Again, thank you so much and welcome to our webinar series at the Center for Open Science. Today, we have a great topic, demystifying the data anonymization process, myths and best practices. We were joking that everyone should try to say that three times backwards. We are recording this webinar, so just wanted to let everyone know it will be made available for distribution afterwards for anyone who is not available to attend live. We also have enabled the transcription service below for those that that is a support and we will make that transcript available as well. So just want to take a quick second and introduce myself. My name is Marcy Reedy. I'm a community manager here at the Center for Open Science. Hope to support initiatives around our STEM education hub that we have worked with through support from the National Science Foundations. And just to start off, I wanted to provide some additional resources and information that would be helpful to people as they embark on their open scholarship journey. The first of which is a STEM education hub page and in there it is a trove of valuable resources that you can go to if you are searching for training and deep dive supports into open scholarship. There are deep dives into pre-registration, into open access, collection of our previous webinars including on data visualization, supporting early career researchers and open scholarship and overview and licensing and copyright procedures. So that is a great resource to bookmark and go to if you are looking for information. As well as I wanted to share a quick link to a hub we have created on the OER Commons website that we are calling the Open Scholarship Knowledge Base which is a repository of the what, when, how of open scholarship. Everything that you might need to know. It not only allows you to search for resources, it also allows you to add your own if you would like to support colleagues that are in their open science journey. So we invite you to visit that as well and bookmark it and take advantage of the resources there. So with those resources shared and without further ado, a couple housekeeping tips. We did, it seems like the Q&A has already been found, yay, thank you so much Phillip. We did want to encourage everyone to take advantage of that and share questions as the webinar proceeds. We certainly want to make this active and engaging and responsive to the audience. So we encourage you to take advantage of that. Also we will be monitoring the attendee list and if you see there is a raise hand function. So if you prefer to actually make a comment and for us to call on you we would be happy to do that. So I will be monitoring it. Feel free to raise your hand if you would like some clarification or question about what is being presented at that time and we will try to keep track of that and monitor it pretty closely. And so without further ado, because no one wants to hear from me, they want to hear from our guest Dr. Michael Altman today and we welcome him. We thank him for joining us and sharing his valuable perspective and expertise. Thank you so much for joining us Dr. Altman. Dr. Altman is a social and information scientist at MIT Center for Research in Equitable and Open Scholarship. And previously he served as director of research for MIT libraries and at the Harvard University as the associate director for the Harvard MIT data center. So hugely impressive background, amazing person to speak on this topic about data anonymization and we thank you so much for joining us. And invite you to take it away. Thank you Marcy and hello COS community. I'm really pleased today to have an opportunity to talk about the research and practice we've been doing and to share some of it. This is informed both by some of our research with a number of collaborators and by previous work both as a social scientist and as a head of a social science data archive. In this talk we'll reflect on the fact that there's more information from individuals that's available than ever before and that the laws, technologies, uses are all changing rapidly. So what I hope to do here is to look at how we integrate information protection into the research life cycle and deal with those ethical, legal, statistical and methodological considerations and particularly to talk about what are the needs for information protection to help characterize key concepts and to identify some next steps for you. So before we go further, there are a few caveats for this talk. This work represents my own perspective. It's not MIT, not our funders, not the library. Further, we're making predictions about where information and privacy and anonymization is going to go. That's tough to make, especially when you're talking about the future. So to summarize, if there's anything that's wrong in this presentation, it's entirely my fault. And if there's anything that you like, it wouldn't have been possible without many, many collaborators, some of whom outside the MIT library for hosting earlier research and some of our past funders for supporting many research projects in this area. And of course, Sanos Giganta and Humoris Incidentis, the project builds upon scholarship and many others, only a few of whom could be directly referenced in this presentation. So one of the facts of research now and of the world is that personal information is everywhere, including where it isn't wanted. And that includes information about what we do, what we say, what we think, where we go, history, health, property. All of this information is much more commonly observed, recorded, shared. It's the subject of research, it's the subject of commerce. And a lot of this is voluntary. This is a chart of the growth of monthly active users in Facebook in the million. So there are 3 billion active users on monthly active users on Facebook, seems like a lot. Sharing all sorts of information about themselves, their friends, their activities. Now this is not only consented information, but even within this framework of consent, there are externalities, such as my sharing something that might contain information about you, picture perhaps with you in it. There are network effects. Facebook is really the only game in town for social information sharing of this sort because the value of the network grows with the number of people in it. And they've got 4 billion people. And then asymmetric information because Facebook knows a lot more about how they can use your information and what the threats to you are than you do when you post a photo or send a message. So even voluntary information that is consented may not be done so under sort of full informed reflective entirely uncoerced consent. Sometimes information has consequences that the availability of information has consequences that are entirely unexpected. This is one example, it's a mudshot database. It illustrates that nominally public information can become universally discoverable rapidly. And actually about 10 years ago, especially in the U.S., a number of county records office started putting arrest records on the internet, part of transparency. Now these were nominally public, you had a right to see them as public records, but it usually involved going down to the county court office during a specified window of time when they were open and asking to look at a particular person and paying for the copying fees. Having these all just heaved on to the internet had some consequences, made them discoverable, which created new opportunities for aggregation, analysis, and use. That inspires new business models such as creating a database of mugshots so that you might maybe support criminal search or maybe because you don't want to be in a database of mugshots and you'll pay to have your mugshot removed. So an intentional misuse can arise as well as unintentional misuses in order for you to discover that you're in this database of mugshots. Well, you have to find it. How do we find people find out this information typically through Google? So there were these mugshot databases bought last name records, last name advertisements, and said when somebody searches in the common last name, put it up an ad so that they'll know that we have their mugshot and they'll pay us to take it off. But people tend to click on these ads more frequently when they see black first names than white first names. It's based on work by Latonya Sweeney. And so what ended up happening was that the ads, the ad algorithm adjusted to only show ads for these databases when there was a combination of a white first, a white, black first name and a last name. Even though the mugshot database people did not have any intention to discriminate by race. And legislation then comes around, works at the edges, changes things. But you will still see advertisements for criminal records on Google, though the racial bias is now, in that particular case, is now more controlled, right? There have been a lot of other data protection issues in the headlines from international disputes to breaches and unexpected breaches and anonymity to claims about group control over information, controversies over consent, problems with hacking and identity theft. And my favorite, that was my second favorite, that reading privacy policies will take you 76 days of your life. So there's another aspect of consent, although technically you've consented to all of the web privacy policies and click-throughs, you've never read them. Information threats are changing in a variety of ways in the current environment. Information travels wider and faster, cyber attacks are increasingly common. Common platforms for information collection, storage, et cetera, expose information in new ways, and privacy leakage accumulates, even when people use disclosure control methods. One aspect of this that is becoming increasingly important is how aggregate information can reveal things about us. So if we think about how unique am I as an individual, if you know there's someone whose birthday is the 31st, whose zip code is 02145, whose gender is male, have you identified them? Well, pretty close. There may be two people there with those sets of attributes. So if those attributes are public, even though we have not used a name, we've accumulated enough aggregate information to learn something about them, for example, that they're in this data collection. And it's not just numbers and databases that reveal this. This is a statistical graphics of disease incidences. And it turns out that given the, and this is simulated, but this is from a study that looked at graphics like this. And you can look at a disease incident chart. And given the criteria for having had that disease, learn a lot about whether particularly individuals are likely to have a disease in that area.  So regardless of the form of the information, whether it's a map or a picture or a story, we can accumulate privacy losses and learn things about people in aggregate. So there are specific challenges of anonymity. And that's what we're going to focus on for the most part here. One is around the environment, the rapid change in how much data is collected, how fast dissemination and broadly dissemination occurs. This doesn't fundamentally change the problem, but it brings some fundamental constraints into sort of a harsh light. And one is that anonymity isn't about naming. It's not really about finding Micah Altman in the dataset. It's about learning. If you don't know, you didn't learn my name from the dataset or learn that I was record 236, but you did learn that I was in the study. And the study is of ex-criminals, you've learned something about me. Or maybe you've only learned it, maybe you only learned that I'm probably there. This accumulation of learning, however, can create the sorts of harm that we typically think anonymization is preventing. So anonymization is really about learning about individuals, not about acquiring specifically their names and identity, etc. We've also learned that the other perfect privacy is possible. It involves throwing away all the data. So if we want to have useful information, we can't have perfect privacy. We will always learn at least a little bit about people who participated in the data, in the computation. And what we need to do is to minimize that amount for the value of what we're learning. But even when we minimize this, privacy losses add up. And so we have to manage those losses cumulatively and conscientiously. So as researchers, we're responsible for information privacy and all of the consequences of sharing information, at least ethically. Many countries recognize information privacy and some recognize data protection as a universal human right. This involves not only necessarily anonymity, but also characteristics of intrusion into your life, dignity, reputation, and control over your information. And researchers have ethical responsibilities in general. But the point of research is informational. It is to gather information and able in order to learn. So when we are doing research on human subjects, on humans, we have to be concerned about the information we gather. That's a central part of what we're doing. We tend to gather that information. We're going to benefit from it. And it should be protecting, it should be a core concern. People participate in research because they view it as a public good. And we have an ethical responsibility both to protect their privacy and to make sure the benefits of the research compensate for the inevitable privacy loss. Even when we minimize it, that will be involved in conducting research. Furthermore, there are legal risks and requirements. And I assert that researchers should treat the law as a supplement to ethical responsibilities. You need to comply with the law. It is part of being ethical. It is not the beginning or end of ethical responsibilities. To do this, you'll need to incorporate data security and privacy planning during your research design, both to minimize the legal risks to you and your institution and the ethical risks to your institution and data subject. Now, there are many different laws. I am not a lawyer. This is not legal advice. And they place different sort of requirements. I'll talk about some of the privacy concepts underneath the law and hope that this presentation will help you identify some possible legal issues. But it is not a substitute for legal advice. And the requirements and triggers for these requirements and even the definition of the same word say anonymity varies from law to law. So in summary, there is a responsibility to understand individual rights and interests and anticipate harms that may result from participation in your research. And you can address this through research design, data management planning, selection and use of protections. And we'll focus in the rest of this talk on some of the key concepts to identify and yes, we will have a slides after the will be disseminated along with the recording. Thanks. And we'll address this through planning informational controls throughout the life cycle. So let's dive into some key concepts. Actually, key concepts in this area derive from three domains. And these domains have grown organically. So the separation is not always that clean. But it's useful to keep track of whether you're using a particular word or concept in one domain or another, even when the same word may be involved multiple. So at core, there are a number of policy concepts, one of which are called informational harms and benefits general sense of what are what are the overall goods and bads that come to individuals in society from from a particular activity and privacy and informational rights that we are protecting. And those are in essence policy concepts that are implemented through technology and through the law. On the technical side, there are concepts of information security, anonymization and utility. And sometimes again, these words are used in other domains, but I'm going to use them primarily as technical and legal side, there are concepts of things like the identification, scope of authority, personally identifiable information, sensitivity, none of which are strictly defined in terms of the tactical, the statistics of or computer security definitions of privacy, but but are regulated by law. So let's dive into a few of these. So informational harm, informational harms occur when others use from research, when other use research results or data, learn something and then violate the rights of others or negatively affect social welfare. And this is a very broad definition. And anonymity just a kid anonymity doesn't take care of all of these. But some examples of these harms are linking a deidentified health record to an individual, find a data set you managed, managed to pin it to Michael Altman, I am denied employment or I lose my employment because it's discovered I have this condition. That's an anonymity harm. Perhaps you do a statistical analysis on some aggregate data tables.  And all of them participated in the study. And so you know that, you know, the whole households of interest in that area participated in the study of sex offenders. So you haven't really identified a particular person, but you know, they're in there and you've learned something about them. That could be considered an anonymity, though maybe not individual. Another is you use biosamples collected for analysis of diabetes. And, and then you extend that to estimate inbreeding among indigenous people. And that contributed to stereotype work. Was it ledged to contribute to stereotyping stigma? We're farther away from anonymization here. You, this could have happened whether you, if you had completely deidentified the data. So anonymization would not be a protection against this, but we might agree that it's an informational mark. Second, what another is analysis of exercise data shows what popular running paths exist. And it also shows you where classified military bases are. This happened with the Strava application. Again, probably not anonymization, at least not in the way that it's typically thought of. Or you build really good machine learning models. You train them on user data. You develop something profitable and you don't share the results. Well, potentially, you know, an economic misappropriation, but not an organization. Information privacy, more broadly, is about the interests that individuals and groups have in controlling information about or from them. Let's, who might be harmed from an information release? We could talk about harms that come, any of these harms coming to the data subject, to not necessarily the result of the data subject, but to a vulnerable group. For example, the harm of stereotyping from using the diabetes data for inbreeding, arguably is and does not rest on a particular individual as much as it rests on a group and doesn't rely on the participation of a specific individual so much as it relies on the participation of the group. We also make care about harm to institution and often that's where legal and institutional authorities are focused as well as on data subjects. And there are, and we have a obligation to society, individual protection of information may still lead to unwanted social harms, surveillance or dual use of data or all sorts of things. But for this, we're focusing on, for the concept of anonymity really focuses on the data subject. Although informational harms more broadly can involve any, can involve those other actors, anonymity harms are in reference to the data subject, research subject. Now let's dive into some technical concepts. Information security is about the control and protection against unauthorized access use, disclosure, disruption, modification. Someone hacks into your castle and steals all your records. That is an information security violation. If they, if they hack into and it is also probably a privacy violation because it involves the control protection over the extent and circumstances of collection sharing and use. Someone breaks into your information castle and burns it all down. It's a security violation, but it's not a privacy violation. And anonymity is a sub case and a more technically well-defined sub case of privacy, which is focused on what others can learn about participants in the data as a result of their, of the data collection processing analysis. Someone learned something about you because you participated in data. They learned that you've gotten, you're likely to have lung cancer because you were in the data and they looked at the data and they found some heightened area and your zip code traced it to your household. That's an anonymity. However, if they learn something, if they learn that you're more likely to have lung cancer, we're not, not as a result of your participation. For example, maybe the study just shows that people who have your profession are more likely to have lung cancer. They might have learned that whether or not you're participating. That's not anonymity. So all useful computations provide some ability to learn about the individuals measured from the data from which the computations were made. We say anonymization fails when others learn more than a minimal amount because the person was involved in the data.   That's a good question. So there's a question about how you distinguish the type of knowledge that is likely to be gained without participating in research versus when you participate. And one of the answers is the privacy concept you're using. Distinguishing between these two things is at the core of the concept of differential privacy, which I'll talk about a little bit in this. So in response to this question, there are different stages of thinking about identifiability. In the mid-60s and 70s or so, the state of the art was where is Waldo? We thought about anonymization and identifiability as being able to link to a particular person in the database. If I can match you to record 17238 in the database, a broken variable privacy. Now, of course, that's generally true if I can match your record to a specific database and if that database has useful information that I didn't know of before, but turns out that although that's a useful attack method, that is not a necessary condition for definition of privacy. A second sort of 1990s or so concept is like indistinguishability. Maybe if there's a large enough group of people that you can't tell something about, then that's privacy. Well, and the idea was that the realization that even when we didn't link you to record 748, the fact that we learned that you were in the dataset and you were one of 30 people who had committed, who was in the subset of data who had committed horrendous crimes, meant that we learned something interesting about you. It turns out that sort of like thinking about the crowd of people to which you are identical is still not a great like core definition of privacy. And the most sophisticated, the most modern definition of privacy, which is where differential privacy and its variance or focus are limiting what adversaries can learn. And you can do this very formally in a statistical and crypt with statistical and cryptographic analysis. And it's actually possible to prove that for some particular data computation processes that you can limit the amount that an individual contributes to the result. So the sensitivity of the answer, say the mean income of that district, if that can be guaranteed not to be affected by any individual by too much, then you can say that if you just publish the summary statistics, you can limit the statistically how much people can learn across all possible background knowledge and distribution.  Of course, there's a trade-off between information utility and privacy. Perfectly anonymous data is perfectly useless data. And there's no... Well, there is a very formal way of describing the information privacy that you lose in terms of the posterior log odds of how much more you're changing the distribution of belief over somebody's properties. There's no single definition of utility. You can talk about mean square or you can measure these trade-offs, but this will vary from case to case. And so privacy protections always balance usefulness and privacy. There's also a number of legal concepts and some of these sound like technical and policy concepts, but it's really important to distinguish them because legal concepts are sometimes at odd with the technical definitions. So sensitivity are conditions under which the law expects some higher expectation of harm and usually requires additional scrutiny or protection. For example, the federal law may declare that data about criminal history is more sensitive. So when you ask questions and you collect measures in that space, there are more required protections. You may expect more risk and so you may need more controls. Scope of authority talks about the conditions under which information is regulated by specific law. And this is typically related to the properties of the data subject, the data collector, the data user. For example, if I'm a resident of Massachusetts and the data collector is an organization doing business in Massachusetts, then they're subject to the Massachusetts personal information protection law. Otherwise, the information doesn't come under the scope of the law. And finally, the law generally has some concepts around identifiability, often referred to as de-identification. These specify the conditions under which the law considers outputs to be anonymous in scare quotes. And it often, not always, it implies under that law that the outputs are not subject to any further regulatory requirements. Often this is based on some complementary definition of PII, or personally identifiable information, say a list of attributes that if you get rid of them, it'll be anonymous. And this is where the tension between legal concepts and technical concepts are most important currently. Because technically, what you can learn is not dependent on specific attributes. You can learn things from any attribute and you have to look at the combination of information and the computations in order to understand learnability. You cannot simply say if you take out the name, the first name, as you can in the Massachusetts law, you take out the first name and everything is okay. It's anonymous. It doesn't work like that in statistics, so it may work like that in law. And there's also sometimes an underlying legal assumption that anonymization is equivalent with zero risk, which is also not true. That's a matter of technical reality, not legal reality. So for example, FERPA, which is the US Federal Law Protecting Education data, defines identifiability in terms of a direct list of PII, so specific attributes like name, that if they're present, imply that it's identifiable. And then a notion of linkage, that there's some indirect information that together could also identify a person, though it doesn't specifically tell you how to tell when something is linked or not. HIPAA, but to be de-identified, it has to both eliminate PII and not be directly linked. HIPAA, it's an either or. You can eliminate 18 identifiers in a list or you can verify that it's you can't link it through a quote statistician, which I think is a GS13 statistician, which means you've got some number, you have an undergraduate degree and some number of credit hours and statistics. And the common rule, which is where a lot of our research and where our IRBs come from, research is governed and IRBs come from in the US, has a standard readily identifiable. They also have concepts of sensitivity. For anything that is not a defined as a directory information, directory information is okay. It's not sensitive, so there's no harm, even if it's identifiable. Anything else is sensitive. HIPAA, it's going to be medical information. And common rule depends on the harm that you'd expect from the information, how sensitive it is. And then the scope, FERPA applies to data collected by institutions receiving federal educational funding, HIPAA to data collected by institutions designated as health providers, covered entities, and the common rule to data collected by institution free receiving federal research funding. So if you have a private company and you collect data to do research, you're not covered by any of these and you have no legal responsibilities under any of these laws. So let's talk about the processes of anonymization. And protection should be viewed as a process. Effective data protection is a result of an effective process. It's not strictly the property of a data output. You can't, if we look at the number 721-071-426, is that the average wealth of the zip code in which Bill Gates lives? Is that a privacy violation, if it is? It is impossible to know given that number. And in fact, even if you had an entire data set, just looking at that data set, you cannot say this is, this is de-identified in a technical sense or this is like statistical average in technical sense. For both of these things, you need to understand the process that generated the outputs. And more generally, we can think about data protection in every life cycle stage from collection through post-processing. And that number is a social security number, by the way, but the person is not covered by law. So we're good. There are different opportunities to protect the different parts of the research life cycle, including at the research design stage, the research implementation stage, the research analysis stage, and the post-analysis stage. These include things like evaluating privacy and security of measurement and data collection, how you store data, what you do for disclosure limitation, and the auditing adverse event monitoring data destruction that you do afterwards. We're going to focus, although these all have some importance for the overall data protection information form, we're going to focus on the disclosure for anonymization. You can think about not only the stage, but the level of harm in terms of a continuum from sort of minimal risk. And this is just a guide for thinking it is not a official legal standard. To grave risk of harm should that data be linked to a person, learned about a person, and found by an adversary. So maybe if someone knows my favorite flavor of ice cream, even if it's fine, even if they figure out that mine is fudge ripple, nothing bad will happen, but if they know that I am a sex offender, it could be a grave risk to me. So the consequences of breaching anonymity will vary. And so how we protect the data will be a factor of both how identifiable the data is, what the risk of learning about individuals from that data is, and the harm, the sensitivity of that data. And so for either harmless data, even if it's identifiable or really formally protected strongly anonymous data, we might choose to release it without any other protections. But if something is either less well protected, maybe because there are no formal methods that you can use for that particular analysis, or has a higher risk of harm, you might want to combine things like statistical disclosure control with restrictions on use, secure data enclaves, legal agreements, auditing, and other sorts of controls. And generally, there will be multiple, you want to plan for multiple ways of getting the data for tiered access. So there'll be some outputs that either because of their anonymity or lack of sensitivity you can make available for the public, some which you may need to have gate and some which are necessary to support particular uses, especially like cutting edge research uses, but that you need many levels of protection for and simply like trying to anonymize the data and disseminate it will not be sufficient for those types of research. Let's think, let's drill in this end part into disclosure limitation for data publishing. You can think of it mechanistically as you apply a set of transformations at a particular stage to execute a privacy goal and it results in some output. So that's a sort of mechanical timeline view of it. The important part here is really the privacy concept because it's the privacy concept like differential privacy that dictates how protective the result is going to be. Regardless of the transformation, the processing stage, or the particular output, it's this privacy concept that's creating the protection guarantee. But we'll look at some example transformations. So one is like can set, we just release it, redaction, domain generalization, we limit the values of the pixels. We've got synthetic data. You might still be able to recognize me. Aggregation, we've aggregated lots of pixels, noise, these are all transformations that are used in commonly used in all sorts of different disclosure control processes. This is a different category. This is an example of conceptually of using differential privacy as a solution concept. Here, it's not just that we're using noise, but that we have an idea of using noise to produce an aggregate result where the input doesn't affect the output more than. So this is not my face blurred, it is the average face. So that's where this idea of formal protection comes in, is that you are reporting results, averages, model results, etc., and the input from a particular person does not affect the output too much. Of course, this is perfect privacy where we remove everything. Here's an example of a particular dataset with some nastiness in it, and here we've removed some fields, aggregated, generalized others, suppressed others, and averaged others. This is a result of applying aggregation, suppression, and generalization. We considered favorite ice cream flavor to be non-sensitive, so we didn't do anything to that. Hopefully, nobody figures out that I like crunchy frog as a flavor and matches me somewhere else. All of these transformations reduce utility. There's a tension between maximizing the breath of future uses and minimizing risk for targeted uses. So if you know exactly what you want, you can focus on a method that protects privacy for that particular use. You're trying to create a general reusable synthetic dataset. It's not going to be as useful for every specific use. And if you don't say how you anonymized it, and you don't provide the measures of the uncertainty you introduced, you're going to get biased analysis. This is true no matter what method you use, and it's always been true, but it's becoming more obvious, and the debate over the census result highlights this. But very quickly, some next steps are to articulate privacy principles, identify the legal institutional requirements, then nominate informational harms that are part of your research, develop a principled life cycle data protection plan, and select and apply privacy protection tools. And really, this set of slides is just a set of links for useful resources to get you to the next step. So articulating the subject rights, there are resources for that, but data protection is to protect subjects. You should consider and articulate at your project who you're protecting and from what. Data protection doesn't involve just disclosure control at the end, but is part of a whole life cycle. And that involves both design principles for what you are protecting and what you are enabling, and how you're measuring both. For legal and institutional requirements, you're going to need to identify your institutional policies, national law, if you're in member states, there are resources for each of these. Informational harms generally a qualitative process. The information landscape is large and rapidly evolving, and we can enumerate categories of harm, but understanding what particular risks are most important to your subjects and your research is a qualitative analysis that you need to conduct and revisit. Then designing the life cycle data protection process, including particular information controls and particular disclosure control methods. And so a general warning here, this is an area where the state of the art has substantially outrun the state of the practice, and some extend the law. The textbooks are outdated, they cover the 70s and 90s methods fairly well, but not methods introduced and the new privacy enhancing technologies and formal methods as well. So there's some introductions. And the software, the shrink wrap software handles again the 70s to 90s methods, and this is a fairly comprehensive list of the shrink wrap software available by the way. But for things like differential privacy that goes beyond using differential privacy to compute means of tables or things like that to or secure multi-party computation or other privacy enhancing, you know, more advanced privacy enhancing technologies, you'll need to get into development libraries and the like. And it is, you know, I guess the good news is that it is generally possible to get to legal compliance with the, you know, for now with the 70s and 90s methods, but that's not future proofing you for risks that can even legal risk that could hit you or and is not protecting against all the possible risks in the subjects. You can find more information about how to contact me and some of the working papers on my website, and I've seen a number of questions, you know, we've had a number of questions in the chat and we can open up for more questions now. Yeah, thank you so much, Dr. Altman. We do have a number of interesting questions, very fall-provoking. One I was really interested in from Ryan says that he uses data from continuous glucose monitors, which collect glucose levels every five minutes. What are your thoughts on entering a bit of non-significant error to throw the folks trying to link data off the trail? So there's a deep insight into that and that's both like that's a great idea and not great idea at the same time. So noise is a fundamental, introducing noise is a fundamental tool for a fundamental transformation method that can be used in data protection. However, the introduction of noise has to be engineered so that it is known to fit a particular privacy solution concept. It is easy to inject noise in a way that makes it really easy to compute, like, to recover information about the individual or subgroup. For example, if we have a, suppose that glucose monitor had a measure of your location, I know this is a strange thing to have, but suppose you just recorded the location sample you were and you noise that. In fact, you only recorded the day and the day plus or minus a week, the date plus or minus a week, and the location plus or minus 100 miles. If we had a sequence of five or 10 of those, that would be over a week or a month. That would create a unique fingerprint that we can match to any other database. So if we could observe that person even with that level of noise somewhere else, we can match them and so they start. So the noise has to be governed by a higher level algorithm that is engineered to provide privacy. Another good question we had was how the anonymization process would work with the study involving interviews. What if the participant's answers could be identifying? Yeah, generally, that's a, there's a life cycle consideration. When we think about about what are we trying to learn and what are the outputs, there are a number of risks from like collecting survey information. One is that the first is that people might be observed while they are being interviewed. So whether or not the answers are identifying, then there's that information, the raw data might have identifying information either directly or indirectly. The platform on which it is used, like if you go through survey monkey, they may be collecting IP addresses. So that could be identified. So you have to look at the whole process of how are the inputs related to your outputs? What are you releasing in terms of your final analysis, data products, publications, etc. And do you have a process that limits what people can learn from that? And that might, you know, if it were people's, you know, if you needed open-ended answers, it might involve coding those answers and releasing the topics. There, even if you redact information from answers, if the answers are long enough, they can be analyzed stylometrically.  So you have to think of it as an overall life cycle and sort of balance the goals of protection against what you're releasing. If there's no other questions, could you please elaborate on the idea of a privacy concept that one could apply to research data and the difference between the privacy concepts you introduced? Yeah, so I think the core privacy concept that to focus, that we focused on right now is anonymity, which is technically defined in a modern framework as what you can learn about an individual because of their participation, right? That is a different privacy concept from, say, a legal concept. Can I prove that you are a record number of 33? Or it is also a different privacy concept than, say, a group privacy concept. You may sample from Ashkenazi Jews, like me, and you may learn about breast cancer mutation in them. It doesn't violate my individual privacy. So it is, in that sense, individually anonymous. But it may be that you are interested in group information. Or you may have, you may have a privacy concept that involves control over data purpose. Maybe you've anonymized the data and nobody knows it's me, but I didn't authorize you to use it for machine learning and building profitable models or for research into genealogy rather than medicine. So there are different sorts of end goals that you may be trying to maximize with those different sorts of modifications to the data and protections from the life cycle. What is the basic or first step towards anonymization is to be taken in the case in which to public the data set supplementary to scientific publication that contains patient data. For that, I would refer back to the two anonymization textbooks, I think, particularly the first textbook link that provides the basic, how can we do some basic checks to make sure that they're not, you know, obvious individual identifiers that some of the standard attacks to link can't work. It's still, there are other things that will be necessary to provide sort of formal protection, but that's a good step. Big step indeed. Well, with that, we are at 303, so we have reached time. I know we could go on forever with questions. It's such a rich, rich topic. And we will follow up, have contact information. So please, attendees, feel free to reach back out to us with other questions and follow up. We hope to continue this conversation. It's a start, certainly a progress we're going to continue to work on. But I just wanted to take this time to again thank you, Dr. Albin, so much for joining us. We really appreciate you leading this discussion and sharing all of your expertise. Well, this is a, you know, this is a topic that I find very interesting and I think is really important to researchers and research subjects. I thank everyone for, you know, having, paying some attention to it and diving into the details of it. Thank you very much. Yes, thank you, everyone. Have a great day.


any PVC glue but I do have some polyester resin I know that sticks if this were a standard 4 inch schedule 40 pipe and this was a 2 inch and these are three-quarters these will fit in between there and it'll all work right however this is not a standard size I got it from some garbage somewhere I don't know what sizes but anyway the walls are slightly too thick so I need to either carve some of this out or carve some of the outside of this well I guess I could carve these smaller but there's 11 of them so this is the easiest thing to do so I'm gonna put this on the lathe and cut it down a little bit Jenny what are you doing well I'm having a minor electrical issue and I don't feel like fixing it right now well I need Sun for one thing anyway doesn't matter why I don't have electricity right now and yeah I could take the lathe to the house or the boat or whatever but I can just turn this by hand it'll be done in ten minutes it's already pretty good it's gonna loosen up more as the the rollers inside wear themselves around her I wonder how much weight that can handle one two three four enough for my pedals


Hello! My name is Emily. Thank you for joining me today for some yoga. For the past few days it's been rather rainy. It's the spring in Vermont, so that happens. So let's have a little fun with some rainy day yoga. So we'll get started with our Namaste song. We'll do some warm-ups, some playful movement, mystery bag, and then closing. I might need some help today too to help me with some rainy day friends. All right, so let's get started with a big breath in. Ah, nice big hug. Are your little ones close? Feel free to give them a nice, loving squeeze. Let's bring our hands up and over the head. Hands coming in front of the heart. Namaste. Namaste. This is the way we start our yoga day. The light in me honors the light in you. Extend and stretch. Fun. Let's have fun. Reach for the clouds. Reach for the fun. Let's have fun. Let's get into some of our warm-up, some of our movement. So today let's reach for the clouds. Just come up slightly to just look around. Something's big out there. Then push on back. We're gonna come up into downward facing dogs. Oh, if you have a dog, feel free to bark.  You just got away.  Fours. Let's drop the belly, lifting the head. Oh, now opposite, lifting the back. Last one. Hope you're feeling a little warmer. I sure am. Still raining, but we're hoping for flowers and plants. I even see a rainbow. I love the rain. Feel free to sing with me and move with me if you'd like. I'm singing in the rain. Just singing in the rain. What a glory. Let's do yoga again. Please think of a rainy day, friend. Just singing in the rain. Did you think of any ideas? You know what? My daughter said the same thing. She thought of worms because we always see worms after a rainy day. Let's try doing the worm pose. So I'm gonna come onto the ground.  I can put my feet together. Can you lift your feet just a little bit? And you put your hands up.  Let's try that again. I'll put my feet together, lift them up slightly, lift my hands up slightly, and now let's wiggle like a worm. So nice. I think I need to go sing in the rain again. It's time to put on the rain boots. Maybe my rain coat. I'm singing in the rain. Just singing in the rain. What a one. Let's do yoga. Can you? A rainy day, friend. Just singing in the rain. Day friend, you think of a frog? I love the water. I feel like they're out even in the rain. All right, let's do it. Let's get into our frog pose on the count of three. Let's jump as high as we can to try to touch the clouds. One, two. Oh, that was awesome. Let's try jumping a little higher. One, two. So good. Now, do you have one more super duper froggy jump? Feel free to get help. Maybe from your mom or dad or an adult close by. One, two. That was it. Some good froggy jumping. Awesome. Shall we sing one more time? Let's sing in the rain one more time. I'm singing in the rain. Just singing in the rain. What a one. Let's do yoga. Can you?  Just singing in the rain. Of a duck. Oh, have you ever seen ducks out on the water? On a rainy, rainy day? It doesn't bother them at all, does it? I'm going to come onto my knees, get my hands on my hips. These are my ducky wings.  Ah, quack, quack. Oh, let's take a big breath in. And let's go. Quack, quack, quack, quack, quack, quack. Maybe shake the water off your back. There you go. Stretch out your wings if you'd like. Oh, nice. Thank you for singing in the rain with me. I would love. What's inside the mystery bag? The mystery bag? The mystery bag. What's inside the mystery bag? Tell me, do you know? It doesn't sound like water. Any guesses? Maybe some rain? Some drops? It's hard. Let's take a look. Oh, it's not water. It kind of looks like a rain drop. Oh my. Have you ever seen these little magnetic guys? This looks like a rain drop. If we think about it, or use our imaginations, we can imagine it's falling from the sky like rain. Oh, so I have two of my little magnetic toys. Oh, I'm going to sit, crisscross apple sauce. And let's start at the top of the head and we'll work our way down. Drip, drop. There is rain on the top. On the top. Breathing in the rain. Tending for the rain. I'll make our rain fingers. You feel pretty relaxed and pretty good. Let's take one more big breath and our rain fingers come rain down. So nice. All right. With my rain drops, I can even pretend to make a rainstorm. Drip, rain. On the top. Drip, drop. Drip, drop. There is rain on the top. Now what is this? It's a quiet rain. What if it's a real thing? I'm going to pretend it's raining on my face. Let's look up and just, oh, it's raining on the face. Oh, and one more big breath in. And we'll have our rain fingers come down. Oh, nice. Do you have three to grab your rain drops? Let's come over. So feel free to just lay down. Something's comfortable and you can stay right here if you'd like or if you fight, we can do feet up the wall. Ready? There we go. I put that rain drop right on my eyes. We can put it on your head, on your belly, wherever you'd like. Let's bring our hands to the side. We'll just focus on our own breathing. You can join us. Let's bring our feet down and we'll come to a criss-cross applesauce position. Here we go. And with our namaste song.  Namaste. Namaste. This is the way we end our yoga day. Delighted me. Honors the light in you. I hope you have a fantastic week. Enjoy the spring and enjoy the rain. Looking forward to the beautiful flowers when they are here.


For those who do not understand the questions. If at all anything is there, please share with me and I'll Help you. Okay. Okay. So all of you focus on your Accuracy once again, so we'll count the accuracy guys. Let me see These accuracies are being monitored for all your future purposes including participation in acceleration. So hence Please maintain your accuracy lower accuracy means automatically you will be out of Big game. So hence Okay, so we'll start eight o'clock it is and Yes, so the first question is on your screen First question on your screen Okay, so last 10 seconds these kind of questions you'd have seen in your previous grades as well Very good. So everyone has any ways voted but still Not everyone could get it right. So this was very simple question and Okay, so 745 So, you know the clock this is minute hand and at 745, let's say this is six and This is seven and this is it Okay, so each Each hour corresponds to 30 degrees and Since it is 745 the hour hand will be exactly three fourth Three four doesn't it divide into four parts Four part each each of them is seven half degrees. So it's 30 plus 7.5 degrees Answer is 37.5 Yeah, this is the answer. So many of you have not got it So answer is 37 and half. Yep. Also the options were pretty much Indicative of that. This is not possible. This is not possible because it cannot be a regular angle at What I mean by order is the minute sign is between 7 to 8 so it will not be making a very perfect angle Okay, yes, so options were very obvious, okay, so the first Need a board of me. So mention your accuracy. So obviously one by one or zero by one One by one or zero by one Okay Next question on the board Be ready Here is the next question. Okay, so here is the response. I Hope you would have noticed there was a slight Yeah, I can I could sense that so most of you have made it wrong. I know most of you would have fallen for the trap which was there in the question and I told you the questions would be easy But options would not be so the question was to find out the compliment of the angle and Most of you have found out the angle itself Okay, so as I told you Right, so hence answer is 60 degrees And it was very simple to solve half of the compliment of an angle That means if x is compliment x is the angle 90 minus x is the compliment 90 minus x by 2 is equal to fifth of the supplement So 180 minus x is the supplement and divide by five So it was plain and simple linear equation But I knew that you will not read the question properly and you will fall for trap So 45 minus x by 2 is equal to 36 minus x by 5 So hence 45 minus 36 is x by 2 minus x upon 5 So 9 is equal to 5x minus 2x upon 10 So x is 30 degrees if you solve it you will get x is 30 degrees right, but the question was the compliment of the angle is 60 degrees, okay, so the answer was 60 degree and Response clearly shows the questions appear to be easy. Oh good Next question on your screen. So these are degrees minutes and seconds, right? So 36 degree 43 minutes and 9 seconds. Okay, so last five four three two and One Okay, so the question was very simple and easy. You don't need to calculate anything but still not many of you could get it so I need to explain this to you and So you have to read it properly. It was supplement of Compliment of this Okay, supplement of the compliment of this so supplement of compliment of this is nothing but 180 minus 90 minus this number 36 degree 43 minutes and 0 9 seconds. So you don't need to calculate anything So it was simple 180 minus 90 plus 36 degree 43 minutes and 0 9 seconds 180 minus 90 is 90 so 90 plus 36 126 and the game was done Okay, so Yep, so you don't need to you know many people would have got disturbed by these figures But you actually didn't require this in the question Yeah, tell me So basically they asked the supplement of the compliment so first find the compliment then subtract the supplement from the Exactly what I was hinting upon Sunaina. I don't need to do it. You will save time And then subtract again it will be waste of time, right? So hence this was the demand of the question and the demand of the question helped me actually So now I am adding this angle to what 180 minus 90 which is 30 So it is very simple to add 30 to 36 degree 43 minutes and 8 second I'm sorry No, no, so what I'm just I was giving you examples so adding a few a integer to this will be much easier Then subtracting it Right Okay, so hence this is the answer 20 questions today My wish on why what happened? So here is the next leader board Okay, so this is the new leader board Rita Tanvi Srijan Nishant, Raghav, Pooja, Anuya, Maverick. Who's Maverick? Identify please Who's who's this guy Maverick? Jhagrav Next Vignesh and Tony Next question on your board instead of wasting time on chat Please focus on the question spend time and solve it. Please take time and solve it. There is Something in the question. So all of you say easy in the beginning, but the response doesn't show that so here is the Final if it is so easy Maximum people are Making it wrong. Okay, so Now, you know why why such questions are set Okay, so here is the question in an examination student made a mistake of calculating the complimentary of given angles So let's say the given angle was X and he found out 90 minus X, but he should have found out 180 minus X. This is what he wanted to find out find out the incorrect answer So this is incorrect answer was one-third of the correct answer so Sorry Yes, the incorrect answer was one-third of the correct answer. So this is the equation Okay, so hence 90 minus X is equal to 60 minus X by 3 Okay, so hence what will happen 30 is equal to X minus X by 3 So 30 is equal to 2 X upon 3 Right. So X is equal to 45 X is equal to 45, but then you have to find out the correct answer not the angle The question was not to find out given angle. The question was to find out correct answer and correct answer was supplementary of X So hence answer was 135 degrees Okay, so hence Please as I keep saying Durga Dhani, so please be focused when questions are easier It's more tough Okay, next and people are also not performing every time. Okay Next question on those on the screen guys, please again Stay away from unnecessary chat easy peasy and all that stuff easy is when when you celebrate after your win not before that. I Hope the image is clear. Otherwise, I will demonstrate here in my screen. So let me show you Suchir stay away from unnecessary spamming So I couldn't see one of the angles and I'm Like the nine look like a zero and I messed up the question Does it look like 69 degrees So but like when you see my mentee, it's like looks like a zero Not everyone is able to get this why less than 50% Yes, so it was easy very easy so You did not do anything actually Clearly M is 69 degrees M is 69 degrees and why is that why is M 69 degree what philosophy which law which rule says So L is parallel to N So M is 69 degrees because of corresponding angles and then this angle was to be found out And this is nothing but that series X X is Nothing, but 65 degrees plus 69 degrees. That's it. Which law which rule says this What is this rule called which theorem? Exterior angle theorem suggests that the exterior angle will be equal to interior sum of Interior opposite angles opposite to this exterior angle is these two So if you sum them you will get X and that's what was asked so right It should be very Should be done very easily But never mind Let's see this course Sorry, we could just draw that line in between and then Sorry, sorry could not get you just We could just draw the line in Like we could draw a line extending from all like on two sides, so Then 180 minus 16 and 180 minus 65 you don't need to do that because again you have to do 180 minus This in the same time Yeah, yeah, yeah, so how does it help so this is 65 69 degrees. Yeah. Yeah 55 degree same thing Yeah, you can do that with also You can show Yeah, sorry, someone is saying something image horizontally Can you give the image I change the image direction you're saying yes, sir. Yes, sir. It's better when you turn in 90 degrees either way What? Yes, sir, then we draw the figure again It's tricky. It's tricky. You make it tricky Hey, come on guys, do you think they will ask you before putting that past, you know diagram Take a screenshot go quickly open it and rotate it No best way is to get accustomed to these instead of wasting time on all of Right, so hence all those who are trying to you know see none of the seed This is where you don't understand the idea is to trap you there where you are most vulnerable Right, so hence Their questions in all the exams will be like that where you are most vulnerable No, none of the competitive exams will give you a question where you are strongest Possible candidate not at all. So better you get equipped or you know accustomed to these Rather than trying to change the pattern of the question. Okay, so hence now that you have told me I will make sure that I'll give you these kind of questions only you should not have told me this Anyways now Okay, so Okay, yes unnecessarily comments will be barred and you will be thrown out of the quiz, please let's maintain the So this is inception this is Jurassic Park, sir angle D is 34 degrees, right? Angle D is not 34 angle. This angle is 34 here So Drop this no gang shang thing away from unnecessary commenting That's the only reason why your accuracy is not 100% you guys are distracted Just Stay focused on the question. So most of you are at least this is the first question after so many easy questions where I'm seeing 38 out of 58 people Giving the right answer so that suggests that none of the topics are easy. Okay, but it was very Easy so this is 34 and what all do you know? So who knows B is 76, right direct B is 76 degrees You don't need to know if you calculate 76 are only option C Is D is not 76 B B. I'm saying B is 76 degrees. Okay, so Clearly what all if this is 34, this is 76 C is how much handle some property 180 minus 76 minus 34, which is 70 Right, so C is 70 much of this ruled out this ruled out Okay, the moment C is 70 D is also 70 and Yeah, B B was 76. How because of this is 76. This is 76 Right, why are these two equal? Corresponding angles, right? So this is 76 then this has to be 76 alternate interior so Now easy, so if it is So D is also 70 So just in case if you want to solve it properly so 76 plus 70 now And in fact, you don't need to do all of that a is directly equal to 34. Why alternate interior? Right, you don't need to calculate anything else. So a crazy directly. This is alternate to this So a is 34. So immediately out of these two, this was ruled out. So C Okay, so easier one. Most of you have got it also. So nice Yes, I Stated that in the very beginning itself Hmm Okay Some shuffling is happening. Shallow next question guys. Good decision. Very good. Nice. So last five seconds and Let's see how many if you have solved this one and even if you have not been able to oh Most of you have good. So, you know this already. So Formula based question actually so we know that If there's a regular polygon regular polygon is that polygon which has Equal sides all sides are equal is regular polygon. So regular polygon The internal angle is nothing but n minus 2 by n into 180 Okay, this is what the formula is, isn't it? So this is equal to 150 degrees and how do we arrive at this formula?  What do we do? What do we know? So this is 180 degrees when n is equal to 3 Total sum of the angle is 180 degrees if you add one more triangle, that is if you make a quadrilateral It becomes n is equal to four four sides are there But two triangles mean n minus 2 into 180 degrees. So Correct, this is how Total the sum of the angles some property of any polygon is there. So if any polygon of n side is there so total angle is one n minus 2 by 180 degree and One angle will be divided by n and this is given as 150 degrees. If you solve this equation you will get n into 180 minus 360 is equal to 150 n Right, and then I'm writing here So this is 30 n is equal to 360 degrees Right, so hence n is Excuse me, sir. Yes, sir. Sir. I got disconnected. Can you tell me the answer last question? Last question was C Oh, thank you Okay, n is equal to 12. So doh decagon doh deca This is a new Okay, doh decagon. So 12 sides of the Polygon revolutions per minute is the usual unit of Rotational motion you would have studied in physics as well Motion rotation is RPM so you now know in How many minutes how many degrees? So in three seconds, how many degrees? Someone's mic is on me. I'm mute. Please read on mute Jagarov, would you know me? Sorry, sir. Okay, so Let's see mixed response. Many people didn't know the answer. Let me explain So a fan is rotating at a speed of 600 revolutions per minute. That means in one minute that is in 60 seconds How many revolutions it is completing 600? 600 revolutions full circle. So in one second, how many revolutions will it do? It will do 10 revolutions In one second, how many revolutions 10 seconds 10 revolutions. So in three seconds It will do 30 revolutions Isn't it now in one revolution one revolution is equivalent to what 360 degrees? one full sweet 360 degrees Okay, and multiplied by how much 30? So 30 into 360 should be the answer So can we assume it another way like it makes 600 revolutions per minute So the answer will be number of revolutions into time Revolutions into time. So you have to reduce the time change the units of time. No, yes, sir You need this is seconds. You have to convert them Yes, sir. Yeah, so that's that's how it has to be done. So hence So basically if you talk in physics that is given as angular this is called angular displacement actually Angular displacement is nothing but angular speed Just studied right into time This is the Formula angular displacement angle is called angular displacement, right? So angular speed Yes, sir. It'll be angular distance because angular displacement is zero Angular angular displacement is zero Yes, come to accelerator then I'll discuss. Okay, it's not zero. So angular displacement is angular speed into time Okay, so How about I thought that a displacement is supposed to be That displacement is In these are two different things. Yes. So one is called linear displacement. What you guys are studying right now is or Translational this is rotational motion. What you are studying is right now is Translational motion Translational motion Okay, when you come to rotational motion Then we'll talk about angular displacements Okay, these are two different There are three types of motion we study in Physics or you know in mechanics translation motion rotation motion and oscillatory motion Okay, so right now in ninth grade your syllabus covers This when you come to 11th grade both of these you have to study Okay, anyways, so then we'll discuss angular displacement is equal to angular speed into time and here angular speed is rpm But rpm is not the right unit. It has to be converted into radians per second But then I have just transformed the question for you because it's an it's an angle based question So hence so hence I didn't want to introduce this formula to you right now But you can solve it like this also right so total number of total angle swept by the blades will be this so much 3 into 36 is one not 8 and double zero degrees So this much Angle D. Yeah Next question guys on the board. Let me show you the question here. So this angle is 130 degrees This angle is 40 degrees So my thing Sorry Your voice is a coincidence Oh Yes, sir, so my my My software did not allow me to click it clicked on its own. Oh glitch Okay, so most of you have got it but again not 50% So this is the Well, I showed the leaderboard first never mind. Oh my god.  So so many people did not I would like to see that first once again so this was the answer and this was the So one two three four five people could not get the right answer. Oh Okay, never mind. So here was the explanation to this I hope I think most of you would have done this one that you draw. Sorry. So I don't know how to So let's say You draw another line parallel Okay, so this becomes 40 and This becomes 50 why 50 because consecutive interior angle if there are two If there are two angles if there are two You know Conceive interior angle sum is 180 degrees. That's what we learned in lines and angles. So hence this D is equal to 90 degrees D is 90 so D is 90 2d is equal to 180 degrees and That's a straight angle. There was 2d not D Okay, so hence the right angle was Okay, so once you get 50, how do you say that's the right angle? This angle this is this hole is this hole is right angle. Why because this is 40 here This is 50 here. So 40 plus 50 is 90 Got it on Yes, sir here. So that is 90 so that the moment it is 90 D is 90 do is 90 means 2d is 180 180 So straight angle Good next question, please. So here is Next question, okay, let me show you Yes Leftmost okay, let me write this. This is X Cool, so most of you are actually I wanted to rescue this question But I could not While I was preparing this question I was solving as well and I had left these marks over here This was these were not part of the question actually, but anyways, you got the advantages anyways any which way it was easy question So this was not given these X were not given. So you have to Say that this is this equal to this because Corresponding angle and this angle is equal to this angle because alternate angle, but I know X plus Y plus Y is 180 degrees Right, so hence that's why I'm wondering why there was such a perfect text and it's weird X Now you understand, right? So I was solving that question at you know sometime back when I was preparing the slide and Probably mistake that those marks I'm sorry So It is yes 90 minus X upon 2 Very easy question. Chalo never mind But still some people could not get it. I had written the answer there But you could not pick it up never mind Next question Okay, so next question is here. Hope you are able to see this. This is X This angle is X this angle is 25 degrees and this angle is 105 Degrees What's your accuracy? Those who are saying easy now. I'll check their accuracy level back. I can't pay. I have all the data. Don't worry Sundar If you are if you know you are correct, you're correct Yes, who's this one's the true false things start After 12th question Yes So most of you have got it correct. So this was very simple there were multiple ways you could have solved this one is directly Pluse it to this Okay, so this is X because of corresponding angles, right? This angle is also X. So that is X 130 degrees Thank you I am also doing the same thing. So this X is 105 plus 25 because exterior angle. So these are interior opposite angles So 105 plus 25 is 130 degrees. Yeah, you could have done that or you could have done this also Right. I don't know how to Point our options eraser so Yes Then now this angle is 105 again so Let me write it here. So this angle is 105 again and again X is the exterior angle to some of 105 plus 25 any which Okay, so 130 is the right answer. Oh, sorry Gargi if that's happening as have been have been happening So Those things are happening. No problem Next leaderboard Next question on the board guys. Let me show you this here So, let me write these angles. This is X plus 15 This is this angle here is 3 y and this angle here is 2 y plus 25 So X plus 15 is 2 over 25 are vertically opposite angles. These two are, yes What's involved in the question that I didn't take my accuracy for 9th and 10th question You didn't understand Tanya. So time is up sir. Time's up Okay, so still many people could not get it right Okay, so it was very very simple question actually so X plus 15 is equal to 2 y plus 25 first of all Okay, and 2 y plus 25 supposed to be 85 It is supposed to be 95 because there's a question I got 85 Find the supplement of Okay, let's see so 3 y is equal to how much 3 y is 2 y plus 25 so y is 25 Okay, so if y is 25 So is if y is 25 what how much is X so you can you can calculate from here? So this will become X plus 15 is equal to 15 2 y is 15 plus 25 So X is 16 am I right? Yeah X is 60 and Y is 25 So X plus Y is 85 X plus Y is 85 and you have to find out what supplement of this. So this was the answer right, let's see see lines and angles are Inherently very easy topic.  Okay, so I'll set for the MCQs Not MCQs 2 and 2 and follows. There are 8 questions 8 seconds per question. You will not get much time to think it is Obvious or not obvious. So here is the first question on the screen. So the statement was false But still many people have got it So statement was very much false. Why because compliment of an acute angle is compliment will never be obtuse Compliment is never going to be obtuse because some of the two triangle is two angle is 90 degree Okay, so if you see X plus Y is 90 degrees If two positive angles are added and you are getting 90 so either of them will be less than 90 So it cannot be obtuse Cannot be obtuse at all. So false Okay Next so you have to be quick now. So we saw the accuracy part. Let's see the Quickness how pick you are So stay calm stay focused don't get distracted by don't look at chat at all look at chat after the 8th question Okay, that's how you can score well. So next question Don't get distracted again. I'm telling you focus on the question. So the answer was true So a compliment of an angle cannot be equal to supplement ever Okay, so Very easy it was Because if you see 90 minus X if it is equal to 180 minus X that will that will say 90 is equal to 180 Which is not true never possible. So hence not possible never Okay Understood by all. So these statements you should remember as if they are, you know, you should be part of your okay Part of your knowledge base, okay Next time someone throws this question to you don't think that time It's as good as you know, which fit as common as you can't divide by zero in mathematics like that. It's undefined So remember like them next exterior angle is external angle. Okay, that statement was false So good, yes, they can be acute as well why you can see Many cases actually so if the if the sum of the interior opposite angle, so let's say this is Bad drawing bad drawing wait, so let me draw up obtuse Let me draw an obtuse angle obtuse angle triangle. So this is an acute angle, right? So let's say this is greater than 90 So this angle which is some of this plus this is less than 90 so it can be acute Can be acute Okay, so next questions next question on the board now some previous stuff Let me see if you remember these so I remember the answer Still Fifty-fifty oh yeah, why why? Clearly a minus one is root three I gave you in last centaur also last time it was two over there. This time I put a three over here So a minus one cube Is equal to root three cube which is three root three, which is an irrational number? So this is false Right. It's a false statement Okay So previous stuff also has to be revised guys It shows that lots of how many of you have again Forgotten all those things Okay, next question. This treatment was true statement. Isn't it so? If there's a polynomial FX FX is equal to let's say We had to be power a n xn if you go by the Regular definition which we talked about Finally a 1x plus a 0 Right now f 0 is 0. So if you put x equals to 0, you're getting 0. That means all will become 0 So it will that means a not is also 0. So the constant is also 0 So any function or any polynomial any polynomial where F 0 is happening or F 0 is becoming 0. That means there is no constant term in that FX, I hope you understood this so Remember this Any polynomial where there is No constant then FX will be equal to 0 or f 0 equal to 0 and the vice-versa Next it was very very again identities. You need not Do all the expansion and other things and you must not forget the identities also So a plus b is equal to c means a plus b minus c is equal to 0 Right, and you square both sides. What do you get a square plus b square plus c square minus or sorry do a b minus 2bc Minus 2ac is 0 That means a square plus b square plus c square is equal to 2 minus 2ab plus 2bc Plus 2ca right you Yeah, so glitches I can understand but please understand me this thing How do you you need not do all these calculations either in the in the right? You know and the you know exam or something. So what do you need to do is? This will never be possible. You have to remember this This will never be possible because if a plus a and if any one of them is Negative then at more at most two will be of negative sign not all will be same sign So this is never this is never possible. So please understand this unless a is equal to b is equal to c, which is 0 So only when Right, okay Next next question ready four four plus two three is equal to one plus three true or false Very good It's true. So most of you would have tried Solving it you need not solve it. You'd have simply squared it Square this what will you get one plus three plus two root three done fast four plus two root three, which is here. So true Okay, so Don't try to win. This is this is the game Right, so you're just square it. You need not find the square root Okay, and you'd have got this true. So statement was very much true problem is remembering Nani Next and the last question of the evening the answer was yes true and most of you If you remember we had discussed this Now to solve this third point three one bar is simply 31 by 99 and 68 bar is 68 by 99. Isn't it yet? We had done this Okay, add this one. So you'll get 99 by 99 one Okay Understood. So you have to retain all of that what we have learned previously I told you did I tell you that if this is 0.21 bar, what will this mean? This is simply 21 upon 99. You don't need to calculate anything Right. So these are all shortcuts So you can add them will give you one right up so on yeah, so but you can't add something which is under the bar Right, it is repeating. What does it point 3 1 bar mean 3 1 3 1? If you add them, you'll get 9 9 9 9 9 9 9 9 9 9 9 9 ok, but but actually that is limiting to one, so hence answer was true, so that brings out or brings the last question is over, so hence closure to the quiz and here is the final leader board, so Tony, now who, who won, Tony has the highest number of points, very good, Tony Srejan, Raghav, Anuya and wait one minute, let me see once again, so who are, who all are there, so Tony, Srejan, Raghav, Anuya, Nishant, Karun, Vihan, Vinesh, Haritha and Nithin, no new entrant in the top 10, very good guys, keep it up, good, please remember the previous accuracy, please let me see the score on accuracy, all of you, accuracy 16 by 20, okay, next, all of you please put your accuracy results here, 15 by 20, okay, come on, come on, 12, 16, 17, so far 17, 17, 17, 17, 17, maximum is 17, someone said 18 also, anyone 18, anyone who got 18, Tony, Tony, okay, so what is the learning guys, learning is stay calm, don't get distracted and stay focused, you will be able to solve the questions, more you are distracted, more you lose on, so many of you, if you just reflect back just after this quiz, there will be two, three questions, definitely you have lost just because you didn't see the question properly, one was that, so three questions, yes sir, next time can you put like two extra regular questions instead of true and false, why, so because like true and false is really fast, so like, or can you increase like two to three seconds time, so just let me draw an analogy, so let's say you are Sachin Tendulkar, you're not able to play the bouncers, let's say just, just in case, so will you go to Slyvector or Malcolm Marshall or Alan Donald that hey, don't bowl bouncers to me or what will you do, you'll go to the next and ask your team members to, what, bowl bouncers only to you, so that you are ready for that, is it, so instead of, again, don't try to modify or alter the background, you yourself get accustomed because this is reality, today or tomorrow you are going to be in such spot, then what will you do, so it's better, the more you sweat in peace, the less you bleed in war, so remember that, okay, so nothing is going to change, in fact it is going to be more drastic and more, more dangerous, so that you guys are trained, this is the training, this is not the real battlefield, you will learn or you will get the benefits in the real battlefield, so hence, so is there a general awareness this Sunday? So can we have a general awareness or geography? So many, so many, so let's do geography because that will aid to your missing as well, instead of astronomy, so yes, okay fair enough, so I'll do biocentamard, that's on Saturday, can we do an astronomy centamard, please, astronomy, oh my god, so I have to, I don't know that much of astronomy, so I'll have to invite my again friends from... Sir, no astronomy, sir, nobody will get anything, she will be like the only person who answers. Geography or Saturday or Sunday, astronomy is so... Yes sir, no astronomy, astronomy is nice sir, sir, it's really good, it's about the space, it's amazing, nobody knows about the space, sir, general awareness, you're supposed to know about space, guys, silence, I'll give you all silence, please, I'm here, don't worry, so don't fight, both, you know, general awareness on Sunday, geography, guys, we will be, see, our geography quiz was half done last time, so let's complete that because otherwise, you know, so those two will be anyways benefited out of that, so let's do that first, general awareness anyways will do no problem, so we'll do that, don't worry. No, Saturday or Sunday? Saturday, there is a bio quiz, a bio, this thing, centamard, first day we'll have physics centamard, all these things we'll do on Sunday, okay, let's go, bye, take care, stay safe, see you guys. Thank you sir, take care, bye.