Thank you everyone for joining us for the final Projects Exchange session. This is the second session for the platforms. My name is Kerry Leavitt. I think I've met most of you. I'm the Platforms Program Manager. So we'll get right into it. Our first presenter today is Bernie Pope. Kerry, do you want me to share my screen? Oh, sorry. Am I not sharing? Oh, sorry. I thought I was. Great. Thank you. So I'm going to be talking about the global technologies and standards for sharing human genomics research data. A short title is the Human Genomes Platform. And my name is Bernie Pope, and I work with the Australian Biocommments. And I'm also at the University of Melbourne. And you can see our partners. There are many partners in this project. I'm not actually going to list them all in the interest of time. You can see their icons there. Next slide, please. So the problem that we are solving is that there are tens of thousands of human genomes that have been sequenced in Australia to date. And this is predicted to grow rapidly in the next few years, tenfold by the year 2025. Global projections are that to estimate 50 million human genomes will be sequenced by the end of this year. Large cohorts are often needed for statistical power in research, especially in rare diseases and cancer. And this necessitates national and international data sharing because individual research groups rarely have sufficient cohorts on their own. And they need to share data with others. Current systems in Australia for storing, analysing, describing and sharing human genome data are bespoke in-house solutions. They have manual laborious systems for granting access to bona fide researchers to obtain the data and using their own analyses. And generally do not conform well to fair principles. Human genome sharing requires high levels of assurance around data access controls due to the sensitive nature of the data. Current inefficiencies are hampering research progress and reducing the value gained from nationally funded research genomics projects. Next slide please. So in this project, we propose a solution that we are describing as a services toolbox, which is based on emerging global standards. And it is comprised of five features. The first feature is a system for identifying virtual cohorts of genomes nationally. So this describes a method whereby individual research institutes can make available the metadata and data that they have in their genome cohorts. And we propose a mechanism to make that searchable by other researchers in the country across those cohorts together, virtual cohorts together. The second component is semi-automation of data access request approval. At the moment, data access requests are achieved through a data access committees which are located with institute data. These processes are generally quite laborious, manual and time consuming. And so we aim to introduce systems that will actually improve these processes and reduce the cost to people being involved. We are investigating as a third component authorization and authentication systems that are appropriate for human genome data sharing, and that address the sensitive data requirements. In the fourth component, we are looking to develop streamline methods for metadata and data upload to established international genome repositories. So this is where research data that is located in research institutes in Australia is then uploaded to international, standardly used international repositories for sharing in the world. And the fifth component is documentation and training. The outcomes and benefits of this and impact of this project are threefold. The first of those is that this project will vastly improve fairness of Australian human genome data. The second component is that genomic data from thousands of Australians will be shared securely and responsibly nationally and internationally, ensuring their full research value can be realised. And thirdly, the platform will provide a working template that any institution in Australia can adopt and deploy. Next slide, please. So how will we build this and what technical architecture are we using? So I'll start with the right-hand side, which is where possible we'll be adopting technologies that adhere to standards being established by the Global Alliance for Genomics and Health, otherwise known as GA4GH. The GA4GH is a policy framing and technical standards setting organisation. It seeks to enable responsible genome data sharing within a human rights framework. This consists of 600, actually more than 600 members across not more than 90 countries. And several of the partners involved in this project are members of the GA4GH. Across the actual sub parts of the project, we'll be deploying various technologies that have been developed nationally and internationally. These include the Gen3 system for data sharing and developing virtual cohorts. That was developed by the National Institutes of Health in the USA and also Vectis, a similar system that has been developed in House at Garvin. For data access approval automation, we'll be considering the resource entitlement management system known as REMS, which is developed by CSC, IT Centre for Science in Finland. Also, we'll be considering the data use oversight system called JUOS from the Broward Institute in the USA. For authentication and authorisation, we'll be considering passports and the authorisation and authentication infrastructure from the GA4GH. We'll also consider the Research Service RAZ from the NIH and lastly, CI Logon from the National Centre for Supercomputing Applications in the USA. Lastly, for the component of streamlining data upload to international repositories, we'll be considering to use the EMBL EBI European Genome Phenome Archive. Thank you for your time and that gives us you an overview of the project. Thanks very much, Bernie. Next, we have Tim Chatches. Thanks, Kerry. Excuse me. Yes, so the Australian Cancer Data Network is a project with many players. The three main players are the Cancer Alive and Queensland, the AusCat project at Liverpool Hospital, South-Western Sydney, local health district, and the Savard project also in the same place. We have partners in CSRO, University of Melbourne, University of Western Australia, and many others too numerous to note. And you know that we're missing a logo at the moment. We have a competition in progress and we expect to announce a winner in about three weeks. The next slide, please. So the problem is that we have so much clinical data these days, but so little of it is actually used for research. And as most of you probably know over the last decade or so, clinical information systems have largely, and very much belatedly, compared to other industries, replace paper-based medical records in many of the most healthcare settings, but particularly in cancer care. But despite the vast amount of really detailed clinical care and outcomes data that's now in the captured in those systems in machine-readable form, there's little use of those data for research purposes. The data is certainly being used for quality assurance purposes and healthcare management purposes, but for world-class research there's revenue little use. And the speed and extent of that use has really happened by lack of access to the data in analysable research already formed. The backend systems are vast, sprawling and complex and not something that most researchers can grapple with directly within the lifespan of an NHMRC or ARC-thundered project. And also, very importantly, research really needs to involve multiple sites and research results as opposed to quality assurance or health management results, which is based only on data from one site is almost certainly biased and irreducible and may actually do active harm to patients if it's used to inform treatment. So we need to really be able to use these data to answer questions such as determining the risk of cardiac toxicity for lung and breast cancer patients following radiotherapy and chemotherapy. And that question itself impacts to hundreds of some questions. What sort of variation is there in practising across patient cohorts and treatment modalities in Australia and internationally? We know that cancer care is protocol-driven, but there is a huge amount of variation as to what patients actually receive. And more technical issues such as can radio that is imaging MRI and CAT scan features extracted from imaging be used to help predict radiotherapy outcomes in specific cancer patients. Next slide, please. So what we're proposing to do is in this project, and this is really just a starting point, is to harmonise three leading Australian cancer data initiatives with each other and also with similar projects internationally. So the first and the initiator of the project is the Australian Computer Assisted Theranostics Network. Theranostics is a portmanteau of therapeutics and diagnostics. And they've been running for about 10 years at Liverpool Hospital led by Lois Holloway, who is the chief investigator on this project. Lois isn't presenting because she is ill at the moment. But they have established a platform for distributed machine learning across data drawn from quite a few different CATs and good information systems around Australia, which is completely interoperable with the EuroCAT initiative based in the Netherlands by drawing similar data from hospitals across Europe and a few in the US. And that's been running for about 10 years and they do machine learning on distributed data routinely. But it focuses very much on radioomics and radiotherapy aspects of cancer treatment. The second one, which is really the elephant in this project, is the Cancer Alliance of Queensland, which is a clinician-led consortium, but it operates the Queensland Cancer Registry on behalf of the Department of Pilth. It collects core data on every single cancer diagnosed in Queensland residents, as well as operating additional databases which links those data to lots of other core clinical, diagnostic and outcome databases. So it's a huge database which has been running since 2004. And finally, let me know that the newcomer is the Cancer Variation Sabah project, which I'm involved with, which is developing next generation machine learning power pipelines to streamline all of this extraction and loading from the source clinical systems directly into common data models, in particular the OBCOMOC common data model and its associated vocabularies. And while doing that, also developing oncology extensions to that model in conjunction with key players overseas. So the goal of all of this is to create a national resource which is interoperable internationally of research ready syntactically and semantically interoperable cancer data that works with both the OSCAD and NeuroCAT projects and also plugs into, operates with the very large OBCOMOC communities, which can not just cancer care, but all sorts of health care at international. And last slide, please. So how are we going to do this? So we're going to go to Scott Stader, but we have some fair ideas. In fact, we have a technical workshop in the fourth week of March, but basically we're trying to use open source software stacks everywhere. There's a lot of legacy software in some of the systems that may not be replaced, but everything new will be open source. Focusing on the usual suspects of Python for all the data wrangling, using things like SQL relational mapping, Metro language processing by the fabulous spacey library, which is written by an Australian SQL backend ignore stick. But very much the focus is on code sustainability because very easy to set up data extraction and transformation systems, which involve lots of different statements and a very, very hard and time consuming and labor intensive to maintain. So we're aiming to wherever possible to use both simple and somewhat advanced machine learning methods to transform the critical data into our target common data models. And that the reason for doing that is that enables the content matter experts, that is the clinician, data managers and so on, to participate in an ongoing fashion in the task of data transformation rather than having to engage an endless stream of contract programmers to write yet more how to maintain code. That's our aim, and we're making some progress on that already. And finally, we're very much focusing on making data analysis easy because common data models are great, but they do have a little secret, and that is that they can be hard for researchers to use, harder than just a usual data table. So we're developing open source libraries for both our and Python, which addresses that issue with respect to the cancer data, but we'll probably have use elsewhere. So I've already mentioned the very standards. We also get Euracat interoperability specifications for the streaming learning based on RBF triplets and sparkle queries and the common data model and vocabularies which subsume very large sets of standard vocabs so SNAMED CT, ICP, RxNorm, Loink and so on and so forth. So it's very much an international and a vocabulary set. And then finally, we're leveraging other ARVC further projects. So we'll be using the Euracat cloud host to secure remote access health data analysis environments that are being set up on a platform project that was funded last year by ARVC where we can actually pull the data and do collaborative analysis on it. We're working with the Cata project around fire safe governance, workflow, streamlining. All of this will be RAID enabled. I won't explain what RAID is, but it's another ARVC initiatives for identifying research projects. And then in the second phase of the Sander, which is another ARVC project to make better use of clinical trial data, we'll intend to participate in that. I think that's probably my time. Thanks very much, Jim. It's great to see all the linkages between the different projects. So now we have Anita Cannon. Thanks, Kerry. Is that better? Okay, sorry about that. Thank you, everyone. I'm Anita Cannon. I'm the Director for Research Platform Data Strategy at Monash University. First, I want to thank ARVC for co-investing and partnering with us on this project because it's a generalized commitment to data governance. And we've got several partners up there and thanks to all the partners for getting involved with this project as well. On to the next slide, please, Kerry. Thank you. Before I get into the problem itself, I want to quickly touch upon what data governance covers. Data governance itself is a term that includes the policies, roles, and responsibilities around data collection, data management, use, and data protection. And this is more important than ever for sensitive data. Now, in terms of the problems that we are trying to address here, data governance is critically important. But it's also quite resource-intensive and time-consuming. And it's critically important because there are there's a lot of shared risks between the researcher, the research project, and the institution. But it's a challenge to address at scale for an institution. And the scale is an issue from a few perspectives. One of them is the variety of data sources that provide data that support research projects from highly sensitive data sources. Collaboration across multi-institutional and multi-jurisdictional research projects can be challenging. And research infrastructure capacity for secure platforms can be a huge overhead. And finally, big data and sophisticated computation requirements for projects like AI and ML over genomics and imaging data sets can be challenging as well. So scale is definitely an issue on several levels. But what happens if we don't actually lower the barriers for data governance is that the data gets locked away in silos and research groups don't really make data fair. And without access to data, all research starts becoming significantly constrained. At the moment, there aren't many commercial solutions or national platforms that provide that secure trusted environment that uses existing institutional research infrastructure and building on infrastructure like the Nectar and the Research Cloud. So on to the next slide, I'll talk about what we are looking at doing. So this project is going to enable a partner institution to establish the secure e-research platform or SERP for short, which is a comprehensive platform that automates data governance in a way that can scale. It's a combination, in our experience, it's been a combination of technology and processes that reduces the burden of data governance on research groups and it also de-risks the institution, particularly given our obligations around data protection and data breaches. In fact, some of our key research users now tell us that they are able to sleep at night knowing that their data is protected from misuse and they've been managing this in quite a resource-intensive way now for many years now before we had access to SERP. So there are two parts to SERP. It's in that box within the dotted lines there. There's a data custodian component which provides data governance and management. It allows data to be brought in, data to be linked, allows data catalogs to be published and also data extracts to be shared very securely with research partners. Now for a research user, it's a second, the data analysis environment that is a remote environment which is configured with tools for analysis and that environment is also controlled, monitored and fully audited. So as a data custodian, they have full control over exactly what data goes into that analysis environment, what data is taken out and every action within that analysis environment is fully audited. There is potential to integrate with other platforms as well and this is something that we would love to explore further and see if we can enable collaborations particularly across jurisdictions and across projects nationally. We've got some key work packages that are going to be delivered as part of this project and I've highlighted the ones in blue there. The first one is the deployment of SERP for partners. The second is onboarding of research projects and the third is establishing a community of practice. The community of practice I think is going to be really useful to share best practices around data governance but also tools, techniques, templates, standards and the second diagram there talks about the impact it's not very clear but that's a pipeline of projects we hope to, we plan to onboard during the course of this ARDC program and across all the partners. And one of the things I want to highlight in that is the data coming in highlighted if you can see this when it's shared is this data says coming from university partners from government partners from industry and as well as health services and government departments. So we see this being useful for research across multiple domains. So this slide is really about I won't go into the details but SERP has been developed at Swansea University and it's the outcome of millions of dollars of millions of pounds of infrastructure investment for a decade. It is very mature and it has quite advanced capabilities. At Monash we've had a research collaboration with Swansea over the last two and a half years to adapt SERP for the Australian context particularly the Nectar Research Cloud and we've demonstrated that it can scale across the entire university. We've got over 400 users across domains, not just health but all kinds of sensitive data looking at using this platform and our partner Curtin University has also developed the link smart component that it's a linkage capability that exists in SERP so we hope to be able to adapt this to further to the Australian context and share that as a national capability. That's it for me, thank you. Great, thank you very much Anitha. Next we have Michael Hall. Hi, so I'm here to talk about the Australian text analytics platform so thanks to ARIDC for supporting our project. It's us at UQ working with people at the University of Sydney and Annette on this project. So the problem we're dealing with it's sort of a problem of connecting up the bits and getting people to use things that are already out there I would say is a very high level summary of it. So in many research disciplines humanities, social sciences, natural sciences we actually rely on text data of some sort so it could be spoken, written, signed, multimodal forms of language and research communication. And so examples of that could be something like we have language corpora and linguistics which are actually fairly structured but you have grey literature policy, government reports and social sciences. You have oral history interviews which are used in the humanities you have field notes which are used in all sorts of disciplines, geosciences environmental sciences and so on. And when people talk about this data it's often called unstructured data as a linguist I kind of rail against that description because actually it is structured but it's not structured in the way that a computer scientist would think. And so we have to kind of match up these different worlds of what we think is structure. But what we could say is across many of these disciplines researchers experience bottlenecks and text data processing getting text data sets into forms that they can work with in a computational environment and also with text data mining how do they get information out of it. There are lots of solutions out there so often I get links to this one of the issues that they're scattered across many different providers many of them are actually commercial or generic and so they're not readily adaptable by researchers necessarily but another kind of part of the issue is that amongst Australian researchers themselves there's this need for accessible training in text analytics so people might researchers might have an interest in it but they're just not sure where to start so there's kind of the idea to bring together users and providers so perhaps the next slide would be good. So our solution I suppose or the beginnings of a solution one shouldn't know the promise so the platform the idea is to bring together users and providers of text analytics by providers I mean or we mean researchers who are quite good at developing scripts for processing and text data mining and there's quite a few people working in the open access open source world who do this it's difficult for us to work with commercial providers in fact we can't because our commitment is to open science but there are a lot of people working who are providers and there's obviously a whole bunch of users how do you connect these people up so our aim is to develop this integrated collaborative cloud based environment we want to use integrated notebooks platforms for the actual processing and mining of text data so the idea is each notebook does a particular task and you string together a bunch of notebooks and different workflows when you're trying to solve a particular problem also I think importantly we want to be developing at the same time training resources and how to use text analytics I think from the very beginning if a whole range of people from different degrees of sort of skill and computational methods if they can't engage with it then we're not really doing our job so we're aiming for quite a wide scope of people we're not really aiming for the professional person working already working in this area they should be able to figure it out themselves actually so our aim here is that broader range of people in the humanities and social sciences and also going out into the natural sciences where there's folk working with text we're wanting to increase accessibility transparency so the way we describe our notebooks is it's like a car you get in and you drive it if you want to lift the hood and see how it's working you can do that if you'd rather just drive the car you can do that too so that's the transparency bit and also that the research you're doing can replicate this research so the idea is really to increase capacity amongst our researchers to use text analytics so the final slide it's actually fairly simple I noticed compared to everyone else's slides which is because we're actually aiming for a fairly simple technological environment it's really about transforming research by people getting to use these techniques we know the promise to them but they just aren't used enough by researchers at many disciplines so the technology is really just Jupyter notebooks which incorporate these open source scripts for cleaning transforming visualizing mining text data we have a data sandbox where researchers can import their own text data sets which remains secure there we'd also like to start working on how we might access national collections through AIF which we can do already in some cases and the last which is actually very simple technology there's a web based online training environment which connects in so the idea is people brought in through a web based training environment you're brought into this mysterious world of Jupiter notebooks let's say mysterious for lots of people in humanities and social sciences and so you kind of lead into it progressively and on the other side this is our kind of conceptual structure at this point thanks thanks very much Michael okay now we have Bill Pasco hi hello everyone I'm Bill Pasco from TLC map at the University of Newcastle on the system architect TLC map is a digital humanities platform for spatial temporal mapping problems yeah so one of the problems we have in humanities is that individual researchers often have very different and idiosyncratic projects and needs across disciplines and individuals and also that although in humanities we can use scientific and mathematical methods we're not limited to that and there's some pretty fundamental metaphysical and epistemological differences to STEM fields which I won't go into in only three minutes but because GIS tends to have a STEM focus or a commercial focus we often find that there's gaps in what we'd really like to do and what is possible to do so I mean you would normally find that because needs are idiosyncratic then you require a bespoke solution but that's really expensive and in humanities we don't have very big budgets so another issue is there tends to be a lack of cultural layers in data sources so for example national map if you go there there's lots of great information about science and various areas in science but there's not much culture and also if you go to Google you'll find lots of commercial layers but not so much in the way of culture and another issue is that in Australia there's a general lack of meaning of place compared to other countries anyway we grow up in homogenous suburbs and go to homogenous offices we don't really know much about the history of a place and its importance and that affects how we value things and how we understand our place in the world and it's kind of ironic that there's that situation since the idea of country and connection to it is so important in indigenous culture and so in trying to address that we do prioritise Aboriginal and Torres Strait Islander projects and First Nations so next slide solutions so these researchers need easy to use tools they usually don't have the time or inclination to learn a whole GIS system or to get deep into mathematics so if we could automate some basic common things that would probably have a great impact for humanities but there remains that problem of idiosyncratic needs it's hard to find things that are common so what we did the different types of digital mapping activity in humanities from natural language processing to virtual reality there's all kinds of different things that's not just putting dots on a map and try to identify what the next step would be in each area and then prioritise all that we don't want to build one thing that tries to do everything or to make a new GIS system and repeat functionality we try to add to or modify existing systems where possible and build new systems where there's a lack by looking at this as a software ecosystem we're able to let each system do what it does well at the same time as ensuring there's a wide range of functionality for different areas so that means we have to focus on interoperability and produce some relatively simple criteria for TLC map compliance so that you can a user can take data from one system process it in another system and then take it from there and put it in another system depending on what their needs are and you might go from text analytics all the way over to virtual reality for example and we also try to ensure that our development are practical solutions by using prototyping and ensuring we don't develop any platform that doesn't have a project as a proof of concept and to put it to a real world test and also make sure that any project we do that in such a way as the software can be reused for other similar projects so in terms of impact we hope that this means there's humanities issue temporal and that the genetic will benefit from being able to easily see and assess and appreciate that research and next slide so in terms of the technical architecture there's probably not too much that's strange or unexpected for people working in research at universities in software development MariaDB MySQL Postgres that sort of thing so probably the thing worth mentioning that are a little unusual are that we contribute some development to allow other systems that are not under our control to be interoperable and enhance some of their features rather than trying to do everything ourselves and well it's worth mentioning also that the strategy of working sort of an ecosystem approach does have the drawback of completely in that we have to learn and support so many different technologies and also I added people there just as a the machines that actually you do need to consider who's going to support that so at all Thanks Bill, sorry you're breaking up a bit so I'm just thinking you're finished Yeah, sorry I hope I just wasn't talking No, no it might be me the wifi can be a bit flaky in here even though I'm in the office Thanks very much Thanks, oops Okay, now we have Marisa Takahashi Hi Can you hear me? Yes, we can Hello everyone, Marisa Takahashi from Queensland University of Technology or QUT QUT is the project lead for this Australian Digital Observatory and our partners are the University of Melbourne University of New South Wales Queensland Cyber Infrastructure Foundation and Google Cloud I would like to thank ARDC for co-investing in this project Next slide please, Gary Okay, so in recent years researchers from both social and natural sciences have started to incorporate dynamic digital data into their research we define dynamic digital data as continuously streamed data from technical platforms such as social media platforms like Twitter and Facebook and gaming platforms such as stream or other continuously updated data over the worldwide web There are many challenges facing researchers who want to use this type of data. For instance data collection can be costly which is a big barrier for researchers with limited funds and those researchers who are less technically savvy face issues ranging from data preprocessing storage and extraction of the relevant dataset and even when they have their data they still face the issue of analyzing this type of data they may need support in the selection and the execution of appropriate data analytics tools and further challenges involve data governance which covers the ethics of using and sharing this data and finally we have researchers doing ad hoc collections and with this type of collections there is the issue of data quality and replicability of research to determine the demand for the type of service that we plan to offer in this platform we sought an expression of interest from researchers from various universities across Australia and we receive an overwhelming support for the establishment of this type of platform service as you can see from the user base list Next slide please Gary So to solve this challenge as mentioned our project aims to establish Australian digital observatory which will be a national platform providing data bank and data services to researchers seeking to work with dynamic digital data so the benefits gained from establishing an Australia wide platform are reasonable costs and availability of the datasets technical and analytical data services to researchers that's enabling them to focus on their research and incorporating dynamic digital data can provide new methods and insights that's enabling new forms of research there is also cost effectiveness that can be achieved by pooling resources across various universities and finally achieving a critical concentration of skills and expertise will enable us to establish a community of practice so these benefits will create impact by transforming and accelerating research project that use and analyze dynamic digital datasets another impact would be the creation of an interdisciplinary team of researchers and support staff at key locations in Australia who can provide transferable skill sets to support innovative projects across many research locations Next slide please So this is not the technical but rather a functional architecture of the Australian digital observatory as you can see there will be four components the data sources where we will be ingesting the dynamic dynamic digital data from the digital observatory platform that will be the back end technical implementation of the functions described there which then enables the front end portion consisting of the data bank and data services which we will then offer to the research communities so the data will be collected from various data sources as shown depending on the demand from the researchers data can be collected via APIs and web archiving again depending on the relevant terms of service we envision three distributed data nodes in Queensland New South Wales and Victoria accordingly the data bank will be distributed data banks at each of these nodes but we will operate with the harmonized data governance which will provide oversight on ethics and data sharing protocols so the rest the researchers can avail of the data services such as data engineering through to data analytics depending on their needs as interface to researchers there will be a formal process of project onboarding as well as designated access protocols of course training and support will also be provided to researchers and finally we will be designing and implementing a business model to ensure sustainability of platform and the current ARDC funding cycle thank you thank you very much Marisa and finally we have Tom Johnston how is this any better am I coming through or not yes I'm not actually seeing any share I guess you're restarting the yep to that that comes up on my screen no problem sorry I was muted that's why you couldn't hear me saying there you go these are the latest slides no problem thanks a lot I should mention to everybody this is my fault for getting the slides done so late so it certainly not carries anyway so I won't waste any time I'll get started just talking I'm Tom Johnston I'm a professor of cognitive neuroscience at Swinburne University and at Swinburne we're also a node of the national imaging facility and our focus at Swinburne really is on MEG and EEG data so that's magnetoencephalography data and electroencephalography data and related techniques using electrophysiology and the platform that we've established is really addressing the need across the electrophysiology EEG and MEG research communities for an advanced analysis platform or solution because currently there simply isn't one unlike many other domains of research now partly this probably reflects a bit of the history of EEG research which is where really things started the research groups themselves are very diverse they span industry and clinical settings within medical field outside of it there are researchers you know spanning from artificial intelligence engineering and looking at robotics and brain computer interfaces to many many researchers in fields in psychology such as social psychology, sports psychology and the challenge there of course is that their backgrounds or academic backgrounds their level of technical expertise and experience is vastly different many many of the researchers come from relatively small labs spread out across the country and they have limited access and experience with Linux systems with supercomputers and most of them most especially from the smaller psychology side of fields are locked into proprietary software that was made available provided with the hardware they used to acquire the data and whilst that worked okay in the early days of course that sort of proprietary software hasn't moved with the times it doesn't often encompass the most advanced techniques that are available for analysis and it certainly doesn't allow for very much interchange of data sharing of data, sharing of analysis pipelines and reproducibility is pretty awful because once somebody's software license goes out of date or the software they have a license for only runs on a Windows 95 computer and not even beyond that then there's absolutely no hope to actually reproduce the sorts of analysis that they've done and that's really the existing state in many many places really in stark contrast to that there is a lot of open source software that wasn't available 10 years ago that is now widely available for analysis of these types of data and it's rapidly expanding it's largely based on Python and various Python toolboxes it increasingly focuses on combining EEG, MEG, electrophysiology data with other types of data such as imaging data from MRI also peripheral measures of physiology that are commonly acquired and so really the challenge here is trying to address this need for a powerful open analysis platform that allows for reproducible and shareable analyses but one that is easy and accessible and portable that can be used by people in these small labs with very few technical resources if you like okay our approach really simplicity is underlying everything here everything has to be made simple for people to use we want a portable working environment that can be installed on somebody's own PC on a workstation in their lab on a virtual machine in the clouds and a Nectar virtual machine but also can run on a on a supercomputer giving them access or ability to scale their analyses from small data sets up to large data sets from simple analyses up to more complex ones we want to containerize the open source software that is available and we want to provide automated container building and sharing for new analytic pipeline so that when people develop a pipeline they don't have to worry about the technicalities of building containers using Docker or Singularity we want something that is far simpler than that more than anything else we want something they can install with basically one command on their computer and then they just launch into it and make it work and through this we hoping that we can foster the creation of far more findable structured data in EEG and MEG reproducible analysis pipelines which really lag behind for example neuroimaging and create a platform that is accessible by researchers from a wide, wide diversity of settings including regional universities and small labs with less technical staff we built in interoperability with other analysis platforms such as the Australian imaging service, the characterization virtual library, also Brain Life which is an effort that's been supported by the NIH in the United States based in Indiana and through this we hope that the analysis can be scaled up to address some major challenges because the data itself is extremely valuable in fields such as epilepsy stroke traumatic brain injury and dementia this is a little bit of the architectural diagram and you can see here what we're trying to do is cater for people who either operate the columns basically represent different types of analysis different types of analysis approaches so we have interactive processing in the middle column there where there's a requirement for low latency visualization of fairly complex data the data sets however might be quite small and this is the sort of thing that people can typically do on their own PC or on their own workstation in the lab but we also want to provide the ability to provide to have interactive processing and more computationally intensive small and large data sets and here we might need things such as GPU enabled virtual machines we also might we also want to integrate what we're doing with the characterization virtual lab which can sit on top of our performance computer system giving them all the warmth that that provides on the other side we also want to provide them an easy transition in the batch processing for computationally intensive and repetitive data set analysis and here's where we are integrating with the Australian imaging service but also BrainLife.io which is this US based platform and the vertical screen you see down the middle gives you some idea of our approach here and it starts off with a very lightweight Linux desktop which can be pretty much installed anywhere as I said with one command that's based upon an open platform architecture called NeuroDesk which has been developed for brain imaging and we're expanding into this to this domain of analysis and then we want an easy containerization system where people can check containers or download containers easily from the registry and know that those are going to function because they're running on the same basic platform as everybody else and with that I've swept through this very very quickly but hopefully that gives you a picture for what we're doing. You can see on the standards on the right there some of the standards we're doing the bids especially the brain imaging data set format has now a data structure format has been extended to electrophysiology, psychophysiology, MEG and EEG and that is built into our platform by default so all the pipelines that we're going to provide in containerized form will be compliant with bids which we think will be reproducible and open and accessible with the platform. Thank you very much. Thank you very much Tom and thank you to everyone who's presented today and thanks to all of you who have come along to hear about these fantastic platforms some really exciting projects here


Hey everyone, I'm Bianca Renee and you're watching Bianca Renee Today and today I'm reviewing some new hair products by Curl Keeper. You guys follow me on Snapchat or Instagram as you should. You know that I use Curl Keeper gel and their original all the time and I always get amazing curl results. So I was really excited when I found that they have new products and this product will help detangle our hair. Yes, one of the many curly hair struggles that we have to deal with is detangling and they knew that so they made the slip. This is literally the Curl Keeper slip. Slip is in the title and it's their 30 second detangler. So this baby right here is going to make our life a little bit easier. So let me show you exactly how to use the slip and how well it works. So here's me in the shower, post shampoo and post conditioner. So what I did, I rinsed out my conditioner and then I grabbed my Curl Keeper slip. So all you do is spray this onto your hair while it's soaking wet. I did one section at a time and then after you spray it all over your hair, you're going to let it sit for 30 seconds. So while you're waiting those 30 seconds, it's going to instantly detangle all those knots, lock in hair color and it's also going to be used as a lightweight leave and conditioner. Now as you guys may know, if you are a loyal subscriber, if you're not, you still can become one.  But I don't really use leave and conditioners because I feel like it kind of is an extra step that weighs down my hair and could probably give me product buildup. But the great thing about this spray is that it's very lightweight so it does not weigh down my hair at all. It does smell really good and it's also helping to tangle our hair at the same time. So after those 30 seconds, I then grabbed another new product from Curl Keeper. This is their Flexi Brush and as you can see, it's very interesting looking because there's no back to it, it's all hollow, which is great because if I do look at my other brushes, there's a lot of product buildup, gunk and bacteria that's just kind of living in there that I've been ignoring. But this one, it doesn't have a back for any product buildup, making it really easy to wash and this is also really good to detangle. The Curl Keeper Flexi Brush will make a weird kind of hollow sound when you brush. I don't know if you guys could hear this, but just because it's hollow, it might sound like you're ripping your hair out, but don't worry, you're not. It's actually helping with minimizing hair loss as you detangle. So when I detangled one side, this is the only amount of hair that I really lost, which is actually less than normal for me. So as you can see here, as I detangled, it was really easy to detangle your hair.  After I detangled my hair, I left it on, you do not rinse it out, and then I applied my styling product. And if you have a conditioner that really gives your hair good moisture, it smells really good, maybe it's just really cheap but it's not that good at detangling, this is something that you need to add to your routine to make detangling a lot easier. The Curl Keeper Slip comes in this new designed sleek blue bottle, has a really easy spray nozzle, it's 8 fluid ounces and is 1750. The Flexi Brush is also available on their website for $16. One of the best things about the Curl Keeper Grant in general is that none of their products leave any product build up. That's the only reason I'm able to have my curls last till day 4, 5 or 6 because my scalp isn't driving me crazy and I'm not itching all day because it doesn't leave any product residue. So as you can tell I am a very strong Curl Keeper advocate, I definitely recommend you guys try their products. This is another one you could try if you're someone that is struggling with detangling their hair and if you're looking for a brush that's not going to rip out all of your hair. These are the products that you should try, you can get both of them on FrizzOff.com, I'll make sure to put the link below in the description box so you guys can get it if you want to try it as well. And if you do, please leave me a comment, let me know how well it worked to detangle your hair. Before you go, I do want you to notice that I did recently hit 150,000 subscribers so thank you all so much for subscribing to my channel and coming back every week for makeup and curly hair videos. If you are new to my channel, make sure you join the family and click that subscribe button so you can get makeup reviews on Fridays and more curly hair product reviews on Sunday. I do have a giveaway coming up so make sure you follow me on Instagram, Snapchat and Twitter at MsBiancaRenae so you know what prizes I'm giving away. I hope to see you all next week. Thanks for watching BiancaRenae today.


What's up internet? A couple of months ago, TerraMaster sent us a NAS and we liked it a lot and still use it in the shop now. But that particular model was really overkill for what the average home user needs. So for this video, TerraMaster sent us another NAS, a 2-bay model which is much more in keeping with what the average customer would need. What's a NAS and why should you care? Basically, it's a big USB that's attached to your network. So for example, you download video files using your desktop, save it to the NAS and then you can access those video files through any device, TV, mobile phone, tablet that's attached to your network. Hard drive filling up with work files, photos, videos, dump all of them onto a NAS you can still access them anytime but it frees up storage on your local device. And since it's attached to the network, you can access the NAS through the internet so even when you're not at home, even when you're not connected to your home network you still have access to all of the files on the NAS. So a NAS is super handy to have, it's like having personal cloud storage but is it easy to set up? That's what we'll be tackling in today's video. This particular model of TerraMaster, is it dummy proof? And that includes me because it's the first time that I've installed the NAS. Is this the ideal model for beginners? I know you're excited to get on with the NAS but first things first when you buy a NAS you also need to buy the drives, the storage that you will install into the NAS regardless of brand that's industry practice, the drives are sold separately a little annoying but from the point of view of the manufacturers iba kasi yung gumagawa, iba yung mga brands nung mga NAS versus yung mga brands for storage and you do need to take a look on what drives are recommended for your particular NAS this isn't like RAM where usually most RAM can be stuck into most systems there are very clear models of storage whether hard drives or SSDs that you want to be using in particular NAS enclosures and storage brands have specific lines dedicated to being used in NAS so that's the iron wolf line for Seagate, the red line for WD and other manufacturers call them different things but they usually have a dedicated product line for use in NAS turning back to Terramaster, out of the box I would have liked printed instructions what you get is a QR code and it's a generic QR code butisana when you scan it you get sent to the instructions for your specific model but you just get sent to a generic page where you have to pick your model and it's not that easy to be honest to find out what model of NAS you have yes of course you bought it, you might be expected to know it but again if you're a super beginner all of these letters and numbers can very quickly blur into each other the Terramaster did come with some nice stickers and nice meaning they are useful because you can stick them on the drive to label your hard drives to make things more organized but the stickers themselves don't come with the model number and you have to actually look at the unit dun sa technical specifications on one side to find the model number again very easy for techies but if you're a beginner you might be sweating a little bit at this point again all of those letters and numbers can be confusing but once you get sorted out the instructions are useful straightforward the pictures make sense pull out the drive tray, install the hard drive or the SATA SSD, slide the tray back in you're pretty good although I had a little problem one of the rails wasn't on properly so medyo maingay nung pinasok ko yung drive tray into the NAS but everything worked out with a little pushing so again I am 100% a beginner in all of this also which is why I found the viewpoint of is it good for beginners very interesting one loophole not addressed in the instructions is where to plug in the NAS for techies again it's common sense that you would plug it into your router so that everything on the network can attach it all of the time but for beginners that's not immediately apparent and some people might plug it in to their computer into their desktop you could do that but that's not very useful when you turn off your desktop there goes a connection of the NAS to the network so a little more handholding would have been helpful even with this very basic step once everything is set up on the hardware and setting up the NAS itself is relatively straightforward there was some scary messages about incompatibility again depending on what drive you use and I did get one message saying that the NAS couldn't read my drive but I guess it sorted itself out because at the end of the installation process okay na siya I was asked to name the NAS and supposedly you can use that name in order to access it but that didn't work out with me provided IP address works just fine this is very familiar to anyone who has had to access their router and so again the theme if you're even a little bit technically inclined setting up the NAS is pretty straightforward if you're a complete beginner it's still doable but it takes a little courage once the NAS is set up the UI is also straightforward very similar to Windows or Apple you can create folders drop files in there are status bars on the transfer of files everything is intelligible if you've used a modern computer so overall this is very doable even for the most basic tech user yes there were some bumps along the way yes there was some knowledge that was assumed where it shouldn't have been assumed it could have been smoother but overall the NAS does pretty much work straight out of the box and if you're a beginner that wants to experiment with NAS is something you might be interested in even for the most basic level computer user the setup is doable with some courage and we'll probably do a future video on the cool things that you can do with the NAS for now I just wanted to give a general overview of the unit and see it from the point of view of a beginner starting out because a NAS is super useful even if you're not super techie thanks for watching saan may nagtatanong kumikilala ba kaming computer shop na trusted yung hindi kalolo ko hin actually meron kaming full service PC store ang hardware sugar nagbabenta kami ng PC components nagbabenta rin kami ng fully assembled rigs we clean computers kasama na rin yung excellent cable management namin and CPU cooler repasting sa cleaning we also clean and repaste GPUs na sa makati yung physical store namin and you can also buy from our site www.hwsugar.ph na 100% palaging up to date yung inventory dun kung instock yung item sa amin available yung sa site we also ship nationwide thanks for watching and maybe one of these days magkita tayo sa shop


OK, so then I start. Good afternoon. Well, we already saw each other this morning. So today, we essentially have the last lecture about rings, maybe not completely finished, but almost. And so we start out talking about Euclidean rings and principal ideal domains. There's some sort of marks on this, principal ideal domains. So last time, we had seen the division with rest for polynomials with coefficients in a field. And everybody knows the division with rest for integers. So Euclidean ring will be an integral domain where you have division with rest. So an integral domain, division with rest. So if we have an element a and b in this ring r, then we can write a is qb plus the rest r. And in a suitable sense, the rest should be smaller than b, than the thing we divide by. You like if you divide a number by another, the rest is smaller than the number you divide by. And so we have to find a way to measure this. And this is done by a certain function from r to z bigger than or equal to 0. So let me define it. So an integral domain r is called Euclidean ring. If we have the following, so if there's a function, which is what measures how big the rest is, d from r without 0 to, say, the negative integers. Such that the first thing is that we can write whenever I'm given elements a, b, and r, and can make division of a by b with rest. So I can write, so then there exists an element q in r, such that a is equal to qb plus r. And r should be, as I said, smaller than b. In a suitable sense, so that either r is equal to 0, or d of r, d of small r, is smaller than d of b. The second condition, which is somehow less important, says that this d is compatible with the multiplication. So the second condition is that if b is an element in r, which is not 0, and a is an element in r. So maybe like this. Then we have that d of a, b is bigger than d of a for all a in r without 0. That's the same statement, but it's different. So whenever you multiply, this d gets bigger. So if that's the thing which measures how big our element in r is, somehow the elements get bigger whenever I multiply by a non-zero element. Yeah, this must be true, because this would otherwise be, obviously, wrong, is not a unit. Thank you. Because obviously, otherwise, for instance, if b is equal to 1, then this can never be fulfilled, as you can see. Yeah, I copied it wrong. Anyways, clearly, it has to be that. So we have easy examples. So for instance, if we take z and we take d of a number n, is for instance equal to the absolute value of n. This is a Euclidean ring. And up to the convention of how you define, you want the sign of the rest. This gives you the usual division with rest. And also, we had seen that if k is a field, and so then kx with d of a polynomial f is equal to the degree of f, is a Euclidean ring. So this was essentially what we did the last time. Now, when we had the division with rest was precisely so that the degree of the rest is smaller than the degree of what we divide by. And in the second condition, it's also obvious, because a polynomial is a unit if and only if its degree is zero. And the degree of the product is the sum of the degrees. And I want at least one other that we do not know. We look at the z of E. So these are the set of all E, so n plus m i, complex numbers such that n and m are integers. So these are just, if you look at the complex plane, these are just the points which have coordinates integers. So this is obviously a subring of the complex numbers. i is the usual i, square root of minus 1. Then, and so we want to say that these are called the Gaussian integers. They claim it's a Euclidean ring with, well, if I take t of n plus i, which one do I want it? i m equal to n squared plus m squared. So we have to see why this is the case. Well, so this, for complex numbers, this is just the restriction to the Gaussian integers of the square of the complex absolute value of the complex number. So we can extend d to the whole of c by, obviously d of a plus i b, where a and b are real numbers, is equal to a squared plus b squared, which would be the square of the complex absolute value. As you have no doubt learned in the complex analysis. So in particular, we have that d of a plus i b is different from 0 if a plus i b is not the 0 in the complex numbers. And it is well known and easy to check for say z and w in c. We have that d of z times w is equal to d of z times d of w. You can immediately check this anyway from the formula if you remember the product of complex numbers and what you hopefully do. And so we have this, you can easily check this. So now we want to make our vision with rest. So let's say now z and w the elements in z of i. So this is whatever n1 plus m1, i, n2 plus m2, i. Anyway, it doesn't matter. So we take two elements. So we can certainly, we want to divide z by w with rest. So we first just divide it in the complex numbers. So let z divided by w, which I write as a plus bi, be the quotient in c. So obviously w is different from zero. So what does it, and we then just want to find as the kind of quotient in z i, something which lies close enough to this. So we choose say nm in z such that say a minus, so the absolute value of this difference is smaller equal to one half and the absolute value of b minus m is smaller equal to one half. We can certainly do that. Just shows the nearest one, the nearest integer in the corresponding direction. And we put q equal to n plus im. So we have our element in z of i, and this is supposed to be the quotient. So can first compute this difference between if I take z minus w minus m plus in. What is it? Well, according to the definition, this is a minus n squared plus b minus m squared. And so this is one half squared, one quarter, one quarter. This is smaller equal to one. No, no, I think in the notes we have the other notation, but I think this is consistent with itself. Okay, so we have this, and so we can, so we put the rest as z minus. n plus, here I have added it wrong. n plus im times w. So this is supposed to be the rest. So let's see whether it works. So this is the rest. So we can write, now we can write z. Obviously is equal to, we just put on the other, we write n plus im w plus r, so this is our division of the rest. And what we have to see that d of r is smaller than d of w. So d of r is equal, well, we can, so if you just multiply this here, it's just this divided by this. So this is d of z divided by w minus n plus im times d of w. Because this is just this r, it's just this multiplied by w. And we know that this thing is actually one half. So this is certainly smaller than d of w. We know that this is smaller equal to one half. Okay, and so we find this. And the second statement is, obviously we find that this is indeed a Euclidean ring. Okay, so now I wanted to, so one of the things that Euclidean rings are is principle ideal domains. So that means every ideal is principle. So that means every ideal is generated by just one element. And so in particular, for instance, every ideal in z is just the multiples of one integer. So definition ring, so I think I want an integral domain. It's called the principle ideal domain. And as this is a bit long, one usually always just writes PID. If every ideal, i in r is principle. So that means by definition, as we have already seen, that i is equal to a for some, which is the same as a times r for some a in i, okay?  Well, it's actually quite simple. So we just have to use this division with rest to do it. So let's take a principle ideal domain, a Euclidean ring, and we chose ourselves an ideal. So now we want to see that this ideal is principle. So if i is just a zero ideal, then it is obviously principle because then i is equal to the ideal generated by zero. So that's principle. So thus we can assume that i is different from the zero ideal. And let a be an element in i, which is different from zero. But we choose a particular one, we have this wonderful d. We choose an element which has the minimal d of a, minimal a in i, whatever. So we choose an element in i for which this d of a is the smallest possible one. We want to claim that this generates the idea. Well, so let b be an element in i. We have to show that b is a multiple of a. So we can do division with rest. So then b is equal to qa plus r with q. And the small r is equal to zero, in which case we are done, because b is, we have found that b lies in, or d of b, d of r is smaller than d of a. But we know, but if you look at it. But by this equation, we have r is equal to b minus qa. These are two elements of i, so this is an element in i. And under this assumption, it would be non-zero. This, so this d of r smaller than d of a is a contradiction to the choice of a. So this is a contradiction to the choice. Because d of a was supposed to be the smallest. d of something for any element in i, which is different from zero. So it follows r is equal to zero. So that means any element b and a is a multiple of a. So that's b in a. If I take an element b and i, it's an element in i. So i is equal to a. Okay, so in particular, we find that these Euclidean rings that we have just introduced are pids. So in particular, we have that z, z of i, and k of x for k field are principal ideal domains. I don't know whether it has an apostrophe or not. Okay, so we can also talk about principal, about great and greatest common divisors in principal ideal domains. So I had defined great common divisors in integral domains. And I said it's not always clear they exist. They only give a definition, but it doesn't mean they have to exist. But in principal ideal domains, they do exist and are actually quite simple. So this is a proposition. So let r be a PID and let take some elements a1 to ar, some elements in r. Then there is a greatest common divisor of a1 to ar. It exists, so maybe I call it d, exists and is of the form of the form. Can write it as a linear combination of these d equal to a1 x1 plus ar xr with x1 to xr is r elements in r.  These a1 to ar generate an ideal. This ideal is a principal ideal. It will be generated by one element, which I call d. And this element d will be the greatest common divisor, or one candidate for the greatest common divisor. So proof. So we choose an element d in r such that if I take the ideal a1 to ar, d r generated by these, so all linear combinations of these, that this is equal to the ideal generated by our, I mean, we know that every ideal is a principal ideal, so also this one. So we can write like this. And the claim d, the claim is obviously that claim d is a greatest common divisor. This is basically obvious. Just look, check the definitions. So by definition, we have obviously that each ai lies in the ideal generated by d for all i, but what does it mean? That it lies in the ideal generated by d means besides that's divisible by d. Whatever, okay, that's just what it means to lie in the ideal. And so it is a common divisor, is a common divisor of a1 to ar. And to be the greatest common divisor, it has to be, it has to be that every other common divisor divides it. So let e and r be a common divisor. So satisfy e divides ai for all i from one to r. Then I have to see that e divides d. But if it divides all of this, then e divides ai. It divides say xi times ai. And if it divides all xi times ai, it divides the sum of all of them. So e divides a1 x1 plus a r xr. Because it divides all the ai and therefore, which is after all d. And so that's fine. So it's a greatest common divisor. So for instance in z, we have that if we take the ideal generated by four and six, this is the same as the ideal generated by two. And two is the greatest common divisor of four and six. Okay, so that was a rather simple remarks about this is all. Wondering whether I missed something. No, it was all. So now I want to start to talk about irreducibility of polynomials. We will later, we talk about field extensions. So you have a field and you want to construct a bigger field which contains the original field. And you do this somehow by looking with the help of an irreducible polynomial. And so we want to have a way to construct them and to check that polynomials are irreducible. So first I talk about irreducibility in general. So definition, so this I'm talking about irreducibility of polynomials. And so first I define what irreducibility means in general. So definition, let's say R being integral domain. So an element A and R will be called irreducible if it cannot be written in a non-trivial way as a product of two other elements. So the trivial way would always be that you write it as a product of something with a unit. So therefore, an element say Q in R, which I assume it's not 0, is called irreducible.  And if Q is equal to A times B with AB elements in R, then either A or B is a unit.  So for instance, say, so maybe first I finish. So it is called reducible if it's not irreducible. So if Q is again is not a unit and not irreducible, it is called reducible. So this means in other words, if one wants doesn't want to say it in such a direct way, obviously just in indirect way, it obviously just means that. So Q is reducible if it exists AB in R which are not units. None of, so without units such that Q is equal to A times B. So for instance, in Z you find that the prime numbers are irreducible. And in fact, you can easily check that all the irreducible elements in Z are plus minus P where P is a prime number. So I want to give you a few more. So, okay, so I can even write it again, example. An element Q in Z is irreducible if and only if Q is equal to plus minus P where P is a prime number. That's almost by definition. Then if you have a field, if K is a field, it has no irreducible elements. Of course, after all, all elements in K without zero are units. And so no, and zero also was excluded. So there's no chance. And then let's look, so again in KX, we have that, I claim that. So AX plus B is polynomials with A, an element in K which is not zero. And B, so K is always a field. And B, an element in K is irreducible. Well, this thing is not a unit and it's not zero. So it is irreducible if it cannot be written as a product of two elements which are not units. And so if AX plus B is equal to F times G for F and G polynomials, then we know that in the product, the degree is additive. So the degree of AX plus B is equal to the degree of F plus the degree of G. Now the degree of AX plus B is evidently one. So the degree is at least zero. So one is the sum of two non-negative numbers. So at least one of the numbers must be zero. So thus the degree of F is equal to zero, or the degree of G is equal to zero. And now as this is a non-zero element, it follows that F and G are not zero. So it means a constant polynomial is a unit in KX. The constant polynomials, the non-zero constant polynomials are units. So it means that either F is a unit or G is a unit. Namely when it's degree is zero or G is a unit. And so this means precisely that this thing is irreducible. So I come back for one moment to this PID. Then we use this for the polynomials. So if you have a principal ideal domain and you have an irreducible element, then the ideal generated by it is a maximal ideal. And therefore if you divide by this ideal, you get a field for position. So let R be a PID, principal ideal domain. And P in R, an irreducible element. Then the ideal generated by P is a maximal ideal in R. And we know that being a maximal ideal is equivalent to the quotient by this idea being a field. So the less second part is obvious and R mod P is a field. So this is just a reminder of it. The statement is this one. Okay, again this is quite simple but we will later use it. So almost by definition. So let's see, so let's do the proof. So we take our irreducible element. And so we want to show that the ideal. So let I in an ideal with say P contained in I. So this contains means, not necessarily strictly, it's contained in I. So this ideal is a principal ideal. So you can write I equal to A. So that P is contained in the ideal generated by A. It means that P itself is contained in A. So that I can write P is equal to A times B for some B in R. So now there are two possibilities. Either this element B is a unit or it's not. So either P is a unit. We have seen that if I have a unit, then an ideal generated by one element. And the ideal generated by the same element multiplied by unit gives you the same ideal. So if P is a unit, then P is equal to A. Because if I just multiply this A by a unit, it gives you the same ideal. So that's one possibility or B is not a unit. But this was actually not what I wanted to do. Let me see. Yeah, yeah, but I'm kind of, I understand. So I think I want to, let's try again. So, well, maybe you can repeat what you said. Yeah, yeah, sorry, obviously I have to use my assumption somewhere, no? I have assumed that P is a prime element. Obviously I'm not trying to prove that this is true for any element. But the assumption was that it's true if I have an irreducible element. So yeah, obviously I have to use my assumption. So P is a prime element. I have written it as a product of two things. So if either B is a unit or A is a unit, because P is a prime element, or B is not a unit, then A is a unit. Yeah, sometimes, but then because P is prime is irreducible. So then obviously if A is a unit, the ideal generated by a unit is the whole of the ring. And so we have seen that if our irreducible element is contained in an ideal, then either that ideal is equal to the ideal generated by P or it's the whole of the ring. So that's precisely the definition of a maximal ideal. Yeah, amazing. Okay, so we want to use this to construct new fields from old by use of polynomials. So basically if we are given an irreducible polynomial, we get in this way a field. So corollary, let K be a field, and F, the polynomial in Kx, an irreducible polynomial. Then we know that after all, the ideal generated by F is a maximal ideal. And so then Kx, the ideal generated by F, is a field. And I can view it as a field containing K as a subfield, so which contains strictly speaking a field isomorphic to what I just say K as a suffering. So by what we said before, if F is an irreducible polynomial, then Kx modulo F is a field. And because this is a maximal ideal in Kx, and so we have the constant polynomials. So if I take the map from the constant polynomials to this quotient, this is an isomorphism onto the image. So the map, so on, so for, let's see, A and K, we have the class of A, no, so the map, restriction Kx to F to K, which are the constant polynomials, is an isomorphism onto the image. So we know that this, so restriction of Kx, pi, so we have the canonical map to the quotient. So if I restrict it to K, then the map is injective, because the, it would have to be either, so as K is a field, I restrict the map to K, it would either have to be the zero map, which is obviously isn't, because the constant polynomial, because K does not lie in the ideal generated by F for an irreducible polynomial. And so it is an injective, this map from K to the image here is an injective homomorphism of fields, and so therefore it is, you know, so it's an isomorphism onto its image, which is a subfield of this. And so later we will be concerned with the question, we are given a field and we want to study larger fields which contain this given field. And here we have kind of found a way to always construct such. So if we are given ourselves an irreducible polynomial in our field, then we get a larger field which contains the field where we start it. And for instance we will see later that we might want to find a field in which a polynomial has a zero, and we will find that somehow surprisingly in this field this polynomial F will have a zero. So somehow in a, anyway, but this we'll look at later, so we'll come back to this later. Now as we have now found this, so this somehow is one of the reasons why we're interested in irreducible polynomials, because they allow us to make fields. So bigger fields from smaller ones. And so now it would be useful to find some criterion for a polynomial to be irreducible. And so we will do this only for the case that k is equal to q. But we also have to do it then at the same time for k equal to z, because that is what makes it work. So we want to study irreducibility over q and z. So we have polynomials in qx and in zx. And we want to find out about irreducibility by comparing what happens in q and z. And the first result about this is due to Gauss. So we have first the lemma and then, so first we have a lemma which is the first step towards this. So we first make the definition. So obviously for polynomials in z, if you take an irreducible polynomial in z and you multiply it by a number, by an integer which is not a unit, it will not be irreducible anymore. So because you can after all divide it by this number, and this number was not a unit. So therefore, we want to first look at polynomials which are primitive, which means that their coefficients have no common divisor. So the polynomial equal to sum i equals 0 to n ai z, and x to the i is called primitive. If the greatest common divisor, so this is a polynomial in z of x. So the ai are integers. So if the greatest common divisor of the ai is one or. So if the a 0 to a n are relatively prime. Prime, which by definition just means that a greatest common divisor of the coefficients is one. So we don't have any common factors for the coefficients in that case it's called primitive. And the first lemma of Gauss is actually quite simple, it says that if you have two primitive polynomials then their product is also primitive. Seems kind of obvious but maybe it isn't. So let f and g be two polynomials with coefficients in z, which are primitive, then f times g is also primitive. So what we just tried to see whether we assume it's not primitive and then we will quite easily bring this to a contradiction. Let's see, assume f times g is not primitive. Well, I can first, but I need to do some notation. So maybe we write f equal to sum i equals what I want 0 to n ai. X to the i, g equal to sum i equal to 0 to m. Whatever, b i, x to the i. And so we assume that fg is not primitive. So then if it's not primitive, then all the coefficients of fg have a common divisor. So there's a number which is not plus minus one, which divides all the coefficients. And so we can take this number to be a prime number. There's a prime number which divides all the coefficients of f times g. If there's some number which divides all the coefficients and this number is not a unit, then I take a prime number which divides this number which divides all the coefficients and this will divide all the coefficients. So then there is prime number p, which divides all coefficients of f times g. But on the other hand, it does not divide all coefficients of, it does not divide all the ai, and it does not divide all the bi. So therefore, we can take the smallest i for which it does not divide it. So let i be minimal such that p does not divide ai. And let j be minimal such that p does not divide bj. So it takes the smallest such index of which it does not divide it. I know it doesn't divide all, so there will be some. It doesn't, but it can take the smallest one. So maybe I call c of i plus j the coefficient of x to the i plus j in f times g. So what can I say about it? By the formula for the product, we can express it in terms of the ai and the bj. So you have that ci plus j is equal to ai times bj plus the sum over all k, which are bigger than i, ak bi plus j minus k, and plus the sum over all k, which are smaller than i, ak bi plus j minus k. So this is just the sum over all albm such that l plus m is equal to i plus j by definition. And so I can do it in this. But now, if I look at this here, when k is bigger than i, then this number here, i plus j minus k, is smaller than j. So this index is smaller than j. So that means p divides bi plus j minus k. So it divides every sum in here. When k is smaller than i, then k, obviously k is smaller than i, and therefore p divides ak. So we find that p divides this whole sum, p divides both sums. But it does not divide ai, and it does not divide bj. So it does not, as it's a prime number, it does not divide ai times bj. It's not divide ai times bj. So therefore it does not divide this one. And so this contradicts our assumption that f times g was not primitive, and therefore we could choose such a prime number. So this is a contradiction. And so we find that indeed, f times g is primitive. So this is then mostly used to prove a theorem which is also called Gauss-Lemma. So it's a lemma for Gauss-Lemma, which says that if I have a primitive polynomial with coefficients in z, then it's irreducible in zx, if and only if it is irreducible in qx. So if I can write it as a product of two polynomials in zx, I can also write it as a polynomial of two polynomials in qx and vice versa. And so let's see.  Then f is irreducible in zx, if and only if. f is irreducible in qx. So if I cannot write it in a non-trivial way as a product of polynomials with integer coefficients, I also cannot write it in a non-trivial way as a product of polynomials with rational coefficients. And that doesn't seem to be so obvious. So there are, I mean, it's equivalent. So there are two directions. First, we do the easy direction. So if f is reducible in zx, so it's by counterposition in zx, then you can write f is equal to g times h, where g and h are both non-units in zx. Yes. So if the degree of g is equal to 0, that means g is constant, then it means that g is a non-unit in z. And we have that this number g is a common factor of all coefficients of f equal to g times h. Because after all, g times h is just obtained by multiplying all the coefficients of h with this number g. And so f is not primitive. So it follows bigger than 0. And the same argument applies if the degree of h is equal to 0. Now it's symmetric. So thus we also have the degree of h is bigger than 0. So we have written f as a product of two polynomials of positive degree. So it means it is, this also describes it, this polynomial as being reducible in qx. So we have f h bigger than 0. That means f is reducible in qx. Because this is a way of writing it as a product of two units, two non-units in qx. If I have a polynomial, OK. So this was the easy direction. Because we just have to take the same. Now we have to use the other way. So this is the most surprising part. You have to see that if you cannot write it as a product of two polynomials with z coefficient, you cannot write it as such a product with r coefficients. What? Yeah, yeah, yeah, certainly. Yeah, yeah, no, I finished. I mean, this is the argument. But what is the, yeah. Well, that's what I proved here, no? This is the direction I proved. No, no, no, but the units are different, no? So if you cannot, so let me see whether your argument makes sense, well, I mean, in some sense. But you have to realize that there are, in zx, there are, if I all right, more irreducible elements. If you have a constant in zx, which is an integer, which is not plus or minus 1, then this is irreducible. So yeah, you need a tiny argument. You have to use that your polynomial is primitive, because otherwise it's actually false. If you take the polynomial 2x, for instance, if you take the polynomial 2x, this polynomial is irreducible in qx, but not in zx, because it's 2 times x. And these are both non-units. So I mean, the argument here is very simple. But you just have to see that they have no common factor. If you assume it's primitive, it's, you know, I also haven't given very much of an argument here. The argument is precisely more or less what you say. But you have to just exclude the possibility that they have a common factor. But obviously, you are right that this is supposed to be the trivial direction. And it is almost as trivial as you say. But anyway, so now let's go to the other one. So again, we do by a contraposition. So suppose that f is equal to gh, where g and h are now polynomials in qx. And we assume these are polynomials of positive degree. So then we have to, so it means the polynomial would be reducible in qx. We have to see that it's also reducible in zx. So we have this. So now we can, so these are, so g has some coefficients. So some ai x to the i, they are some rational numbers. So we can multiply with some integer so to clear all the denominators. So we multiply with all the denominators of the coefficients here. We multiply with all the denominators here. And we divide by the greatest common denominator. So let me say it like this. So clear the denominators of the coefficients of f and g. And divide by the greatest common divisor of the new coefficients. So then we will get that f is equal to somehow a divided by b, g prime, h prime, where g prime is g multiplied by some rational number so that it is so that with g, g prime, and h prime primitive in zx. So I mean just as an example, whatever, if you have, if f is equal to 7 fifth plus 3 divided by 8. So x plus this, then you would multiply here by 5. So in this case, you would get, you have to multiply by 40. And you would get that you can instead just take f prime. So this was maybe g, would take g prime to be 7x plus 3. So it's a polynomial which is the same up to multiplying by a, no. Hopefully you do not believe that. So yeah, yeah, yeah, 7 times, so this is 56x plus 15. I think that's more likely to be true. And yeah, obviously, should not be caught forgetting what one learned before one went to high school. Anyway, OK. So anyway, I just replace this by this multiplied by some rational number, this by this multiplied by some rational number so that these two are two primitive polynomials. And the product is like this. So maybe just try it again. So we have g prime is equal to alpha times g. And h prime is equal to beta times h with alpha and beta are some rational numbers. That's how it works. And then you can do it in such a way that they are primitive. And so now let's look at it. And I can also assume, obviously, here we have a rational number so I can clear the common factors so that we have a and b are relatively prime. Relatively prime. You can just put it like this. So in particular, we can also write this by a very complicated transformation. We can write this as bf is equal to a times g prime h prime. So but now what do we see? Both f and g prime h prime are primitive. f is primitive because we have assumed it to be primitive. And g prime and h prime were both primitive. And by the lemma we had before, the product is primitive. That's why we proved that lemma. So if we look at this equation, we see here a greatest common divisor of all the coefficients is 1. So a greatest common divisor of all the coefficients in this product is b. Of coefficients of pf is b. And the greatest common divisor of the coefficients of a g prime h prime is a. But how is it possible this is the same polynomial? So the same polynomial, the same coefficients have as greatest common divisor b and a. So we know that greatest common divisors are uniquely determined up to multiplying by a unit. The units in z are only plus and minus 1. So it follows that b is equal to a or b is equal to minus a. So in other words, f is equal to g prime h prime or f is equal to minus g prime h prime. In any case, we have found the factorization of f as a product of polynomials as integer coefficients, not irreducible. So this was this statement. It is reducible in zx. So we want to now make a few criteria for irreducibility of polynomials. So one of the things we usually will be interested in the irreducibility of polynomials with coefficients in q. But we do it by checking it for cross over z. So the first result is the Eisenstein criterion, the theorem, Eisenstein, so some job of mathematician, criterion for irreducibility. So it's something which one can sometimes apply to show that the polynomial with coefficients in z is irreducible over z and therefore over q. So let f be a polynomial, so sum i equals 0 to say n, ai, x to the i, be a primitive polynomial in zx.  So it's not constant. And now we assume some strange condition. Assume there's a prime number which divides almost all the coefficients except for the leading one. So with p divides a0, p, maybe I just say, divides a1, and so on. p divides an minus 1. But we have that p does not divide az an. It does not divide the leading coefficient of degree n. And the square of p does not divide a0. So some strange condition about this divisibility. Then f is irreducible, first in z of x, and therefore in q of x. We know that these are equivalent. This is a well-known criterion to check that the polynomial is irreducible. It's a bit special, so one cannot apply it all that often, but sometimes one can. So let's see. So we assume, again, that it is reducible, and then we want to find the contradiction. Proof, assume f is equal to g times h with g and h, some integer polynomials. And we have to show that either f or g is constant. So let's write down, not f or g, g or h. So let's write down the coefficients of g of h and h. So write g, so sum i from 0 to what we want, k, bi, x to the i, and h, sum i from 0 to, say, l, ci, x to the i. So we have fixed the coefficients, and we assume in each case that this really is the degree. So b of k is different from 0, and cl is different from 0. So we know that the constant coefficient, a0, is divisible by p, but not by p squared. So as p divides a0, but p squared does not divide a0. We know that, and we have that a0 is equal to c0, p0, c0. We must have that p can only, must divide one of these two, but it cannot divide both. Because if it would divide both, then the square would divide it. So we have that, so and this, we have that p divides precisely one of p0 and c0. So thus we can assume, obviously, the role of, which we call g and h is up to us. So we can assume that the one, so we can assume that p divides p0 and p does not divide c0. So let's see. Now we look instead at the highest coefficient. So an is not divisible by p. And obviously, if the degree we have that we have an, so obviously we have n is equal to k plus l. And an, again by the product formula, is ak times bk, is it k, times cf. And we know that p does not divide an. So thus, p does not divide bk. So we know p divides p0, but it does not divide bk. So there must be kind of a last one which it divides. So thus, there exists a maximal element j between 1 and k, such that p divides bi for all i smaller than j, and p does not divide bj. So we can find the first one which is, it does not divide. Now we want to compute the coefficient aj. So aj is, again, by this formula for the product. This is equal to pj c0 plus pj minus 1 c1 plus p0 cj. So if the number l is smaller than j, we can add some zeros. The later cj is equal to 0. So it's this. So and now it's a usual thing. So by definition, so by our choice, we have that, we know that p does not divide c0, and p does not divide bj. So p does not divide bj c0, but it divides all the smaller bi's. So it divides each summand here. Well, the conclusion is that p does not divide aj. But now we have to remember what our assumptions here were. The assumption was that p was supposed to divide all of the aj's except for the last one. So it follows that this number j must be equal to n. But what does it mean? It means j is a non-zero coefficient of the polynomial g. So it means that the polynomial g has degree n, the same as f. So thus j is equal to n, and therefore also k is equal to n. That means the degree of g is equal to n, and the degree of h must be equal to 0. So we have found, we have actually shown that h is constant. Actually, we was not there. And so this shows that our polynomial was indeed reduced. So now I have gone a bit over time. So maybe I stop here. I can just, so you can, for instance, if you just take any polynomial x to the 5 plus 16x plus 4, this would be irreducible by this criterion. And obviously, if you wanted to check directly that it cannot be written as a product of polynomials of lower degree, that would be difficult. That actually is, now you should have contradicted me. Maybe I put 2 here rather. I was assuming that 4 is a prime, which is a kind of rather rash assumption. Thank you very much.


Well you circle games on the calendar when heading into the season and tonight is certainly one of them for the midgy boy soccer team ranks ninth in class 1A and coming to town the fifth ranked team in class 2A Duluth East. It's a top 10 matchup under the lights. Let's head to Cheddar Interestadium. We go in the Greyhounds put pressure on Bemidji early but look at Adam Locke so come out for the big save. That'll keep the game scoreless and it stays that way to the 18th minute but Nolan Friday is gonna get his own rebound finishes here with the goal 1-0 Duluth East and just two minutes later look at this strike Nick Lanagan my goodness the blast puts the lead to 2-0 that would end up being the final 2-0 with Bemidji's first loss of the season. If you've enjoyed this segment of Lakeland news please consider making a tax deductible contribution to Lakeland Public Television.