Entrepreneurship is not easy, especially if you are a solopreneur you often are isolated working on your own. And so when you have difficulties and failures, quote unquote, when launches don't go as you hoped, when you do some kind of outreach and the response comes back. Well, no response or very little. It's easy to get discouraged. And you might be tempted to quit. So, in this video, I'm going to share with you a recovery method way to bounce back from your so-called failures or setbacks and continue the path of entrepreneurship, because only if you continue, can you learn and grow enough to make it successful. And I talk about this from my own grounded perspective experience because I have been full time as an entrepreneur, a solopreneur since 2009. And in all that time, all these years, I have launched dozens of group programs, online courses. I've announced my one-on-one services dozens of times, if not hundreds of times on social media through email newsletters, etc. I've reached out to many potential clients to potential collaborators, colleagues, joint venture partners. And from all of that, you might imagine that there are a lot of ups and downs. There are a lot of times when I've done some kind of outreach or promoted some product or service or program or event. And I've gotten very little response, sometimes no response. So if you have had that experience, you are definitely not alone. Join me in the community of failed entrepreneurs. Well, I shouldn't say failed entrepreneurs, but those who have experienced some disconnection between our hoped for result and the real actual reality that happened. We are never a failed entrepreneur. We are only a in progress learning entrepreneur. Right. There is no failure only be direction, if we're willing to see it that way.  But if you always continue trying and, and take on a growth mindset, a learning perspective, then it's all opportunities. It's all data. It's not speaking anything about who you are as a person, your worth, your potential. What it speaks to is, Oh, you had some expectation, and that expectation turns out not to be realistic. So how can we, you know, ideally have little expectation except for what happened the last few times when we did the exact same thing. There's no realistic expectation, but anything else is who knows, right. And you simply have to try experiment and learn so that you can experiment a little bit better next time. So, still to this day, I experienced some setbacks and so called failures right now as of this recording, I am relaunching a program that my opinion was kind of a failure compared to my other programs because the response and the engagement was far lower than I had expected. Right now I'm actually launching, launching another major program, and the response is much lower than I expected compared to in fact compared to previous years. And it's because I made some big changes to the program and that that was part of it, but, but still to this day, I experience so called failures. And I want you to know that because maybe you see me as having a stable business, maybe some of you see me as having successful business, and I do for the most part. I always, I, the only reason I mentioned any number is because some of you actually find that interesting and, and grounding and helpful so my revenue in my business is between two to 300,000 a year. My take home is, you know, well over 100,000 a year it's between 100 200 K after expenses after all expenses paying affiliates and everything. So take me on after taxes, it doesn't matter I live very comfortably, even in San Francisco, you know, one and more expensive cities in the world, I live comfortably, I'm not I wouldn't say I'm wealthy, especially not compared to my neighbors around here. But I'm certainly middle class in my city, I would say. And as a solopreneur, I do have a couple of assistants that work for me a few hours per week that that's actually relatively new just this year I've ramped up my, my, my working with certain assistants and helpers but I've been solopreneur most of my years. So, I'm, you know, I'm successful as most solopreneurs might consider it, and yet to this day I experienced failures.  Those of us who are so called experts or professionals, and who have succeeded time after time after time in various launches. You don't see all the typically you don't see all the failures that we don't promote and tell you about. We launch things and we don't see don't see us usually say hey that was a failure, yet another failure yet another failure. So, truly, the, the professionals and the experts and the leaders are often the ones who are willing to so called fail the most, but bounce back and fun and have a resilience process that allows them to continue trying, growing, and therefore create more and more and more successful systems and processes over time it takes years, and a lot of you don't realize this but you will as you as you keep trying. So, as promised, let me share with you this resilience process that kind of came to me one day when one of my failures I was very discouraged and this word came to me just breathe. That was the word breathe. And I said, okay, yes, breathe. Yes, that was helpful. But then I thought maybe there's something deeper here maybe maybe breathe could mean something more than just take a few deep gentle breaths which is always helpful. Over the next few days I reflected on this word, and I love acronyms so I turn it into an acronym for other resilience process that I'm going to share with you now. So, it stands is, you know, breathe. What is it seven letters, and each letter stands for one part of the process so be stands for breathe. And simply like when you're discouraged when you're feeling down when you're feeling maybe like a failure or tempted to quit. Please don't. The first thing you should do is take a few gentle deep breaths and just that act of bringing some more oxygen into your body and your brain will just instantly shift a little bit your energy towards hopefully a little bit more, a little bit more perspective than the immediate state of negativity that you might be in initially so a couple of large gentle deep breaths. That's the first step breathe. That's B for breathe are stands for rest. And if you have been watching my videos for a while you probably have heard that I take multiple naps a day. I love taking naps. So when I say rest of to me that just means go and take a nap. It's going to be okay to go and take a 15 minute 20 minute nap. I don't take naps more than like 25 minutes definitely not more than that because I get I feel groggy the default the rest of the day but 15 minutes is pretty good. It's nice.  I imagine some kind of energy healing from the earth, or from the divine source as I'm laying there and gently breathing and relaxing horizontally. So that's our for rest, rest at whatever way makes sense to you but just take a take a moment take 15 minutes, or half an hour if you can to just rest and do anything else just relax and kind of try to feel some some energy healing from from your divine source or from the earth. So that's our for rest, he stands for extract the good. So he for extract the good. What do I mean by this is that no failure or no experience that feels like a setback, or no, no thing that you've tried that didn't work. Is ever 100% failure. So let me say that again, whatever you did, whatever you tried, whatever action you took, there is something good from it that you can. You can say, you know, sure, it didn't turn out the way I expected, but I'm glad I did that, or I did this at least or I learned this. Okay, so he is to extract some, some goodness from that action or from that situation, whether it's from something you did that some part of what you did that you say you know what at least I did that. At least I can be proud of this at least I tried that, or maybe that aspect of it went well, you know and I'm going to keep doing that next time but I'm going to do this other things differently. What can you learn what what can you appreciate from from the from the situation from the activity and also what what might you learn. So he stands for extract the good from that situation. A stands for ask for guidance, ask for guidance. So you might have a friend you can go to or a coach, or a community of people that you trust. And I just encourage you to go to someone as well actually even before you go to someone.  Ask that source that invisible source for guidance and just close your eyes and sincerely take a moment to say, if you have hard time extracting the good you can ask for guidance for that like what can I gain from this situation, what is something good from the situation, like make a sincere ask, and also ask, what shall I do next for the highest good of all. What shall I do next for the highest good of all, including my highest good. And ask your invisible source for guidance and, and then take the next step and ask your visible sources for guidance go to your friend coach, supportive group. You know, colleague, who, who, who you have a great rapport with and say hey you know what I'm feeling discouraged. I had a setback and I just wonder if you have any words of encouragement, maybe even guidance for me. And people, your friends, you know, want to help you. They do you have friends and supportive people in your life, you do, and who want to help you. And we just don't ask often enough, and something simple as this like hey I'm feeling discouraged and wondered if you have any words of encouragement for me I tried this and it didn't work out. I have no words of encouragement or guidance I'm super grateful. Either way thank you for being a support of my life, something like that just just do that. It's so helpful to get in touch with another human beings, please please do this. Please do this right. So as to ask for guidance. T is trust. If you've extracted the good or tried your best you've asked for guidance. It's time to trust that the guidance will come to you. Maybe you sent you set a prayer, and then you also sent a couple of emails or messages no don't ask just one person by the way, ask at least two or three because it'll take them time to get back to you one person will get back to you faster than than another, maybe one or two people will be so busy they didn't see the message and only one person. So ask at least three people. Really, promise me, you'll do that okay ask at least three people. This this kind of question and then T is to trust trust that the guidance is coming to you. It is. Better days are coming to you. I believe with all my heart. I really do I believe 150% in the fact that we are being guided. This is sharing my worldview and you might believe something different but you can indulge me for a moment and imagine this. Maybe true who knows that I really believe that there is invisible guidance all around us and through us. You might call it like I said angels spirit guides, God, the universe. You know, guiding spirits who are incredibly powerful, more powerful than us actually, but they try not to interfere with our free will, and our ability to make our own decisions and experience our own life, including all the failures and setbacks. That's an important part of life for whatever for whatever reason we, I believe we incarnated here to experience all the ups and downs because, and hopefully they, they, they, I think are, are wishing that we will learn from it we will grow from it because why, because the background of all of it is it's truly all good. In my life, I believe our consciousness continues into a better body and into a, you know, into a more powerful perspective, like, there's no death, in my opinion. In my, you know, I really believe this there's no death or consciousness just like a doorway and the body dies sure but then consciousness keeps going oh my god it pops out of the body and go wow, everything's all good. It's all love, it's all power. It's all love and I'm part of the all and I can now go anywhere in the universe and. Anyway, it's, this is just this life in my opinion is just a virtual simulation it's like a very tiny moment. Anyway, I'll stop there with my ramblings about spirituality and just say trust. Trust that if you believe in an invisible source and guidance that's coming to you really is more powerful than you can imagine, they don't they only whisper to you because they don't want to be too loud and interfere with your own free will. Trust also the visible guidance is coming to you right because it just if you want to talk about secular I mean just your brain as you asked for guidance your brain is going to be primed to look for the guidance that you asked for so trust. That's T. H stands for help someone else. It is really remarkable that when we are feeling feeling down and negative it's a downward spiral, and the downward spirals related to focusing on ourselves ourselves ourselves our problems our problems our situation our situation. And that's truly the downward spiral is in into more and more egoism, and I don't mean to judge those of you who are feeling depressed and sad and angry or frustrated or confused or whatever. But someone's got to say it to you, whenever you're feeling negative depressed angry that that that that that that who are you focused on your focus on yourself. You are willing. I know it's hard I mean you don't like to hear this you think I'm judging you think I'm being mean. I'm just speaking what I what appears to me to be the truth, which is what because I know the experience myself. It's focusing on myself. And when I focus on somebody else. There's always someone who is less fortunate than you, of course, we are we, most of us watching this video live in so much privilege, compared to other people in the in the in the world.  Otherwise, anyway, there's always someone that's kind of extreme. There's always someone you can help in your own community in your own circle. And I'm not talking about going feed the hungry and, you know, heal the heal the stick and, and that's, yes, if you can do that but I'm talking about something as simple as going to a Facebook group and being helpful there that's all I'm saying it's something you can do right now. You don't have to go and travel to war torn country to help out I'm just asking you to take a moment after you've done the breathing resting and the good asking for guidance trusting. Now just take a take 10 minutes and go into a Facebook group that you enjoy and try to be helpful.  Go on social media and comment on comment supportively on someone's post there's always someone.  They do right same thing. You've seen many comments in you don't have time sometimes or energy to respond but you feel a little uplift when someone comments supportively and appreciatively do that. Do that for someone it's going to take you five or 10 minutes, try not to get sucked in the social media too much, but just set a timer for 10 minutes. And so I'm just going to go and be a supportive commenter on a couple of posts. Just appreciate them for who they are appreciate what they said. And just by doing that you instantly I think will come out of your, your, your kind of your shell or your downward spiral and spiral upwards again towards the whole community towards the greater all that you are So that's H for help someone and then E finally is experiment E for experiment. Once again.  Now it's time to experiment again don't take too much time to rest, meaning you know don't don't wait too long to experiment again. Because the secret, you could say of entrepreneurship is to experiment as much as you can try another tiny tiny launch, try posting another piece of content. And the experimentation mindset says I don't know how this is going to work. I don't know if people are going to like it or not, but I'm going to try. I don't know all that means. I don't know, but I'm going to experiment I'm going to try to play with this new idea I'm going to play with this format I'm going to just try to put something out there without judgment of whether without judging myself, and without expectation of what's going to come back it's an experiment. Let's see what happens. Stay curious. By doing these steps, you hopefully will recover and get out there again into action that's the key. You kind of like start off by taking care of yourself, and then you end up getting out there again with action because that's how we continue to learn to grow. And by doing so, we find out what authentic success means for us. We discover the methods that work for us, the systems that we want to grow and develop. And therefore, you become more and more of a seasoned and effective entrepreneur. The key is to have a quick recovery process of resilience process just like the way I've described it, you're welcome to borrow this completely use this teach this to other people, or modify it, and make it your own. You have to have a quick resilience process because the next setback is inevitably coming I know this myself from my own business, and you can't just expect if you have success or something. No, if you if you're willing to experiment, which which is needed for your potential to be reached, then you're going to have a setback or a mismatched expectation versus reality at some point, and having a tool like this to bounce back quickly is so essential. So, I hope you'll give it a try. Or if you have your own resilience process that works well for you. I welcome you to comment below it might really benefit somebody else. So thank you so much for joining me and I appreciate and honor the entrepreneurial journey that you're on. And this community this larger global community historical community called entrepreneurship, that you are in this with us, and we're all in this together. So, I hope that you will continue on remembering that no matter what somehow in some way, all is well. And if we just trust the process, know that all will be well, keep learning, keep trying, keep growing. Thanks for joining me. And I'll see you in the next video. Take care.


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Hello everyone. I'm Jun Jie-Liao from Cornell and the title of our work is Namediability Against Poinomial Temporary. And this is a joint work with Marshall Boe and Tomah Kim from Columbia and my advisor Ishan Chatapati, also from Cornell, and Leon Tan from Stanford. So first let me tell you what is a Namedibot Code. So Namedibot Code is first introduced by Jim Boski, PR Trek and Wix in 2010. And it contains an encoding function and a decoding function. And we'll consider a temporary experiment which take input message s and encode it into a codeword c, and then there will be an adversary who tempers this codeword c to a temporary codeword codeword c. And then we'll apply a decoding function on codeword c to get the temporary message to the s. So our goal in this temporary experiment is we want to guarantee that either the temporary message s remains unchanged or it becomes something unrelated to s, which means it gets destroyed by this temporary experiment. So formally we will consider a temporary function family f, which we want to protect against. And then we want to grant it two properties. So the first one is the correctness, which says if we take a message s and then we encode it and decode it without any temporary, then what we get is exactly the same message. And the second property is a Namedibility, which says for every function f, there exists a simulator df for the corresponding temporary experiment for f, which means the temporary message s will be roughly equivalent to applying this simulator df on the original message s. And furthermore, this simulator df should be a distribution over identity function or constant function. So here identity function means the message will remain unchanged. And constant function means it will be changed to something completely unrelated. In other words, the message gets destroyed by this temporary experiment. And a simple observation here is it is impossible to construct a Namedible code, which is secure against arbitrary temporary function f, because otherwise the adversary can just take the temporary function to be first decoding the code word to get the original message and change it to something related and then re-encode it, then this will break the Namedibility. So some restriction on this temporary function family is necessary. And next, we will see some temporary functions which have been considered in previous works. So the most well-studied one is probably the split state model. So in a split state model, a code word will be split into several parts, and the adversary is allowed to temper each part of the code word individually and arbitrarily. And there are a lot of great work in this line, and remarkably, a recent result by Agarwal and Obromsky shows that it is possible to construct a Namedible code with constant rate in the two split state model. And another line of work which recently received more attention are the global temporary functions. So in a global temporary functions, we can apply, the adversary can apply a function, temporary function on the full code word. However, there should be some restrictions on the temporary function that the adversary can apply. So some examples include permutations and biflipping, local functions, affine functions, modep circuits, modep decision trees. And there are also some other beautiful works based on some possible cryptographic assumptions, but in this talk, we will focus on conditional information theory results. So the first result in our paper also falls in this category. So we construct a Namedible code which is secure against polynomials over a prime field FQ. And formally, the code word in our Namedible code will be n elements over a prime field FQ. And then the temporary functions will be degree d polynomials on unbearable over a prime field FQ. So if the adversary choose p1 to choose degree d polynomials p1 to pn as a temporary function, then the temporary code word will become p1x, p2x to pnx. And our first result is we show that for every integer m and d and the sufficiently large prime Q, there exists a Namedible code which is secure against degree d polynomial temporary. And interesting corollary of our result is our Namedible code actually also works for arithmetic circuits. So in an arithmetic circuit, it's a circuit which takes some variables and some constants. And in this circuit, each gate will compute the product or the sum of its two inputs. And so we will consider the temporary function to be size s arithmetic circuits on unbearable over FQ. And we define such a temporary function family to be E and Qs. And here the size s is the number of gates in the arithmetic circuits. And it's not hard to see that size s arithmetic circuits actually compute a polynomial with degree at most 2 to E s. So this means this temporary function family E and Qs is contained in F and Q 2 to E s. So our result for against polynomial temporary will also give a Namedible code which is secure against arithmetic circuits. So note that there is the restriction of the prime should be larger than a polynomial in 2 to E s. However, the code the length of the code word is unlock Q, which means the length of the code word is actually only have a linear dependence on the circuit size s. So this restriction on the prime Q is actually not unreasonable. And our second result is the Namedible secret sharing. And before we introduce our result, first let's briefly review what is a secret sharing. So a secret sharing scheme is first introduced by Shamir and Blockley in 1989. And in the T autofund secret sharing scheme, there are two functions, a share function and a reconstruction function. And a share function will take the secret s and produce n shares. And we want to guarantee two properties. The first one is the correctness, which means given any t shares, we should be able to apply the reconstruction function on it to get to reconstruct the original secret. And the second property is a secrecy, which means if we are only given less than t shares, then these share together should reveal no information about the original secret s. And the recent work by Goyal and Kumar consider a Namedible secret sharing, which is basically a secret sharing scheme with an additional Namedibility guarantee. So in Namedible secret sharing, we will consider an adversary who can temper the shares. And what we want to guarantee is if we take t tempered shares and apply the reconstruction function on it to get a tempered secret, then this tempered secret should either be identical to the original secret or it should become something unrelated to the original secret. So similar to the Namedible code, it is also necessary to play some restriction on the tempering function that the adversary can apply. Otherwise, the adversary will be able to reconstruct the secret and then temper it and then reshare this tempered secret, which will embrace the Namedibility. So in prior works, the most common tempering model is probably individual tempering. So in individual tempering, the adversary can temper each share individually and arbitrarily. So the first tempered share will only depend on the first share and the second tempered share will only depend on second share and so on. And there is also another model which has been considered is the joint tempering model. And in a joint tempering model, the adversary can split the shares into two disjoint sets. And then the adversary can temper the shares in each disjoint set jointly and arbitrarily. But still, the tempered share in the first set can only depend on the shares in the first set and the tempered share in the second set can only depend on the share in the second set. And finally, there is another model which is global tempering function. And in global tempering functions, we allow each tempered share to depend on all the input shares. However, we will play some restrictions on the tempering function that the adversary can apply. So some examples include a fine tempering, which is by Lin at all, and the composition of joint tempering and the fine function, which is by ShadowParty and Lin. And our second result is also forced in this category. We construct a nominal secret sharing, which is secure against a polynomial tempering over a prime field FQ. So our second result says for every integer m and dt and some sufficiently large prime Q, there exists a t-out of a nominal secret sharing scheme for an m-bit secret against a degree d polynomial tempering.  We allow the adversary to adaptively choose a tempering function. More precisely, the adversary can first take t minus 1 shares and then use the information from these shares to choose a tempering function F, then the adversary will apply this tempering function on all the shares to produce the tempered shares. And note that each tempered share can still depend on all the input shares. However, this choice of the tempering function can only depend on t minus 1 shares. Otherwise, the adversary will be able to apply a reconstruction attack, which is impossible. And so this adaptive choice of tempering function is actually a pretty strong security guarantee because it allows the adversary to temper these t minus 1 shares jointly and arbitrarily. And furthermore, the adversary can use some information from these shares to choose some suitable tempering function for the other shares. So the adversary can actually do a lot with this adaptive choice. And also, as a corollary, this nominal secret sharing also works for arithmetic circuits. And next we will give a brief overview on how we get these two results. So both of our results are based on a C less amenable extractor against polynomial tempering, which we will introduce in the next slides. And then with this basic building block, we will apply the reduction by traction and Guzwami to get a amenable code. And then we will apply another scheme by Lin et al. to get an amenable secret sharing. And also, in order to apply these two reductions, we also need an efficient inverter for this amenable extractor, which we believe to also contain some interesting new techniques. And also to achieve the adaptive security guarantee in our amenable secret sharing, we actually use a specific and non-trivial instantiation of the Lin et al. scheme instead of just applying it as a black box. So next let me define what is the C less amenable extractor? So a C less amenable extractor is first introduced by Tchaikovsky and Guzwami. And it is a function which will be applied on a source S to produce a distribution which is closer to uniform. And in other words, this is the randomness extractor. And furthermore, it needs to satisfy an amenability guarantee, which says for every temporary function F from some temporary function family, if we apply this temporary function F on the source to get a temporary source and feed this temporary source into the amenable extractor, then what we get should be identical to the original output of the extractor, or it should be independent of the output of the extractor. So Tchaikovsky and Guzwami show that if we have an amenable extractor for uniform distribution, then this will implies a amenable code. And the encoding against the same temporary function family. And the encoding function in this amenable code will be an inverter for this amenable extractor, which takes a uniform sample from its preimage. And the decoding function will be exactly this amenable extractor. So our main result is we show that for every integer M and D and the sufficiently large prime Q, we can construct an explicit C-less amenable extractor, which output an MB string, and which works for uniform distribution and secure against the degree D polynomial temporary functions. And furthermore, we also show that there exists an efficiently computable inverter for such an amenable extractor. So with these two results, we directly get the amenable code against polynomial temporary. And actually what we prove is a stronger result. So we show that this amenable extractor actually works for a skew of fine source, which we will define the next slide. And this stronger result is actually important to support the adaptive choice of temporary function in your amenable secretory. So we say a source X is a skew of fine source if it is a uniform distribution over a fine subplace. In other words, it is a fine source. And also it needs to satisfy the property that none of its coordinates are constant. And another way to view this skew of fine source is we can consider it as a uniform source conditioned on some fine leakage, and which doesn't reveal any single coordinate Xi. So this view will be useful in our construction of an amenable secretory, because we will consider the shares leaked to the adversary to be some fine leakage with this source. And more details can be found in our paper. And next we will give a brief overview of this extractor construction. So the construction of our extractor will be of the form which first apply a low degree polynomial edge on the input x1 to xn. And then we will take the last n bits of the output of edge to be our extractor output. And this construction have appeared several times in the context of extractors. And what we want to do here is we want to choose a proper polynomial edge such that it is this extractor is actually not amenable. So a first attempt will be choosing this extractor to be the same as the Gabison-Ross extractor, which was for a fine source over a large point field. And in such extractor, this polynomial edge is taken to be the summation of Xi to the Ci for some distinct integers you want to see. However, such extractor is actually not amenable because it is vulnerable to a linear temporary attack. And more precisely, we will choose some proper constant beta i such that beta i to the Ci equals to some constant k, which is different from 1. So this will imply that if we temper each xi to beta i xi, then the tempered output of edge will be exactly k times edge x. So this even after we truncate to the last n bits, there will still be some correlation between the original output of edge between the original output of the extractor and the tempered output of the extractor. So this will break the numerability. So our next step is to try to change this construction to something different which prevents this linear attack. So we will choose edge to be the summation of xi to the Ci plus xi to the Ci plus b, where b is the constant chosen to be co-prime to the q minus 1. And why we set two terms for each xi and make the difference of the degree to bb is because with such construction, it is actually impossible to find a beta i such that beta i to the Ci and beta i to the Ci plus b are the same and it's different from 1. So therefore a linear attack doesn't work for this construction. And so actually we will take an edge to be the summation of xi to the Ci minus 1 plus xi to the Ci, where Ci is a properly chosen arithmetic progression with common difference b and b. And we don't have time to talk too much about why we choose this, but we will give some brief ideas about how we prove that this works. So the basic proof idea is first we will use some exponential, some techniques to show that when this edge is taken to be a low degree polynomial, then the only possible correlation of the real output and the template output is the linear correlation which we have seen in the like as in the linear attack for the original construction of Gabith and Ross. And this can be proved using the well-bound from edge-backed geometry and the generalized XOR lemma by Raoul and Dodie Settle. And then after proving this, we only need to show that the polynomial edge we construct, this will never happen for the polynomial edge we construct. So we will do some case analysis which we don't have time to go through, but we will briefly talk about like how we prevent all the possible attacks. So first having two terms for each xi will prevent linear tampering as we have seen in the previous slides. And then the choice of Ci being an arithmetic progression will prevent the non-linear tampering, like suggest quadratic tampering. And this is based on a lemma by the VR, Gabith, and Wickers. And finally, because we restrict the input of find source to be skew, so this also prevents attacks which set some, which set some xi to be a constant. Okay, next we'll briefly talk about the efficient inverter which will be the encoding function of the non-linear code. So note that our non-linear extractor consists of, is a composition of a function sigma which truncates the less than bit and the polynomial edge. So to get the inverter for this, straightforward construction is to first take a preimage of sigma to, which is y, and then we will take a preimage of edge of y, for y. And to, so taking a preimage for sigma is trivial, and taking a preimage of a polynomial edge can be based on an algorithm by Traptory and Chocolati. However, there's a problem in this construction. So because we need a uniform preimage from the composition of sigma and edge, so we actually cannot sample this preimage y uniformly. Instead, we need to sample y with probability proportional to the preimage of, to the preimage size of y. But, and a simple way to achieve this is by rejection sampling. And the similar approach have been adopted by Traptory and Chocolati in the work which constructs a template state non-linear code. However, this doesn't work in our setting because in our setting, our polynomial edge works on unvariables, and this n can be pretty large. And a large n will be especially useful in our construction of non-level secretary. And computing the preimage size of edge will be expensive. So in order to solve this problem, we will actually, we observe that the algorithm by Traptory and Chocolati is also a rejection sampling. So we can embed this rejection sampling step into the Traptory-Chocolati algorithm. So we are actually applying a rejection sampling on the, on this, on this composition of sigma and edge. Finally, we briefly go through how the non-level secretary scheme work. So the linear to all scheme works by first taking a shear function to be first applying an inverter for the non-level extractor to get x, then takes a erasure, the encoding function of the erasure code to produce n shares. And so in our setting, it will be, we will take the non-level extractor to get a t out of n-secretary, we will take a non-level extractor which works on t elements in the prime field F2. And then we will use a erasure code which produce n shares of a prime element of n, which produce an element in the prime field FQ. And also we will take this encoding, decoding function to be a systematic MDS code. And this will actually implies that any, any t minus one share together will be some, a finite leakage for x, which doesn't reveal any single coordinate in x i. So in other word condition on these shares, the, the source x will still be a skew of my source. So the nominability still applies. And finally, we go through some open problems arise from this work. So the first open problem, so the first future direction will be trying to improve the parameters in our non-level code n-secretary, such as improving the information rate or the error. And the second interesting open problem would be trying to achieve nominability against polynomial over a field with smaller characteristic such as F2. And note that we, this should, if this is possible, then this should be very different from our approach, because our approach rely on a well spawned, which is only non-trivial when the, over a large prime field. And finally, it will also be interesting to achieve nominability against other polynomial, other global tampering functions, especially those which already have some interesting average case for a problem, such as small waste branching programs or AC0 circuit with parity gates, et cetera. Thank you for your attention.


Maike lynaszini yng Ngai L transmission. Mi foreigner iksau aishkai mae betu. Lansi Dragons, Rai We love the fact that virtually in every city we're 20, 30 minutes away from some of the most wonderful landscapes on the planet. We enjoy that melting pot that special environment, safe environment, natural environment. I suspect it's a privilege. Being Kiwi is actually everything because it's actually who I am and to an extent I feel an obligation that I'm carrying through the stories of the various generations that have come before me. So for me to be Kiwi means to love life, enjoy the people I interact with, enjoy that we can do whatever we like done here and really make a beautiful world. We're a unique country. We do have a lot of tolerance here. To be ambitious, to be surrounded by people who've got ideas and what feels like a really young country, a country that we're still making, a country that has a proud history and a proud heritage. One thing I love about New Zealand is I think most Kiwis would agree that anyone who really considers themselves a Kiwi is in and it's not about where you were born or where your parents were born or what you look like that it's about are you in this community, is this who you are and if so then you are welcome. Sometimes all we need is just a face-to-face, you and me having a cup of coffee and just going, who are you, who am I, how do we create a bridge together. I travel a lot around the world but I have decided or concluded that actually my voice can only come from this place. I was brought up in Auckland, the biggest Polynesian city in the world. For me that's pojun. It means a lot for me to be a Kiwi.


So, the title of the session is what, why and how of concept maps. We are going to use this idea this technique of concept mapping and learn two or three diverse issues related to it. One is the technique itself and why it is useful and how to do it. And second is how do we use it for course design and how do we connect the syllabus and the learning objectives in our course. And thirdly what technology tools can help us actually create a concept map. So, what you have done in terms of course planning so far is we started by discussing and looking at the need for learning objectives, started with the mismatch between teacher and student and so on. Then you wrote learning objectives for a topic in your course and today in fact you wrote learning objectives at various cognitive levels for a specific topic or unit in your course. The next steps of course planning is that you need to think about the learning objectives for the entire course or at the course level. What I mean here is that the course your course or the subject that you are teaching has various modules. Usually it is about 5 to 8 modules per 40 hour course is a very standard number. And then each module has topics or subtopics again there are 3 or 4 or 5. So, totally there are about 40 or so subtopics because if it is a 40 hour course we usually do one subtopic in every class. And what we wrote learning objectives for were at the lower as in were at the more detailed specific level. And now we have to think about the entire course and see what are what is it that we want our students to be able to do at the end of the entire semester at a synthesized level. So, before you write your own course learning objectives let us look at a few examples. So, I have examples from 3 different courses and this example is on fluid mechanics. Again I have just chosen 3 diverse topics. So, let me tell you what these are. So, perhaps you will be able to connect to one or more of them. One is on fluid mechanics, one is on basic electromagnetic theory may be a first or second year course and the third one is a first year course on computer programming. So, hopefully a large number of few will be able to follow at least one or more than one example. So, for this course on fluid mechanics what the teacher wants the students to be able to do at the end of the course finally, is describe physical properties of the fluid and explain the consequences of this these properties. State some conservation principles, create models of different types of fluid flow and determine basic forces and moments acting on different profiles and shapes in a fluid flow. So, if you look at these they are actually at various cognitive levels. The one which says state the conservation principles are at the recall level. So, as we are looking at the objectives let us also try to pinpoint which cognitive level they are at. This is not written in order in terms of hierarchy, but it is perhaps written in order in which they appear in the course. Whereas describe properties of the fluid is and explain the consequence could be at understand level. Determine basic forces could be an apply or analyze level objective and create models of fluid flow can be at the highest create level. So, the other thing you want to observe when you look at course level objectives is that they are written at a broad perspective. It is not we are not saying any one specific topic or one specific application, but these this is these are techniques and knowledge and skills that we want our students to be able to learn and do after the entire course. So, I will just pause for about 10 seconds so that you can read this and then we will go to the next example. So, the next example is a course on electromagnetic theory again this is a basic course perhaps even at 12 standard in some in some curricula they might do it, but definitely at the first year level a lot of departments run a course like this. So, if you look at how it starts it says given an electromagnetic field problem in the sense all the objectives are with respect to a situation where some electromagnetic fields are described exist. Given an EM field problem students will be able to use the principles of electromagnetic theory to conceptually describe behavior of the charges and currents. So, the first bullet here is it is actually at an apply level, but it is saying that qualitatively and conceptually students should be able to reason. The second one says apply Maxwell's equations to quantitatively solve problems and the third one is derive expressions for energy. So, it is only three objectives, but this is all the problems and all the examples in the entire course usually will fit either one of these or some objectives that are under these. In the sense to be able to conceptually describe behavior of currents and charges the students should know what is a current and what is a charge and should know the laws and so on. Those are not stated here they will come in the unit level objectives. Finally last example and the reason I am showing you all this is because the next activity is where you will write your own course objectives. So, in this last example this is a course on computer programming it can mean any language it does not matter students should be able to trace code and predict output of a given program. So, they should be able to read a program understand what it is saying and be able to predict what the output of that program is. What kind of a program the ones involving pointers functions parameter passing and so on. They should be able to write a C plus plus class for such applications here they give an example. They should be able to design and implement applications that means they have to write large code and they to be able to create a simulation for an example like this. So, again I am going to pause here since a number of you might be teaching a computer programming course. So, that you get an idea of how to write course level learning objectives. The next activity is for your own course what you need to do is write a few learning objectives and I have said 2 to 4 it is it is ok if you write 5 do not go to 10. So, somewhere between 2 and 5 learning objectives at the course level please write this and what you have to say is that at the end of my course of this course name students should be able to and write these the way you saw the examples earlier. So, you can here I will give you some flexibility either do it as an individual activity or find somebody who is going to be teaching the same course. This exercise will work best if you choose a course that you will be teaching in the coming semester. And after you do this what you can do is the coordinators can post a few of course level objectives just so that we get an idea of what kind of objectives you are writing. So, let us say about 5 minutes for this activity again if you have any questions feel free to post it on chat ok. So, it looks like a number of you have been writing and sending let me first talk about one set of course learning objectives that came on chat which is actually not very helpful most of it most of what is there is useful and is written in the proper way, but there is one which is not and the reason I am talking about it is if you know what not to do you will always be able to do what you are supposed to do well. So, it is not trying to say that somebody did something wrong, but this is what you should not do. So, this is for a course on DBMS it is ok if you do not know what it is, but just listen to the words wording of the learning objective. It says that students should be able to get the fundamental concepts necessary for designing using implementing database systems. So, I think that the idea is more or less in the right direction, but the moment you say that students should be able to get the fundamental concepts it is no longer a performance outcome it is no longer written from the perspective of what students can do because as a teacher I do not know students get it or not get it. So, instead the way to reframe this is that students should be able to design database systems using fundamental concepts of DBMS or students should be able to implement database systems by doing something. So, keep thinking of what you want to see the student be able to do you know it is a performance think of that word perform. Similarly, it says clear understanding to solve practical problems that is not valid we saw there are lots of problems with the word understanding it is not bad, but it is not wrong, but it is really very complicated this beast called understanding. So, instead if you say that students should be able to solve practical problems such as given example using DBMS concepts then you are back on the right track. A number of you have written learning objectives at two the most common ones I see are applying concepts to solve problems and designing systems or designing circuits designing algorithms and so on. And this is not surprising because we are talking of engineering courses where solving applied problems and designing systems are two very common tasks two very common goals that all engineers have. So, it is good that we want our students also to be able to do it. In programming courses of course we want students to be able to write programs some of you have said that many of you have talked about students should be able to explain the working of either a system or working of a particular protocol and so on. So, all these are valid here is one from mechanical engineering I think this is again fairly comprehensive that students should be able to identify different boiler types they should be able to classify different types they should be able to calculate boiler parameters. So, course objectives also here have been written in increasing order and there is one last objective in this set of boiler which says which is a skill level objective. So, that is again something I want to highlight it says students should be able to interact with various tools using SQL. So, both content specific and two skills using tools are important ok. So, I think you can stop sending your course objectives now you have almost all the tools you need to do course design. So, let us go to the next point now. So, now here is a situation that a teacher faces where most of us are at this point that you wrote learning objectives for specific topics and modules you also wrote learning objectives at the course level. But the next point all of us need to be need to pay attention to is make sure that the topic level learning objectives and the course level learning objectives are aligned with each other because one is at specific level in the course the other is for the course as a whole. These cannot be independent they cannot be separate and they have to be exactly aligned to each other. So, this is one point one requirement that the teacher has to fulfill while doing course design. The second requirement is that in most courses these days 40 hour course semester long course complicated topics you have a large syllabus lots of topics and not just lots in terms of numbers, but there are lots of interconnections between these topics and what we want students to be able to do is actually see these connections make these connections themselves between the different topics and different concepts in the syllabus. So, as an expert in the domain and as a teacher you have an idea of what these different topics are and how they connect, but for a novice student who is learning it for the first time being able to see these interconnections is not very easy and when we think of our syllabus even if we print it out in three or four pages and give it to a student a syllabus has a long listing of topics one after the other and what is missing in a syllabus is these interconnections for a novice as an expert I am sure you can do it. So, there is a problem or not a problem there is something lacking in the in a syllabus the way we write it even though the syllabus is where we start one is that the syllabus does not have these objectives and it is a little hard to align these if only if all we have is the syllabus and secondly these interconnections are not clearly visible in the syllabus. So, what is needed is a back and forth connection between the learning objectives at all levels at all cognitive levels as well as at course module unit class level and the syllabus. So, these two ideas these two concepts so to say have to be interlinked and so far what we have done in actually in all these sessions what we do is first we set up the problem we say here is a situation faced by the teacher here are some gaps or here are some needs and then we think of the solution. So, here the situation faced by the teacher in the slide is actually the problem and one possible solution is actually given by the concept map. So, what the concept map or the technique of concept mapping helps us do is fulfill these requirements that we just talked about in the previous slide same these are the same requirements that teachers need to make need to make sure that the learning objectives at course and module and unit levels are all aligned and students should be able to see the connections. So, the way we are going to solve this problem is by actually creating a concept map of our own courses. So, at the end of today which includes the session and the lab after this students will be able to at the end of this course you will actually go back with a concept map and learning objectives for your own course ok. So, now let us come to what is a concept map we have been using this word for the last 15-20 minutes and the word itself is a little evocative it says map and there is a word concept. So, the moment you say map you get an idea that it is something visual and graphical. So, concept maps these are definitions are graphical organising tools they are visual they are actually a form of a static visualisation which are used for organising and representing complex bodies of knowledge. So, this in the first bullet it tells you what the concept map looks like we will see an example in a moment and in the second part it says what is the purpose of this concept map and I will just quickly I will give you a preview of a concept map and you will come back to it the preview will show you how complicated it actually looks. So, this looks this is a concept map and I am sure you cannot read it which is completely ok. So, it is visual it is a visual tool there is some organisation there are different concepts they are all interlinked and so on. So, it is clear that the body of knowledge is complicated it is also clear that the concept map is a visual tool for organising this. So, we come back to that slide in some more time ok. Concept mapping when we verbalise this noun is a technique to understand relationships between key ideas of a concept and we create visual map of these connections. So, creating this concept map by linking different ideas that is the concept mapping technique. So, let us actually now work our way through an example which finally leads us to that concept that horrible complicated messy diagram that you saw it is not horrible of course it is very useful it just looks complicated. So, every concept map exercise starts with a question and the question is called the focus question it is not simply draw a concept map off a computer, but usually there is a question and the question helps focus your focus the different concepts to come together. So, the question here is what are the different parts of a computer. So, this is something in all school level computer courses maybe at fourth grade or sixth grade we teach our children and it is a very simple example. So, I just wanted to walk through all the steps. So, we will do these slides quickly. So, the moment you say different parts of a computer you can start thinking of the parts and the way you do it is you simply list them first. So, I will keep clicking on slides from 12 till almost 30 hardware motherboard and you just list them and it does not matter which order you list them first you simply list all the ideas that come to your mind when you say when somebody says parts of the computer booting, ROM, memory, instructions, motherboard, CPU, operating systems ok I will just click on a few one by one this these parts are being added. So, let me pause here I think this is all the ideas together. So, you can take a look this contains most of the important parts of a computer. This is still not the concept map these are just the various ideas. So, various concepts which now we have to link together. In the next step what we do is we organize these. So, right now it is unorganized it is all all these ideas are just put together on the page. Now, let us try to organize these together. It looks like this printer and mouse or output devices keyboard there is something about an input device and it is up to you how you want to think of organizing them. So, let us see how the person who made the slide organized them. So, they have said ok hardware and software that is really at the top and they have put things like the parts that actually help the computer run CPU, motherboard, OS all these also hierarchically they are at a higher level than let us say printer or hard disk and all. So, these people have decided to do a top down hierarchical organization. Once this is done what is done next is to link each of these words which is in a circle. So, those are the concept, concepts link them using lines and this is what you get I am going to zoom in. So, right now I just want you to see the zoomed out view try to observe the picture. Those concepts we wrote in those circles are here this one there are lines and you cannot read it, but you will see that there are some words in between the lines. So, the words are what is called the linking prepositions that link one concept to another. So, I want to zoom in into different parts and hopefully you can read it better now. So, this is just some part on the left. So, there is hardware and it says broadly categorized as output device input device CPU and there is something else there. If you come to input device it says input device are examples of or contains examples of keyboard and mouse. If I go back to the previous slide what I would like you to notice is that this concept map has a top down approach like that. There are no loops, but it starts up here top center and it kind of goes outwards and downwards. That you can see in the zoomed out view that it has this top down approach ok. Let us zoom into some other part this is where it started it says computer consists of hardware and software. Software is broadly classified as system software and something else ok. So, what a concept map does is it has these let us actually dissect it a little bit more. What does a concept map contain? It has these concepts usually these concepts are enclosed in circles or boxes like this. It says computer software hardware and all the all the different circles that you saw here each of these is a concept. In addition a concept map has links, links are just lines connecting to concepts there should be an arrow it and it should be a unidirectional arrow there is there are whatever bidirectional arrows and concept maps. The direction is from the top or the more general to the bottom then there are things called linking prepositions. So, on each link there is a word which specifies the relationship between two concepts and this is a very important aspect of a concept map. You may be familiar with this technique and this idea of mind map where it usually looks like a radial diagram and people use it while brainstorming some ideas for something new. So, there we just write associations between words and often those diagrams are radial. So, mind map is also a useful technique, but it is not as structured and specifically a mind map does not need to have these linking prepositions, but in a concept map between two concepts you have to say how this idea at the top is related to this idea. So, here you have prepositions of the type consists of is an example of causes, effects. So, there is some verb some preposition which links these two and finally, if you look at this concept map most even though most of these arrows go top to down occasionally you will see arrows and lines which are horizontal these are called cross links. So, what cross links do are take a concept which is at one end of the map take another concept which is at some other part of the map often far away and it connects them again with a link and a preposition. So, this is why a concept map is rich and useful because it helps connects ideas which come from different parts or different angles, but later you know that there is some interlinks between them and this is extremely useful during while doing course design because you might be teaching chapter 5 and you realize that there is some concept in chapter 2 which actually is very relevant and which needs to be linked in chapter 5. So, that a cross link between that concept of chapter 2 and chapter 5 is what a concept map helps you to do. So, here is a summary of the features of a concept map we have talked about all of these it is a visual representation it is a hierarchical organization of knowledge this hierarchy also is useful in a concept map because it gives a top down view of the entire complex body of knowledge. So, hierarchy means the concepts at the top the ones you first write are more important and they are more generalized and the concepts at the bottom usually are examples and they are more specific ok. You cannot read it here, but let me just tell you what is at the top and what is at the bottom. Here it says computer it is the most general it is what you start with here it says software and hardware. So, if you think of the words the ideas of software and hardware they are broad they are generalized they are different because there are several types of software it is not a single idea hardware again there are different types for different purposes whereas, if you go all the way at the bottom here it says hard disk RAM and ROM which are more specific. So, the examples and the specific cases are at the bottom and the generalized terms the broad terms are at the top. If we had to pick the most important thing in a concept map my choice would be that it is the preposition that links the concepts because simply saying hardware, software, RAM does not tell you how they are related. So, these prepositions that we saw is a part of belongs to includes reason they are the ones that tell somebody and that help us understand how two concepts are related and the cross links that we talked about which connect different concepts across the map ok. Some logistical points so, usually it is top to bottom it is not radial and usually it does not go upwards it is just a convention. The top down also indicates the hierarchy usually we do not have upward or backward arrows and there are definitely no loops. So, this is not an algorithm it is a static picture of the entire complex interconnected body of knowledge. So, in terms of what is a concept map this is as much as we need to know as to what are the features how you know what comprises a map. So, let us do an activity where actually you create a concept map and this has nothing to do with your course this is an exercise it is actually a fun activity. There will be a video and the way the easiest way I think is I will provide you a link to the video and if you can play the video at your end watch the video think share activity as usual watch the video and as you are watching the video note the key concepts into it. So, keep jotting down the key concepts in your notebook you can play the video twice in fact I think that is a better idea it is a video from National Geographic on climate change and how astronauts seek a climate change. So, we wanted an example which all of you can understand which and which has nothing to do with our domains and teaching so, that we understand this we are able to apply this idea of concept map. Then pair up with a partner and you actually create a concept map for a focus question that I will show you in a moment and finally, in the share phase we will do something new which we have not done so far we will do a peer review of the concept map with another pair. So, as experts in the domain and as professionals you know the importance of peer review and you also know as a teacher that it is hard to assess complicated or open ended tasks. So, you might be wondering how will I do a review of a diagram. So for that we will provide some criteria and the main idea you want to take away as a teacher is that it is actually possible there are techniques to assess open ended tasks such as concept maps and diagrams ok. So, this is the summary of the activity and we will now we will do it phase by phase. So, the first phase here. So, here is the video it is called changing earth here is the link. So, if the coordinator could please play it on your on the screen and what the participants each of you need to do individually is note down the keywords and the key concepts. So, this video is about 1 and a half minutes long you can play it twice or 3 times will give you 5 minutes for this activity because it is it is important that you note down all the keywords. So, that in the next phase you can actually create the concept map. I could play the video from here, but you would not be able to hear the sound. So, that is why it is best if you play it at your end. So, what I will do is let us do it in two phases now. We will go to the next phase and if you have been able to see the video start working on the pair phase. If you could not see the video I am going to try to play it from this end and I will try to share my desktop and you can view it then. So, those of you who could see the video turn to your neighbor and based on the videos and keywords create a concept map with your partner to answer this question. The specific question is what and how have astronauts witnessed about the earth's changing climate. Let us move on to the next phase. Here you would actually be looking at each other's concept map and trying to trying to do a peer review. So, I am not going to call this an evaluation because it is not about one is better than the other, but there is an instrument there is a tool and what we mean by tool is let us say there is a technique of assessing open ended tasks such as diagrams and so on. And the technique is called a rubric and a rubric usually looks like this it is a table firstly. The columns or the first column here talks about the criteria along which the review will happen. So, in case you are not able to read this clearly I will just read out some of the criteria. The first criteria for reviewing a concept map is comprehensiveness. Does it completely cover the topic which was read by you or which was seen by you? Second criteria is organization which is to arrange by systematic planning. So, is the concept map systematically and hierarchically organized and the third one is correctness which says does it conform to the facts or to the truth. So, what you can do here again this whole exercise is to just give you a feel of how to create a concept map and how to review a concept map. The actual exercise you will be doing in the lab is where you will take your course and do it. But before you get to course level concept mapping where you have to think about both your course and the idea of concept map what we thought is you should get a feel for how to draw concept maps and how to review it. So, how to draw concept maps you have done in the first two phases and in this phase what you will do is find another pair and become their partner and you can exchange your concept maps. Remember that all of you will have different concept maps here. One of the two no two concept maps will be identical though they may be similar because it all started from the same material and use these rubrics here to peer review each other's concept maps. So, again I will let us spend about five minutes on this and then we will go to the next part of the session. If you learnt any new ideas it will help you to connect the new ideas to the knowledge you have. It helps you to organize ideas in a logical fashion but it is not very rigid because the concept maps can have different shapes and as you saw different people may have different concept maps. This last point is what the concept maps are recommended for the most and especially if you think of using concept maps as a tool in your course for not for course planning but if you want your students to be able to use it. It is said by doing the activity of concept maps a student can move from some road learning to more meaningful learning. So, in your particular course the reason to use concept maps are that it will help you create a big picture of the course and we said earlier that different elements of the course need to be linked to each other. Let us look at the first point first and then we will come back to the second and third point. So, we will do an example here. Before doing the example I am going to just pause on this slide. This is how exactly the steps you will use to construct the concept map in the course. The same list is there in your lab assignment also. But what I would like you to know is this list and my colleague Madhuri Mahadeva will do an example for you on how to construct a concept map and she is doing it for her course. So, she will in fact follow these steps in order and as she is doing it you can try to connect it to these ideas.  So, she will identify the key concepts and then she will rank these concepts for the most important or most general to the next most important and to the next most important and so on. So, tell us which course we are doing and what the concepts are. So, I am starting with the digital logic circuit. The same course where I have given example for learning objectives. The first step is identify key concepts in your course. Yeah, so the course is on digital logic design. So, the first one is the digital logic circuit for which I will write a, this is the course for which I will write key concepts or we can say that since we are generating it for a course level, definitely the modules which will go and what are the lessons. So, in order to write key ideas, I will just start writing key ideas. When I talk about a digital logic circuit, the key ideas will be, one of them is sequential circuits. Then there can be combinational circuits. Then we can write basic gates. So, you can see that I have listed few concepts here for digital logic circuits. It can be sequential circuits, it can be combinational circuits, then basic gates, number systems, truth tables, flip flops, then basic gates like AND or NOT gates or it can be even universal gates like NAND nor gates. There can be finite states machines. Then arithmetic circuits will be there, multiplexers, demultiplexers, then there can be decoders, there can be binary, octal, hexadecimal or even conversion of systems and arithmetic circuits. So, these are the key concepts or the key modules which I have noted. Now, the next step in drawing concept map, that is the next step. I have to identify which are the major modules or the important modules that we have to, I have to write down first. So, I have written few of the modules as a first module or I will write it here. So, after writing this concept, the first one or first module which comes to my mind is the number system and definitely it is as per syllabus. So, this will be the first module. Then comes the basic circuits or I can say that logic circuits that is its second idea. The third important idea is the combinational circuits. Now, the fourth important idea is the sequential circuits and the last one are the memories. So, this is how from the digital logic circuits, I can write this as includes number systems, logic circuits, combinational circuits, sequential circuits and memories. So, these are the most important modules which are there in the course of digital logic circuits. Now, further to write a secondary level concept in number system itself, I can further write as classified as is a preposition. Now, number system is classified into binary, then octal, then hex system. So, definitely as a teacher, if I start with this module, then the next part which I will follow is teaching this system that is I will teach all this number systems. If I take a second module suppose, then what I will write is logic circuit includes basic gates like then all and or not universal gates as well. So, this is the secondary level concept in the concept map. Now, in order to if I just follow this link, now this basic gates, how am I going to realize them? Realize using two tables. So, this is one link which I will follow. I am going to make a quick comment here. See, when you are showing the example, it is not so much to teach you what are logic circuits. So, we are not trying to focus on the content. We are picking a topic which may be familiar to at least half of you, but even if you are not exactly familiar with the circuit, what you want to try to follow in the demonstration is how starting at a general or top post topic, one can draw a concept map all the way to the less to the more specific topics. So, even if you do not understand the topic, you should be able to follow the key ideas of drawing the concept map and if you look at the demonstration demonstration. If you look at this, you saw how starting with the top the four most general topics were identified. They were drawn, circles were put under a preposition called includes was put on the top and then logic circuits was then further detailed. There was a preposition, another preposition called includes next set of concepts, another preposition called realize and the final set of concepts. So, this is the type of this is what you want to be able to see. So, right now we will do one more such branch and then we will just connect it to learning objectives. Now, if I select now this is being the fourth chapter in the module. Now, sequential circuit contains flip flops. So, this is another concept. Now, in order to realize this flip flop, you will require concept of basic gates as well. So, this is being a second chapter, flip flops can be realized. So, basic can be or you can say that basic gates can be used for flip flops. So, here is a cross link that is if you teach basic gates, student will able to realize flip flops as well. So, there is a connection between a second chapter and fourth chapter if we. So, this is a cross link actually. So, from basic gates we can say that flip flop can be realized. So, which are the part of chapter number 4. So, this is known as a cross link. Here earlier the only thing I would like to say is that in this live demonstration what you should have seen is that starting at the top. There were next level concepts identified, repositions included and then cross links between topics a little far away were put in. So, when you do your course design, this is exactly how you will do it. From the top go down all the way at the bottom. So, for digital logic circuit suppose there is one of the course objectives and design of student will be able to design different digital circuits. So, design of a digital circuit if it is the course level objective. Now, in order to fulfill this course objective I have to include which chapters I need a logic circuit, I need a combinational circuit, I need a sequential circuit. So, at logic circuit level I may include recall and understand type of learning objectives. Like I will first this is being a introductory chapter. I will write that student will able to draw logic diagrams, they will able to write to table or they will able to even construct a logic diagram for given situation. Now, once they are able to do this then using once they know how to do logic diagram then here I may introduce they may able to implement circuit or arithmetic circuit. So, this is little bit at higher level, apply level. So, probably I will choose only two learning objectives here and in order to develop this chapter I will go to the apply level. So, there is a possibility that one design level course objective can be fulfilled using chapter 1, 1, 2, level 1, 2, chapter 3 using third level, chapter 4 or 5 I may go with the higher level. So, this is how I can split one course objective into different levels across different chapter. So, it is not necessary that I will try to fulfill this learning objective or this course objective using only one link. There are links between the content. So, for every lesson I will try to set up a learning objective which will ultimately lead to the final course objective. Okay, so that brings us to the end of this session and what you will do in the lab is to create a concept map for your own course in the manner that the demonstration was shown now except that you would not do it on paper you will explore tools. So, earlier a number of you were asking on the chat window are there any technology tools? Yes, there are several of them and many of them are available in as free software. So, the lab assignment tells you gives you an example of one set software where you can actually create these bubbles it is called bubble.us you can create these concepts and the cross links and the prepositions and so on. So, you will explore technology tools you can do it collaboratively and you will create a concept map for your course using this tool and then in that concept map where you will essentially take your interlinked ideas and the syllabus you will include some learning objectives at the course level and at different levels and you will see how the how the entire picture fits together.