Welcome to the panel, our panel, the library, your Swiss Army knife for getting it all done. So just to let everyone know this is going to be, this is recorded. This is being recorded. It's also being transcribed live as well as live streamed on YouTube so that folks can watch it later and get a refresher on all of the information that we're going to be sharing today. So my name is Caitlin Maxwell. I'm a student engagement librarian here at Western Libraries and I'm going to be sharing some great resources on how you can get support for your assignments, just student life in general, as well as technology, all sorts of things.  So with that being said, we're going to go ahead and go through all the panelists. And then as folks think of questions, please feel free to drop them in the Q&A and we have someone monitoring the Q&A and they'll keep a list of all the questions. And then we'll get to, after all the panelists are done, we'll get to the question part of the panel. So with that, let's go ahead and get started with our first panelist, Stephanie Morgan. Take it away. Hi, I'm Stephanie Morgan. I use she, her pronouns and I supervise all the students at the circulation desk in the libraries. Circulation is a place where you can get help finding materials and picking up holds, as well as checking out materials. We are also a great place to ask questions. We are happy to be the starting point for all your library and campus inquiries. And currently we're available by phone and email. We are also the place that houses all the library reserves. And reserves are electronic and physical materials that are needed for coursework. This may include any library or instructor-owned texts, articles, videos, audio recordings, and other relevant resources that support classroom instruction. A list of all these materials that are available for your class can be found on your Canvas page for that class. Physical reserves aren't going to be available this fall due to COVID-19, but please always check with circulation to see if we have access to what you need in our physical collection or if we can help find it somewhere else. In addition to our collections, Western libraries also partners with all the other nearby libraries and schools, meaning that any materials from the Bellingham Public Library, Whatcom County Library System, Northwest Indian College, Whatcom Community College, and Bellingham Technical College can be returned to Western and any of our material can be returned to them. When our buildings are open, the circulation desk is a place to turn in and to check for all lost and found items. We get everything from cell phones and textbooks to earrings and shoes. The circulation desk is also the place to reserve and check out group study room keys when we're open. Group study rooms can be checked out by two or more people in our great place to practice group presentations or work collaboratively, and these services will be available again once the buildings reopen. And our most popular service is our hold shelf. If you place a hold on an item through the library's catalog, it'll be waiting for you at the circulation desk, and you can place holds for our summit items, which we hope to resume offering soon. Our summit is our partnership with 38 libraries across Washington, Oregon, and Idaho, and then we can also place holds through our interlibrary loan system, Iliad, and we partner schools all around the world for this. And now I'll show a quick little video of how to place a hold in our library catalog. Hi, in this brief video, I'm going to show how you can request print items for curbside pickup or mail delivery from the Western Library's collection. Starting from the Western Library's homepage, go ahead and search for the items that you're looking for. If you're doing general searches where you're just looking for lots of different items and trying to see what kind of books we might have on a subject, it can be helpful to change these limiters so that you're focusing on Western items rather than including our summit partners, since those are not yet available. When you found a book that you want to request, go ahead and click on the title so that you can open up the item record, and you'll want to make sure that you get signed in if you're not signed in already. Once you're signed in, you'll see that there's an option to request WWU copy. At this point, you'll see two options, one for curbside pickup, where you can pick it up Tuesdays or Fridays, 10 a.m. to noon, or you can have it mailed to your home address. Once you've chosen your preferred option, go ahead and click request, and your request will get sent in, and we'll process it as quick as possible. Just keep in mind that we do have a limited amount of staff that can be in the building at a time, so it may take a little bit longer than you would normally expect. All right, and now hand it back over to Caitlin. So now we have our slides back up, and next we have Pipa from the studio. Thank you, Pipa. Yeah, hi, so my name's Pipa. I also use she, her pronouns. The studio covers basically anything that you're working on that has words in it. It doesn't matter what subject, doesn't matter what level, we probably do it. So at the studio, we think that nobody should have to do projects alone. We all do much better when we can bounce ideas off of other people. And because all of us bounce research and writing ideas together all the time, we've built up a massively huge number of tricks and strategies that you can use to make research and writing easier, not to mention other things like reading faster, smoothing out group projects, and also applying to majors. All things that we all have to do at some point. But the most important thing that we do is probably helping people figure out how to customize their own strategies so that it would suit your own learning style. So you can drop in to use the studio as an online study space anytime you want to. Talk with a studio assistant if you get stuck, or if you get tired of working alone. Some people even like to use us as like accountability so that they can stay focused on their projects. And we have several different ways that you can choose to work with us if you're wanting to study or wanting to ask a question. So you can choose between them all. Some people like to chat with us online or text us a question on their phone. Some people prefer to show us what they're doing on Zoom. Some people like to send drafts as they get to the next stage as they've written something out. And then you can also sign up to work with a partner if you'd like to for the quarter, like if you're focusing on a really big goal, for example. So try out one of those ways that seems useful to you. Check it out and make your life easier in the long run. It'll be very, very helpful. Okay. Thank you, Pippa. Okay. So next we have Katrina from the Tutoring Center. Thank you, Katrina. Hi, I'm Katrina Buckman. I'm the head of the Tutoring Center and also used to her pronouns. And like Pippa said, you shouldn't have to work alone. And it's really so helpful when you can find someone else to work with. In the Tutoring Center, you'll find many different ways you can collaborate with either other students or with tutors and peer advisors who are students that work at the Tutoring Center. So at the Tutoring Center, you'll find an online now virtual learning community where you can work with other classmates, you can work with a tutor, you can join a study group, or you can boost some of your study skills. Our drop-in tutoring covers mostly math and science, GURs. Those are the general undergraduate requirements that all Western students need to take. And so if you're taking one of those classes and you're looking for some support, drop-in tutoring is a great place to start. Study groups are also great. Those are more of an opportunity for you to work with other students in your class or in other sections of your course. And you'll have the support and guidance of a tutor who will mostly just be encouraging you to verbalize some of the concepts that you're working on with your other group members. We have something new now that we that are we're just introducing as of this summer, which is appointments. So if some of our drop-in times don't work for you, then you're welcome to make an appointment. For those of you who aren't taking math and science to your courses, we have study skills support available for any class at any time. And that is there's some great best best practices and strategies for time management or active learning, reading, test taking, and other types of metacognitive strategies to make sure that you're really understanding your work and you know what you need to get out of it. And those are also available by appointment. So we're just going to check out on our website now. And if you go to our website, which I'm going to bring up in just a moment, you will find how to make an appointment, how to connect with a tutor at that, or how to connect via Zoom. So on our website when we're open, which these are our summer hours, but our fall hours are Mondays through Thursdays from 10 a.m. to 9 p.m. Fridays from 10 a.m. to 5 p.m. and Sundays from 5 p.m. to 9 p.m. Anytime you're during those hours that you come to our website, you'll see this chat with the TC. And if you click on that, that will connect you with one of our peer advisors or tutors. If those times don't work for you and you'd like to make an appointment with one of our tutors outside of that, you can click on schedule and appointment. And if you stick around our website long enough, you'll get a pop-up box asking you if you need some support. If you go to our services and drop-in tutoring, our services menu is located on the left and drop-in hours is the third item down. If you click there, you'll see a list of all of the courses that we support and the times that we are open to support those courses. So for math, chemistry, and physics, we're open almost every time that we have a tutor on for those, almost every time that we're open. But for some of our other classes, some of our availability is more limited. So definitely be sure to check our drop-in schedule, which will be posted on our website under services drop-in hours. Okay, that's all I have on the tutoring center, but we hope to see you there. Thank you, Katrina. So up next, we have Kona from Disability Access Center. And just a second as Kona starts sharing their screen and we'll get started in just a second here. Sure. And actually, I'm not going to share anything. Our website might be changing a bit. So I don't want to have something shared and then it'd be changed on a person. So my name's Kona. I'm a combination manager over at the Disability Access Center. Our office serves any student with a disability. If you have a disability, you're eligible for services at our office. I think last year we served just under 2,000 students through our office and we serve, we have the ability to help students in all aspects of the student experience, whether it's academically in the classroom, housing, if you are in a class or program that leaves campus, field work. So pretty much any part of the student experience we can help out with. Some questions that come up often are just how do you get the accommodation process started. And there's a few things you'll need to do. And one of those things is submit an application on our website. And I've put that website in the chat and it's also going to be on a slide that will be available to you at the end of the presentation. So you go to our website, which is disability.wwu.edu. You can also call our office at<PHONE_NUMBER>.  Also, information you might want is any previous accommodation information, also any documentation from a care provider if you do have that. If you don't have any of those things, that's fine. You can still call our office and make an appointment to meet with an accommodation manager. And we'll be able to help you through the process even without those documents. Another good question that folks ask are what accommodations are available. And something to keep in mind is that we don't necessarily have a list of like a menu list of accommodations. It really is based on what barriers a student experience is based on their disability. And that will determine what accommodation or modification we might make to allow full access to a class or to housing or to whatever the student is trying to achieve, whatever their goals are. So I have to tell students just come to college, come to class, come to school, and pursue what you want to pursue. And if you come across a barrier, then our office is the place to come to figure out, well, how can we get you involved in full participation in those programs or activities? Because we're doing a lot of remote learning, a question that folks, I'm getting, just I guess a lot of people are asking questions around remote learning. And one of them is do accommodations apply to remote learning? And the answer to that is yes. And it goes along with what I had just previously said about how accommodations will be, they're evaluated based on the given situation. And so if you, if you have a barrier even in remote learning setting, we work to figure out how to alleviate that. And so it's very much applicable in their remote learning and online learning. So I think that's about it for now. And if you have any other questions, just feel free to contact our office. Thank you, Kona. Okay, so up next, we have AJ from Student Technology Center. So take it away, AJ. Hello, everyone. I'm AJ Barse. I'm one of the managers of the Student Technology Center. And normally I usually have my normal stick that, you know, we're on the second floor of Haggard Hall. But unfortunately, we are closed. But that does not mean the STC is closed. We have moved and pivoted to online. And as such, I have some resources for everybody to kind of keep in the back of their minds, should they run into any technical snags.  But at the bottom, you'll see the, what are our hours of operation are going to be through the quarter and stuff. The biggest thing that I want to point out is while we're open, and even when we're not, you have our live support chat, which will show up at the bottom of your screen. And this allows you to chat during business hours to any one of our student staff. We have about 25 students and staff this year. And they'll be able to answer your question live.  The answer is yes. And when my crew will jump in and answer whatever your tech questions are. Also, out of this, if you run into a technical snag and you need somebody to help walk you through things, all of our crew is equipped with TeamViewer and also teams and all of the tech goodies that allow for my crew to help interface with any student's machine, whether that be a PC or a Mac or a Linux box, so that if we need that hands-on training that you used to get when you came up to our wonderful front desk on the second floor of Hagrid Hall, we're going to be kind of mimicking it digitally. So that's one of our resources so that you can still get the same one-to-one or peer-to-peer tutorial help that you might have once had in the physical realm. Now in the digital realm, the other thing that we used to do a lot of is workshops. So this year we have been working to digitize all of our workshops and put it into the wonderful, miraculous place known as Canvas. So if you are looking for training for any of the applications that you see on a typical ATUS machine, such as, you know, your faculty makes you have to, I don't know, do something in Excel and you don't want to completely fake it, you can come in and self-enroll into our course and pick any of the modules and just go through it. Basically our crew has created individual trainings based off of the application as well as the skill and this is kind of a big change for the STC. Now you don't have to kind of sit through an hour or an hour and a half workshop just to learn one little thing that you need to learn. You can jump directly to a specific attribute of an app. So for instance, if you needed something, I just picked on Teams because, you know, everybody's working remotely these days. And let's say you needed to know how to do something as simple as just sending a voicemail or accessing something. So no longer do you have to kind of go through an entire sit-down training in this digital environment to get the skills that you need. And then also for faculty, if your faculty is able to take any of our modules and integrate it directly into a course. So there's one of two avenues that you might be getting training from the STC. From your faculty or directly from us. To access the Canvas course, all you need to do is self-enroll and the self-enroll link is really simple. It's bit.ly slash STC Canvas. And that'll take you directly to the enrollment and anybody in the Western community can do this. Students, staff, faculty, because we just want everybody to learn and be cooler online. So Caitlin, back to you. Okay, thank you, AJ. Let me get my screen up here. All right. So up next looks like we've got, sorry, it looks, I thought we were in a different order, but we've got Dennis from Maps. If you're ready, Dennis. Hi, everyone. My name is Dennis Matthews. I am the manager of the Map Collection. Just a little bit about the collection. We have over 75,000 individual sheet maps in the collection. We also have a small collection of globes, reference materials, atlases, as well as access to numerous online resources, which I'll talk about a little bit here when we get through the slides. Types of maps that we have in the collection include USGS topographic maps, Canadian topographic maps, nautical charts, recreation maps, geologic maps. So we have a pretty large selection of different types of maps that you have access to in the collection. As far as the, you know, I have a slide on when to use maps and why you can use maps. I give different examples of the why you use maps, but I want to focus a little bit on when you, when to use maps. So inevitably you will have classes, writing classes, writing assignments, presentation, stuff like that. So, you know, depending whether you're in English, geology, environmental science, history, for example, think about using maps as a way to help articulate some of the, you know, what you're trying to convey in your reports. So now as far as research assistance goes, what we can do for you, there's a couple of ways that you can reach us and ways to get help. So the first one is you can contact us via email, or you can call us with voicemail. So we are here remotely, even though we're not here in the building. If you choose to do your own sort of research, you have a couple options. You can use one search, which is the library's online catalog. What you can do there is you can type in your named geographic place followed by the word maps. And then once you get your search results, then you can limit by a physical map, online map, where the map is located, time period. So there's lots of different ways that you can limit, you know, your search. Also, if you do find a physical map in the collection, there are scanning services available for students. So just send us the information that the map that you find or maps that you find, and, you know, we can scan those maps for you. Now there might be copyright restrictions, so depending on the map, you know, we'll have to see what's available. Another option for you is to use our online resources page from the map collection. We have a number of local, state, and federal resources available for students that deal with different cartographic materials. So depending on what you need, there might be something available for you out there. Again, if you have questions, you can always reach out to us and we'll be happy to help you. And finally, if you want to learn more about the map collection, you can always click our link, which you have there, and that'll take you to the map collections landing page. And from there, you can learn a little bit more about the map collection or if you need to contact us again, there's our email as well as our phone numbers. Thank you. Thank you, Dennis. Okay, so up next we have Rachel Thompson, who's going to talk about Heritage Resources. Hi guys, I'm Rachel. Obviously, I use she her pronouns. And today I'm talking about Heritage Resources and what we can offer you during your academic career here at Western. So Heritage Resources, and if you don't mind jumping to the next slide, that'd be awesome. Thank you. So Heritage Resources is actually three separate units. What we all do is collect and preserve materials, historical and primary source materials. So things like rare books, manuscripts, correspondence, diaries, audio visual recordings, oral histories, institutional records, and much more. So we collect primary source materials. And I'll get into, I have a slide with a link to more information about primary sources coming up in just a second. Thanks, Caitlin. As I mentioned, Heritage Resources is made up of three separate units, each one with a slightly different focus. Special Collections is the first unit on the list, and there's a link to each one of our web pages on this slide. Special Collections acquires rare books, personal papers, manuscripts, oral histories, photographs, and other materials that document the history of Western Washington University, as well as materials that are related to children's literature, Northwest history, the history of the book, fly fishing, Russian and Mongolian culture, Jewish culture and history, and some other topics. So it's got a wide range of materials. So if you're doing research into any of one of those topics, definitely check in with them and they may have some great primary source materials to help you with your research and with your various projects. University Archives and Records Management is the second on our list today. Again, we have a link there that you can go to with, to go to for more information about what we do. But in brief, the University Archives is the official repository for the institutional archives of Western. So we collect university records in all sorts of different panels, sorry, in all sorts of different formats, and from all parts of the institution. So if you're doing research on how Western responded to something in its history or the history of the university, definitely want to check out the university archives. Finally, last but definitely not least, we have the Center for Pacific Northwest Studies. The Center for Pacific Northwest Studies collects a wide array of materials such as private papers and organizational and business and institutional records about the region. And when I say region, I mean the Pacific Northwest study, sorry, Pacific Northwest, and ranging from pre-European contact to the present. So particular emphasis in their materials is given to documenting economic developments, cultural and social history, environmental history, and other historically significant trends in the region. If you have any questions, you're not even sure where to start where, you know, if you have a research topic in front of you and you're not sure who to talk to out of those three units, you can just send us an email at heritage.resources at www.edu. And that I'll bring up a slide at the very end. Well, Caitlin will bring up a slide for me at the very end of my piece with our contact information, but I just want to let you know that we are, we're here to help and don't be intimidated. If you just shoot us an email, we will contact everybody who needs to help you out. So don't be afraid of us. Caitlin, if you could go to the next slide. I mentioned primary sources and without getting into a whole lot of detail right now because I'll take up the rest of the time. I just want to give you guys a link to a video tutorial that we have talking about what are primary sources and how do you use them in your research and in your academic career. So if you have questions like that, check out this video tutorial. But once again, I say this in every single presentation I ever give, contact us for more help, for more information. That's what we're here for. And Caitlin, if you could jump, I have one more slide. And we're right now, obviously access to our collections is limited. Our buildings aren't open to the public right now. So however, the good news is that a lot of our content, a lot of the materials that are in one of the three units of heritage resources are in our online platform called Mabel. Mabel stands for Multimedia Archives Based Electronic Library. Don't expect you to remember that. Cool fact that helps me remember the name is Mabel. So Wilson was the first librarian of what later became Western Washington University. So we named this great resource after her. If you're interested in using Mabel and finding online content, online primary sources, check out this video tutorial. It'll kind of walk you through how to use Mabel. And I believe some of the things that are actually in Mabel. All right, Caitlin, I have, I lied, I have one more slide. And this is the important slide. This is our contact information that I mentioned before. So once again, I just want to leave you with the knowledge that we're here to help. If you have a research project or really any type of project that you think or you've been told or you think would be benefited by using some cool primary sources, come to us. Our email is heritage.resources at www.edu. And like I said, we can direct you to the folks that you need to talk to. You don't need to figure out which one of the three units to go to. Just contact that number or excuse me, contact us through email. Or you can also leave us a voicemail at the number listed on the screen,<PHONE_NUMBER>. And we'll get back to you as soon as possible. So thank you very much. And hopefully we can help you out in your academic career here at Western. And back to you, Caitlin. Okay, thank you so much, Rachel. And thanks to all of the panelists for sharing this awesome information. In case folks are wondering how to find this information again or how to get in touch with folks, we do also have some slides on how you can get in touch with us if you have questions or if you just need to know, or if you're not even sure who to get in touch with, we can point you to the right person. And we also have links, websites for everyone, all the resources that have been talked about today in the slides as well. And a link to the slides will be available in the description for the YouTube recording when that's when that's ready. So thanks again, for sharing all that info. So now is a good time for some questions for our panelists. So were there any questions from the Q&A or the chat that we can bring up and ask folks? There were a couple of questions that came up. Hi, everyone. My name is Elizabeth. I am she, her. Some of these, at least one I think was answered, but I'm going to kind of ask it again just to make sure. This is for Katrina and the tutoring center. There was just a question about scheduling drop-in sessions. So maybe if you just want to address that one more time, so we make sure that that's covered. Yeah, great. So our one-on-one tutoring will start on the first day of classes fall quarter. So you can head to our website and check it out. And one general piece of advice is I would say go before you really need it. Go before you're feeling frustrated or worried. And that way you can get used to the system. You can connect with a tutor, connect with a peer advisor, ask a quick question.  And this is how it's going to work.  But yeah, it'll be open, the one-on-one tutoring, appointments, and both of those things are open the first day of classes. Any study groups will be announced usually by week one or two. All right, thanks. How do people sign up for study groups? So the study groups are going to be announced based on the classes. Not every class has a study group. And so usually someone will get an email from me, Katrina Buckman, and it'll say there's a study group for your class and you can click on it here. Another way is also just to go to the Tutoring Center's main website and again, click on the bottom left of the screen to connect with a tutor and or connect with a peer advisor and just ask them because they're great resources of information and they are always happy to answer questions, even if it's not a specific math or science question, but a question about how to use the resources. Okay, next question. This is for AJ and the STC. So you talked about the trainings, the one-on-one trainings. When did those start? So the Canvas course is actually up now. We won't have our staff back until all the other students come back. So you can expect to see that the STC kind of come back to life that first week when everybody rejoins us digitally on campus. Okay, I'm going to ask a couple follow-up questions if you don't mind. So looking at the resource mention links, the slide that's up now, I do see one thing. I see the subject librarians. Can you tell us a little bit about that, maybe, Kaitlyn? Sure. Yeah, so let me go back to that slide actually because I kind of clicked on it before I started talking. Okay, oops, there we go. Okay, so the subject librarians here, and I'm just going to click on this link that's available on the slide. The subject librarians are basically a group of librarians that are dedicated or that work with different subject areas at Western. So we actually have three teams that include about two to three librarians, including arts and humanities, which is a team that I'm a part of. There's also a team for science, and there's also a team for social sciences and programs, which includes Elizabeth. So one thing that you can do if you are running into questions around finding research or if you have a big writing project for a class that you're taking and you'd like a little bit more directed help on finding resources in that subject area that you're researching, you can contact us. You can get in touch with the subject teams in a lot of different ways. I think earlier when we were looking at the tutoring center page, there was a pop-up chat box. You can totally just use that pop-up chat box to get in touch with us via chat, and then it'll get directed to the right person. So if you're just curious about finding more resources for your classes, for your subject areas that you're interested in, if you're wanting to explore a major a little bit more, you can definitely get in touch with the subject teams. All right. Those are the only other questions. I'm wondering if any of the other panelists have questions for some of the other panelists. And I've got some too. Okay, when we have a moment. But yeah, let's see if other panelists have questions for the other panelists, because this is a chance for us to get to know each other better too. I have a question for Stephanie. So Stephanie, I know there might be students in the area this fall. Can you talk a little bit about curbside pickup? Yeah. So curbside pickup right now, it is Tuesdays and Fridays from 10 a.m. till noon. And what you do is, like the video showed, you go to our catalog, find the item you want, place a hold on it, and then you can show up any time between 10 a.m. and noon and give the circulation desk a call, our number is<PHONE_NUMBER>, and it's also on the library's website and the slide that I was talking about. You give us a call, we'll check out the item, and then we'll bring it down to you. We'll have a little area set up right underneath the skybridge in between the two buildings, and we just come set your books on a table, go back inside and you grab them. It's real easy, real simple. Yeah. I actually have a follow-up question to that, Stephanie. How long do I have them checked out for? Right now, the standard due date for everything is September 23rd. It may be a little longer if you're a grad student or a professor, but that's what we're going with right now. What about during the fall quarter? Then it will be about a six-week checkout. Great. I actually have a question for Kona. For example, I know that when I was a student, I had a lot of anxiety around tests. Is that something I could contact the DAC about? It is. Some students have experience in, if you're coming from a high school environment, some students may have been given maybe more informal accommodations, and if that's the case, maybe you were getting a little extra time from instructors, but did not have an official IEP or 504, which are accommodation documents. That's definitely something that you can come chat with our office about. Our office is pretty open, so pretty much if you've got a question around, is this real? Is this not real to me? Typically, people's experiences are real to them, and there seems to be a lot of question about, well, I talked to some students who think that they've experienced something for so long. They think that's just the way it is, and oftentimes they don't realize that, oh, there is something different. There is a barrier that I'm experiencing that I've just been kind of putting up with. If you've got questions around that, say you had some anxiety around test taking, a classic indicator of that would be something we often talk about is just not finishing exams. If you're someone who just doesn't finish exams, then that might be something to come talk to our office about, and we can help you navigate kind of what's going on. And you might, starting right now in the remote learning setting, I know that not as many students will be moving physically to campus, but that doesn't mean that your environment where you're at is going to be the perfect environment for remote learning either. And so there might be a, there are different stressors happening that are causing students or family units, different types of anxiety or stress. And so if something is, if an anxiety or a symptom of something along those lines, there is affecting the way that you're able to participate in the classroom, whether that's digitally or in person, that's definitely something you can chat with our office about. Thank you. So there's a follow-up question about the DAC, Kona. Do, so do you have drop-in sessions or do, do people need to make an appointment to come in to see you? We do either. If in the fall we're hoping to have the ability as we're trying to streamline the drop-in session with some video, just kind of like how we're doing right now in Zoom. But basically if you call our office, you can get transferred to an accommodation counselor potentially right there if you've got an immediate question or if the front desk can't help you. But making appointments always great, just call the front desk. Anyone can make an appointment at any time. We're just as much as a resource for students as we are for other partners on campus as well. So also if you're, you know, if your family member has a question, we'd be able to take those appointments as well that we wouldn't share personal information about students. So that's a little shift from family involvement in a high school setting to a university setting. So, but we'll take an appointment for, for many ones. So yeah, just give our offices a call and you don't have to have an application completed or anything and we'll be able to be happy to chat with you. Great. Thanks. Great. And I actually have a question for, for Pippa from the studio. So can you, so let's say like, let's say I have like a draft of a paper and I'd really just like someone to take a look at it. Is that something that studio can help with? Yeah, absolutely. A lot of people send us their drafts through our online send us the draft form. It's very conveniently named. And so what we do is you'll be able to give us your draft, you can tell us about the assignment, you can tell us about your questions, things you're concerned about, and we'll respond with feedback and strategies that you can use focused on either your questions or else something we see like, oh, we're about this also. So it's, it's a really easy way to pop your, pop your assignment into the internet and then the internet will spit something back out two days later and you'll have a next step you can take. It's not always two days. Sometimes we're fast and it's only like half a day, but it could be two days. So we like to give the range of times. So another question for AJ and the STC or and also possibly Stephanie. Is the STC of the library checking out any tech this fall like laptop computers and that type of thing? Yeah. So originally the STC we had our racks and racks of laptops and because of COVID we've shifted all that down to classroom services because the first floor of Haggard in their area is going to be open. And in the fall, there's going to be a special like checkout schedule and procedure. I don't know if that's been released yet of what room is going to be, but it'll be on that first floor and stuff right now during the summer. They've actually been having like they've been doing all their checkouts out like in a tent outside of Haggard. So they'll be bringing that back in presumably when you know the Pacific Northwest starts to deluge on us like the day after the term starts. But no, so A2S has most of our kit, but you can't get it from us. You have to get it from classroom services. Thank you. That include calculators as well. I know STC and the circulation desk and the tutoring center all used to provide calculators. Can students get calculators from A2S? Yeah, they should because they're going to have our stuff. Yeah, no. So anything that the STC had or the bigger items, the small bits and bobs like our cables and stuff, you know, that's still locked up on second floor. But the bigger ticket items we intend to have in the loan pool for general student use. So I have a question for Rachel. So, Rachel, if a student finds a resource in heritage in one of the three heritage resources sites, if it's not digitized, can heritage resources scan or take a photo and get that information to students? Yeah, so we are doing some limited scanning of resources. I say limited just because one little research question can uncover a whole bunch of materials but we can work with you to figure out exactly what you need and to get the material scanned to you. It won't be an immediate turnaround but we can definitely do that for you. I have another question for Pipa. Pipa, on the research writing studio slide there was a mention of the studio partners. What are studio partners and how would a student get connected with one? Yeah, so studio partners, so normally in the studio we function on a primarily like a drop-in basis because it's really flexible. People can come and stay as long as they want or as short as they want and ask a quick question or just keep working for a long time. So we created the different studio partners for people who want to work one-on-one with someone for longer amounts of time throughout the quarter so that you can really get to know someone and focus together on whatever it is that you're trying to tackle. So a lot of times students will sign up for a studio partner if they are for example trying to develop their writing skills to pass like the standardized test for becoming a teacher for example or they might be trying to work really hard on an application to a major or tackle some challenge that they've been facing for a while. So that tends to be when studio partners can be really useful but there's no like requirements or anything so you can request one on our website even if you just would like to work focused with one person instead of multiple people. Yeah, I'm not sure if we want to like show the website or what but it's really easy to access you click on connect with us and then studio partner. I wanted to this is Elizabeth I wanted to follow up on that a second in addition to the studio partners we also have a library practicum called library 341 it's a practicum in academic literacies and it's where you can get some personalized help similar to the studio part the studio program except for this is where you have a learning plan that is really developed for your specific needs it's often designed around your specific classes so if you have classes that have a really strong or heavy research and writing component it's a really good program to sign up for class to sign up for it's one credit to kind of go along with your other classes so if you want something that's a little more structured than the studio then the studio partner that can work oftentimes people will sign up for a studio partner like halfway through the quarter because they realize they need some specific help and then they will sometimes migrate into the and then move into the the practicum because they realize they need something a little more structured so they often kind of go go hand in hand yeah thanks a little bit it's kind of like the informal formal version depending on what you want most at the time and what's the most flexible for you okay any other questions for our panelists from our panelists or from the attendees one other question that came up that we might want to that I think we should address is about student employment and I'm just going to give a quick overview normally the the library does employ a significant number of student employees I believe we still will be having some student employees in the upcoming fall quarter I don't know for sure how many all of our student jobs or student positions are advertised through the the student employment site so if you are looking for a job whether it's it's this quarter or next year the student employment site is is the place to go to look for student employment in the library thanks for that Elizabeth and I'll do a little plug to both the research trading studio and the tutoring center usually do our hiring in the spring for the following academic year and I will say that one of the things that we look for in our tutoring center future employees is whether you've been to the tutoring center before whether you've used our resources and you're familiar with them the tutoring center is definitely not a place like we're only struggling students go there's no stigma attached with it and there's you know sometimes you go when you're struggling but sometimes you go when you want to maintain you know a really good grade in a class and we really look for students who understand that struggling is a normal part of being a student and they get that and they're wanting to support other students who are going through that so yeah definitely look if you're interested in being a tutor or a study skills peer advisor look for us in the spring and consider dropping by and using our services so you're more familiar with what we do when you do apply I'll do a little plug for my area to I usually hire in the summer around July and we do post through student employment and the jobs I offer at the circulation desk so if you like customer service and helping people it'd be a perfect place for you but on the flip side to that if you hate talking to people and want to be in the stacks all day I also manage the what we call the return room students where you can just shelve books and tell your heart's content and not talk to a single soul so yeah I hire in July and hopefully I'll be hiring again whenever the buildings open up okay well I'll jump on this wagon to you can I just say ditto from the STC I mean we pretty much say the same thing the only difference is we're currently hiring our application actually closes at the end of this week so if students are are interested in working for the STC obviously remotely please put in your application and yeah bonus points if you've actually been to the STC and know our mission and you know know what we do the other thing that I want to throw out is kind of a misnomer like the STC you do not have to be a geek to work with us we hire across the board we have everybody from performing arts majors to CS majors to CBE folks like we take everybody because we want genuinely people who want to help other people because we see people when they're the most stressed out which is right after they've gone to the hack or research and writing studio and have a draft of their paper with all of the resources the libraries provide you and clippy eats your homework so you know we have to deal more specifically with the human side of technology before we get to the tech side so if that's an interest of you do apply to the STC so that's my shameless plug okay so lots of opportunities to possibly work in the library the STC if you're interested so definitely check those out keep your eye out okay so if there are no other questions which I'm sure there are tons of questions I'm going to go ahead and stop the recording and we'll make sure that this is up and available on YouTube with all the links that you might need and thanks again to all of our fabulous panelists you were wonderful and thanks for all this great information can I say one more thing of course just one more thing I want to add I always like to end with just something fairly simple and that's that every single person that works in the library whether you can see them or not is here because they want to see you see you as students succeed and so please don't hesitate to contact us at any point when you need help whether it's the beginning whether it's at the end whether you're stressed out we are always going to be here to help you in some way shape or form kind of get through especially your first year and especially a very unusual quarter as we start moving into it so again please don't hesitate to contact us if you need help thank you okay


Before we got started today, so I'm going to come back to the learning objectives for today. I wanted to briefly talk about the motivation for PCA again, which we did yesterday. I think late in the afternoon to the requestions, when do you do PCA? Why are you doing this? Why are we? This is useful. And I'm here to tell you it is very useful. Okay, so here's a major application in human genomics. When you have a data set with people of different ethnicities, and I don't just mean people with different continental recent genetic ancestry, even fine-grain ancestry, like if you are doing population study from one of the Nordic countries or something like that, you are going to have biases because of recent, you know, sort of, because of the genetic structure being different between these populations. This phenomenon is called population stratification. And if you do not control for it, you are going to be reporting a genotype effect that may be related to the population of your cases versus controls. Okay, so what you're seeing here is a PC plot, PC1, PC2, for SNP data, right? So genetic polymorphisms. And this is sort of a sampling of global populations, right? So you've got individuals from Africa, recent sort of African ancestry, American ancestry, European and so forth. Okay, and this is PC1, and this is PC2. And you can see they're completely spread out, right? You can see all the yellow dots are kind of together, all the pink dots, purple dots, and these represent different populations. What happened if I, you know, wanted to do sort of a disease study for whatever my disease of interest is? And I don't control for this, right? So there's a slight difference. My cases have slightly more American, you know, people of American ancestry, and my controls slightly have people of Asian ancestry. I'm going to be reporting population differences, not disease differences. So it is very common in genetic studies to take, you know, the first 10 principle components and add them in your model. So that model we talked about yesterday where you say, you know, whatever disease is a function of SNP or vice versa, you add multiple models for 10 principle components. The plot on the bottom is actually showing you the PCA for just individuals from, you know, the Han population in China. And even there, you can see that, you know, individuals from sort of different regions seem to cluster together in the PC plot. So this is one example.  Okay. Yeah. Yeah. Is that, I guess, kind of from like, I remember like, So yes, they are low, but how low is your signal compared to that? So it depends on, you know, what, what you're looking for. So I would take the same data, and I would color code the sample. And I would color code the sample. Suppose you're looking at effective some environmental perturbation, right, and you're like the people exposed to air pollution versus people not just say I've got air pollution on the money these days. So, so if you color coded them right, where would they, what would they look like, would they be mixed in here. And, you know, is that going to swamp your signal or not, right. So that's, I would make a judgment about the relative magnitude of the signal you're looking for. And these, I can tell you population stratification, you want to just really, really control for it. In practice, you might want to run your model with those terms and without those terms and see if your effect is robust to that. So that's another thing. Even though it explains 0.2% or whatever, there is structure there. They're not, you know, yes, that number is small, but look at the look at the clusters, right, they're separating, they're separating out. And so if you have a very slight bias, just because of the nature of data collection, you have a slight bias, your controls tend to be slightly more from the south, and your cases tend to be slightly more from the north, then is that going to influence your results.  Here's another example where we use PCA. Okay, this is a case control study. We were looking for sort of biomarkers in the DNA methylation layer in schizophrenia and bipolar disorder from postmortem brain samples. Okay. And so what you're looking at is the PC plots of DNA methylation data from a microarray, and each of those points is a sample, okay, and each of them has a long text because the sample ID is being plotted there instead of circles the way we did yesterday. Okay, and so what you can see is this is principle component one, principle component two, principle component three, right, and you can see there is a separation there's like two blocks here. And, and, you know, here we've color coded them based on which microarray slide they were on, whether they're case control status, whether they're male or female. Oh, look what's happening here with the PC to right. And what tissue bank we got the samples from. And, and you use this sort of as, you know, and then notice there's just like one sample. That's kind of sticking out. Right. So, you know, the thing that I'm not mentioning here is that these samples were either obtained or, you know, we took the brain tissue and we separated into neuronal cells and non neuronal cells. And so the first principle component showed that this one outlier sample was mislabeled as being a neuronal sample and it was actually a non neuronal and the PC plot picked up on that right. Males and females that gets mislabeled as well. You pick up on that right duplicate samples, you can pick up on that as well because you're like sample a has perfect correlation with sample be, and then you look into it and this happens. This happens a lot more often than you think so these tools are important to make sure your data are what you think they are, and then the inform you additionally about what not you know variables you need to build into the model. So, in addition to methylation we did snip arrays on these samples, and we took the first three principle components, and we built that into our methylation model. And this is how you use PCA, and this is you use it for data exploration, and you use it to kind of find the extra terms that you need to build into your model.  Okay, that's a motivation. And that's what your model looks like for example right at DNA methylation is a function of disease, and these three genetic components post mortem interval to vert tissue harvesting etc etc model grows and your sample size stays the same. And today we're going to talk about generalized linear models. This is an extension of linear models so you do you folks cover linear models in the intro to our course. Okay. So, so linear models are used for when you are trying to fit, you know, to continuous valued variables, and, and, you know, and linear regression seems to make sense. If you are, you would use the LM function. And I'm going to go over this notation for models. You know, but here you've got data that I've simulated, you know, why versus X, and the noise, which is this variation, which is always there in real world data there's always going to be noise. And the assumption is that this noise is sort of got a normal distribution like a belt distribution about each point on the line. Okay. But sometimes you have data where, you know, you've got a binary outcome, like survived or not survived has diabetes does not have diabetes. Right, and you've got some continuous valued exploratory variable. So if you try fitting a line to this, it's probably not going to be the best way to explain these data. Rather, you're looking to fit some kind of a step function, right, which has got an S shape. So this is called a sigmoid sigmoid is like S like, and, and at some point, you know, there's sort of gradual switch from the off position to the on position.  Right. So when you want to fit some other kind of shape. You know, then you don't necessarily need to reach out for a linear reach out for a linear model. So this is how it goes. We talk about linear models, because they're very, very simple, well defined, and they actually fit the data well in a number of cases, but you cannot take a linear model and apply to all kinds of data. Right. And so you've got linear models. You've got a broader class of models called generalized linear models, which means that the data are not, you know, linear. But if you apply a transform for them, you can make them linear. And then you have a third category called non linear. When I say you can make them linear, I mean, you can make them fit the assumptions of a linear model. So, you know, why are we introducing this here, it's because it's a very common experimental design. We have binary outcomes and we have continuous value values that were exploratory variables, right. So for this, we tend to fit, you know, what's called a logistic regression. And in our, instead of saying LM, you use another function GLM for generalized linear model. And in this case, you tell it what flavor of generalized linear model you're using. And for this particular scenario, the binary. Yes, no, it's a it's a coin flip model, right. So, the more the increase in exploratory, explanatory variables, the higher the chance that the coin is going to come up heads. So we say it's a binomial family of GLM. Another very common one you're going to see in genomics is for count based data, such as that from next generation sequencer, right RNA sequencing what we generate is counts. And then we want to compare the counts of all the genes between groups and B. So for that, you need to use a different flavor model called a negative binomial model. You don't need to know all the math. The key thing is that the nature of your data informs the model choice, and you cannot fit a line for everything. So different kinds of generalized linear models are this logistic regression formula and this negative binomial. Okay. So model selection must be data driven. A bit of a notation for model fitting in our. Okay, so, for example, if we want to say, you know, we want to, we want to model income as a function of percent literacy. And we say, oh, we think this is going to fit a line. Then you use LM, and you say, you know, my why value my response variable, and then you use this tilde, you know, as a function of this explanatory variable, we don't use this intercept term are kind of understands that it's going to fit an intercept. And then we say, use this table and fit this line. The Y is income, and the X is percent literacy. Yes, that's just the notation. When you have something like a logistic regression model, where you got a response variable here diabetes yes no, as a function of blood glucose levels and say pregnancy status. And now we said this is a generalized linear model. We're going to use GLM, but the notation is similar. Why tilde and the explanatory variables. We don't have to put in these beta terms, these coefficients, because our just does that for you. And then you give it the data as before. And because GLM lets you fit different flavors of generalized linear models, you need to specifically say, for this case, I want you to use the binomial family equals binomial. So that's how it works. Okay. So now we are going to go to the online example. And just as we did yesterday with the dimensionality reduction class, we're going to follow along with the work examples, and everything is just going to work.


You know what I mean? Listen bro. That's my hat, man. Oh, god damn, we can't beat this nigga here.  These motherfuckers hiding the cable bill.


Practice makes perfect. So the more you exercise, the better you are when it comes to execution. And training as you fight is something that we always do. So going overseas and pretending to do what we would do in the real world definitely helps when you go to do your actual mission. Swift Response 21 is a multinational exercise that's taking place with our allied partner. From getting here to on-ground Romania, we had to pick up our equipment coming off the aircraft and then we had to set up our trucks, set up our computers, making sure that we had sufficient power so we were able to plug our computers in and talk to our partners. We're just making sure that we can deploy safely in a COVID environment and do our job across seas with our allied partners. Our experience working with partners has been great. Our partners in peace in NATO countries have phenomenal team players. They're very professional. They're friendly. We love working with them. My favorite part about doing missions like this is actually being able to travel the world. When I joined the Army, that was what I wanted to do. And so now we're actually able to do that and I get to see other countries, how they work and how to do my job in those countries.


Please, let's welcome Sirov Shatizy for his seminar presentation. OK, so thanks to the organizers for the invitation to his very nice workshop. So I'm going to talk about a method for lower bounds on fluctuations of random variables. So as we know, there are many ways of getting upper bound and fluctuations. So this is this broad field of concentration inequalities and variance bounds. But as I realized, well, thinking about a question that Yuval Peres asked me, and which is part of the talk, actually, that there are very few methods for lower bounds. So in fact, when I was thinking, I figured that the only ones I know are the following. So first, you can try to prove some kind of distributional convergence, a central limit theorem. That's great if you can do that. Then you have upper and lower bounds matching everything that you want. If you cannot do that, then you prove a lower bound on the variance. So there are some techniques for getting lower bounds on the variance. But you have to also prove a matching upper bound on some higher moment to apply this second moment method. So just a lower bound on the variance doesn't tell you that the fluctuations are of that order. There is a coupling method due to Swanti Jansson, which I didn't know. After I wrote my pre-print, I sent it to Mike Steele, who told me about this. So Swanti Jansson has an idea, has a lemma which he used with Bella Bollebach to prove a lower bound on the fluctuations of the longest increasing subsequence before everything was known about it. So there is a method. And then there are problem-specific methods. So there are various papers that have been written. And so you get a survey of all of these in my pre-print, which is on archive now. However, as I was thinking about this question that you've all asked me, I realized that there are many other open questions. That's not the only one. And there are many modern problems where none of these methods work. So I tried in various things that didn't work. I'll tell you about a new method with applications to the following things, first passage per collision, then traveling salesman and minimum matching, and the random assignment problem, some spin glasses, and finally, for this workshop, a little bit of application to random matrices. So first, what is meant by a lower bound on the order of fluctuations? If a lower bound on the variance doesn't tell you, then what does? And the most sensible way to talk about lower bound on fluctuations is through this notion of levy concentration functions. So if you have a random variable x, its levy concentration functions defined as follows. f of some number h is a probability that x belongs to an interval of length h. And you take supreme overall all intervals. That's the levy concentration function. And we'll say that a sequence of random variables xn has fluctuations of order at least delta n. So here's a sequence. Delta n is another sequence. If there is some positive constant so that the limsup of fnc delta n is strictly less than 1. So otherwise, you can find a sequence of intervals of length of order delta n so that the random variable, or actually the low of delta n so that the random variable belongs to these intervals with probability tending to 1. So the fluctuations are much smaller than delta n. So this is the notion, this is the sense in which I define the notion that a sequence of random variables has fluctuations of order at least delta n if this happens. Any questions about this? All right, so now that we have fixed one notion of a sensible notion of fluctuations of random variables, here is the main lemma. And the proof is very simple. So I'll show it in one slide. The lemma is a following. Suppose x and y are two random variables defined on the same probability space. Then for any interval a, b, the chance that x belongs to a, b is bounded by half times this 1 plus the chance that x minus y is less than b minus a plus the total variation distance between the law of x and the law of y. So the idea is that you want to show that probability x belongs to an interval i is uniformly bounded away from 1 for all intervals of length bounded by some delta. If you want to show that, you construct another random variable y so that the total variation distance between the law of x and the law of y is small. And x minus y is at least delta apart. If you can do these two things, and here small doesn't mean going to 0. Small just means that this sum has to be less than 1 so that this whole thing is bounded away from 1. So to show that a random variable x is fluctuations of a certain order, you just have to construct another random variable y on the same probability space so that the total variation distance between the laws of these two random variables is small. But they are far apart. They are apart by at least delta with some substantial chance. That's all you have to do. So as I mentioned, there's this coupling technique due to Swanty Janssen. And there's a similar approach, but in Janssen's lemma, he takes y so that the law of x and the law of y are exactly the same. And this lemma somehow gives you much more flexibility, as we'll see. Why do I have the total variation distance instead of something else like the barrier scene, the Kolmogorov distance or something like that? There are specific reasons. There is a distinct advantage of using the total variation distance. So we'll talk about that. Any questions about the statement of the lemma? So as I said, the proof is very simple. You take any interval, a, b, call it i. Then one is bigger than or equal to the chance that x belongs to i or y belongs to i, which by inclusion-exclusion, you have this. Now, the probability that y belongs to i is at least the probability x belongs to i minus the total variation distance. So in case there are some students here who don't know what's the total variation distance, if you have two probability measures, mu and nu, the total variation distance is the following. You take any event a, mu a minus nu a, take the difference of the probability of a under mu minus the probability of a under nu. And absolute value takes a premium over all events a. That's the total variation distance between two probability measures. So from that definition, it's clear that this is the case. And also, this intersection probability is bounded above by the chance that x minus y is less than the length of this interval. Because if they are both in this interval, the difference is bounded by the length of the interval. So if you substitute these two inequalities in here, you get this, which is just what I wrote down in the previous slide. Yeah, yeah, so Kolmogorov distance would be fine, too. But there is a reason why I'm using total variation. So we'll see. Yeah, you could have substituted total variation with Kolmogov distance. That would be fine, too. OK. So here, let's see a quick example, very quickly, before going into any kind of complexity. Suppose you have x1 to xn iid Bernoulli, half random variables, an essence of sum. We all know it has fluctuations of order square root n. Can we get a lower bound using this method? So what you do is the following. You define xi prime to be equal to xi with probability 1 minus alpha times 1 over root n, where alpha will be chosen later on. And xi prime to be exactly 1 with probability alpha times 1 over root n. So xi prime is either xi or it's 1. So for a small fraction, for a 1 over root n fraction, you kind of set it to be equal to 1 randomly. Now, the nice thing about the total variation distance, so sn prime is the sum of these xi primes, the nice thing about the total variation distance is that it has this projection property. So the law of sn, the law of sn prime are complicated objects. You know, you need the central limit term to understand those, or at least the binomial theorem. But since these are functions of these random vectors, you can bound it above by the total variation distance between the laws of these two random vectors. And that's much easier to compute. These two probability measures can be explicitly written down. And there's a formula for the total variation distance between probability measures in terms of differences of probabilities. And you sum them up over all atoms. And you can compute. So this xi prime is different from xi at roughly root n places. But still, the nice thing, and we'll see the reason why this is true. So this isn't exact computations. This is just a little bit of analysis. You write down the whole thing. You do a little bit of analysis. And you just have to use Chebyshev's inequality nothing more to do this upper bound. But this upper bound doesn't depend on n. It's just some universal constant times alpha. Where this alpha was this alpha here. So if you do this computation, you don't do it now. But if you do this computation, you'll see that this is bounded by constant times alpha. On the other hand, you see what's happening between sn prime and sn. So sn was sum of x1 to xn. Now you chose roughly root n of these xi's. And you set them to be equal to 1. Now when you're setting them to be equal to 1, some of them, half of them are already 1. But the other half are 0. So you are increasing by root n. So you're increasing sn by root n when you're going from sn to sn prime. So sn prime minus sn is of order root n. Because you're increasing them in this artificial manner. So therefore, by this lemma for any interval of width less than root n times alpha, the chance that sn belongs twice bounded by half times 1 plus this total variation distance plus this probability. And this probability, we know that it's going to 0. C2 was chosen in this manner. So if alpha is chosen small enough, this is uniformly bounded away from 0, from 1. So choosing alpha small enough, this right side can be made uniformly bounded away from 1. And this shows that sn is fluctuation of order at least root n. The only thing I didn't show you is this calculation. But we'll see how to do that in greater generality, this kind of total variation calculation. Any questions? OK. This is the basic example just to give you an idea of how this is done. So you construct something which is substantially away from your original thing, but yet it is done in such a manner that the total variation distance is not too much. It's kind of small. OK. So let us now see how to get this optimal lower bound and the fluctuations of the length of the optimal tour in the traveling salesman problem. So this is a much harder example. And we'll slowly go through the steps. So the traveling salesman problem, again, if somebody here doesn't know, so you have the stochastic traveling salesman problem. You have n random points on the plane according to some distribution, i.e. points. And you want to find a tour through these points. So there's a salesman who is traveling to all of these cities. And he has to have a tour where he ends at where he started from and has to minimize the total distance traveled. So that's the length of the optimal tour. And then you ask about the fluctuations of that. So this can be in two dimensions. It can also be in D dimensions. So there are a few steps to this. And these are systematic steps. So we'll see how whatever I'm outlining carries over to many other problems. It's not just for this one. The first thing is this Hellinger affinity. Let mu and mu prime be two probability measures in the same space with densities f and g with respect to some probability measure mu. And of course, mu can be mu plus mu prime over 2. So you can always find a probability measure with respect to which these are both absolutely continuous. So suppose these have two densities. Then the Hellinger affinity between mu and mu prime is defined as the integral of square root fg d nu. And by Cauchy-Schwarz, this is bounded between 0 and 1. And the closer it is to 1, the closer these two measures are, mu and mu prime. And one can show that this quantity doesn't depend on the choice of this measure mu. So this is independent of that. That's called the Hellinger affinity. Now, why is this useful? Suppose you have measures mu 1 to mu n, mu 1 prime to mu n prime. And you take these two product measures. Mu is mu 1 cross up to mu n. Mu prime is mu 1 prime cross up to mu prime. Then this bound is very well known to statisticians. It has been used very effectively in theoretical statistics. The total variation distance between probability measures, these product probability measures, which are complicated objects, can be bounded by something which is a much simpler object. So you take these individual mu i and mu i prime, take the Hellinger affinity between them, squared them, take the product, 1 minus that. The square root is a bound on the total variation distance between mu and mu prime. It's very easy. It's just Cauchy-Schwarz. But it's slightly tricky. You have to carry out the argument. But the nice thing about using the Hellinger affinity is that it allows you to get bounds on total variation distance based on simple computations that you can do for the individual measures. So this is one of the reasons why I'm using total variation. Now let x be a d-dimensional random vector with probability density function e to the minus vx on either rd or on the positive orton, 0 infinity to the d. And suppose v is a smooth function satisfying some mild growth conditions, which allows x to be a Gaussian or exponential random variable or many other things, but not uniform. So uniform, if you have uniform on an interval, v has to be infinity at some points. And that is not allowed. And take some epsilon and let y be x over 1 plus epsilon.   So you take the law of x and the law of y. So you take this x is a random vector. y is a scaling of x by 1 plus epsilon. And when you do the computation of the Hellinger affinity, you can write down, so this is the density of y, this is the density of x. You can write these things down, do a Taylor expansion while you have to justify all the steps, of course, but I'm showing this roughly. You do a first order Taylor expansion, you get 1 plus epsilon d over 2. And here you get this, expanding this, you get 1 minus epsilon over 2, something. And then you just apply integration by parts and, kind of like magic, the epsilon terms goes away. So the Hellinger affinity is at least 1 minus c times epsilon squared. And that's very important somehow. So when you take a random vector, d-dimensional random vector with a smooth density, and you do this scaling by 1 plus epsilon and take the Hellinger affinity between the laws of the two things, it's bounded below by 1 minus constant times epsilon squared, not epsilon. This is not true if, for instance, x was uniformly distributed in a cube. Then this is no longer true. It's the smooth density that matters over here. And then from this, now it's very easy to derive. Suppose x1 to xn are iid with density satisfying some conditions as above, and yi's are scalings of epsilon by 1 plus epsilon i. The derivation distance between the laws of these two random vectors is bounded by c times square root of summation epsilon i squared. And this is what allows you to get what you want. So somehow the same thing was at playing the Bernoulli example also. So there epsilon was 1 over root n. It was not smooth. It was a somewhat different setup. But epsilon was 1 over root n. So it is 1 over root n perturbation of the original Bernoulli. But the 1 over root n gets squared. And that's why when it's summed from 1 to n, you get something that doesn't depend on n anymore. So that's kind of what mattered. If you compute the Hellinger affinity between xi and xi prime in that example, and you applied this lemma, then you would get this result. Any questions about this? So now you have this. So you have the x1 to xn points in Rd. You have a slight scaling of those things. And you're total variation distance bound. OK. So now a general class of geometric optimization problems. So suppose you have a function which takes in n d-dimensional vectors and outputs a real number. And it has this homogeneity property. It's a homogeneous function. So if you take fn of lambda x1 to lambda xn, it becomes lambda to the R. So R is some fixed number times fn of x1 to xn. And a surprising number of very complicated functions can put into this framework. So for instance, if you take the length of the optimal traveling salesman path, it satisfies this with r equals 1. So if you take all these points and just scale them down a little, it's the original length times that scaling. And similarly, the minimum matching and the volume of convex hull and all kinds of things have this property. So let xi be these random vectors. And ln be this function. And what's the general lower bound on the order of fluctuations of ln? So here is a theorem. Let Tn be a sequence of constants so that lim in for probability ln bigger than Tn is positive. So Tn is somehow a lower bound on the size of ln. So Tn is a sequence of constants, so the chance that ln is bigger than Tn is not going to zero through any subsequence. So the lim in phase positive. Then ln has fluctuations of order n to the minus half times Tn. So roughly speaking, in all of these problems which have this homogeneity property that I wrote down here, the fluctuations are of order at least one over root n times the size of the object. So the fluctuation of the traveling salesman would be at least one over root n times the length of the traveling salesman path. The fluctuation of minimum matching would be at least one over root n times the length of the minimum matching. The question is whether this gives your sensible answer. That's the question. So it gives a lower bound by this machinery. Well, just a word about the proof, it's very simple. It's using the lemma. So you take the original points x1 to xn. You scale them down by 1 plus alpha over root n. So just a little bit of scaling. And then ln prime, due to the homogeneity property, ln prime, the new optimal length is just the scaling of the original length. And if ln is at least Tn, then you get a lower bound of the difference between ln and ln prime, which is like one over root n times Tn. On the other hand, by the proposition that we proved, the total variation distance between the two laws is bounded by some constant times alpha. It does depend on n. So it can be made small by choosing alpha small. And then you apply just the lemma. So if you take any interval of length, 1 over root n times Tn, this lemma will tell you that choosing alpha small enough, the probability is uniformly bounded away from 1. So the proof is very simple. Once you're given this whole thing, first of all, this lemma. And secondly, this total variation bound using the Hellinger affinity, it's just a few lines. Any questions about this proof? So just to recap, we have these IID points in RD. We have some function which has this homogeneity property. Let's say, if you scale all the points by lambda, then the result will also be scaled by lambda. It can be a very complicated function. And then this argument says that the fluctuations of the output are, at least, of order 1 over root n times the size of the output. So let's see what this gives. So suppose the length is either the length of the optimal traveling salesman path or ln is the length of the minimum matching either of these two. In both cases, the size of ln is of order into the 1 minus 1 over d. And the reason is very simple. It is a well-known result. It's because the nearest neighbor distance in d dimensions is n to the minus 1 over d. And both of these things are lower bounded, at least, by the sum of nearest neighbor distances times some constant. So that's why you get n to the 1 minus 1 over d. So you can take Tn to be n to the 1 minus 1 over d. So the theorem says that the fluctuations of order at least n to the minus half times n to the 1 minus 1 over d, which gives you this. And it is known that, at least for densities with compact support, which unfortunately doesn't include this unbounded densities, this is the right order. So surprisingly, unbounded densities, there are, I didn't see any results in a yaster round and I couldn't find anything. But presumably, if the densities are falling off fast enough, then you can apply this kind of technique and you can get the same rate. So this seemingly, I don't know if I should call it crude, but this technique ends up giving it to this result, which seems like the right result, is n to the d minus 2 over 2d. So I have not seen. So this is actually, I think it's an open problem. It's an open problem because if you just want to apply a Frankenstein kind of bounds directly, you would get infinities. So there is something. Otherwise, I would have just done it. So the only previous result I know is due to once a re, who proved this order 1. So in dimension 2, it's order 1. You see d minus 2 is 0. Re-proof the order 1 lower bound for traveling cell spend through uniformly distributed points at unit square. And just for completeness, I generalize this to d dimensions for uniformly distributed points. It requires a different coupling, this kind of very simple coupling that I showed it won't work. For minimum matching on a compact set, I think the question of the lower bound is open. So I'll mention it again in the list of open problems. OK. So now I'll not show you any more proofs. I'll just show some results that I have in this paper. So this is the problem that motivated this whole research, this question that you've well asked. It's about two-dimensional first passage percolation. So if you're not familiar with the model, so you have each nearest neighbor edge in the two-dimensional lattice is assigned a random weight. The weights are non-negative in IID. And the weight of a path is the sum of the edge weights along the path. And the first passage time from x to y, from vertex x to vertex y, is the minimum weight overall paths from x to y. So you take all paths. Each path is a weight. Minimize overall paths. And that's the first passage time, dxy. So is the model clear to everybody? The question is, one of the main questions in this area is, what is the order of fluctuations of dxy, depending on this distance between x and y, in particular, if the distance becomes bigger, goes to infinity, what's the order of fluctuations? And we know very little about that, although a lot of work has been done, a very deep work has been done. So the best known upper bound is the distance divided by the log of the distance square root, best known upper bound on the order of fluctuations. And this comes as a result of works of various authors. So Kestin proved it without the log. Benjamin Kalari and Schramm proved it with the log for binary weights. And these were extended later to much more general class of weights by these other authors. The lower bound, on the other hand, is in much worse shape. So Newman and Pisa showed that the variance of dxy is bounded below by some constant times log of the distance. However, this does not prove, so this is the question that you've all asked me, so this does not prove a lower bound on the order of fluctuations, because the upper bound doesn't match. So just a lower bound on the variance you cannot use to say it has fluctuations of order at least square root of log of the distance. So Pemandl and Peres, they proved an actual lower bound. They actually showed these fluctuations of order square root log n. But only if the weights are exponentially distributed. And the memory less property of the exponential was crucially used in this proof. So it doesn't seem to extend beyond the exponential distribution. And then using the techniques of this paper that I just showed, you can actually show this, that for a large class of distributions, the fluctuations are actually of order at least square root log of the distance. You just have to take these original edge weights and you scale them, but the scaling depends now on the distance of the edge from the origin. So you have to cleverly choose the scaling, and then this result falls out of this technique. So more on first passage percolation. So first, any questions about this? Yeah, so the coupling is, OK, I can tell a little bit about the coupling. So you take a point at distance n from the origin, and you want to show that the first passage time from 0 to that point has fluctuations of order at least square root log n. So you take a ball of radius n over 2 around 0, and take each edge weight, call the edge weight WE. You replace WE by 1 W over 1 plus some factor, where this factor is 1 over the distance of the edge from the origin times square root log n. So you do an inhomogeneous perturbation. And with that perturbation, it turns out that total variation distance as before is bounded by something that doesn't depend on n, which you can make smaller, small by choosing a parameter small enough. And on the other hand, the first passage time has to decrease by at least square root log n. So this coupling gives you this. So somehow, this kind of coupling doesn't seem to work in dimensions higher than 2. So maybe there is some other more clever coupling that can work in three entire dimensions. I don't know. But so this is just a perturbative coupling. And then you use the rest of the things, the Hellinger affinity and all the other things. But the coupling is inhomogeneous. So the weights vary inversely as the distance of the edge from the origin. Here, the conjecture is in two dimensions, it's x minus y, the distance to the 1 third. That's the conjecture. Distance to the 1 third. And as I said, the best known upper bound is distance over the log of the distance, square root of that. And so even showing little low of that, Burgan told me he tried for a long time to prove little low of that. So that would be a big step to prove little low of n over log n with that, and many other people. So the next thing is shape fluctuations in first passive percolation. So let bt be the set of all vertices that can be reached by time t, all x so that t0, x is less than or equal to t. And there is a result. Following works by Richardson and various other people. There's a result of Cox and Durett where they show that there is a symmetric convex set b0 so that almost surely for every epsilon, bt over t, if you take this all points which can reach by time t, scale that set by 1 over t, well, you have to kind of fuzzy it a little bit to make it a subset of rd.  So there's a limit shape. So the shape of the region that can reach by time t approaches a limit if you scale it by t. So b0 is called the limit shape. And the fluctuations of this object, 1 over t, bt, are called shape fluctuations. And Newman and Pisa define this shape fluctuation exponent, which is naturally indicated by this theorem here. This is the smallest kappa so that bt is contained in t minus t to the kappa b0 and contained in t plus t to the kappa b0 for all large t almost surely. So the smallest kappa. So this gives a measure on how much this bt fluctuates from the predicted limit shape, this exponent. And it has been an open problem, actually, to show that this chi prime, this exponent is positive in any dimension. So this is the most natural thing we can define to understand the shape fluctuations. So what follows from these arguments is that in 2D first passage per collision, under some mild condition of the edgeway distributions, chi prime is at least 1 eighth. The main step is to show that there is a direction in which the first passage time to appoint a distance n as fluctuations of order at least n to the 1 eighth. And as I mentioned before, in this paper Newman and Pisa, they also did the same thing, but they've got a variance lower bound of order n to the 1 fourth in some direction. However, since it does not give an actual lower bound on the order of fluctuations, this cannot be used to get lower bound in chi prime. And it's conjectured, again, to answer Sylvia's question, it's conjectured that chi prime is 1 third in 2D mentions in 2D. OK. Yes. No, no, because it doesn't need an assumption because there is always the direction of curvature. So this is a fluctuation of the whole shape. So if there is a direction of curvature, that's sufficient to guarantee that the BT cannot be in a very thin band. OK.


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