vague, of course, because I don't want to, even to introduce the energy, I want to go to geometry. So this is just, again, a motivation for me. So suppose that you have defined this energy functional. This must depend on the order between the objects in the three-dimensional scene. For instance, in this case, we are imagining, say, a white triangle in front of three disks. Just in front of three disks. So there should be, in the functional, something which depends on the order of, in some way, on the order of the three-dimensional objects. And the minimizer should carry depth information on the order, saying which is the object in front and which is in back. So ne, John, I don't even understand the problem, actually. What is your?  I would like to find an energy function defined on curves, set of curves, graphs, or something like that. The minimizer of which should contain, for instance, this, the boundary of this triangle. And the minimizer says, OK, exactly on this picture. Saying that, OK, a minimizer could be, the boundary of the minimizer could be a triangle. And there is also depth information, which says that this triangle is in front of three disks. This is the aim, one of the aims of this kind of papers of the mathematical literature. Sorry. So, oh, no, it's skipping the next slide. No. It is the one after, check it there, not your, it's not. No, no, oh, I didn't check this. Oh, there is an action, OK. Let me see. No, it's, OK. Let's go on from here. So, the minimal configuration is carrying, probably, a depth order, but these kind of models have a limitation, in various limitations, because the problem is quite intricate, I have to say. This is a very interesting model, but still there are some limitations. One of them is that this model enforces a global ordering on the various objects. So, you cannot, for instance, you cannot model or get into your minimizer, you cannot get an object, which is in front partially to another object, but at the same time, in another region, is behind the object. So, this is a situation which is excluded by the previous model. Again, also, one connected object, which is partially, I mean, this is an object which self-overlap, in some sense. Again, this kind of three-dimensional solid set cannot be obtained as a minimizer of such kind of model. So, in the effort of try to solve and try to include these as possible minimizers, we modified, we tried to modify the energy functional into another energy functional, which, in particular, is defined on possibly overlapping regions, taken to account to self-occlusions. So, self-occlusions, now, in a new model, and more refined, if you want, model, can be considered. Now, it turns out, after some variation analysis, that this new energy is defined on what we will call apparent contours. I will define what it is in apparent contours. Again, we are in the motivation here. So, no details. So, this was a motivation for our study on apparent contours. So, the motivation was trying to avoid the problem of self-overlapping in the Manford-Nitzberg model. And then we come out with a model defined on graphs, suitable graphs, which are apparent contours, and minimization of this function also can carry information on how to reconstruct hidden contours, and how to, which is the object behind, and which is the object in front of. This is an action that I don't want to write here. It is an action depending on several things, depending on the order, on some labeling, on the length and curvature of the graph, and so on. But this is technical, and I don't want to enter into the details. OK, just an example. Suppose that your grid level is this one, in the sense that you know that your grid level is jumping on this curve, this sort of ellipse, and this part here. So, presumably, the Nitzberg and Manford model produces, under certain assumption on the constants inside the model, produces such a minimizer. What is this minimizer? It is just, if you want, a solid ellipsoid in front of another solid object. This is not connected. See, you have two objects, just one in front of the other. But there is another possibility, which cannot be obtained, probably, with the Manford-Nitzberg model, which is this one. And this one is as a connected, just one solid object, which is a connected set, which is just the, this is the so-called apparent contour of a mushroom. OK? Now, you see, here there are some integral numbers. I will explain the meaning of this integral number, these integral numbers in a moment. So, this is just to say that if you have this object, you want to imagine, where does it come, which is the three-dimensional set, the two-dimensional draw of which is this. There could be this possibility, but also this one. And these two possibilities can be captured by the new model, while the first model here cannot capture this second reconstruction. So, this is all about trying to have a computer to recognize images. Yes, of course, of course. So, do you also keep in mind how to compare this with what we would recognize when we look at what humans would see? What do you mean to compare? I mean, do you, for example, I think we would all interpret the top one as the bottom one rather than the middle one. You would interpret it. Do you prefer this? No. You want to think, even if you think that it is one. It is a mushroom. Yeah. Well, that's not even part of the question. No, it is very difficult to say what it is natural here and what it is not natural. What I just can say is that I'm just enlarging the possible minimizers. That's it. And probably the answer to this question is sort of psychological and biological problem. Neuro-physiological problem, which. You like mushrooms, don't you? Yeah, for instance. OK, so now, this is just a motivation, so short introduction. So, let me go on. So, let me define something now. So, I have, suppose that I give you a three-dimensional object, this potato here. I call this E, always in the seminar. And the sigma is the topological boundary of E. Is a solid set. The boundary is a smooth object. Is a smooth surface. OK, then I project it. I choose the projection direction. I put my i here in the direction of minus infinity orthogonal to this plane. This is the so-called retinal plane. It is the plane when I project this solid object. And what I see in the projection, the apparent contour that I will define for you is this curve. In this case is just one curve on this plane, on this projection plane. And this obtained directly from this solid shape in a specific way, I will explain. Notice that this kind of curve here is singular, because you have here a transversal crossing here. And then you have two casps here, OK? So, casps and crossings are very important in this discussion. So, let me try now to define what is the apparent contour. So, suppose that you have given a three-dimensional smooth solid shape. And this is connected, but in general we can allow also non-connected objects. OK, suppose imagine this object to be transparent for a moment. So, this is the same object, but semi-transparent, if you want, just semi-transparent. And then I define what is this graph, which is called the apparent contour of this. So, what is it? So, you have to do the following. You take all points on the surface in three-dimension. So, this is a boundary, a boundary of solid set. This boundary has, there are points on this boundary containing the direction of projection. The projection is in this direction, OK? And all points of the surface, such that the tangent plane at that point contains this direction make a smooth curve on the surface itself, OK? For instance, it is clear that at this point the tangent plane is this, and this tangent plane contains the direction of projection. But this is not only the case for this part, as you see, but there are other points having this property, OK? So, this point give you a smooth curve on the surface, OK? Now, you project orthogonally this smooth curve on the surface, which is a very smooth curve without self-intersection. It's a perfect curve on the smooth surface. You project it on the retinal plane. So, you take a projection on a plane of this space curve. And when you project it, then you get singularities, OK? And which kind of singularities you get? In this specific case, you get, again, this corresponds to a transversal crossing. And this corresponds to a casp, another casp, another casp, another casp. And this is what you obtain. It is a complete graph having kind of singularities, in particular, it has casps and transversal crossings, OK? Now, it is interesting, and this picture shows an interesting fact, that this graph consists of two parts. There is one bold part. And there is another part, which is not bold. This one, this one, and this half circle here is not bold. What does it mean, bold and not bold? Well, the bold part is the visible part. And the non-bold part is the part, which is non-visible, in the sense that you see, you cannot see if this is semi-transparent. But if it is not semi-transparent, you don't see this part, because it's behind a fold of the surface, OK? So this graph, essentially, is divided into two. There is a visible part and, say, an invisible part, OK? Singularity of the visible part are t-junctions, like this. So there is a t-junction. So this terminates here and is occluded by this. And there is a terminal point here and a terminal point. These are singularities of the bold part of the graph. On the other hand, singularities of the complete graph are just transversal crossings. OK? OK, now I need to assign to this graph some label, because giving a graph only is not enough to reconstruct the dimensional shape. So now I want to endow the graph with some label, in particular, integral numbers. What is the meaning of this number here, 0, 2, and 4? We have 0, 2, and 4, and 4. These are even numbers, integrative even numbers, assigned to each region of the graph, or each connected component of the plane minus the graph itself, OK? So this 0, this 2, is simply what? Is simply the total number of folds that a light ray meet starting from the projection plane. So for instance, if I take a light ray corresponding to this point, I intersect the surface twice in the direction of the projection, OK? So you see, here you intersect four times. You have four times, total intersection of all your light ray, 2, 4, 2, 0. 0 is the external region. There are no intersections, OK? So this is just, this number, labeling is quite evident. It's a very easy labeling. And notice that the orientation of my graph, now I consider a graph oriented in which sense, in the sense that on the left, locally, I have the highest number, on the left I have 2 and 0, here on the left I have 4 and 2, et cetera. And notice that these are always even numbers, OK? Where F, I call this F, F depends on sigma. Sigma is the boundary of the solid shape.  And actually, where F is 0, this is called the background, actually this number here can be recovered simply by as a winding number. So it's not really something too deep. It is just twice the total winding number of a point with respect of the, you fix a point, you look at the winding number of the curve and you multiply by 2 and you recover this labeling here. So this is F. But what it is more important in order to uniquely reconstruct the three-dimensional shape is another number. So this F is assigned to regions. Now I assign another number D to arcs. Two arcs. Now, what is this D? So here 2, 0, and 4 is the old F, OK? So now I give you another information, is number D. So D is now assigned to this arc and to this arc, to this, to this, and to this. What is this D? D is the following. In words, D is the number of folds. So you take a point on this arc. This point comes from a unique point on the surface because this is a projection of a critical curve on the surface, as we told before, OK? Now you look at the number of folds. You start from the point on the surface and you look at the number of folds of the surface that you meet, a light ray meet, before arriving to this x, to this point here on the curve. So it is the number of folds of the surface anterior in front of the point here. So let me explain with this example. D equals 0, here you have no, this is the visible part. You don't have here any fold of the surface in front of this point. Now you take, for instance, a point here on this arc, this thin arc here. So this is a point, essentially, here. So this point is the projection of a unique point on this surface here.  You just have one. This part in front is just one layer and then there is the point. So here this one. If I go here, now I have two layers, two folds of the surface in front. So D is 2. And then it jumps to 0, here. This is really what matters. F is not so important, but D is extremely important. So you assume there's no light. No, this is a good question. Everything here in this seminar is under an assumption of stability, say, genericity. This stability is a delicate and fundamental issue in singularity theory. I don't want to enter this, but exactly one of the conclusion is that you don't have any kind of flat part in the projection direction. They are not totally independent. No, they are not totally independent. Let me go on, and I think I will answer immediately to your question. So is this clear? So what? Yes. OK, so look at the point here. I want to define the number D associated to this point, to this arc. Actually, it is constant on this arc, this number. So I have this point here. This point here is the projection of a unique point on your manifold sitting on a curve. And the tangent plane, this curve is defined as the points of the surface where the tangent plane contains the projection direction. So this pointing comes from a point here. Now I imagine a light ray starting from here and going to here. How many folds of the surface I am meeting before going to this? This one, and this is one. This is the number D. This is the definition. As I said, F is not so important. Suppose that I give you a set of curves, and I give you only F. F must be an even number. This is the background, so 0, necessarily. Then I have to jump always by 2, 2 and 4, for instance. But then this cannot identify the topology of this object in three dimensions.  So the number F is not enough. But now if I give you a labeling D, let me call D labeling from now on, F is not so important, but D is more important in this seminar. Could be connected, could not be. Yes, if I give you D and F compatible, I will reconstruct uniquely the topology. And therefore, I can tell you F. No, no, not just from here. From here, no, but from here, yes. So let me give you now not only F, but also D. OK, now I give you D as follows. For instance, F is this, 2, 4, and 0 as before. This is F, but D, this is 0 here, because necessarily this must be visible. So 0, 0, also on this. But suppose that I give you here D equal 2, for instance. So what does it mean, D equal 2? Well, this means simply that the small sphere is behind the large sphere. If D is 0, then this means simply that the small sphere is in front. And with this one, it means that there is a hole. It's a small sphere inside the big sphere. So this is a suggestion of the same. Maybe if I find a sufficient number of conditions, compatible conditions within F and D, then maybe I'm able to say that always this comes from some three-dimensional. This is one inverse. I have not understood. Yes? No, this cannot be a donut. This cannot be a donut, because a donut has a hole here. And therefore, that is visible part. So this is 0. This cannot be 4. This could be 0 here. So let me see that I try to go to explain that one of the question is the following. Locally, essentially, this is one of the pictures that happens at one singular point. So at the transversal crossing locally, we have this kind of situation. There is D, which is not jumping here, but this other D is jumping from D2 to D2 plus 2. Here D1 is constant. And you have that F, as always this structure, the minimum value is, say, here, this is the maximum value F plus 4, F plus 2, F plus 2. You have to imagine this sort of local three-dimensional object. The orientation, you see, is such that the highest number of intersection with the light rays on the left, like here and here. And you see that here D is not jumping, but D is jumping here. Because when you go in this direction, there is a couple of folds in front of the continuation of this arc. So you see D2 at the transversal crossing jumps of two units. And there is a constant here. Oh, sorry. There is a constant, which is this. This kind of inequality. This is fundamental. So locally, the situation is at a singular point of transversal cross type is this. We imagine it is this. And what happens at the casp? At the casp, you see, again, in this picture, we have this constraint here, F plus 2, when I am here F, and then when I'm here inside, local inside the casp, F plus 2. And then if I have this orientation, I could have also D plus 1 here and D. But this is just an example. You see, from this, this is visible. So D equals 0, and here D equals 1. So it jumps of one unit at another singular point at the casp. OK, this is sort of what we imagine to be true when we have a three-dimensional picture of a surface embedded in a tree. We always come to this kind of compatibility conditions within D and F. The point is, are these enough? Are these efficient? Notice that indeed, in the second action function I introduced by just discussed a little bit, if I define my action function on this kind of graphs with leveling, it turns out that these three objects, which are the datum of the problem, I can put on this object a compatible leveling. You see? And the possibility of putting here a compatible D and F on this configuration with the triangle is one indication that if we are able to set the parameter so that this becomes a minimizer, then we end up really with a triangle in front of the circles. So in the second action functional, the action function is defined on this kind of graphs. So it's a complicated domain. The function has a complicated domain, because the domain are graphs with levelings, and also something else. Now, coming to your question, Stefano, is the following. Notional stability is required everywhere here. This is a fundamental point in singularity theory. So for me, the reference book, I am not an expert in singularity theory, but I know a little bit about this book. And there there is everything. Oh, sorry, this is mappings. Mappings is a mistake. So everything we need to write the book was contained, essentially, in this book here. But as a byproduct of this kind of stability assumption that we will make and generosity of projections, stability of shapes, and so on, it turns out that these graphs, apparent contours, the singularity are just exactly only of these two types, transversal crossing and casps in finite number and t-junctions and terminal points, and no more than that. This is a consequence of these stability assumptions. Now, questions are the following. If I give you a plane graph with crossing and casps, is it the apparent contour of a 3D shape? So if I give you a plane graph with a compatible leveling, say? Or another question. When you have systematically analyzed all the possible compatible labels? It turns out that those two are essentially the only compatibility conditions you need to solve this problem here. So they are sufficient, necessary and sufficient. And then this concerns the complete graph. But if I want to, because in my picture concretely, I don't have a complete graph. I just see the visible part of the graph. So the final aim would be, I give you only the visible part. Then from the visible part, is there a way to construct a complete, apparent contour? If it is the case, after that, can we construct a three-dimensional shape coming from this complete graph? OK, this is what we are doing here. The possibilities are finite right now. On what? I mean, in the video now. No, I think that this is a good question. Maybe it's related to this second point. If you give you just only visible part, yes, there will be essentially, no, there will be at least one way to produce a complete graph. And not finite, not finitely many. OK. Now, so these are questions concerning graphs, just graph. Then there are more difficult questions. Suppose that you give you two apparent contours, very complicated, I don't know, 200 casps or 300 crossings. Can I say that these are coming from the same object? They reproduce the equivalent 3D shapes. This is the same question that appears in not theory. And even there is extremely difficult. OK, so this is a situation much more general than not theory. So it is even more difficult. In the class of equivalent meaning now that they are isotopic. Maybe I will define it what it means ambient isotopic later. In the class of equivalent shapes is there one, which is the simplest one. And is it possible to automatize this issue on a computer program? Maybe this is the most interesting part of the book. Are there several moves? Yes, yes, yes. I'm going very slowly, I'm sorry. So let's see examples just to understand. Suppose that I give you this. This is just F, there is no D. But it turns out, you can check, it is not possible to put a compatible D here. So this cannot, a posteriori, cannot be apparent contour of a three-dimensional shape. But if you slightly modify it, this with the same F, OK, there is another region here, 0, this actually you can prove, it's easy, it's easy that you can put a D here. And once you can put a D, there is a hope that this is coming from a three-dimensional object. Actually it's true. So this is impossible, this is impossible again. There is no D, but here there is D. So it's not so, OK, one should try by himself to find a D. Mascherina di macdi carnivali. I don't know how to explain this in English. It is a mask, this is a mask. This is coming from a mask. This is impossible, OK. OK, there is a first theorem, finally. The theorem says that if you give you an oriented plane graph with casps and crossings, and I give you a labeling, satisfying the compatibility conditions that I showed before, just only those, then there exists a smooth three-dimensional shape such that the apparent contour of the boundary of the shape is your G. And the D you get from the 3D shape is exactly your D you have given a priori. So this is an inverse problem. I give you a graph. I reconstruct the topology of a 3D shape, OK. We found some related reference. I think this is a sort of bibliography in computer vision, maybe. This kind of reference related to this problem here. What about uniqueness? So there is, it is possible to reconstruct a 3D shape. Is it unique? Yes, in some sense. It is unique up to transformation in the direction of the eye along each point monotonically. So you don't change the fibers. I mean, you have given any x, you have a transformation which is strictly increasing in this direction and moving continuously with respect to x. It is clear that you have a sphere, but you can modify the sphere like this. And you don't change the apparent contour. So this is the only thing that you can do, essentially. So this is a uniqueness result, OK. OK, the proof of this is a proof based on the cut and paste, essentially. If you want to go into details in this proof, it's not so easy. Maybe for a geometry, it's almost trivial, probably. For me, it's not. And working in the details, it's not so immediate. And let me mention that what we reconstruct is not the roundest, more natural in some sense, which I am not able to define. It is just an object, OK. It's essentially unique. But the most round is another problem, OK. And once we have reconstructed it to see what it is really, is it a torus? It is a torus inside another torus. It is to tori, like this, with the sphere inside. This can be very difficult in general. OK, there is now a program, which is free, which can be downloaded apparent up contour. It's called up contour, this program, which reconstructed topological structure automatically of this three-dimensional shape. And the number of connected components of the boundary and the one characteristic of each of connected component. And also information distinguishing between these kind of cases here. The program, I think it's this kind of program in the number of crossings. No, no, this is very quick. If you do this in a few seconds, you get it, the result is not. But we have not checked this with 100 vertices. Also, because giving to a computer, the structure of a graph is not so easy. Because now I tell you, giving as input your graph is a kind of piece of information, which is not easy to give to a computer. So proving with 100 of nodes, I don't know exactly. So OK, then there is by product. So suppose that they give you your graph and the labeling consistent, compatible. Now suppose that from this theorem, there is a unique essentially unique three-dimensional shape having this as an apparent contour. Then it turns out that the Euler characteristic of the boundary of the shape can be computed just from the apparent contour. So I give you the apparent contour. And from that, it is possible to deduce exactly the Euler characteristic, only from that. In particular, in a special case, when this surface is connected, then it is possible to deduce also the Euler characteristic of the solid set bounded by the surface and on the complement of the set bounded by the surface. All these can be found in this program up contour. We always look inside the stable and generic surfaces. So there cannot be flat, stricter increasing monotonic, stricter increasing must be at any point. OK, to show the difficulty of this kind of problems, let me tell you, let me make you this observation. Suppose that E0 is a noted solid torus like this. Suppose that E1 is a standard solid torus. Suppose that E2 is anti torus. So it's just a sphere, then you remove two disks and you do a gallery inside the sphere, a noted gallery like this. So these are three solid objects. It turns out that they have the same, that the surface of these have the same Euler characteristic. It turns out that also the interior and the exterior have the same Euler characteristic, but they are not equivalent. So this is an example that showed that, of course, knowing the Euler characteristic is not enough, even if you know the Euler characteristic of the interface of the inside and of the outside. So this says that, of course, you have to know to inspect a lot of invariance of this kind of objects, invariance in some sense, like in no theory, essentially. So other invariance of the apparent contour and more interesting of the 3D shape can be considered. Some of them are automatically obtained by the up-contour program, for instance, the fundamental group of the complement of the set, but also the fundamental group of the inside and the fundamental group of the surface itself. So another remark is the following. How to recognize the shape? How to say that this is a sphere when you have an apparent contour tremendously complicated, it turns out to be a sphere. What do you do? Well, again, as in no theory, there should be some way to simplify it, maybe, and to find a sort of elementary, class of elementary moves that modify locally the graph and simplify it, sitting inside the equivalence, isotope equivalence of the 3D shapes. I will explain a little bit about these moves, and this is maybe one of the most important features of this program, because applying these moves is not at all trivial. Now, the software code is devised in such a way to be insensitive to the particular embedded of the apparent contour in the plane. And as I was saying, it is designed in order to capture only orientation relative position of the ashencine topological structure of the apparent contour. You can always modify the apparent contour with an isotope of the plane, with a diffimorphizum, if you want. But this should not be important for the program. So OK. Now, what about the completion problem? Let us try again. Now let me focus on the visible part only of the graph. I want to understand maybe a class of sufficient conditions on the structure of this object in order to be visible part of some apparent contour. For instance, we realize that this cannot be visible part of anything, because this singular point, terminal point, cannot be, cannot terminate in the background. This is impossible. Also, this is impossible because it is impossible that to have a visible part, which has the background on the left, with this orientation. This is, again, impossible. One also realize that the emerging arc here, let me call this the emerging arc, must always lie on the right of the occluding arc. So this is allowed, but this is impossible, at least at the first side. And the theorem says that if I give you an oriented plate graph with t-junctions and terminal points only as singular points, so no casps, no crossings, but only t-junctions and terminal points, and suppose that the previous condition are satisfied, suppose that we do not fall in the example of the previous site, then this is visible contour of something. In the sense that there exists a labelled apparent contour which complete it in such a way that the given k is the visible part of g. So philosophically, we have the following. We start with only a visible part. Through this theorem, we reconstruct at least one complete apparent contour with a consistent labelling. After we have this, we can reconstruct a three-dimensional shape. This kind of property is exactly sufficient and necessary. Yes, you see, you realize that this is impossible, this is impossible, and these are only possible cases. That's it. And this is a characterization. This is the other way round. What I'm saying is the other way round. I say the other way round. So in some sense, we have solved the problem in computer vision in the sense that I can tell you in some sense when what I see on a two-dimensional picture, when this object is a visible part of an apparent contour which is coming from a three-dimensional shape. So I reconstructed a three-dimensional shape just only from the knowledge of part of the contour of the plane on the plane contour. So what else is there possible besides t-junction and terminal points, the principalness? No, the visible part. And that is always like that. Any visible part, always like that. This is due to genericity and stability assumptions. The proof of this theorem, this complexion theorem is constructive. And again, there is a part of the program which is called visible contour, which does this. And the proof is based on Morse description of the graphs. I don't want to enter this direction, but the Morse description of this object is fundamental in every description. Now, this is an important remark. When you do this proof, you have to prove this in any case. So you don't have a specific graph. You have any graph, and you have to prove you can do a complexion with a compatible labeling. This is a global problem, because you do this locally. Any t-junction becomes a crossing, you continue. Any terminal point becomes a casp. But then in the end, you have to close it with a compatible global labeling. This is the difficulty. And our proof produce one solution, but maybe it's not the best, and necessarily the best that the brain, the human brain, does. So the scope of this theorem is just to show that the hypotheses are sharp, and we are able to construct at least one complexion. Examples. So suppose that I give to the program just these two curves. Then the visible contour. This is the visible contour, and not oriented. Then what is the answer of the program visible contour in sufficient orienting information, because the internal circle cannot be implicit-oriented, because it can be oriented in both in two. This orientation is trivial, it's just like this. But this could be in two ways, and so the program cannot go on. Second case, suppose that I give you the same visible contour, but now I add the information that this is oriented like this. Now the clockwise orientation of the internal circle. And now suppose that the background is just only here, not here. So we impose f equals 0, only in the exterior region. The result in the construction cannot be a torus, because this is not a hole now, it's not a hole. So what is the solution of the program? The solution of the program is the following. The program adds a new circle, and the unique solution of that is this. What is this? Is a visible torus, the bold one, and there is a sphere behind. So this is what the program is producing, intermediate sphere behind. Another is the same visible part. And now you force f equals 0, also here, and the visible contour reconstruct the torus, seen from above. Again, same visible contour. Now let us orient this on the left. So if I orient this on the left, it means that f must be higher here. So this cannot be a hole, cannot be 0. f is 0 only here. So visible contour reconstruct the apparent contour. So there are no hidden arcs, as in example 2.  This is what the program gives to you, just only from this information. Now, more interesting maybe now, suppose that I give to the program this visible contour here, and suppose that is in this region, I force this to have 0 f. So I suppose to be inside the background, this small e region here. So this is what visible contour produces, which is exactly our theoretical proof of the completion theorem. When we imagine a Morse line, our proof produces exactly this object. Now, as I said, this is not the most natural object that one could imagine. This is just one solution. But what is this? You see, this terminal point is becoming a cusp, and the completion, this is becoming a crossing, like this. And then everything goes down, and then you have to close it and put a consistent labeling. Is this possible? Yes, because this is a theorem. And what is this? Now, the program is able to tell you what is this. This is not clear. I mean, maybe it's clear, it's a torus. But the program is telling to you that after some command that you give, you simplify it with a list of moves that I will explain at the end. And what the program gives to you is the torus. So maybe we are a little bit happy about this. Now, suppose that you don't force F to be 0 here. Now, what is the solution? So you remove the marking of the small internal region as part of the background. So the background is only this one. You enforce your program, visible contour. Our proof, theoretically, is this one. It's a very complicated complexion where in the small circle there is an F, and the other labeling are the D. This is what we find in our proof. This is what visible contour is doing. And what is this? This is not clear at all. This must be simplified with the use of the moves. And visible contour, after using the moves that I will explain in a minute, must simplify the former 3D sphere, for instance, using the elementary moves. So this is actually is the apparent contour of a sphere, OK? Using the elementary moves that I will explain. So the above example show that it may be difficult to recognize your 3D shape. The topology of what is this is not clear. So it is necessary to find moves that simplify the apparent contours, remaining inside the equivalent shapes, ambient isotopic shapes. So this is one of the main problems in theory, of course. And in that case, these moves are three elementary moves and are called rademeister moves. So here also there are essentially six elementary moves. This situation is more rich. It's a little bit more complicated than not theory. And these moves have been implemented in this up contour. So there is a theorem here that for me maybe is one of the most difficult that says that two 3D shapes are equivalent if and only if you can pass from one apparent contour of the first one to the apparent contour of the second one only through a finite number of elementary moves. Like in not theory, exactly. And which kind of moves are these? These are essentially six moves. This is called t-move. Locally you are allowed to do this. This corresponds to the third move of rademeister. Then there are new moves. So this is, this collapse to casps. And also this collapse to casps. So this is called leap and big to big. This is, swallow tail is this one.  The inverse, OK. There are also this one. And then the other, this k-type, k1, k0, k1, vk, k2, k1, et cetera. These are locally the move of type k. But essentially these are, the theorem as before says that these are only, the old, this set of moves is complete. So these are enough to describe isotopic shapes in 3D. These kind of moves on two planar graphs. So this kind of, OK. These are realizations in 3D taken from a paper of these authors in 206, which shows a sort of physical realization of the moves, OK. This is, I found this nice, sorry, producer. This is the reference. So now the proof of that theorem is, for me, is quite complicated. But it is based on classical and very important basic results of Whitney, Tom Arnold, and others on singularity theory, OK. The program up contour can manipulate these moves and can, in order to simplify and possibly recognize the object, OK. For instance, there is a rule, an action rule. If you ask this, the computer tell you which kind of, I can apply this move, this move, and this move here, here, and here. What do you want that they do? Start from here, and then he tries to go on, OK. For instance, what the computer is doing, if you give the computer this object, you apply moves k1b. So it is possible to push this part inside, keeping the two casps. And then there is a leap move, which collapse the casps together, and you come here, so this is sphere, OK. Now, if you think of a torus, if you look of a torus oblikli, just two minutes maybe, if you look from a torus, you look at torus oblikli, you see four casps. But if you look of a torus from above, for instance, you don't see any casps, you just see two circles, one inside the other, with the proper orientation. Now, essentially, this is interesting to say. It is always the case. So it says that if you have a smooth closed surface embedded in a tree, you can find a set of moves transforming it in such a way that the apparent contour has no casps, like for the torus. So maybe you increase a lot the number of crossings, but at least you can destroy all casps. This is a general theorem again. Is it all in your book? Yes, everything is there. So final remarks, sorry for the delay. We are now trying to understand a little bit better some other kind of invariance of 3D shapes. These are shapes more complicated than knots and links. So it's not so clear for us. We are trying to work on this. But we are going to three-dimensional topology, and I am not an expert really on that. So what I've said up to now does not include cubes, for instance. So, for instance, polyadrolipshits objects. We have plenty of no smooth objects here in this room. And the theory does not include that, unfortunately. There is a new singularity, y-junction in that case. And what about the discussion was concerned with embedded surface? What about immersed manifold, or even less than immersed, with not even immersed, with the singular point, the differential knot of maximum rank, et cetera. There is a lot of literature on that. Maybe everything has been done. So there are just few names on that. OK, that's it. Sorry for the delay. Thank you.