Right, so go ahead and get started. So it's my great pleasure to introduce Sarah Hanson today for thesis defense. And so this is probably one most impressive audiences to assemble for a thesis defense here in a long time. Like a lot of splicing knowledge has space separated into this room. So Sarah joined my lab in 2012, coming from the University of St. Thomas through the IPID program. And my first impression of Sarah was that she's not as tan as someone as I thought who went to college in the Caribbean. But then I learned the University of St. Thomas is in Minnesota, so that helps with a lot of pieces of that together. So Sarah came into the lab with a strong interest in chemistry and chemical biology. And so she began working on an incredibly difficult project but it's one that I've been thinking about now for over 10 years. And the idea is that we've done a lot with single molecule work to study kind of the big picture events which are happening in splicing, but then we kind of need to take the next step and study things in a lot of detail to answer really important questions about how RNAs are recognized by the splicing machinery. And so this is an incredibly challenging project and Sarah has made absolutely terrific progress on this and hopefully the paper will be submitted quite soon on this. And it'll be I think something that will make waves within the splicing community. But she's also done quite a bit of other things in the lab. And so she also has a different project that is in press at cell chemical biology which is also I think going to be quite important for the splicing field and important for those who study splicing in vivo in yeast. And finally, Sarah's also mentored a large number of undergraduates and has been extensively involved in undergraduate teaching here at UW Madison both as a TA for my courses as well as volunteering to be TAs for several courses within the department. And she's won the Denton Award for undergraduate mentoring for all those accomplishments. And the number of undergraduates she's worked with has been really phenomenal and she's not even going to talk about that work but that's all been kind of slowly making progress on one of these splices homo helicases to understand it's basically it's biological function. And she has made absolutely terrific progress with all of them and taught them a lot about biochemistry and chemistry. So I'm extraordinarily proud to welcome Sarah to her thesis defense. And I wanna thank all of you for coming. I'm a little emotional because I see all my babies on the audience but I'll let Sarah take it away. Okay, thanks, Erin. That was very nice. So yeah, so thank you for coming here today. I'm really happy to be here at this point and to talk to you about this graduate research that I've done on intron recognition by the pre spliceosome. So an outline of what I need to talk about today, it is divided between two different research projects and they're united by their being about the pre spliceosome. So we'll start with some background on what the pre spliceosome is. And then the first story is about an in-depth single molecule kinetic analysis of five prime splice site selection by U1SNRP. And then the second story I'm gonna tell you is how we developed a new tool for studying the spliceosome, which targets a protein that's a component of U2SNRP. So to start with some background, so when the vast majority of our protein encoding genes are actually transcribed as precursor messenger RNA, which means that between the protein encoding exons, there's these non-coding intron regions. And these regions have to be identified and removed and the exons ligated together with nucleotide precision in order to get a correctly encoding messenger RNA. And that's the process of splicing. So how are these sequences recognized? Within the intron there are three conserved consensus sequences. There is at the five prime end of the intron where it meets the exon, there's the five prime splice site. At the junction between the intron and the downstream exon is the three prime splice site. And in between there's a branch point sequence. So this is what needs to get recognized. It's also involved in the chemistry that's going to result in these two exons ligated together. And the machine that is gonna do both the recognition and the chemistry of this process is called the spliceosome. It's extremely large. It's composed of five SNRNAs and dozens of proteins. They are organized into these complexes called the small nuclear ribonucleo protein complexes or the SNRPs. And they need to assemble on each intron in a stepwise fashion. And after they are all assembled they undergo dramatic conformational and compositional rearrangements in order to produce an active spliceosome. At which point this machine can undergo two steps of catalysis which produces an intron laryate product and the messenger RNA. After this process that messenger RNA is released and the components need to dissociate and be recycled so that this process can happen again on another intron. And what these projects are united by is that we're interested in how is an intron identified and selected so that it can be brought into this process. So if we look in closely at the process of assembly we're gonna look at this stage which is called the pre-spliceosome. So we have a cryo-EM structure as of this last year and what is happening in the pre-spliceosome there's U1 snrp with its SNRNA base paired to the five prime splice site. However you can see it's a very large complex because it has many proteins as part of its composition. And similarly the U2 snrp has its SNRNA base paired to the branch site sequence. And so overall it makes this very large pre-spliceosome structure. And what we're gonna ask in these two projects are how are splice sites identified? And it's a really important question to understand at a basic level because we know that about 14% of all disease related point mutations can be found at splice sites. And furthermore about 50% of all disease related point mutations change splicing in some way. So we wanna understand how this works in order to go forward and understand what happens when something goes wrong. So with that I wanna tell you the first story about U1 snrp. So U1 is responsible for five prime splice site recognition during spliceosome assembly. In yeast it's a really large complex composed of a single 568 nucleotide SNRNA and 17 proteins. And it's gonna associate with the five prime splice site sequence by a combination of SNRNA, RNA base pairing, protein RNA interactions, and then protein-protein interactions with other components of the spliceosome. And there's a really interesting thing that's going on with this association. U1 snrp has a single SNRNA and it's five prime and needs to recognize many five prime splice site variants. So in our genome we have thousands of variations of the five prime splice site sequence which is represented in the sequence logo. And these nucleotides all interact with the same 10 nucleotides at the five prime end of U1 SNRNA. This sequence is so important that it's perfectly conserved between yeast and humans including two post-transcriptional pseudo-uridine modifications. So how is it possible that it's so important that it's perfectly conserved and yet it has to be flexible enough to interact with all of this variation with the exception of two positions? So to keep in mind, G plus one and U plus two are nearly invariant because they're necessary for the catalytic steps of splicing. So our approach to answering this question is to use single molecule microscopy. We use a method called co-localization single molecule spectroscopy or COSMOS. And so this is a picture of the microscope that Josh Larson who's in the audience and with help from Mad City Labs, Eric's in the audience as well, help build. And what you do in this technique is we fluorescently label biomolecules and watch their interactions one molecule at a time. So in this example, there's an RNA that's immobilized to the slide surface and it has a blue fluorophore on it. And so because it's immobilized it's gonna be there constantly through the experiment. We can put in solution other biomolecules that are able to bind and they're fluorescently labeled. And by looking at the signal from those fluorophores separately we can see when binding events occur. Now to do this sort of experiment we have to first fluorescently label what we want to study. And I wanna study U1 snrp and I wanna study it in a purified system. To do that I worked with a yeast strain where U1 protein, SNU71 is fused to a tap tag and that allows me to use affinity chromatography to purify the yeast U1 snrp complex. In that same strain there's another U1 protein SNP1 that's fused to the snap tag. And the snap tag is used to form a covalent attachment with a fluorescent small molecule. In this case I have a small molecule that's both contains a fluorophore and a biotin moiety. And that allows me to immobilize U1 to the slide surface using stripped avidin. So this process requires me to grow about 12 liters of yeast and in the end what I get is a fluorescent purified complex of about 15 picomoles of U1 snrp, which is not a lot. It's enough to do a lot of single molecule experiments or very, very few biochemistry experiments. And we did do some biochemistry because we wanted to show that we had successfully purified an active U1 snrp. So to show its activity we did in vitro splicing assays. If you take yeast whole cell extract and incubate it with a radio labeled pre-MRNA you'll get the products of splicing as you can see here. And I removed the splicing ability in that yeast whole cell extract by ablating the five prime end of the endogenous U1. And you can see most of the splicing activity is lost. And in that background if I add back purified U1 you can see a return of most of the splicing activity showing that this complex is active. We also collaborated with the Smith Lab here at UW to do some mass spectrometry on what I purified. And we can see that all 17 proteins that are part of U1 are present. And in general you see a trend line where the larger the protein is the more peptides we detect by mass spec. Now in a few replicates I could detect non-U1 splicing proteins but you can see that despite how large some of these proteins are they're not detected frequently they're not detected in all replicates. And so we conclude that they're not there to an appreciable degree. We have purified an active U1 snrp. And so with that we were ready to go forward and do single molecule experiments. And this is what it looks like. So in an experiment I have U1 snrp immobilized to the slide surface and its fluorophore is excited by a red laser. And so you can see in this field of view a bunch of fluorescent spots and each one of those is an individual molecule of U1. In these experiments in solution there is a 29 nucleotide long oligomer which contains the five prime splice site and is labeled with a Psi3 fluorophore. So it is excited with a green laser. And it is only going to be excited when it's bound to U1 because only then is it held close enough to the slide surface and is no longer diffusing so rapidly that it can't be seen. So when we look in that field of view you can see where an RNA has bound to U1 by the co-localization of the two fluorescent signals. And we look at what happens at each U1 molecule over time and that generates a trace which is the fluorescence intensity from the Psi3 fluorophore over time. And when an RNA is bound to U1 you can see that appearance of that fluorophore in the video and a signal in the trace. And when that RNA dissociates you go back to no spot being present and back to background intensity. And the information we're getting from these videos and we're getting hundreds of these data points is the time it takes for something to bind and the dwell time of that interaction. So I'll show that what it looks like in a video form. In the case of this experiment the RNA that's in solution contains the yeast consensus five prime splice site sequence. You can see how it base pairs to U1 up here. And in yeast the consensus sequence actually includes an internal mismatch. So here's U1 on the slide surface. Here's a sped up video of those RNAs interacting with U1. And just qualitatively what you can notice is some of these are very rapid. They're only there for a frame or two and they're gone. But there are other interactions that are really sticking around for a long time. And when I actually analyze the distribution of hundreds of dwell times what I see is that that distribution is best described by a double exponential decay function which is also shown above. And what that means is that within the data there are two populations. There's a short lived population and a long lived population. They each have an associated tau and amplitude. So the short lived population has a characteristic dwell time of about 12 seconds and a long lived of about 120 seconds. This was a really exciting result for me to get when I first got these experiments to work because Josh Larson had been working on experiments where he was looking at how U1 interacted with full length pre-M RNA and mobilized the slide surface. And he was doing his experiments in yeast whole cell extract. So he can ablate some of these interactions by not having ATP in his experimental conditions by mutating the branch site, by having a cap analog that's gonna inhibit this complex binding. And still in these various conditions what he sees is a dwell times that are best described by a double exponential decay function. And my kinetics are also similar to those in yeast whole cell extract. And so what this told us is that there is this behavior that's intrinsic to U1 because I could see it in a purified system and what it's consistent with is a two step binding mechanism for how U1 interacts with the five prime supply site. So when U1 first binds to a five prime supply site it's able to dissociate rapidly and that's what gives rise to the short lift population. So we call that the weak complex. Now this weakly bound complex can transition into a more stably bound state which is slower to dissociate and that's what gives rise to the long lift population. And what was really nice about being able to see this in a purified system is I was able to go forward and interrogate how the sequence of that RNA, how changing the sequence of the five prime supply site is gonna affect various steps of this mechanism. So that's what I did. I designed a library of RNAs that I wanted to test to see how sequence affects this behavior. So the first thing I did was look at how changes to complementarity would affect it. So the five prime end of U1, the single stranded region is 10 nucleotides long so we could have an RNA that's perfectly complementary to the sequence and then just remove one base pair at a time to see where the mechanism falls apart. Now as I mentioned earlier that consensus sequence includes an internal mismatch in the helix and so we also looked at how position of the mismatch might affect the mechanism. And there was one more thing we wanted to look at. So this is with a purified U1 snrp but it has all of these protein RNA interactions that are contributing to the mechanism in some way. So I also designed an SN RNA MIMIC which has the same single stranded region at its five prime end to interact with RNA and solution and so we can look at these interactions when it's just two pieces of RNA binding. And I will say first of all when I put that SN RNA MIMIC down on the slide surface so same distribution of single molecules and put this RNA in solution I get what are the saddest single molecule videos you can possibly create. This isn't a video but it might as well be. There is no co-localization observed above background levels and that's true even when I was doing these experiments with an RNA that's fully complementary. So that wasn't great but we can interpret something from that. We can interpret that U1 snrp with all of its proteins is accelerating the on rate of this interaction. And so beyond that there was something interesting that we saw. The U1 oligo association is approximately the same across many diverse five prime splice site sequences. So something that's fully complementary to something that has very minimal complementarity has a very similar apparent on rate all within one order of magnitude. So that was an interesting thing to see. It says that the association is to a limited degree somewhat sequence independent. You have some minimum sequence complementarity that's required but above that it doesn't increase the on rate. Now that doesn't mean that the protein free experiments didn't bring us any information because what we can do is anneal all of the RNA pieces together in a high salt buffer immobilize the three pieces together onto the slide surface and then do a buffer exchange and monitor the rate of dissociation. So we can see the off rate in this way. And when I did these experiments I found that the RNA only interactions are governed by thermodynamic stability. So the off rate is a single step dissociates in a single step and there is approximately an exponential relationship between how stable that duplex is and what the rate constant is. Now when I do these experiments with U1 and I'm looking at the off rate for the stable complex what I saw was that once again this rate is approximately the same across many diverse five prime supply sites. And furthermore they all fall within the range that was observed in yeast whole cell extract. And so what that's telling us is that U1 is able to modify the stability of these interactions and this is in some cases a very large change. So for instance with the 10 base paired duplex the mean lifetime when it's a protein free interaction is more than 1800 seconds but the stable complex lifetime is only about 140 seconds it's making this huge change. And beyond being able to just modify these interactions it's doing so in opposing directions depending on the identity of the RNA. So it's stabilizing weak duplexes and destabilizing these strong duplexes relative to RNA only interactions. And the question that I had proposed at the start of this section was how does one U1 SN RNA interact with so many variants of the five prime supply site sequence. And so we think of it like the Goldilocks principle it's taking things that are too hot and things that are too cold and it can make everything just right. One thing that doesn't remain the same across a diverse five prime supply site sequences though is the amplitude of the long with population. And the amplitude represents the efficiency at which U1 transitions from a weakly bound complex to a stably bound complex. And we started to look at this in terms of end to end duplex length. So where you take complementarity that is for instance seven base pairs, contiguous base pairing and you treat it the same as a duplex that has six Watson Creek base pairs but also contains an internal mismatch. And if you think of duplexes this way and you look at the data what we found is that in general duplex length increases the efficiency at which U1 transitions to the stably bound complex but there is a sharp cutoff so that when the SN RNA duplex is less than seven base pairs long the stable complex is not observed. So this indicates that U1 has the ability to sense the length of the duplex that it's interacting with. And that is an interesting concept that is very much different from how we typically consider a five prime splice site. So this is a sequence logo for all five prime splice sites found in yeast. So if I show you this and I ask you what is a five prime splice site you would look at it and you would say it's G-U-A-U-G-U it's five base pairs and it has certainly not meeting this seven base pair length. So what we did is we actually went back to all of the annotated five prime splice sites that are in yeast and we looked at them not for their individual sequence but how long of a duplex would be formed with U1 SN RNA if you allow single nucleotide mismatches. And if you look at it this way you see that 85% of introns actually have a five prime splice site that would form a long enough duplex that we would predict they're competent for stable U1 binding. So this really showed us that sometimes you can't look at the aggregate of the data you have to look at things one at a time. And so what about though the 14% of introns that appear to be too short to be competent for stable binding? Well we can't say what's going on in each individual case but what we do notice as a trend amongst these genes is many are known to have low U1 occupancy and there's a significant portion of these shorter duplexes that have either unusual intron features or they're being regulated by the cell. So that's could be some of the things that are going on in the cell that explain why there's this division between longer and shorter duplexes. And overall we think that this agrees with what we are observing in single molecule experiments. So, you know, we had to concede this project and do almost all of this work without any structures for the yeast U1 snrp. We had no cryoEM data until 2018. And when finally we've got a structure of the yeast presplicis zone we had this really great observation that we could make. This is the presplicis zone structure where we're only looking at the duplex between the five prime splice site and U1 snRNA. And there are two proteins that form extensive contacts with this duplex. The first is U1c. It's a conserved U1 snrp protein. And the other is LUX7, which is a U1 protein in yeast but an alternative splicing factor in humans. And the footprint of these contacts between these two proteins in the duplex is seven base pairs long, the minimum length requirement. So this might be the mechanism by which it can sense the length of the duplex. The other interesting thing we see from the structure is that the five prime splice site in the structure contains mismatches to U1 snRNA or non-canonical base pairs. And yet it's in this extended helix. So it's possible that the U1 proteins are in these contacts can compensate for mismatches. And we wanted to know is the long-lived complex sensitive to exactly where the position of that mismatch is located. To test that, I designed RNA oligomers, which are complementary to U1 in order to form a seven base pair long duplex with the same start and end positions but with a different position of the internal mismatch. Now, if that internal mismatch is at the plus four, plus five, plus three, plus four, or plus five position of the five prime splice site, the kinetics are all approximately the same. However, if that mismatch is at the plus one or plus two position, the long-lived population is completely lost. And to be clear, U1 can still bind these RNAs but it dissociates with a single step and it's very rapid and that's consistent with only the weekly bound complex being formed. And what I want you to remember from earlier in this presentation is that these two positions are nearly invariant and it's true for both yeast and humans. And that's because they're necessary for the catalytic steps of splicing. So what our data is telling us is that U1 has evolved a kinetic selection for the conserved positions of the five prime splice site while retaining the ability to be flexible at those other positions. So all together, we think we've put together some rules for five prime splice site selection when U1 is not interacting with other proteins. We need to have at least five Watson Creek base pairs in order to observe binding at all. And then transitions into the stably bound complex are stimulated by additional complementarity. You cannot do this transition if the duplex length is less than seven base pairs or if there are mismatches at the plus one or the plus two position. So we conclude that what's going on in vivo when you have weak splice sites is that they would be unlikely to transition to the stable complex and thus would require other splicing factors to stabilize U1 to the sequence. And this is a starting point, a foundation for a lot of future study about U1. We can ask a lot of interesting questions having done this work. So for instance, which of these steps are dependent on U1 proteins? We can, for instance, delete a non-essential protein such as an AM8 or we can make mutations in the zinc fingers of U1C in LUC7, which contact that duplex and see if they affect certain steps or certain positions of complementarity. Another interesting question is, is there a role for these U1 proteins in the destabilization of some of the stronger duplexes that we tested? And Josh, in his work, actually found evidence in yeast host cell extract that U1C may have a role in this function. This would also be very interesting to go forward and study this mechanism, but with human U1 snub. So do the kinetics differ between a core complex and one that contains alternative splicing factors, such as LUC7, which is a part of U1 in yeast? Okay, so that is the end of one project. I'm gonna take a quick sip of water. And then my second project is how we developed a tool to inhibit the splice's own by targeting a protein called HSH-155. So when we study the central dogma in some of our model organisms, one really useful tool is to inhibit the process. And we have useful tools for small molecule tools for inhibiting transcription and translation, but we did not have a tool for inhibiting the splice's own in yeast using a small molecule. And that is what this project is about. And to do that, we targeted a protein called HSH-155. So this protein is a component of the U2 snub, and it is a homologue of the branch point finding protein SF3B1 in humans. So both of these proteins contact the duplex that's formed between U2 SNRNA and the branch site sequence. And the reason that we are looking to this protein is because SF3B1 is a hotspot for mutations found in several types of cancer, and thus it's been the target for several promising anti-tubor drugs. And we want to adapt this system in the use of these drugs to be used in yeast. Now, these proteins are very highly conserved, and the largest domain in HSH-155 is the heat repeat domain. It's composed of 20 of these two alpha helices motifs called the heat repeat motif. And this domain overall forms a clamp-like structure that binds to the U2 branch site duplex. Now with this duplex, the branch point adenosine actually gets flipped out into a binding pocket that's formed by heat repeats 15 and 16. This binding pocket, which you can see here in a structure from HSH-155, is the same site where these anti-tumor drugs bind for SF3B1. So you can see pladenalide B occupying the same binding pocket form between heat repeats 15 and 16. So that tells us that these SF3B inhibitors work in this way. When they occupy that branch point A binding pocket, this protein cannot form a stable complex with this duplex. There's just one problem. This inhibition is specific to SF3B1. It does not work in yeast. So I picked up this project from another graduate student named Tucker Karocchi. And what he had shown when he was a graduate student is that you can make chimeric constructs of HSH-155. You can replace heat repeats of this yeast protein with the human sequence and yeast are viable. Furthermore, he showed that you can take these yeast and make whole cell extracts and look at the splicing activity. And if you have replaced heat repeats five through 16 with the human sequence, that yeast whole cell extract is able to splice, but it's sensitive to the drug pladenalide B, whereas the wild type HSH-155 sequence is not sensitive to the drug. However, there is no effect in vivo. So if you put this chimeric construct into yeast and you put pladenalide B in the growth medium, you don't see an inhibition of growth. And that's where I picked up this project from because we wanted to develop a method to inhibit splicing in vivo in this important model organism. And the way we were able to overcome this problem, we had hypothesized that it was due to drug efflux. So the drug is getting pumped out too rapidly to observe inhibition. And so we started working in a transporter deletion strain where several multi-drug transporters were deleted and we put into these strains the chimeric constructs that Tucker had developed. So as I showed you before, if HSH-155 is wild type, it's not sensitive to pladenalide B in the growth medium. But now in this background, if you put in that humanized construct, you can see robust inhibition. And so we have developed a way to inhibit in vivo. And furthermore, this yeast strain is sensitive to inhibition by structurally diverse SF3B1 inhibitors. So in the future, this could be used to screen for drugs, to test the optimization of lead compounds. And we also saw that you can test specific alleles of HSH, or SF3B1. So when I put in a humanized construct, but it contained a point mutation that conveys drug resistance in humans, we see that drug resistance in our assay. Going forward, I wanted to look at the binding pocket at what is actually involved in this sensitivity. And so what we had done is overlay the structure of the two binding pockets, yeast and human, and align the sequences of these heat repeats. And for most of these residues, especially the ones that actually line the binding pocket, they are almost all identical. And there's two exceptions to that. There is, N747 is availing in humans and L777 is disparaging in humans. And so we wondered if these two residues could be responsible for the difference between HSH-155 and SF3B1 in binding these drugs. So I made, or I used single point mutations as well as a double point mutation construct and tested them using our assay. So if HSH-155 includes the L777N point mutation, there's no sensitivity. However, if it contains the N747V point mutation, you now see drug sensitivity. So a single point mutation is all that's necessary to see inhibition by SF3B1 drugs and yeast. Now, if you put those both mutations into HSH-155, you see an enhancement of that sensitivity. So L777N, while not being sensitive on its own, increases the sensitivity to this drug. I showed that this arrest of growth is due to the inhibition of splicing by using primer extension. So I put in a reporter pre-MRNA into the yeast strain and grew them in the presence of the drug. Now, if the HSH-155 is wild type, you see robust splicing of that reporter pre-MRNA with or without the drug present. But if the yeast contains the double mutation, the splicing of the reporter pre-MRNA is inhibited by about 90% in the presence of this drug or box of dying. So this together shows that we've developed a system that is a way to potently inhibit splicing in vivo and could be an important tool for the splicing community. We also looked at how these changes to the active site might affect its function in binding the U2 branch site duplex. And I did this with an undergraduate in the lab named Brandon Nikolai, and what we did is we put in an Act 1 Cup 1 reporter into these strains. So this reporter pre-MRNA, if it is properly spliced, you get the Cup 1 gene in frame and that encodes for copper tolerance. So the more efficiently this pre-MRNA is spliced, the better that yeast can grow on higher concentrations of copper in the plate. So if that pre-MRNA contains a consensus branch site sequence that's perfectly complementary to U2, we see no difference in growth between yeast that contains wild type HSH155 or the double mutant. But when we start making point mutations in the sequence so that there are now mismatches between the branch site and U2 SN RNA, we start to see a difference. If there are mismatches at the one or two positions upstream of that branch point A, yeast that contain the double mutant HSH155 actually grow better. So what we see is that the same residues which convey sensitivity to SF3B1 inhibitors are improving the splicing of branch sites that contain mismatches with U2 SN RNA. So the conclusions that we drew from this work. So SF3B1 inhibitors can arrest splicing and yeast growth when the binding pocket of HSH155 is humanized by the replacement of 12 heat repeats or by a single point mutation in that binding pocket. Mutations in that binding pocket convey inhibitor sensitivity and increase the use of branch sites that have mismatches with U2 SN RNA. So we believe this will be a powerful tool for the splicing community that wants to study what happens when you inhibit the splice's own in a living cell. And some of those things that we can, or that people will be able to test. So one question we're interested in is using RNA-seq, are certain genes or certain branch site sequences affected earlier or more strongly by this inhibition? Another interesting question that I think a lot of labs would be interested in using this technique for is what happens when you decouple splicing from other processes that are occurring in the cell, such as the maintenance of chromatin state or the RNA polymerase, which we know is coupled to splicing? One question that I would be very interested in is what happens to U1 occupancy when pre-splice's own formation is inhibited? So, yes, with that, that's all the research I have to present to you today. So first and foremost, thank you, Erin, for your help during this project. It was a difficult one, and I feel like we got through it together at difficult at times, great at the end. And thank you for your mentorship, and I want to thank the whole lab for the support that I've received while I was here. I have some great lab members, some of which helped very directly on this project. So Brandon Nicolai is an undergrad in the lab who helped a lot with the HSH-155 project. I stood on Tucker's shoulders to get that HSH-155 project. So thank you for all the work you started towards it. For the U1 project, we collaborated with Floyd Smith Lab and Mark Scalf to do the mass spectrometry. So I've been supported by the integrated program in biochemistry, and I've received a lot of support from the chemistry biology interface training program as well as funding from the NIH. Here's our happy lab. We do a lot of fun stuff together as a lab. We have a lot of fun lab activities. And just a lot of opportunities to travel and go to really fun places and talk about research and hear great research. And I think that the lab, I chose the reason I got to have all of these opportunities. And furthermore, we didn't just interact in the lab space. This was a great group of people that I met in the lab or friends that I made or brought with me to graduate school and that friendship blowing off steam when it was necessary was a really important part of getting to where I am today. So I mean, I had people who flew in from Yale, Johns Hopkins and University of Washington to come in to see me defend. And I appreciate that so much to have fun and do some of this one more time. But I think the most support that you receive is from your home life. So I think Vlad has literally carried me at times through the last six years. So I think, I don't know why you were surprised when you saw the dedication page and you're like, you dedicated your thesis to me. And I was like, yeah, I didn't get here except for you. And so, yeah, thank you, Vlad, first most. And to my committee, just so you know, you might want to take this into consideration. Vlad and I did say that once one of us successfully defend, our cats get honorary PhDs. I'll just say in their defense, that one can open doors and that one can scam out a second dinner out of a second person. So they're kind of smart. So, but thank you for coming here today. I really appreciate getting to talk to you about my work and I'd love to take questions about this. Thank you. Yeah, Heidi, I saw your hand go up first. I don't know if you need to replace 12 or 12 heat repletes. I think there is work coming out of the areas lab too where they just replaced heat repeats 15 and 16. And I think there's drug inhibition in vitro as well. So Tucker was just looking in his previous paper at what chimeric constructs were viable. And he found that this particular chimeric construct is both viable and sensitive to in vitro inhibition. So that is why it became our starting point going forward. I think there could also be a role for the U1 SNRNA structure in limiting this influx of light. Because I recall it's the five prime supply side binding that is very close to a four helix junction or an extensive secondary structure in the RNA which I'm wondering if that might help prevent recognizing too far into the exosail of light through the light forward because you would be further away. Yes, I think that's very possible as being a limitation for how far base pairing can extend in this region. So one thing that we are testing going forward before we publish the paper is shifting the seven base paired duplex to see what happens. So for instance, the big question there is, is it any seven base pairs of complementarity or does it need to be precisely positioned? Because I agree there could be constraints that come from having helix one start just a few base pairs upstream of the five prime supply side. Yes, hi. Yeah. The connect. Mm-hmm. Josh's work did show that the branch side is contributing to the association of U1 with the five prime supply side. If he deletes both the branch side and the pseudo branch side, it significantly reduces the long lift population. And so there is, when I say the kinetics are approximately the same, that's what we're kind of getting at is that they're not different by an order of magnitude. They're two-fold different and that purified U1 keeps it at that same level across it. So it definitely is shorter in yeast-hole cell extract if you don't have interactions with the branch point binding protein. No, I haven't. I think that's very interesting, but we haven't looked at that yet. I think we have all the data at hand. We just haven't analyzed it in that way yet. Yeah, we got, we share the. Are there any other questions? I'll ask it. Yeah, hey. Yes, in yeast. Yes. Oh, you're saying where that base pairing is of the short duplex? That's possible. I don't know for sure about those short duplexes. One of the unusual features we see is actually a long five prime exon, short one, but that might be a mechanism, both the length of the exon and the weaker five prime splice site might be a mechanism of controlling that particular transcript, but I can't say anything about the particular genes. Into the closed session, but I think that's an interesting question. So normally, like when you have something that's conserved, conserved's a particular sequence for a particular job, but here, it conserves spliceisome. It's conserved, but it seems like from your talk, it's conserved in order to allow variability. Yeah. So that's kind of interesting. It's like a little backwards from normal. And I wondered what the selective advantage is of nature doing it that way instead of having nature just make all the splice site sequences the same, which would have been the more obvious thing to do. I think the advantage of this is that it allows for other steps of regulation where you won is not the ultimate regulator of how well a particular intron is spliced. It's saying this has a GU and it has the minimum amount of complementarity that it could very well be a five prime splice site, but it also gets defined by other features like the cap binding complex, branch point binding, and then before catalysis by the spliceisome, it's exchanged with U6. So I think that why wouldn't there just be one sequence that's always used? I think it allows for transcriptional control. So some of these introns that only, you only want to be spliced and expressed at levels during meiosis, for instance. You can control that by maybe having a low level of affinity baseline for you one, but then you express other factors during meiosis that will promote that interaction. So you have all these protein-protein interactions that can be dependent on cellular context and control. Because it gives you flexibility in changing the splicing when you want to by having other factors get kicked in. Yeah, so you can be inefficient under some contexts and efficiently splice that transcript under other contexts. Yes? That affects splicing. And so if you go back and sort of map the splice sites, are there any patterns that jump out that? I'm not sure about that. And that 50% figure means mutations that will put a point mutation into a splicing factor, like a mutation that'll make HSH-155, a cancer associated mutation. So, yeah. You know, I can't think of any off the top of my head. And I don't know if there's, I don't know if there's a very particular pattern. Thanks, Sarah, for the wonderful talk.


business needs now. Cashless transactions rose by 44% year-on-year to heat 117.33 trillion Naira in the first four months of 2022 and that's according to data from the Niger interbank settlement system NAPS. From January 2022 to April this year 117.33 trillion Naira was processed through electronic channels which is 35.79 trillion Naira more than 81.54 trillion Naira that was processed in the corresponding period of 2021. Cashless transactions are monitored under NAPS through the Niger instant payment system and point-of-sales terminals. In January 27.22 trillion Naira was processed electronically in the nation. This increased to 27.76 trillion Naira in February 35.52 trillion Naira in March and 29.84 trillion Naira in April. In January 2021 18.99 trillion Naira was processed electronically 18.79 trillion Naira was processed in February 22.55 trillion Naira was processed in March and 21.19 trillion Naira was processed in April.


Stevenson and Elizabeth town finish in a 2-2 draw line Clark now with Stevenson the head coach Tati Korba Coach, I guess if you could try to measure for me the disappointment in not coming away with a victory versus how you feel about your team Showing the fight and digging their way out of a 2-0 hole today. Yeah, I thought great resiliency You know to be down to nothing and to come back and generate a lot more chances and have a couple cleared off the line and You know sometimes I You know, it's I think it's just been that kind of season for us I know it sounds repetitive, but we're doing a lot of the right things Made some corrections at halftime. I think that that were important but again, I think just just great fight to come back and You know again, or the record is not indicative of how we're playing and sometimes in soccer, you know the results Take care of themselves in some ways We'll continue to you know to keep fighting and honestly to keep playing the way that we're playing We've got some adjustments we can continue to make and to improve some things, but You know proud overall of the effort today once again One of the things that jumped out at me the play Keegan-Caffery in the first half She had the one that sort of leaked out and landed the rebound opportunity And I think a lot of players maybe would have been doomed by something like that But she really dug in and made the plays when you needed them to be made after that and was very sure-handed the rest Yeah, I mean this is only Keegan's you know, maybe sixth start. She's a sophomore and We've just been so impressed with with where she is and Mentally, I agree. I thought it was just a great rebound You have to have a short memory as a goalkeeper and I thought Keegan did a great job just kind of putting that behind her and coming out strong and Refocusing on the next one and made some some nice saves second half I saw a lot of creativity on the corner kicks today and it led to that goal that sort of got things started in the first half I guess what where's your bag of tricks? How much do we still have in there? Did you have you thrown everything at us yet on the corner kicks? Definitely not something that I'm going to tell you Or share but we have been working a little bit more on corners You know, we've been generating a lot and feel like that's a good opportunity for us So we'll continue to mix things up and hopefully generate some more goals from there work today coach I guess we say congratulations on what ended up being a result after where it could have been down to nil best of luck moving forward on Wednesday Thank you. She's Toddy Korba. I'm Glenn Clark for go Mustang sports calm


Welcome Traders, Patrick Munley here with another Tick Mill chart. I'm going to draw your attention to a developing opportunity on the four-hour chart. This is the Kiwi Dollar potential test here of descending trend line resistance coinciding with predicted daily range resistance. Looking at this 6610, 6620 area, we're trading below the weekly pivot, sorry, just at the weekly pivot, below the monthly pivot. So I'm looking for a rejection candle here on the four-hour timeframe from this 6620 area. I'm looking to set short positions, headed down for a retest of the lows here at 6510. If we get through there and through predicted weekly range support at 6496, look for the test of descending trend line support 6350. As always, Traders, plan the trade, try the plan, most importantly, manage your risk. Until next time, thanks very much.


This is Stockmer 11095. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used like-duty truck headquarters. Today we are checking out this Super Clean 2015 Ford F-150 Crew Cab 6.5 foot box. This truck has the 3.5 liter V6 EcoBoost Twin Turbo motor which pumps out 365 horsepower. This truck has been fully safe and inspected by our service shop per the state of Wisconsin inspection process. It has a fresh oil and filter change. All the fluids have been checked and topped off and this truck is 100% ready to go. Ignite silver is the color. We shoot all of our videos in 1080p 60 frames per second so if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is definitely your best way to check out the quality and condition of the truck before seeing it in person. And if you'd like to check out all the photos on this truck in the upper right hand part of your screen is the link to our website. Click that and check us out. There it comes with the 20 inch polished aluminum rims and it has like new Michelin 275 55R 20 tires with just about all the tread left. I'd say at least 90% of the tread left on those tires. Very very new. Front fender is in excellent shape. I didn't see any dents or dings on that. This one does have the LED headlamps, the LED running lights and the factory fog lights. Front bumper is in excellent condition. I didn't see any dents or dings on that. Headlight lenses are nice and clear and you do get that platinum front grille. The hood is in really nice shape as well. I didn't see any major dents or dings on there and the passenger side front fender is in excellent condition too. This one does have the 360 camera, passenger side rim, no scuffs or scrapes and also has the sensors and everything for parallel park assist and as you go down this side of the vehicle you can see just how clean the body is how reflective and mirror like that paint is. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down but you're still interested in purchasing the truck you can see the truck hear the truck and have confidence in the vehicle that you were looking at before you even get here so that when you do get here there's absolutely no surprises and that is why we offer the Summit Auto Fastpass option in the upper right hand part of your screen. A link right to our website where you can apply for financing, get pre-approved, see a payment quote even appraise the trade all from the comfort of your own home so when you get here all you got to do is drive the truck love it and you'll be all set to go. Back tires are just as new as the front tires and you can see just how clean that frame and underbody is absolutely no corrosion and it's like that all the way underneath. It has the power running boards lower rockers all look really good bed rail covers on every F-150 and it does have the chrome tipped exhaust that's in really nice shape as well. Rear bumper is in great condition I didn't see any major imperfections on there it does have the backup parking sensors full towing package which includes a receiver hitch four pin and seven pin wiring has the power drop down tailgate so you just press the key twice and it'll come on down like so it has the shock down assist so it's never going to slam on you this one does have a bed mat a uws toolbox and you do get the led bed lighting back here you can turn those on with that button and it also has side box tie downs also turns those cargo lamps on up there tailgate shuts nice and solidly and that tailgate is in really nice condition as well you can see it's got the nice platinum applique on there down the driver's side just as clean as that passenger side didn't see any dents or dings on the box and for full disclosure this back rim is in pretty nice shape as well it does have the capless fuel fill which is a nice feature and as you go down the rest of this side of the truck looks really good no dents no dings it does have the driver's side door code entry we do have the code for that has the blind spot monitoring in the mirrors led side lights and these mirrors telescope out like so they also power fold in and I'll show you how that works in just a second get power windows power locks power mirrors memory driver seat speaking of those seats you get kind of a burgundy brownish leather interior with the black accents no rips or tears on the sides there looks really good you got the platinum button or insert on the back there memory driver seat and then this is your lumbar and massaging seat controls which are pretty cool I'll show you those in the second factory floor mats has auto headlamps power pedals and then those led side lights as we hop inside the truck here we'll turn on the ignition so you can see everything on the instrument cluster you get the animation at the beginning there this one has 41,401 miles and you get the digital speedometer compass display there as well and of course all your different apps that you could do in some instrument clusters very nice and clean this one comes with the heated leather wrapped steering wheel bluetooth and audio controls on the right cruise controls and information center controls on the left it also has adaptive cruise control turned dial four wheel drive push button start this one has the ford my touch radio and it has am fm and serious xm radio capabilities on here you also can do your climate controls where you get heated and cooled seats as well as your heated steering wheel button and of course all your climate controls and then it does have the factory navigation system so you got to press the button on the seat here to get to the massaging seat portion or the adjust for your lumbar and that's honestly it'll like pump up the seat and the backrest for the massaging effect it's actually my favorite feature on these platinum f150s and a really cool thing this one does have stability control it does have the sony sound system and it does have the 360 camera which is also a very neat feature and then if you keep pressing that camera it'll change which camera so that's the front of the vehicle and then you get a side down the sides of the vehicle as well and um of course it does have a backup camera too down here is your cd player and your more tactile climate controls you also have heated and cooled seat buttons factory brake controller and then two usb's and an sd card slot has the automatic transmission shifter there lane departure and then parallel park assist so if you press that button on there you can get your parallel park assist i think you got to have the vehicle on for that to work anyways you get 110 volt 400 watt max plug-in and then the passenger side format and seat are in excellent condition as well that passenger seat massages too and the headliner is in really nice condition on this truck you do get the home link buttons for your garage door security systems and lane systems power sliding rear window button and of course your map lights up there we'll take a quick look at the back seats and then we'll start it up back seats are just as clean as the front seats no rips or tears back here these back seats are heated on the outboard sides you do get the latch child safety system for any child car seats power sliding rear window with the built-in rear defrost these headrests do fold down or you can just remove them for better visibility and you do get those platinum badges on the back rest back here as well very nice condition these seats do fold up for extra storage looks like it has an extra air filter in here and then you do have heated seat buttons back here as well as another 110 volt 400 watt max plug-in child safety locks on the back doors and we'll start it up and take a quick look under the hood also has power tilt and telescopic steering wheel show you those led side lights as long as we're heading up and light up everything on the side of the truck pretty good chrome trim mirrors and I would personally like to thank you for checking out the video today and hopefully from this hd video you'll have been able to tell just how clean this truck is all the way around inside now under the hood we have the 3.5 liter v6 eco boost twin turbo motor engine based very clean runs very smooth this truck has been fully safety and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off has a motorcraft battery usually a good sign it's always been serviced at a Ford dealer and this truck is 100% ready to go and to see more pictures of this truck or one of our other 450 new and used cars trucks scvs minivans wranglers half tons three quarter tons one tons you name it we got it go to that website right there www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summitauto.com and if you'd like to check out more hd videos you can go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos that you see there in fact in a second you'll see link to subscribe to our youtube channel on your left a link to more Ford f-150 vehicles like this one on your right if you've not been to our website on the bottom link to this vehicle on our website click those check us out we really look forward to helping with this super clean 2015 Ford f-150 crew cabs six and a half foot box platinum addition and ignite silver metallic thanks again for checking out the video


Hi, I am Zor. Welcome to Unizor Education. Today's topic is quantity among different fundamental concepts of mathematics. Well, everybody, I'm sure everybody knows what actually the common term quantity is, but in mathematics it's it's special as everything else. Quantity is a rather complicated object in math and I would like to start from a very philosophical standpoint. If you, let's say, consider a set of six buildings and six cows, well, they don't have anything in common, right, except the number six. So if you have two different sets, probably one of the very probably the only property which they have in common or they might have actually in common is their quantity. Okay, so fine, number six in case of six buildings is a property of a set and number six is a property of another set. Here are houses and the buildings and here are the cows and this is the common property. So what we can actually say that at least finite sets might have certain common characteristic. Now, how do we establish that the number of elements in a set of six buildings is exactly the same as the number of elements in a set of six cows or six anything? Well, for this purpose there is a concept which is called in mathematics one-to-one correspondence. So let's just spend a little time and explain what one-to-one correspondence actually is. If you have certain set of elements and I'm not actually talking about finite set sets anymore, I'm talking about any set which contains certain elements and you have another set of elements and you have the rule which from each element of one set you can always find a corresponding element of another set and what's very important is that different elements of this set which we can call the source if you wish, if they're different they are corresponding to different elements of another set. So if these are different then these must be different as well. So this is half of the definition of one-to-one correspondence. Another half is just an opposite. If you have all the elements of this set then for each one you should be able to find the corresponding elements of this one. So this is A, this is B. So we have a correspondence from A to B which is unique. Different elements should correspond to different elements from the image and it should be inversible which means for every element of the set B you can find corresponding elements of the set A and again different elements from B should correspond to different elements of A. So this is a mutual unique correspondence, unique because if sources are different the images must be different and it's mutual because the inverse is supposed to be true as well. Now if these rules, these correspondence between the elements does exist then we can say that there is a one-to-one correspondence between sets A and B. Now here is a very interesting detail. It's just one of the particular case of correspondence if you wish because if you take all the elements from A and map them to elements of B and if we assume that elements of B are completely filled up which means there is no element in B which is not filled by this particular correspondence then we can always say that inverse correspondence also exists because for each element of B since it's an image of something from A we can always say that the corresponding A element is the source which actually corresponds to this element of B. So in this case instead of drawing these two different errors, well actually I can use this, I can use the same but bidirectional error. So every correspondence can be bidirectional. Now this is a particular case of one-to-one correspondence. It's not actually necessary that it will be the case always and here is an example. Let's go back to the buildings and cows. So let's say you have a square building, a triangular building and a round building and cows are called let's say A, B and C. The correspondence between the buildings and the cows can be this and inverse correspondence can be this. This is our case I was just talking about but at the same time I don't have to really establish the inverse correspondence exactly in the same way as I established the direct correspondence. I can always say that in reverse they are this way. So there is a rule which are errors directed down which establish the correspondence between the buildings and the cows and two different buildings are corresponding to different cows obviously. Now the inverse correspondence also exists from A to triangle from B to a circle and from C to a square and it's also a unique correspondence because different cows correspond to different buildings. So depending on how I establish the correspondence it can be of this particular kind when it's just mutual or it can be of a different kind but in any case it's still one-to-one correspondence. So I would like actually to be very very clear that one-to-one correspondence is number one bidirectional and number two it does not have to be bidirectional in this particular way which means if element A corresponds to element B it's not necessary that B also corresponds to A. It can be something else like in this particular case but it's important is that both directions should be unique which means different sources should correspond to different images. Okay now let's talk about finite sets. Now in case of finite sets there is an obvious statement that only the number of elements is the same then we can establish one-to-one correspondence. Now why? Well obviously you can consider let's say you have two different finite sets. One is with three elements and another is with four elements. Now this direction can be unique without any problems because you have only three elements and you have four choices so you can always find a unique image for every source element but when you go backwards you have to have a unique correspondence between four elements and three images of these elements and obviously I think there is a name actually in this principle it's maybe Archimedes some kind of a mathematician. The principle is that if you have more elements in this set than in this then there is always something left it's like musical chairs you have a certain number of people and the number of chairs is less than the number of people somebody will be out of chair so there is some element in the bigger set which will not be which will not be corresponding to something which was not really touched before by this correspondence because you have three elements here three elements here but the fourth element will not have any unique image. So if the sets are finite then the one-to-one correspondence is related to the number of elements. Now another very important property of one-to-one correspondence is it's transitive now what it means is the following if a one-to-one corresponds to b and b one-to-one corresponds to c then a is in one-to-one correspondence with c now how can that be proven well actually it's quite easy let's say you take an element a now using the direct correspondence you get an element b now from b you get c now what you can say is that a to c establishes the correspondence from a to c now is it unique well let's just check if a and b are if a one and a two are different then b one and b two are different because this is a one-to-one correspondence between a and b now since b one and b two are different then c one and c two are also different so this correspondence for different for different elements from a produces different elements from c one and reverse is obviously true in exactly the same way so one-to-one correspondence is a trend that's very important now let's go back to quantity now we all kind of used to the fact that the word quantity is related to counting and obviously with finite sets we have established that the quantity is something which sets can have in common completely different sets can have in common and that's the number of elements that's the quantity actually by definition so if you want to say what's the quantity of elements of certain finite set well you have to establish the one-to-one correspondence between this finite set of elements and another set which is one two three up to m natural numbers so if there is a one-to-one correspondence between your set and set of the first n natural numbers then we can say that the quantity of the elements of this set is equal to m this is the definition basically that's it so the quantity is defined as a correspondence of the elements of our set with a subset of the first n natural numbers that's what quantity equals n means and from this actually we can say that the quantity of two different sets which have the same element which means they are mapped to the same there one-to-one corresponding to the same subset of natural numbers so if this is quantity n and this is quantity n and then we can say that the quantity of these two sets is the same they are equal in their quantities if you wish so that's the quantity of the finite set but this is just the beginning as always there are much more complex things and mathematicians always find something to to exercise their brains a little bit further so where are the complications complications are in the infinity okay now you know what the quantity is and you probably feel quite comfortable with finite quantities let's talk about infinity well the first infinity which we might deal with well first of all infinity is something which is a completely pure creation of our mind there is no such thing as infinity in the real life i mean yes there are some physical theories about infinite universe etc but this is all kind of theories you cannot in a normal way in a regular practical way establish the fact that something is equal to infinity so we are talking about creation of our minds infinity is in our minds so what's the first set with infinite number of elements which we can deal with well obviously this is a set of all natural numbers etc what's important is this in fact this is etc that's what make it infinite change the market all right um how big is it well it's infinite right but we would like to compare infinite sets in exactly the same fashion we compared the finite set which is one-to-one correspondence well let's talk about another infinite set let's talk about natural numbers but not all of them but only let's say even ones so it's two four six etc this is also infinite number and it's obviously smaller because this is a subset of this so we took only every second number so it should be smaller right well wrong it's not smaller first of all the words smaller or larger bigger or whatever they are not applicable to infinity there's no such thing as a smaller infinity however there is a way to compare different infinities we're just not using the word smaller bigger infinity we're using some other words which i will introduce in a little while so first of all let me talk about these two infinity infinities my statement is that there is a one-to-one correspondence between them and if there is a one-to-one correspondence between them we cannot say that one is more infinite than another they are both equivalent to each other so there is a new word called cardinality there's nothing to do with church cardinals so the cardinality is basically an equivalent of the word quantity but applied to infinite sets so my statement is that the cardinality of these is the same and because they are in one-to-one they can be put into one-to-one correspondence well how very easily now this direction is y is equal to two x where x is element of this and y is element of this now this is basically a correspondence a unique correspondence from this to this why is it unique well because it's defined on every natural number which is an element of this set and two different numbers using this function will correspond to two different even numbers so this is the rule basically that this correspondence should be number one complete it's defined everywhere and unique so two different elements would correspond to two different images now how about the way back well actually in this particular case we can have the way back using this function so for an element two of this my corresponding element would be one for four it will be two for six it will be three etc etc in this case by the way this particular correspondence is double double error because if this element corresponds to this using this transformation corresponding rule of correspondence then the the way back is exactly what this particular thing is so using these two correspondence rules we have established one-to-one correspondence between these two seemingly different sets because this is definitely a subset of this however both are infinite and both infinities are in some way equivalent which in in in more precise terms sounds like the cardinality of this set is exactly the same as the cardinality of this set which cardinality means it's a it's a replacement of the number of elements or quantity but four for infinities so the same cardinality means that there is a one-to-one correspondence between two sets but maybe all infinities are of the same cardinality maybe I can always find the correspondence between all the different infinities is it right well this is definitely wrong there are more infinite infinities and less infinite infinities if you wish and I'll just give a couple of examples for instance the number of points in a segment cannot be put into the correspondence into one-to-one correspondence to a number of natural to a set of natural numbers now this cardinality of this is definitely greater now why well I can definitely put this correspondence how well there are many different ways but for instance I have divided this segment in two halves and call this point corresponding to this then I divide this into two halves and I made the correspondence with a number of two etc so every time I divide by half and I can find from and for each number I can find a point so from this set to this I can find the correspondence which is unique and defined everywhere but not the vice versa why it's a different question and it's not easy but that's actually a true statement there is no correspondence unique correspondence from each point on the segment and and natural numbers so the next lecture I will actually talk about different examples well primarily infinite examples of different sets and I will compare their cardinality but for now I think this is enough to basically introduce you to a concept of quantity and cardinality applied to infinite sets just as an introduction to the whole concept so that's it for this particular lecture and don't forget that there are problems in the next lecture associated with this one which are very very important to understand this whole business of quantity and cardinality better okay so that's it for today unizord.com is where you can find this and many other interesting educational materials and parents are definitely encouraged to use this side to supervise and control the educational process of their student okay thank you very much and good luck


Form 8862 may be required, so if your CTC child tax credit, refundable or non-refundable depending on the tax year, ACTC additional child credit or ODC other dependent credit for a year after 2015 was denied or reduced for any reason other than a math or clerical error, you must attach form 8862 to your tax return to claim the CTC child tax credit, ACTC other child tax credit or the ODC other dependent credit unless an exception applies. So you can see form 8862 information to claim certain credits after disallowance and its instructions for more information including whether an exemption applies. So effect of credit on welfare benefits. This is always kind of an issue when you deal with these kind of programs where you're going to get something that kind of looks like income or you have multiple different kind of welfare programs then the question is well if I have income from this other source is that going to mess up the my other kind of income sources that I have set up and note this is obviously one of the problems with the benefit or welfare kind of programs or incentive programs often times they actually incentivize people to not be able to work or not to go into work because if they were to get some income they would lose a lot of benefits they might lose more benefits than the income that could actually be made. One of the ideas to kind of combat that was the earned income tax credit where you actually have to have some earned income the idea being that it would incentivize people to get some earned income and get back into the workforce but many of the credits and whatnot are not set up ideally so you have these kind of issues with one system having an effect on another benefit program and so on. So that's what we have here. Any refund you received as a result of taking the ACTC additional child tax credit cannot be counted as income when determining you or anyone else is eligible for benefits or assistance or how much you or anyone else can receive under any federal program or under any state or local program finance in whole or in part with federal funds. So typically that's usually a good thing for the people that might be getting funds from these other benefit programs which you would think would have a limit depending on your income level and therefore you would like to like reporting taxes you would like to have the actual income but it'd be exempt from having to be reported because having income would be bad for most of these tax taxes and these welfare kind of program systems to be able to participate in them. So these programs include temporary assistance for needy families that's the TANF Medicaid supplemental security income SSI and supplemental nutrition assistant program formerly food stamps. In addition when determining eligibility the refund cannot be counted as a resource for at least 12 months after you receive it. Check with your local benefit coordinator nature to find out if your refund will affect your benefits. Okay.  So again the general idea here we have a dependent the question is what's going to be the benefit from taxes of the dependent. Usually the child tax credit would be the biggest benefit if not then we move on to the other dependent credit. Okay. So to claim a child for the CTC and ACTC the child must be your dependent under age 17 at the end of 2022 and meet all the conditions in step one through three who qualifies as your dependent in your instructions for form 1040. So this kind of dovetails into the discussion of who qualifies as a dependent because one of the major benefits of qualifying as a dependent could be the child tax credit. So example your child turned 17 on December 30th 2022 and is a citizen of the United States and claimed as a dependent on your return. You cannot use the child child to claim the CTC child tax credit or ACTC additional child tax credits because the child was not under age 17 at the end of 2022 for each qualifying child for whom you are claiming the CTC or ACTC you must check the quote child tax credit in quote box in column four of the dependent section on page one of form 1040. So that page one is where you're going to put basically your dependent so you've got yourself your social security numbers everybody's information all your personal information on page one of the form 1040 they want it right up front there including the dependence and then you check off if they qualify for the child tax credit the actual calculation of the child tax credit being on the second page of the form 1040 which will take a look at in the future with some examples adopted child and adopted child is always treated as your own child and adopted child includes a child lawfully placed with you for legal adoption credit for other dependents this is the odc so remember the strategy here we have a dependent they qualify as a dependent possibly then the question is well are they qualifying for the child tax credit if not then other dependent credit much less but still beneficial so the odc is for individuals with a dependent who meets the following conditions one the person is claimed as a dependent on your return so that goes into the instructions for being a dependent again to determine if an individual is your dependent begin with step one under who qualifies as your dependent in the instructions for form 1040 which you could find in the iris website to the person cannot be used by you to claim the ctc or a ctc so in other words you have this dependent you can't claim the ctc or a ctc the child tax credit or just additional child tax credits because if you could you would do that because it would be more so if you can't do that then then that's one of the thing the restrictions because you're not being able to do that that's why you're going to take the odc other dependent credit so see credits for qualifying children earlier for that one three the person was a u.s. citizen u.s. national or u.s. resident alien for more information see publication 519 if the person is your adopted child see adopted child later example to your siblings 10 year old child be lives in mexico and qualifies as your dependent be is not a u.s. citizen u.s. national or u.s. resident alien you cannot use be to claim the odc other dependent credit for each dependent for whom you are claiming the odc other dependent credit you must check the quote credit for other dependents in quote box in column four of the dependent section on page one of form 1040 or form 1040 s r for the dependent in other words you have your dependent all the stuff on page one you've got yourself all your personal information your social security number your spouse's social security number and their name all your children's social security and numbers and names are on page one to which would be your dependence and then all your dependents would be would be there as well and then you would check next to your dependents name if they qualify for the child tax credit or the other dependent credit you can't check both of them because they can't qualify for both they can only qualify for one or the other that's why we had one of those restrictions here for the other dependent credit being that they don't qualify for the child tax credit or additional child tax credit and then on page two you calculate the credit of course so adopted child we'll see examples of that later by the way adopted child an adopted child is always treated as your own child an adopted child includes a child lawfully placed with you for legal adoption if you are a US citizen or US national and your adopted child lived with you all year as a member of your household in 2022 that meet that child meets condition three earlier to be a qualified person for the odc other dependent credit so limits on the CTC and odc child tax credit and other dependent credit so the maximum credit amount of your CTC child tax credit and odc other dependent credits may be reduced if you're one or two apply either one or two apply number one the amount online 18 of form 1040 1040 SR or 1040 NR is less than both credits so if the amount is zero you cannot take either credit because there's no tax to reduce but you may be able to take the ACTC if you are claiming the CTC so the additional child tax credit if you're claiming the child tax credit if you cannot take the ACTC if you are only claiming the odc in other words okay so C part to a additional child tax credit for all filers later so this has to do with the refundable and non refundable portions of it so remember the idea is that this is an income tax normally you can't get credits that take your liability below zero


Ralphie, you want to tell them the good news?  Cats, am I right? Well, hello everyone. Sarah Lane here. Just wanted to let you know of some hopefully very good news. Myself and my co-host Eileen Rivera have decided to launch an Apple show. And we're calling it Apple Vision Show. Get it? Get it? Yeah. This is not only an Apple Vision Pro show, although we will talk about the headset and we have ordered one. It went off without a hitch this morning as I record this on Friday. But it's going to be all things Apple, lifestyle stuff, tips and tricks, fun stuff about software, hardware, ways that you can consume content using all things Apple. Apple people already know kind of what we're going for here. But we hope to have as many of you as possible along for the ride. We really are excited about this. Anybody who's kind of followed me for some time knows that I have previously done quite a few Apple shows. And it's been a while and I'm really happy to get back in the saddle. And Eileen is just the greatest co-host and I'm so happy that we're doing it together. She's also a very good friend of mine and we've known each other for a long, long time. So, what we're going to do on Monday, that would be January. Let me look at my calendar because math is hard, January 22nd. We are going to have a live stream immediately following Daily Tech News show, which wraps up its live stream at 2 p.m. Pacific Time. So, starting at 2 p.m. Pacific Time on Monday, the 22nd. We're just going to get in the stream. By the way, this is youtube.com slash Daily Tech News show. And just kind of kick around some ideas because the show is going to work unless we make a show that everyone wants to watch and or listen to. Either way, we're going to give you both options. So, we want to hear your thoughts. We want to get your tips. We want to thank you for those tips. We want you to be part of the show. And that's it for now. And we just hope you come along for the ride. So, again, Monday, January 22nd at 2 p.m. Pacific Time. That's whatever time you're in. Do hop on over and join our live stream at youtube.com slash Daily Tech News show. And let's make a show, shall we? All right. Bye-bye.