Well, thank you all for attending this science seminar. These seminars are presented by the National Science Foundation's National Ecological Observatory Network, operated by Patel. Our goal with this monthly series of talks is to build community among researchers at the intersection of ecology, environmental science, and neon. Today, we're very excited to have Teresa Cremins and Alyssa Rose-Martin from the University of Arizona to present on the USA National Phenology Network. But before we turn it over to the speakers, a few logistics. We have enabled optional closed captioning for today's talk. And if you'd like to use this closed captioning option, please find the closed captioning button in your menu bar. The webinar will consist of a presentation followed by a question and answer period. As you think of questions, please add them to the Q&A box. Moderators will facilitate the discussion at the end. I'm one of the moderators. During this time, there should be an opportunity to ask questions over audio. Neon welcomes contributions from everyone who shares our values of unity, creativity, collaboration, excellence, and appreciation. This is outlined in our Code of Conduct. These guidelines apply to neon staff as well as participants external to the neon program. Please review our Code of Conduct, which can be found on the DEI page of the neon website. This talk will be recorded and made available for later viewing on the Neon Science Seminar webpage. And finally, to compliment these monthly seminar series, we're hosting related data skills webinars where you can learn more about how to access and use neon data. These monthly science seminars are held kind of in every two weeks alternating with the data science seminars. So the next data skills seminar will be on November 29th and will focus on working with neon plant phenology data. And so for those who'd like to register for the data skills webinars, you can do it on the same page as the science seminars. So now it's my pleasure to introduce today's speakers, Dr. Teresa Crimmins and Alyssa Rosemarten. Teresa is a faculty member in the Integrated Climate Research Ecosystems, Water, and Weather Vertically Integrated Project at the University of Arizona. Teresa's research addresses patterns of drivers and drivers of phenology as well as facets of citizen science and engaging non-scientists documenting the plant animal life around us. Teresa is also the director of the USA National Phenology Network, which we're gonna hear about much more about during this today's talk. I'd also like to introduce Alyssa Rosemarten. Alyssa is an application specialist with the USA National Phenology Network and coordinator of research collaborations at the University of Arizona. So thank you, Teresa and Alyssa. We'll pass it on to you now. Super, thank you so much. Let me just, of course. Does the slides look good? Look great. Okay, super. So yes, Teresa and I are very excited to be here today. It gave us this, preparing for this presentation gave us a great opportunity to reflect back on, you know, 15 years of collaborations between the USA National Phenology Network and NEON and we've really just worked together in so many cool ways. And so it's exciting to get to share this with you and have a conversation about it as well. So in case you're not already sold that phenology is the coolest thing since sliced bread, we are into it because it is a great way to understand climate impacts. It offers feedbacks to climate connections to hydrologic cycles, carbon cycling, ecosystems and many aspects of global change. And we're also perhaps more in the last five or six years really focused on the use of phenology in decision support like invasive species control, agricultural applications, human health like pollen and allergies and then cultural events like flowering festivals. I mean, how those are changing with changing seasonal temperatures and preset patterns. So our organization, the USA National Phenology Network exists to collect, store and share phenology data and information with an overall purpose of advancing the science of phenology, supporting decision-making, communicating and connecting, bringing new audiences to observe and connect to and understand patterns in the seasons as they're changing around us. And then we're also focused on growing an equitable and inclusive network and ensuring that we're delivering benefit equitably to all demographics in the U.S. And we can really trace our origin story to a neon connection that we hear from the people who wrote the original research coordination network for the USA NPN that it was envisioned as a complimentary network to neon at some early neon planning meetings where neon's work would be intensive with all the amazing co-located sensors and the USA NPN would be only phenology focused but extensive across the country. And indeed, I think we have been really complimentary over the years. We've had many long and rich collaborations with many people on the neon staff but especially with Katie Jones and Sarah Elmendorf. And then on our side, it's been Ellen Denny, Kathy Gerst, myself and Teresa who have been particularly involved in fostering the collaboration with neon. We started working on shared protocols early on so which I'll talk about a little bit more in a minute. Approaches to data quality, sharing ideas and code and approaches for data quality. We've worked a bunch on data integration and access to make it easier to use both data sets together. We've collaborated on the development of novel analytical methods and then on indigenous approaches to phenology as well as data equity. So I'll talk in depth a little bit more about most of these. The shared protocols, I'm not sure how familiar everyone is but essentially what the USA National Phenology Network and NEON do is status monitoring. So instead of saying the date of the first milkweed bloom was June 15th, we say on June 15th, there were blooms on the milkweed. So it's presence or absence of a phenophase on a given date. And then we also have carefully worded definitions when we say there's leaves on a plant, we all mean the same thing by that. It's unfolded, you see the leaf base and it doesn't include dead leaves for the example that I've put here. And if you want the further resource, the Elmendorf et al paper from 2016 has the full monitoring design for NEON for phenology. So for us at the National Phenology Network, we've implemented those protocols through our Nature's Notebook program. So we have over 1600 species of plants and animals. We have extensive training materials and support for observers. So we have people, volunteers across the country collecting phenology data, people in the parks, backyards, natural areas, volunteers as well as park staff, refuge staff who collect data as part of specific projects or part of their work. We also have local phenology projects which are locally or regionally organized efforts where there might be a particular question like when are the mesquite pods ripe because the extension master gardeners want to grind the mesquite flower and they want to know when that's ready. So there's usually like a specific set of species and a local question that drives these local phenology projects. And then the middle part of the slide is a screenshot from the mobile app where people can download and submit data either on their own or as part of one of these groups. And then in NEON, which I'm not sure how if everyone on the call is already like, oh yeah, we totally know how the NEON phenology design works. But at each NEON terrestrial site, there are a series of phenology plots that are co-located with the productivity and biomass areas and in the tower air shed. And so this is in contrast to our program, this is like highly designed in terms of a sampling design around the questions that NEON is getting at, whereas our observers tend to be more opportunistic or organized around a local or regional question. NEON's program in phase one focused on, or is focusing, I think the transition is, Katie can speak to this more, but I think it's happening now, but in phase one, three species, 30 individuals of the sort of dominant species at each NEON site. And then phase two, which some sites are transitioning to now, is the community phonology. So up to 20 species at each location with a minimum of five individuals and selected based on abundance, as well as the science priorities, so species of management concern or species targeted by other sampling programs. So the NEON phonology program so far has 4 million records, 16,000 observation amounts for 541 species at 93 plots and 47 sites. And these records, because everything's compatible, because we've worked together for so long to make the protocols and the data structure compatible, these are served concurrently through the NEON and USA NPN data portals. So when we step back and look at the nature's notebook data and the NEON data combined, we see we have 30 million records across the country with 25,000 observers and 18,000 sites. And so I didn't double check this, it's very likely that a number of those bigger bluer circles are NEON location. So we're getting what we sort of dreamed of, right? Like deep intensive, well-sampled phonology for dominant species at NEON sites and extensive covering area in between those sites with the nature's notebook data. And then because we have integrated the data, that means that you can look at both NEON and nature's notebook data combined in our visualization tools, as well as our download and other tools. So this is an example of an activity curve where we look at the total, this is for milkweed, how many open flowers there were and for the monarchs, how many active individuals there were. Or this is the total number of, sorry, this is the total number of plants with positive observations for flowering over the course of the season. So it enables cool data exploration by having the two datasets combined. And then this was a specific NASA funded project that we collaborated on with NEON and other partners to develop a publicly available repository of source code workflows and APIs that could enable people to get at multi-scale data. So one of the great things about NEON is that there's the in-situ data camera, phenocam data, and we also have MODIS data from NASA for the same locations. And so how can researchers that want to use all three of those get access to them more readily and integrate them more readily? So that was the idea with this project and it resulted in a series of our packages which are shown here at the bottom. One of these is the phenocent project which shows you a phenocam view shed and allows you to visually select what pixel might be the best pixel to use to be for comparing phenocam and MODIS-based phenology as well as ground-based phenology. So it helps you both select the data that you might be interested in using and then also download it all together. And that's covered in the more set at all ecological informatics paper for more detail. And then another dimension of our collaboration that has been really meaningful to me, especially is that our work in the Indigenous Phenology Network. So also I think actually sort of transitions from the prior slide, it was Jeff Morris that originally invited me to a Rising Voices meeting in 2014. And I met Katie, no, I must have already known Katie but we got to, we're here in this picture, right? Like this is me and oops, and Katie next to Kalani who led the network for many years. So this group formed out of the Rising Voices as an NCAR-UCAR-led effort to bring together Western and Indigenous scientists in a way that is equitable and respects and values multiple Indigenous approaches to phenology, recognizes Indigenous community members and scholars as the first phenologists on this continent. And so Katie and I have learned and built so many relationships with others and many great collaborations have come out of this group. The core focus, like everything keeps coming back to relationships, to being responsible, to being a reciprocal, good relationships with each other, to engaging equitably. One of the Katie and I co-organize a symposium at ESA in 2020 called Indigenous Phenology, New Mindsets for Working Among Worldviews with Thal Small and others to really bring to the fore some of the amazing Indigenous scholars who are doing work in phenology. It's just also been a really great connection point because many tribes and Indigenous communities see, think deeply about phenology and close observation of the natural world through the season. So it's been, I've learned so much through this. This is some of Katie Jones' work following on, I think the growth that we've both been through through the Indigenous Phenology Network and the Sensing the Earth Tribal Climate Science Partnership Summit. There was a workshop in June and there's another one this month with the idea to build partnerships between tribal college faculty and our science institutions to support data-skilled curriculum and climate research. And then there's also that, she's also working on the NSF-funded Earth Data Relations Working Group, which advises on exercising Indigenous data governance in open data repositories. So those are two of the things that Neon is bringing forward in terms of data equity and working with tribal partners. And then for us at the National Phenology Network, we have a few things going on. One is the use of our protocols, but without our data management system. In the Great Lakes Fish and Wildlife, Indian, Great Lakes Indian Fish and Wildlife Commission is doing a study on important, traditionally important species that they harvest, including the wild leeks shown here. But the locations of those plants are often, they're in seeded territory where they have hunting and gathering rights. And so they often don't want to show the specific location of the plants that they're gathering. So to respect data sovereignty, we sort of explored this. We thought maybe we could make a protected data system, but ran up against the Freedom of Information Act. And feeling like since we have federal funding, we would likely would be obligated to share locations if requested. So they're managing their own data. And then sort of, but another example where they are using Nature's Notebook because the location is at College of Menominee Nation in Kashina, Wisconsin, where they have a knowledge learning path that's open to the public. The location of the plants is not an issue. And so they're using our data management system as well as our protocols as well as traditional protocols for observing and names for observing those plants. And then on the right side, there's just two more recent Climate Adaptation Science Center funded projects. One about returning cycles of renewal, returning good fire to the Shumash homelands in Southern California. And so the phenology dimension of this is focused on the timing of when to burn and the ecosystem response in terms of basketry materials and how phenology post fire. And then time to restore is in the South Central US looking at the timing of eight species that are important to pollinators and working with tribes and others to collect, store and share that information in ways that respect indigenous data sovereignty and help inform management for pollinator restoration. And I'll just a quick pitch for the Foundations of Data Equity class that I took through. We all count was really a powerful set of tools and lenses for thinking about equity in data collection and use and storage and interpretation. And I think with that, I will pass it over to Teresa. Thank you, Alyssa. That was fantastic. It was like a total whirlwind blast through what the NPN is and our longstanding history with neon and it's really cool to reflect on. As Alyssa indicated, because of the very intensive sampling efforts at neon, the data set that we manage and host at the USA NPN is progressively larger with every day that passes. And I was estimating today, I think that that neon's responsible for about a quarter of the data that's coming in on any given year these days, which is pretty exciting. And as Alyssa described too, they're so complimentary because we've got the deep, really static data sets that are being collected there at the neon stations contrasted with the broad scale observations that are being collected by observers across the country. And that has enabled all sorts of cool science and management advances to be undertaken. And so I'll just talk about a couple of these really quickly to kind of give you a sample, but by my count, and I am certain that it is far from comprehensive because we have, it's challenging to keep track of every time someone uses the data for sure. By our account though, it's well over 100 papers approaching now 150 papers that have used the phenology data contributed to one or both of these systems. And that's just the peer reviewed literature. Really, there's lots more outside of the peer reviewed literature too. So I'll just highlight a couple of examples here for fun here to be inspirational, hopefully. Alyssa, are you gonna advance? Okay, great. So the first one I wanted to mention is, it's tricky to make a slide to support this because it's just not a very visually appealing effort, but this is a manuscript that emerged from collaborative effort with Sarah Elmendorf who is someone that Alyssa mentioned earlier in the presentation. She had been a staff scientist with NEON several years ago and we undertook this analysis collaboratively, several of us prior to the establishment of the connections between our two databases. So she actually had to pull the phenology data from the two separate databases in order to analyze them together. But the aim with this particular effort was to try to apply hierarchical modeling or Bayesian approaches to see if we could establish drivers to leaf out and leaf color change in the observations that have been contributed to both datasets. That may seem like a funny question because there are so many papers that have addressed the drivers to leaf out and leaf color change, but in truth, there's still a lot we don't know about what the specific drivers are to these phenological events and especially when you get down to the species level and especially to once you drift away from temperate forests. Eastern temperate forests we have dialed in reasonably well but once you start getting into water-limited systems it really becomes a lot more challenging to know specifically what the conditions are that plants need to be exposed to in order to trigger either leaf out or leaf color change or any other phenological event. And so this effort was novel at the time that it was undertaken because it took advantage of all of the observations that we had for leaf out and flowering for over a hundred species in the two databases combined across 15 different eco-regions. And the approach that we used, the hierarchical modeling was undertaken because it can tolerate messy data basically, situations where you maybe don't have a prior no preceding the first time that someone says yes to yes I see open flowers or in this case leaf out. It also can tolerate infrequent and irregular sampling which again is less of an issue of course in neon observations but definitely an issue in the observations contributed through nature's notebook. And by pooling all those data together you can draw strengths on that larger dataset to try to basically address the gaps and I'll be honest I'm not the mastermind behind the Sarah was that's my limited understanding of the why we undertook it. We really wanted to see whether this technique could perform better than the more traditional model building techniques. And it was interesting. I will say that there weren't any massive surprises that emerged.  And so it really didn't come as a surprise to us that growing degree days or accumulated warmth in the spring and day length had the greatest impact on promoting leaf out and then it varied by species but frost and precip kind of had a suppressing effect. And then when we looked at the fall chill degree days which is basically the accumulation of cool temperatures after the peak of the summer season had the strongest effect on driving leaf color change. But though I think we kind of were a little disappointed because we didn't feel like we solved the problem of being able to identify drivers to these phenomena. It was a first attempt and in truth the database has grown significantly substantially probably doubled since the time that we did this. And so it's certainly an open opportunity for anybody who may have an inklinger and any enthusiasm around taking this further because we really it would be much easier to do now since the data are combined and there are lots more data. Next slide please. Okay, another cool, I really wanted to draw out papers like the last one where it was very obvious that neon data were front and center. In truth, a lot of people that use the phenology data that were there especially when they're pulling it from our site, I think it's fairly transparent to them that some of the data originates from neon sites. However, I think it's transparent at the point of pulling the data. I think it emerges in the analyses because suddenly you start to see there are particular sites that have very good regular sampling and don't seem to miss events where again, and persist year on year which is definitely something that varies with volunteer observers. That said, there are so many cool examples of analyses where researchers have endeavored to capitalize on the breadth of all of the data. And so absolutely it may be not so much that in the manuscript the people called out neon but absolutely it's embedded in here and it was part of the story. And so in this particular recent paper that I really think is fascinating the investigators explored whether urbanization has an impact on fall phenology. And so the motivation for this question is really what's the effect of urban heat islands on phenology? So we saw in the previous slide that temperature really is important for driving phenology in the spring again warmth. The presence of warmth is so important to initiate activity. And then at the end of the season, the accumulation of chill plays a pretty significant role in driving the senescence and abscission. So leave color change and drop in species. We know too that urban areas tend to be warmer than their surrounding less developed locations. And so these researchers just said let's take advantage of all of those observations that have been contributed on leaf color change and leaf drop and see if the timing of these events vary based on whether the location where the trees were sampled was urban or not urban. Next slide please, thank you. And so this map shows the all of the different locations and I'm sure there's some neon sites in here where leaf senescence observations were drawn from over a basically a 10 year period and there were over almost 200,000 observations here that these researchers pulled on. Go ahead and go to the next slide please. And this is just a quick summary of the results. On the X axis of this graph here, we have effectively urbanization, the degree of urbanization. They used human population density as a proxy but and it's long transformed here but on the left of the axis it's low. And as you move to the right, it's increasingly more developed. And on the Y axis we have the day of year that the leaves senest. And then the color of the lines that we have graphed here reflect the annual average temperature. And so the purple line on the bottom, it reflects locations at the highest latitudes or elevations where the annual average temperature is the coolest. And we see a really clear positive relationship here where as locations become progressively more developed, we see that onset of leaf senescence or when leaves are senescing, moving toward later in the year. And then as we move basically to locations with increasingly warmer average temperatures, which also equates to further south or lower in latitude, we see the slope of that line flatten out eventually. And eventually at the end, it actually reflects the inverse relationship. The locations with that yellow line are actually the most southern most parts of the Conturminus United States. So we're looking at Southern Florida and Southern Texas there. But in truth, we actually start to see an inverse effect there. Go ahead. And so I wanted to bring in this next study that just came out earlier this year because it's also related, this particular study investigated the influence of artificial light now. So the kind of addressing that day length control on both the start of the season, again, represented by leaf out and the end of the season reflected in leaf color change and leaf drop. So what we know, what's really well documented in the literature, again, talking about temperate forests here, just nice, well-behaved deciduous plants. And I say that because I'm in Arizona and things don't behave here well at all. We have many bouts of flowering within a single season and it's very hard to model and predict. So sticking with these nice Gaussian curve seasons where things progress through clearly leaf on, leaf off. Basically, we know that temperature is a major control. And as temperatures warm, that springtime is advancing earlier and delaying things later in the season. However, there is anticipated that eventually there's a limit on that. And for many species, it's day length where the species require a certain number of hours of daylight in the springtime to actually be able to respond to those warmer temperatures. And so it's been predicted that we'll see an advancement in the onset of spring activity up until we run into that limiting factor and then we will cease to see things advance. However, what happens when we start throwing a bunch of extra light into the mix? And we actually are doing that because we have so many artificial lights on all night long and that it's quite concentrated and it's broad spectrum in many cases and it's not just pointed down at the ground but they're pointed up into the air. And we have cars driving around with lights on. And so all those extra sources of light can have a interactive effect here as well. Go to the next slide please. And so what these researchers did was pull on a satellite product and I'm forgetting the name of it but it is specifically aimed toward documenting where it's light in the night basically. You can see that imagery in the background where there are clear hotspots of artificial light and it reflects our cities of course. And then what we have layered on top of this are observations of breaking leaf buds on the left and colored leaves on the right. And again, I'm certain that there's some neon sites reflected in here. And what these researchers did was then evaluate what's the relationship here? What's the, is there, does the presence of the artificial light have an influence on the timing of leaf out and leaf color change? So basically in the locations where those observations are being collected if they happen to fall in pixels where we have bright white there, do we see a different timing of the event relative to similar latitudes but not so developed? And it was a very clear yes. It was very clear yes for the leaf out. It was a little more mixed for colored leaves but absolutely the take home message was artificial light does have a effect on the timing. And so therefore this kind of changes our story about whether we're gonna see a limit to how long the growing season can be extended in either direction because we are kind of, what's the right word? We're kind of supplementing that limit. We're subsidizing it, I guess I'll say with the artificial light. And so removing that control on the lengthening of the growing season. Next slide please. Okay, so I only put a couple of examples in here but we have a page on our website and I believe Neon does too where you can explore all of the different papers that have been published using the data. And if you're fishing around for a research question or inspiration, I strongly encourage you to check it out because there's really cool stuff on there and there's more stuff coming online just about every week. And I could easily fill hours talking about all these different examples. It's really pretty cool. But shifting gears a little bit because it seems worthwhile to mention these things too. We here at the USA NPN also develop our developing and delivering a several suites of raster gridded data products too. And these are real time and forecasted products as well as products that have been calculated back into the previous century, previous two centuries actually in some cases. And so those are additional data sources that are readily available and can be combined with the observational data being collected on the ground at both neon sites and other sites through Nature's Notebook for further analyses. One of those products is what we refer to as our spring leaf index or our start of spring maps. This is an example of that map as it was collected from April 18th of this year. And what it is indicating is the color represents the day of year that conditions that are associated with the start of biological activity in the Eastern US really were met. And so it's effectively accumulated temperature from the start of the year that and these particular temperature thresholds were established using observations of flowering, leaf-out and flowering in lilacs and honeysuckles. We have a long historical data set for those that goes extends back into the 1950s. And those plants are among the first to actually undergo activity in the springtime. And so this doesn't necessarily reflect the day of year that all species put on their leaves. It's an index, but it is an index that reflects conditions that are consistent with some activity in particular species in the spring. And so in this map, the color reflects the day of year that occurred. And then what resonates a lot more with folks is the slide, the next slide, the map on the next slide. What we do here is difference that current year map to the recent three full decades. So this is actually incorrect. My label at the bottom says difference from normal 81 to 2010. We actually updated the maps now where we're using the most recent climate normal period. So we difference the current year from the day of year that the event was reached in 1991 through 2020, the average over those 30 years. And then what the map indicates is was this year earlier than when it occurred on average those past 30 years or later and by how much? And so the red tones indicate locations where the onset of that spring activity occurred earlier than it did on average in the last 30 years and the blue tones indicate locations where it occurred later than average. And we find that these maps really get folks engaged because it's kind of a pretty clear distillation of information packaged in a way that makes sense to them. They can just simply look at the map and determine is spring happening earlier or later. It's absolutely not a comprehensive story but it's a starting point for a conversation. And so what we also find is in years where the southern states are shaded blue, meaning spring started later than average, we don't get very much media attention. But if those states like Georgia and Alabama and Texas and Florida are red, then we will get a lot of phone calls from the media because everybody wants to know a spring coming earlier and what does that mean for the allergy season and for the cherry blossom festival and for the crops that we just put in the ground and for mosquitoes and for all the reasons why we care about phenology and the timing of seasonal events. Next slide, please. And so here's a couple of examples of where folks have leveraged those maps in kind of storytelling and engaging with the public. One of the things we do is make those maps readily available in KML format, which is the format that most TV weather folks use. They can grab that file and pull it straight into their software that they use to make their online broadcasts or on air broadcasts. And so the map on the left is a screen capture of where someone did that and they just kind of reshaded it and re-labeled it but it is the data set from us. And they were using it to tell the story about allergies in particular. And then on the right was a similar story where folks were fretting that the cherry blossoms were going to be done blossoming before the actual big event occurred down in the tidal basin area. Next slide, please. Parallel to those, we also offer and deliver a couple of suites of accumulated growing degree day products. And so that's, it's fairly similar to the spring indices but we make these available on a couple of different, with a couple of different parameters. So different base temperatures and different, I guess that's it for now. So the map on the left is indicating how much heat, basically how much warmth has accumulated since January 1st in particular pixels across the country. And these maps are available at two and a half kilometer resolution in the current year. And we also have tools that enable you to go in and pull a time series within a pixel as well. And then on the right, we deliver anomaly maps. So again, similar to the previous slides I showed, this indicates whether we're ahead of schedule or behind schedule in terms of heat accumulation on a given day. And so these maps were from 2020, which was an early warm spring. And so you can see the impact of that across those Southern States where those are, those locations are many hundreds of growing degree day units ahead of schedule. And basically what that means is just the, those locations have been exposed to a lot more springtime warms than typically occurs in the early months of the year. Next slide. Those maps are also, those are, those are useful in and of themselves for sure to kind of tell a story about how the year has been unfolding. But then another way in which they are used and that we make use of them is in, especially in agricultural applications and integrated pest management, it's been established by field research or growth chamber experiments, other experimental approaches, exactly how much warmth in an organism needs to be exposed to in order for it to undergo a phenological transition. And so what we've done is in cases where we've been able to identify a species where it would be helpful to know when something's going to happen, when we can identify that and it's already been established how much warmth needs to be accumulated in order for that event to occur. We operationalize that as a real time forecast by just taking that, that growing degree day threshold that amount of heat that needs to be accumulated and using that as a way for how we deliver and present the maps. And so in this case, emerald ash borers are insects that bore into the heartwood of trees, ash trees in particular and do a whole lot of damage, I'm sure you're aware. And they're fairly hard to control for because they spend most of their life cycles under the barks of the tree. But when they become adults, they emerge from the bark and they fly around for about two weeks and then they lay eggs. And that is a prime opportunity to try to control their spread to additional trees. You wanna really prevent those adults from laying eggs on uninfected trees. And so managers have indicated it's helpful to know, it's helpful to be able to anticipate when is that gonna occur because then we can get traps out there and try to get crews out there to control their spread. It's been established by others that adult emerald ash borers emerge around 450 growing degree days. And so what we simply do is on any given day, shade the map based on how many growing degree days have been accumulated relative to that threshold of 450. And so in this case, the locations that are shaded yellow are locations where that threshold has been met recently. And so we predict that emerald ash borer adults are flying around in those locations at this time. And if you happen to be in the green or the blue tones, you're in locations where you're getting close to reaching that threshold. If you're in the purple tones, you can hang tight, it's not time yet. And if you're in the brown, you're past your threshold, you missed your window. Next, well, just go ahead and click it. One of the things we offer is folks can sign up to receive email based notifications based on their location. And so these maps are available on our website, real time and six days out. And so anybody can come at any point and explore the maps looking now and into the future and even into the past. Not everybody always wants to do that. They want a reminder delivered to them. And so you go in and you type in your location and then it'll prompt, you can sign up and then you'll receive these quick notifications when you're approaching. I think it's three weeks out, two weeks out and one week out, something like that. To try to help folks take most advantage of the information that's available. Next slide, please. The one other, I did want to make mention too because Alyssa mentioned early on in our strategic themes. One of the things we also try to do is just engage beyond just science and management but to ideally everybody who lives in the country to help them understand what phonology is and why it matters and how it's relevant. And so we do that by engaging via various podcasts and with the media and other opportunities whenever we can to help try to demystify what that old fashioned word is. Next slide. So with that, Alyssa and I will be happy to take questions and we invite you to get involved if you're inspired. At a minimum, please explore the data that are, I should have said, neon and NPN data. We have a wealth of curriculum material available for both K through 12 and post graduate instructors. We have the maps and forecasts that I mentioned. We also have several different newsletters that you can sign up for to stay in the loop on all of the great developments that are occurring. And we also always invite collaborations. We love working with data users or data collectors or anyone along that spectrum to just increase the reach and the impact of what we're able to do. So thank you. Thank you, Teresa and Alyssa. That was a magnificent presentation, really interesting. I'd like to remind everyone that you can ask your questions in the Q and A chat. There should be a button at the bottom of the screen where you can enter your questions and we will also take some live questions. I'd actually like to kick this off perhaps. This is a fascinating subject and really, really interesting presentation. As I understand it, there are different partners and stakeholders that are contributing data to the NPN. Is data quality control a challenge given the fact that you have multiple sources of information as part of the network? That's a really fair question, absolutely. Alyssa, do you want to do that or do you want me to? Yeah, either way, you can take it. It's definitely something we think a lot about. Pardon? It's definitely something we think a lot about. I guess I can say a few things that Theresa can time in. Yes, we think a lot about that and we sort of do the QAQC, so quality assurance, like what can we do on the front end to make sure the good data's going in? And so that's a lot about having really clear interfaces, really clear definitions, photographs where we can and then training happening locally. So like for the species that people are watching, like what does that look like? We have a new and updated observer certification course on our website.  And then we do stuff on the back end as well, the quality control where we're looking for observations that are in conflict with each other or that are logically inconsistent and either removing those when it makes sense or flagging them. And yeah, I was, I think, some of those we have in common with Neon, like Katie and Sarah and Kathy and Ellen and like we sort of came up with some of those together that are in the Neon workflow. And some of those, like there were problems that happened for Neon data that don't happen for us and vice versa. So there was, we could make a, we perhaps should make a little slide or flow chart that shows like where we have, where we do quality control measures together and where, and what our separate ones are. Do you miss anything, Teresa? No, there's been a couple of studies that have looked at that and have generally found really good concordance between professional and amateur observers, especially after the beginning of the season or the first few months of participating. Is the, are the Neon sites, the Neon phenology observations used as part of that kind of quality control assessment? Like in the publications? I don't know actually, I don't think so because those were done before the integration, right? And we couldn't unmute Katie anytime too if she wants to chime in. Yeah, but certainly when the neon ops come into our system they go through the same checks that the rest of the, that our data go through. Great, I think people can also raise their hand to ask questions live. I'm not certain how that actually works, but perhaps Samantha or Darcy can page them in once one of the questions are, when there's available time to ask those questions. I do see a question in the chat. Question is from Xian Wang, Wang. Could we potentially identify species based on the phenology variability for example, can we identify annuals and perennials? How much potential is there in doing that? Yeah, I'm happy to try and answer that. So I think the question is asking do we have good representation among these different functional types? And if so, is there the opportunity could we leverage that and see what phenology the variability in phenology might be across those different functional types or growth forms? Yeah, definitely, yes. I don't know off the top of my head what the breakdown is among the different growth forms or functional types. But I know just last week we were asked what's the representation of herbaceous species because there's an effort in an international effort with focus on herbaceous plants because traditionally trees, overstory canopy trees have been dominantly the focus of phenological investigations and studies. And so we quick and dirty during the call calculated it and it's about half and half among our plants where trees versus herbaceous. So it would then be a matter of looking among those which were perennials versus annuals. And then it would also be a matter of that's just the breakdown of the species available for observing in the program. The breakdown then would be how many observations do we have from represented for those different species? And that I don't know but it's absolutely a question worth pursuing and an opportunity, an open opportunity. Cool, I can ask one if no one else has one right now. So looking at your maps, obviously amazing spatial coverage so many hundreds of thousands of records but there are some white faces in there. It's interesting even with the citizen science observers there are areas that seem to be more or less covered. And so I wonder if you think is that something that you kind of actively try to do something about to sort of reach out to people that are more rural or don't live in population centers or don't live near university or you talked about like tribal partners maybe in certain jurisdictions or isn't it just sort of like you take whoever's interested comes to the network and they offer what it is or is there sort of more active from the network outward to kind of fill in the geography of observations? Alyssa, do you wanna jump in or would you like me to? Yeah, no, go for it. Okay, so I would say the answer is both really. Absolutely the way that nature's notebook is set up is that anybody and everybody is encouraged to participate for as long as they would like to participate but you're right that.  And then it's a big ask we really hope for observations on at least a weekly basis maybe more frequently when things are changing rapidly so you can really catch the start and the end of those events with high precision and then ideally to keep it going for years on end so we can have a really fantastic temporal record they're a good time series and it's a lot to ask for and so we recognize that it's a lot to ask and so therefore we say pick a site that's very convenient like right outside your door make it even such that maybe you don't even have to walk outside to make an observation you just stand at the window and so then that definitely leads towards a bias toward more developed more population density it just ends up following population density. We have definitely through particular campaigns and efforts put focus on particular geographic areas or species and that has grown data in some of those less data dense areas but that's of course limited by both available funds and staff and that kind of thing. One thing that we are trying to investigate right now is can we lower that barrier to participation to invite more observations? Recognizing that, just recognizing that what we're asking folks to do is such a heavy lift and we're really only going to get a pretty narrow slice of the population stick with us for a long time and so we've been kind of inspired by some of the other programs it's more like iNaturalist where you can make a very quick incidental observation you really it's very quick and easy to do it on your smartphone while you're out and about could we maybe do something like that for phenology as another way to kind of shore up what we've got in terms of the long-term observations and depending on the type of question that you're pursuing and the analysis that you wanna invoke those observational scattering just random yeses or noes that aren't part of a longer time series at a particular location may be indeed fine and well and good and so that's actually a pretty major shift to the database and the data model and the whole approach that we've evolved over all these years but we're exploring it as a way to kind of grow and really do a better job at trying to fill in some of those gaps. Is there anything you wanna add, Alyssa? Okay, we have a couple of questions from the audience from our own Katie Jones. Thank you so much for your presentation. One aspect of the NPN protocols that I think is very cool is the intensity data, not just whether phenophase is occurring but the extent to which a phenophase is occurring on an individual. Can ask questions about trends and rate of transition across years, species, et cetera, but this is still an underused aspect of both the NEON and the NPN phenology data. How can we promote opportunities to leverage these underutilized data in analysis? Alyssa, you should answer that one. You should definitely talk about the recovery. Katie's teeing me up but I don't even know if we've talked about this. So yes, we have been over the summer with a wonderful undergraduate student. I think the main barrier for people to use the intensity data from our data output tools is that it's been, so how many flowers you see 11 to 100, 100 to 1,000 and then what percent of those are open, five to 25, 25 to 50% and you have to track flowering through time. You have to do a bunch of data formatting and processing to get that information to identify start and end of peak. So we have a new product. We have both hopefully a publication and a new product, a peak phenometric product coming. I don't want to say anything about timeline. It could take years for us to get there but we'll at least be prototyping it and so that you could readily download information on, like this is when peak started for this species, this site, even maybe this region and this is when peak ended and use that data more readily. So I would love to talk to others who are interested in that and definitely something we're thinking about. I think that's the main barrier to usage is just the people understanding the kind of convolutedness of how it is right now and it just needs to be formatted more readily. Great. We have one more question but unfortunately we've run out of time. So I would ask that the person who asked the question stick around for a few more minutes so that we can ask the panelists. But I would, thank you so much for an extraordinary presentation and we really look forward to working very closely with the NPN as we move forward and hopefully everyone got as much out of this presentation as I did and I'd like everyone to, I'd like to open the invitation to our next presentation which will be in one month's time. January. January, okay. We're skipping December, have a great holiday but we will see you back in January. Okay, great. Well, again, thank you both for a terrific presentation and thank everybody for coming.


Today, we discuss closure properties of regular languages. Let us understand what do we mean by this phrase closure properties. Remember that the class of regular languages by that what we mean is all regular languages, no the set of all regular languages that we have been that is the one we have been referring to as the class of regular languages. And now, so this each element of this class is a language and it is regular l 1, l 2, l 3 and so on.  And when you take the union of these two languages you get another language. So, you can think of this way that union is a binary operation on the set of languages for any class of course. Now, as it happens and we note this fact and we will see that once more that the union of two regular languages is regular.  So, what is happening we have this binary operation in this case union we take two languages any two languages from this class and define the new language obtained by taking the union of these two languages. And what do I find that this new language the result of that binary operation is still in the in this class. Because since l 1 l 2 is regular it will occur somewhere in this class itself. So, in other words the operation binary operation union which would give me a language by taking any two languages from here. So, what we are saying once more is that union is an operation a binary operation defined on this class which when performed on any two languages in the class the new language that we obtain still belongs to the same old class. So, in that sense the operation of union does not give me any new language from this class, but the new language formed by taking the union of two languages is inside this. So, another way of saying this what people say that this class is closed the class is closed under union. Because you are not getting any new language when you perform this operation of union. Now, there are many possible operations in particular we will see a few which are binary as well as we will see a few which are unary. And we will show that under all those operation the we never managed to get any extra language by performing that operation on this class. So, therefore, the class is closed under union. So, let us we started with union. So, let us see this the class of regular languages is closed under and here I will provide a list of the operations list of some not not totally exhausted, but a number of operations under which our class is closed. First is union now what is the proof for that fact that the class regular the class of all regular languages is closed under union. Actually, we have seen this proof earlier let me remind you what we did was suppose I have two D F A's M 1 and M 2 and M 1 is Q 1 sigma delta 1 Q 0 and F 1 and M 2 is Q 2 same alphabet sigma delta 2 Q 0 let me put a one here and a subscript and F 2 and one of the classes that we had right in the beginning we had considered taking the product of these two sets of states. So, let me do it here sometimes the new machine M is called the product automation taking the product of these two D F A's. So, this has a set of states and that set is the cross product of the two D F A set of states Q 1 cross Q 2 and what is the idea for this product automaton let me write it here idea is. So, this is the product product we did not use this term, but let me use this now and that we can define in this following manner. The idea is this machine M will keep track of what happens to both the machines M 1 and M 2 at the same time and it does in a very straight forward simple way in its state it keeps track of the two states of the two machine and now when a symbol comes suppose I define this delta in this way delta now see the this state set of states is now pairs right. So, each state here is a pair. So, let me say Q 1 Q 2 is not it a state here is an element of Q and each element here is a pair. So, I wrote like that Q 1 Q 2 and where the first of the pair is a state of M 1 and the second is a state of M 2 right and now suppose I define the this delta in this way which we had seen earlier. This is supposed to give me delta is supposed to give me a state of this machine in the product automaton and suppose we define it as delta 1 of Q 1 A and delta 2 of Q 2 A. So, delta 1 of Q 1 A gives me the state the machine M 1 will be in when it sees a symbol A in state Q 1 and similarly delta 2 Q 2 A defines the state in which the machine M 2 will be when it scans the symbol A on state Q 2. So, you see what is happening you can see that suppose after scanning a part of the string x the two machine the machine M 1 was in Q 1 and the machine Q 2 M 2 was in Q 2 and the product automaton our goal of the product automaton is that it is keeping track in its head. That means in its set of states the what is happening with the two individual machines M 1 and M 2. So, since machine M 1 was in state Q 1 and the machine M 2 was in state Q 2 and now let us say this symbol comes then at this point clearly this will be the state in which the machine M will be the product machine. So, if you define Q and sigma this way Q and delta this way sigma is of course the same sigma as both M 1 and M 2 they have then Q 0 is of course very simple the initial state is what initially the two machines are M 1 and M 2. So, delta 0 the state Q 0 is the pair Q 0 1 and Q 0 2 the index the suffix 1 meant this is the initial state of machine M 1 and the suffix 2 meant that is the initial state of machine M 2. So, initially the product machine will be in this state and now it is very easy to see as we had argued earlier that the machine M on scanning a string x we can say delta hat of for this machine. So, let us say Q 0 and 2 on scanning x clearly it is going to be easy to see delta hat of Q 0 x this is 1 and this is delta hat 2 of Q 0. I am saying the same thing now in terms of the symbol delta hat and what we are saying is that the machine M on seeing x it is going to be in a state whose first component is the state in which the machine M 1 would have been on seeing the string x and whose second component is the state in which the machine M 2 would be on scanning the same string x. So, then it was easy in fact that is what we did for if I now define f as p 1 p 2 such that p 1 is in f 1 this picture or 2 in f 2 remember that f 1 is the set of final states of the machine M 1 f 2 is the set of final states of the machine M 2 and now what does it mean? If this product machine is in one of these states f that means either the machine M 1 has reached one of its final states or the machine M 2 has reached one of its final states. So, that means therefore any string which takes the machine M 1 to a final state or takes the machine M 2 to one of the final states of of course, M 2 then all such strings will be accepted by this machine M. So, therefore clearly the language accepted by this machine M is language accepted by M 1 union language accepted by. So, if you take any two regular languages of course, there will be two D F A corresponding to these two regular languages do this construction to obtain the product machine define the set of final states of this machine in this manner and you have another D F A which accepts the union of the two languages. So, therefore, we can see the class of regular languages is closed under union, but let me give you the same proof more simply now using the notion of regular expression. What do we want to prove that L 1 L 2 be regular union L 2 now that we know the notion of regular expressions and we also know the fact that for every regular regular language there is a regular expression which denotes that regular language can use that fact to prove this much more simply than what we did there. So, let me give you the proof using regular language regular expressions since L 1 L 2 are regular I can claim the existence of these two regular expressions let R 1 and R 2 be two regular expressions such that language denoted by R 1 is L 1 why can I why can I say this can say this because L 1 is regular and we have proved that for every regular language there is a regular expression which denotes that regular language language denoted by the regular expression R 2 is L 2 then by the very definition of regular expressions clearly then the regular expression R 1 plus R 2 by definition L 1 union that is the very definition of the operator plus for regular expressions. Therefore, you see this is a simpler proof for that, but that construction is useful when I want to show some other closure properties in fact the very next closure property that you would like to consider will be intersection. So, here what you would like to prove that if we are given two regular languages L 1 and L 2 their intersection L 1 intersection L 2 is also regular suppose we manage to prove this then clearly I can say that the class of regular languages is closed also under intersection. Now as it happens this kind of proof through regular expressions will not work as simple as that because we do not have any regular expression operation corresponding to inter section. However, this product automaton idea will work what is the class of what is the set of strings which are there in this set L 1 intersection L 2 these are precisely those strings which are both in L 1 as well as in L 2 by definition of intersection. So, what would such strings do to the machines M 1 and M 2 each such string which is both in the language accepted that by the machine M 1 as well as in the language accepted by M 2 all such strings will take the product automaton to a pair of states where both the states are such that P 1 is in F 1 and P 2 is in F 2 that is all I need to do in the definition that is all the change I need from that union definition of the product automaton to the obtaining a product automaton for the intersection of the languages this delta definition remains same q 0 definition remains same and now because of this change this is going to be the language accepted by this product automaton where the set of final states is defined in this manner just change the previous or to add that machine M is going to accept the intersection of the language. So, you see that product automaton became useful in this case and what about you know there are other Boolean operations. So, let me take another one which is complementation now what does it mean that I take a language L the complement recall was defined to be sigma star minus this is an unary operation as opposed to union and intersection which were binary operation on this class of regular languages. Here I take any language I perform this operation of complementation I get a new language and we say that this class is closed under complementation if whenever minus L whenever L is regular its complement is also regular in fact that is the case and how do we know that and again this is a fact something we have seen before if I take a DFA for L I swap the final states the accepting states with the non accepting states the resulting DFA will accept precisely the complement of L we have seen that. So, let me therefore see the class of regular languages is also closed under complementation now there is a binary operation which is something obtained by this notion of difference of two sets and that is set difference if you take L 1 and L 2 two languages which are of course, sets of strings. So, L 1 minus L 2 by definition is the set of all strings such that x is in L 1 and x is not in L again it is the case the that the class of regular languages is closed under set difference which is a binary operation and that is something which is again immediately obvious from this product machine construction again we just need to change the set of final states and now you will say what P 1 is in F 1 and P 2 is in F 2. So, all those strings x which takes the first machine that is the machine for the language L 1 to one of its final states, but does not take the second machine to one of its final states that means the second machine does not accept the string, but the first machine accepts that means if the first machine was for L 1 and the second machine was for L 2. Therefore, this machine will accept all strings which are in L 1, but not in L 2. Actually now that we had done these we could have said it more simply this result without going through the notion of product automaton because you see this another way of saying this would be what L 1 intersection L 2 complement is not this which are the strings which are here all those strings which are in L 1 as well as in L 2 complement that means all those strings which are in L 1, but not in L 2. However, since we have seen that regular languages are closed under complementation. So, if I take a regular language L 2 I do the complementation I get a new language, but that is also regular. So, as we are saying that suppose L 1 and L 2 are regular let me give that argument once more then we have already proved that L 2 complement is also regular and that follows from the fact that the class of regular languages is closed under complementation. So, since L 2 is regular L 2 complement is regular therefore, L 1 intersection L 2 complement is also regular why because in the same thing that I have two regular languages L 1 and L 2 complement and I am taking their intersection and regular languages are closed under intersection. So, therefore, the new language I get is also regular. Therefore, the conclusion is that class of regular languages is closed under set difference once more because I take any two regular languages I consider their difference L 1 minus L 2 and that will be regular because of this argument. See all these operations union intersection complementation set difference these operations are defined on sets. However, there are certain operations which are defined because these are sets of strings. In fact, we know a language is a set of strings and each such string in the set will be finite strings and you have seen some of these two most important concatenation and the cleanies star or cleaning closure will remind ourselves of this definition once more that is we say that we have two languages L 1 and L 2 two languages. Remember what was the definition of the language obtained by concatenating these two languages by definition it was the set of all strings x y such that x is in L 1 and y is in L 2. In other words the concatenation is a binary operation on class of languages obtained by the new languages obtained by taking a string from L 1 taking another string from another string or one string from L 2 put doing the concatenation. And these are the kinds of strings which will be there in the language which is the concatenation of L 1 L 2. Now, can we see immediately that the class of regular languages is closed under concatenation the binary operation concatenation yes indeed because again just think of regular expressions. Since to prove this that the class of regular languages is closed under concatenation again we appeal to regular expressions that will give us the simplest proof to what we will say that suppose L 1 and L 2 are regular then there are regular expressions R 1 R 2 such that the language denoted by R 1 is L 1 and the language denoted by R 2 is L 2 we know that because again the idea is for every regular language there is a regular expression which denotes that regular language. And what is the regular expression R 1 R 2 we know this that this regular expression will denote the language obtained by concatenating the two languages L R 1 language denoted by R 1 and language denoted by R 2 again this is the definition of concatenation for regular expression. So, since I have a regular expression for the language L R 1 L R 2 concatenated therefore, I claim that the regular languages the class of regular languages is closed also under concatenation same with cleanly closure that proof will be very similar only thing then will appeal to the fact that if R 1 is a regular expression then by definition. So, is R 1 star such that the regular the regular language denoted by this is the closure cleanly closure of the language L R 1 where L R 1 is the language denoted by this. So, if I take any regular expression R 1 and I take star of that of course that gives me the language which is the closure of the language denoted by R 1. So, therefore, again the class of regular languages is closed under cleanly closure there is one more example of closure that we had seen earlier which is the operation of reverser. You can see this that this operation is a binary operation on the class of regular languages this is also a binary operation on the class of regular languages.  So, that is a unary operation this is again going to be a unary operation and let me define that once more. So, L is a language over the alphabet sigma then what is L R reversal of L will take this way is the set of all strings x in sigma star such that when you reverse the string x R on reversing x you get x R that is in the language L. We had seen this, but let us remind one ourselves once more by taking a very simple example supposing L is just two strings 0 0 and 1 1 0 if we make it just very simple language with two strings. So, what we are saying then L R would be we are saying that you take a string from here reverse it you write the string the other way round instead of left to write you write it from right to left for the first string of course, you will get the same string back on reversal for the second string you will get 0 1 1 and this constitutes these two strings will constitute the language which is the reversal of the language L like to remind you what we did to show that if L is regular then so will be the reversal language L R briefly what we did was consider the DFA M for L we are recalling what we did to show that if L is regular then so will be L R we said that look consider a DFA for L call it M and there what you do very briefly I am trying to recall what we do is reverse all arrows in the transition diagram of M that is one thing that you do second thing that will do is maybe a picture would be better. So, this was Q 0 in the of M and let us see we had number of final states the second thing that we do is add a new state right and there are epsilon transitions to the old final states from which epsilon transitions defined to each old final state they are now of course, no longer final states. So, they are just ordinary states only final states will be the old initial state and then this new machine M dash we claim would have accepted the language which is the reversal of the language accepted by the old machine M. Now, that was a proof with that we had given then and it was more as an illustration of non-determinism remember non-determinism came about in two ways because you had epsilon transition as well as when you reversed the directions of the arrows in transition diagram from the same state on the same symbol now they could be more than one states that one could go to. So, we would get a NFA in general and that NFA it is not difficult to see would have accepted the reversal language, but like some of the proofs before now that we know regular expressions this proof also can be made much simpler using the notion of regular expression. So, let me provide the proof now again we will see that since a language L is regular you see this is what I am trying to show that if the language L is regular then it is reversal L R will also be regular. Now, this proof will be a little different from the previous ones because we did not have a direct operation for reversal as we had for concatenation as well as for linear start with our regular expression notation. What we can do is that we say that for every regular expression let me claim this write it properly let R be a regular expression then this notation is a little funny because R on top of I am writing R. So, let me make this instead of R let me make it a let a be a regular expression then a R the reversal of the regular expression now this is something I am going to define will accept a L of a but I have not yet defined what I mean by given a regular expression what is its reversal this I will do inductive. I want to now provide the definition of a regular expression reversal and these kinds of proofs we have seen earlier that I want to claim something here I am trying to define something over all regular expressions and we will do that inductively the way regular expressions themselves were defined inductive. So, remember the base cases base cases where that I had the regular expressions epsilon a and now intuitively what we are trying to do is that if we have a regular expression for the language I am trying to define the regular expression for the reversal of that language. So, I have here epsilon this regular expression stands for the language. So, let me write it language denoted by this regular expression is of course this now what is the reversal language obtained from here take the empty string you reverse it you will get back epsilon right. So, clearly let me define reversal of this is nothing but E r. So, this is a definition remember let me write it put it this way. So, that we know that this is a definition we are defining the reversal of epsilon to be to be itself and the same kind of reasoning will be true for these two also reversal of the regular expression a is the regular expression a itself by definition and the reversal of the regular expression pi is again by definition is going to be. So, what I have done that I have defined for the base cases of regular expression definition what the reversal means now the inductive step we call that we build regular expressions also inductively there after the base cases I had three ways of getting new regular expressions out of all regular expressions.  So, this is of course, a unary and this is these two are by. Now, let us see inductively we have defined a 1 r and a 2 r these are already defined then I defined a 1 r and a 2 r these are the reversal of this to be you take the regular expression a 1 take its reversal and now put a 2 take its reversal and similarly in this case and this is again a definition. So, the definition for the reversal of the concatenation language is going to be what and I will come to the reason why we are defining it this way a 2 reversal concatenated with a 1 reversal and a the reversal of the clinic closure is going to be we are defining it as take a 1 and its reversal and then the closure. Now, the claim that we have is see what we have done so far we have a and now we are defining something called reversal of the regular expression and what will finally claim that this regular expression will denote the language which is the reversal of the language denoted by the regular expression a and we will very clearly see this once we understand the motivation behind defining the reversal this way for regular expressions for the base case I have already given you the idea this is what I am trying to ensure. Now, let us take this case suppose I have a 1 and a 2 to regular expression then inductively we have let us assume language denoted by reversal of a 1 the regular expression a 1 is take the language denoted by a 1 its reversal now this is no longer a definition this is a claim because inductively we are making this a claim assume this and similarly l a 2 r is the language obtained by reversing the language denoted by a 2.  So, what is the language because this denotes the language which is denoted by this regular expression and what is its reversal by definition it is the set of all strings right which whose reversals will be denoted by the will be either in let me write it this way set of all strings x such that x r is in l a 1 or x r is in l a 2 remember this simple a capital A is the regular expression a 1 plus a 2.  So, if I just take the plus operation for this two regular expressions then clearly I will have this because by definition the language denoted by this regular expressions will be the set of all strings which are either is in this regular expression in the language denoted by this regular expression or denoted by this regular expression right. So, therefore, the reversal we defined in this manner and now you know inductively I can claim that if a 1 and a 2 are regular expression then the this regular expression a 1 reversal and a 2 reversal will indeed will be the denoted language let me let me write it l right denotes the reversal of what we are saying is if you take the two regular expressions a 1 r and a 2 r simply put a plus between them the new regular expression that you get that will generate all strings which are either the reversal of a string in a 1 the language denoted by a 1 or of a string denoted by a 2. So, therefore, what I am claiming now is that if I have two regular expressions a 1 and a 2 then their reversals their individual reversals if I now just put this in the then how did I define this for this you know it was defined this way and this is going to be the language which is the reversal of the union of the two languages denoted by a 1 and a 2 right. So, you see this is a simple simpler of this example 3 take this case concatenation what we did was that by definition I I had a regular expression a 1 a 2 then its reversal I defined it as take the reversal of the expression which is the regular expression of the second one a 2 reversal followed by the regular expression reversal of a 1. Now, again it is not difficult to see that if you inductively assume that a 1 r denotes the set of all strings which are in the language which constitute the language reversal of a l a 1. So, assume that is language a 2 a 1 r language denoted by this regular expression is language sorry this is a language. So, I need to take reversal here reversal operation is on the language when I do this I am getting a syntactic I am referring to the syntactic expression which we defined in this manner. Now, if this holds then a 1. So, let me claim this a 2 r a 1 r the language denoted by this is indeed the language obtained by a 1 a 2 l of a 1 l of a 2 and the language denoted by concatenate them and now take the reversal is this is also fairly easy to see see what is happening is when you take the concatenation of two languages and then you reverse that language that means initially you will get a string which is in the reversal of a 2 and next that is what you are getting here a 2 r a 2 r inductively will generate all strings which are in the language this followed by you have reversed it. So, now on the reversal finally, the last part will be a string in the language denoted by a 1 and therefore, this will be the situation. So, similarly for clinic closure and therefore, what I am trying to say is that using regular expression we can also prove the fact that class of regular languages is closed under reversal. So, what we have done in today's lecture is that first of all we defined an important notion called closure of a class and then we considered the class of regular languages and proved in fact most of the results were already known by us as examples of DFA NFA etcetera that the class of regular languages is closed under union intersection complementation set difference concatenation clinic closure as well as closed under reversal. And we have also found another interesting thing in this process that the fact that the class of regular languages can be captured by regular expressions that helped us in proving some of these results in a manner which is different or more simple. So, that will be the case always that since for the same class I have different ways of looking at either as regular expressions or as language or as you know or through automata. So, sometimes automata will give us easier proof sometimes regular expressions will give easier proofs for this. We will see some reason why other than of course the fact that these are nice things to know why closure properties are useful.


Hi everyone, in this tutorial you will learn how to check if two strings are anagrams in Python. Here we have two words and in this example we want to check if these two words are anagrams. The main idea of this algorithm is to use sorted function. Sorted function is gonna return alphabetically sorted list from the letters in a string. I'm gonna show you how that works on this example. I'm gonna print the result of this sorted function. We're gonna sort this first word and we get a list with alphabetically sorted letters from this word. So we want to check if the list of alphabetically sorted letters from first word is exactly the same as a list of sorted letters from the second word and if that is the case then these two words are anagrams and if it's not the case then these two words are not anagrams. Obviously these two words are anagrams but we're gonna check if our program is working. I'm gonna run it and you can see that this result is correct. That's all in this tutorial. Don't forget to check other tutorials on our channel. See you in the next tutorial. Bye-bye!


It's got to be a really good feeling when amongst your peers you are Recognized as one of the best especially when you've been putting in work for years. You've been grinding it out and Initially you may not have gotten the accolades and not that the accolades that they confirm anything But the accolade the accolades are a nice little bonus and that's exactly how it's been with one Marlon Humphrey That's Ravens fans. We really saw Marlon Humphrey coming out We we've been seeing how good he has been for a little while now But the world didn't really know about Marlon Humphrey the world wasn't really introduced to Marlon Humphrey But then in comes one Lamar Jackson and of course it wasn't all Lamar Jackson But Lamar Jackson was a huge part of things because in came Lamar Jackson and he brought a lot of attention To the Baltimore Ravens He brought a whole lot of attention and that attention spread through every single part of the team from coaching to players To prime-time games to just the focus being on those Ravens and Marlon Humphrey he got to be a beneficiary of that Now of course Marlon Humphrey with or without Lamar Jackson Marlon Humphrey. He's been doing his thing But now again with a lot more media attention and whatnot a lot more people have been seeing Oh, whoa, this this guy Marlon Humphrey number 44 and he's gonna be keeping number 44 by the way But this kid no Marlon Humphrey number 44. He's pretty good and he got another high level of recognition From one of his peers but not just one of his peers one of his peers that he sees at least two times a year and Boy with Ben Rothesburger coming back is gonna make those match-ups that much more intense Because and just thinking about it Marlon Humphrey Marcus Peters Tavon Young it really all all the cornerbacks of the AFC North They have to go against some pretty tough competition But more so Raven specifically because they face against the receivers of the AFC North Now a lot of times when you think of receivers in the AFC North You might like be like, okay, they don't have any of the top guys but When you think about it, maybe they do they of course got the Browns have Odell Beckham, Jr. In Jarvis Landry, and that is a beautiful one-two combination The Steelers they have Juju Smith Schuster now James Washington, and you know the Steelers They breed receivers like nobody else and now they got their quarterback back That's big Because last year while Juju and James Washington and the rest of the Steelers they weren't really anything serious on offense They were missing their most serious piece on offense but anyway The Browns Baker Mayfield and again like we mentioned Jarvis Landry and Odell Beckham, Jr. And then the Bengals Joe Burrow he's to be determined But they have if he ends up getting healthy. I know he's been sitting out a lot of practice They have AJ Green. They have Auden Tate who catches literally everything They have Tyler Boyd They just drafted T Higgins Like Bengals got a nice group of receivers. So being recognized as you know, let's get to the recognition Could we talking about recognition for all these great players in the AFC North? But not more than Humphrey. So let's see what Juju said. This was from Reddit from Reddit Phillip Milmore said, hey, Juju. Who's the toughest defender you've gone up against and why and Juju from his official reddit account. He responded and his answer. He said Marlon Humphrey Great player big defender plays the ball really well smart Instinctive he has it all as a DB love battling with Ultimate sign of respect Ultimate sign of respect and These are great characteristics of one Marlon Humphrey Great player. We talked about that early in the video big defender Now when he says big defender in my eyes, I don't think he's talking about in stature I think he's talking about that he he comes to defend. He don't play when it comes to defending Defending the territory defending the football just defending his side of the field Because that's him Marlon Humphrey and we've seen it happen before Marlon Humphrey can single-handedly take somebody out the game now There may be a little bit of holding here and then a little grab to the jersey in there, but He takes care of his business And moving on Plays the ball really well now we know Marlon's at that times he struggles with defending the deep pass Sometimes he gets a little lost out there when it comes to the deep pass, but overall Yes, that is very true. One thing about Marlon Humphrey Is what and it makes it why Marcus Peters is the perfect person opposite Marlon Humphrey man Because their strengths like they play off of each other strengths and they can counter each other's weaknesses What I mean when I say that Marlon Humphrey He will his goal is to make sure that you as a wide receiver You don't catch the football. That's his number one goal That's his number one target make sure that you as the wide receiver. You don't catch the football Now Marcus Peters on the other hand his number one goal is that he catches the football That he ends up turning to the wide receiver and he makes a better play on the football than you do And it's this just so it's a perfect pair man. We got that's all we got to get the Super Bowl like right now We should have got it last year, but okay last year's last year got to get it this year Because they ain't gonna be able to keep this team together forever. Anyway So plays the ball really well smart. Well, we know that instinctive Instinctive now the game actually against Juju as well from last year in Pittsburgh that comes to mind When Juju said Instinctive because in that game against the Pittsburgh Steelers Marlon Humphrey He and funny mallet the first two touchdowns of Marlon's career that he gave up because in his rookie year He didn't go up many touchdowns, but it wasn't until his second year I believe that he gave up his first touchdown But his first two touchdowns that he gave up his career came against Antonio Brown and AJ Green I believe but anyway in the Steelers game last year in Pittsburgh Marlon Humphrey wasn't him. Yeah in Pittsburgh Marlon Humphrey He I think it was one of one of the Steelers first drafts Juju caught the ball Marlon Humphrey was chasing him Marlon Humphrey caught up to him Marlon Humphrey tried to punch the ball out And he came up short Juju broke up touchdown And it's like we looking at Marlon we thinking about Marlon like why man? Why would you do that just tackle them you give the defense a better chance? Why you just trying to make this big play? What is you doing man? Come on, man It was like oh this guy so then It's over time It's over time Steelers get the ball I forgot whether it was Hodges or Rudolph it probably Rudolph because it was early in the season Whoever the Steelers quarterback was at that moment. They make a good pass to Juju. Juju catches the ball Marlon Humphrey The play earlier happened where he tried to punch it out and was unsuccessful and gave up a touchdown But he said you know what? I ain't worried about that that happened That was the past and we're gonna leave it just there so he used that same thumb that he used to point at to say that was the past to Try to punch that ball out and this time he was successful and that was the game Winning play of course Justin Tucker still had to make the field going well But that ended up being the a huge game changing play and it took great instincts because he must have felt in his mind I can get Juju to drop this ball. I can get this ball out of Juju's hands. I can knock this thing out I'm about to make it happen. I got to make it happen And that's exactly what Marlon Humphrey did He made it happen and that allowed the Ravens to win that game in Pittsburgh. No, what a game anyway And he also said he has it all as a DB love battling with him So, yeah, man, that's Marlon Humphrey in the in a nutshell, man Juju described Marlon Humphrey to a tee and he gave him his credit and it's that's that's that's a beautiful thing man I love when people Even though they play for opposite teams, they are obviously under the same umbrella the NFL and a lot of them are friends and whatnot But I just I love when people can give credit Where credit is due? I Love that and that's that's a beautiful thing, man. So this was special shout out to Juju, man And I'm looking forward to seeing Marlon go up against Juju and the rest of Steelers receivers and go against Ben Roethlisberger That should be fun. Oh Man this I just want that that Raven Steelers rivalry to get ignited again Because like I said, it has fallen off a bit. It's it's not the same as it once was and I've talked to multiple people about this but it's not the same as it once was and It's not just a lot has to do with the rules and whatnot But I think a lot of the players getting older and retiring moving on that changed a lot But I just I want that thing to get reignited like Browns Ravens. That's that's that's hot right now And I'm loving that But I want Steelers and Ravens to to get that old feel back and it may never get the old feel back But just get something with it. Anyway team keep it clean. Appreciate y'all. I love y'all and Just like the football said to juju Smith Schuster's hands when Marlon Humphrey punched it I'm out