So today I will talk about genome alignment, so just to give you one phrase summary, it's how you place your reads over the genomes, but we'll see more in detail what this means. So what I will try to bring you as knowledge during this lecture, I will give you another small introduction to the idea of technology, so just a reminder of what we already see this morning about doing a jar of the talk. Two, as we try to make you understand what the main classic of the data, what is the problem that we have to face when we do genome alignment, what are the possible sources of error, and also give you some more general knowledge about terminology and file format. And during the practical, we'll see how to run the first step of the DNS pipeline, and tomorrow we'll see how to run the second and third step of the pipeline. So as I say, I will start with NGS technology introduction, so I will try to be fast on that because Gerard explained it really well this morning. So the revolution of the sequencing was made because 10 to 20 years ago there was a batch of major projects for sequencing genomes, and it takes months and years depending on the size of the genome, so years for the human genome, and it costs a billion and a half dollars. We are now with the new technologies for small genomes, we can have the genome with sufficient amount of collagen hours, but in hours, and it only costs thousands of dollars. So what is the next generation sequencing? So as Gerard explained, it starts from the clone-based approach that is presented this morning, so it was you got your fragment of DNA, you put it in a clone, and then you put it in the old sequencer, and it will give you your sequence as a program here. So what the problem is, the number of run you can do at a time, so it's 96 sequence at a time, it takes many hours for each run, so it's really not suitable for large genome. So the next generation sequencing, and it works, it works in the same ID to generate code to use fluorescent code for each basis to be able to retrieve the sequence, but the idea is to do medium of sequence at a time, so it's just a part of a small image of a flow cell, so you see that in the flow cell, each cycle it will take a picture of this gigantic image of dots and try to refine which cluster corresponds, in each cluster which color is each cluster for each cycle. So how it works, so I will present here only the building approach, which is called sequencing by sentences. The main idea is to take your DNA, you share your DNA to a fragment size where you know approximately the size of your fragment, you add some specific adapters, then when you have these adapters you load this fragment on your flow cell, so on your flow cell you've got some complementary adapters that will catch the one you load on the flow cell, so you will end up with some fragment of DNA which is linked to your flow cell, and you will do what we call the bridge modification, so you have the fragment that will catch one side of the DNA fragment, and it will create a bridge between one adapter to the other adapter, and then you will do the amplification directly on the other flow cell. So when you do the amplification then you denature the double strand molecules, and you will have two copies, and so on at the end to arrive to cluster of sequences that represent exactly the same sequence, so for one group of molecules you have the same initial DNA fragment that you have put in the flow cell. Then you do the sequencing, so you start from the beginning, you add fluorescence, for example, be nucleotide, and for each and then you plant it, the fluorescence is catch the same, for all the clusters at the same times, and you will end up with this kind of images, where you are able for each cycle to know for a given cluster, I got a yellow dot, I got a blue dot, green dot, yellow, red, and yellow to extract the sequence. So it works really well, it's really efficient, there are some sources of error as we discussed this morning, phasing, prefacing of the data, but we'll come later on that. So there's actually five marginal players to do sequencing, life technology, which have developed a lot of solid and iron torments, which do solid exides, and my sick, my sick, so except for my sick, it's kind of, my sick is more in between, but this technology do small fragments of sequencing, so from 50, from 30 to 100, 200 base pair alone. Here with my sick and 454, we go in the medium size of, medium size of size of 3, so it's around 300 to 600, so 300 more for my sick and 6700 for 454. What you have to know is 454 is now closed, so we're still at the center of some 454 run of sequencing, but it will be, it will be, the technology will die during the next year. And we have the large REIT technology with Pacific Biocents, we developed the PacBio machine and Oxford Nanopower, we developed the Minion and the ReDI. Just a quick comparison of the technologies, so we talk about this morning, but what is interesting to look when you try to decide, when you have your own project and try to decide what technology should I use? First, the size of the REIT, depending on what you are doing, if you want to do structural variants, you need to have a long REIT, if you want to do assembly, you need to have longer REIT, if you want to do arena sick, you can go with shorter REIT or more general, just classical more general, might be shorter REIT, so depending on your experiments, you need to know the size of the REIT you want to do, the type of error that each technology has. So long REIT and medium REIT really generate more indels, and especially long REIT generate indels around, when you have stretch of the same type of nuclear field, so when you have like 3, 4, 5, 8, for example, sometimes you will only have 4 out of 5 or 6 out of 5. Where for the short REITs, in Illumina, you will have substitution, so mismatch. And what is the type of error? So you have really low error for the short REIT, larger error for the longer REITs, but this is a single pass error, so this is what the row seconds will give you. So we have methods like direct talk this morning, if we do two-day REITs or two-pass REITs for a nanopart, it will decrease to 3%, if you correct CSS approach by value, it will also be able to decrease the level of error, but we will do a bit on this maximum size of REIT you can have. So all this kind of technical configuration, and as Gerard said this morning, all this numbers are probably still out of date because the technology evolves really fast. What is important to think is about advantages and disadvantages. So mainly nanopart and packed values advantages is the size of the REITs and the time to sequence. Nanopart is also advantageous because it's really to use, you just need to open your device and fill the device, but mainly advantages is the low yield, the cost and the type of error and the stability, but not the stability is more and more in progress with nanopart. For Illumina, the main advantages is to the high sequential, the lower cost and accuracy of the data. The main disadvantage is not for use for certain like us is the cost of the equipment. So and the fact that you cannot read some certain type of variant due to the lower size of the data. So just give you an example of what we can do with this type of machine. So this is what we've got, the number of machine we've got at our center. So we've got three, four, three, four, three, all this type of machine. So for the medium, for the machine that give you medium range read lines, usually what we do is that, smaller than what you're sequencing. So it was what we do at the beginning. No, we don't do it anymore, but you can do it. That it won't be a not the best choice, but we do mainly for this type of machine on the consequence in metagenomics and valuation. For the short read and high throughput, what we do, we do everything, which is wall, wall exon, wall genome, wall transcriptome, cheap sex, wall genome by seed fat, and anything of that you need to have a wall coverage of your genome. So you need to have the power of the high yield of our sequence. With the long read, what we do is small and medium to know the new assembly. So long auto type sequencing, targeted sequencing, epigenomics, and validation. And here, sorry, there was a problem with my slide. With the Tendix, so Tendix is not a really sequencing technologies, it's more of library prep technologies. And what we do with that, we do a lot of apotyping, especially for cancer. We do wall genome assembly, but what we really do a lot with Tendix Dynamics, actually the center is a single cell RNA-seq analysis. Because directly with the machine you can put yourself and the cell will be will be catching individually and you could also back up to catch each molecule individually. So it's really efficient for the single cell analysis. So now that we know a bit more about the technology, what are the main parameters you need to sync when you design your experiment? This is a different type of approach. Redance, library type, error profile, barracoding, if you want to put Cheval in the same main or sequencing. So this is a main characteristic that needs to drive your choice. When I meet people and discuss with them, they usually come with these two parameters as a major factor. If you do it, to my point of view, it will not be the best way to design your experiment. But for sure we have not an limited form, so we need still to take it into account. So no, what should we do from data? So when we do DNA-seq analysis, the idea is to start from the fast queue what we will have from the machine to VCF. So VCF is a variant called format file. So it's the file where you will have your variants. So what is the what we have at the beginning where the fast queue? So for each sample you will have usually two files because you have your fragment and you will take on one end of the fragment and the other end of the fragments and each end will be in a file one and each second end will be on this file. So for each sample, depending on the coverage you will have, you will end up with a file that could go from 5GHz to 300GHz of data, so it's a massive amount of data. And in your fast queue, your data will be presented approximately like that because it's sequencer, it's technology has its own set of fast queue formats, but there are some kind of rules you need to respect. So the rule is you will have four row pair sequence. The first one that starts with an add sign that describe that gives you the name of the identity of your sequence. Usually it's linked to the name of the starter, the name of the machines, and you have some personal information regarding where the cluster was taken on the flow cell and usually at the end, we tell you slash one, we tell you which read one, or if you are on read two, you will be slash two, the same ID will be slash two at the end. The second line is really the sequence that you have called from your sequencer, then you have a third line which is used for a second header, so usually it's starting with a plus sign. Usually it's either empty or the same ID, and then you have the quality of each basis. So the quality, as you can see, the quality is a numeric value, but it's a numeric value that tells you what's the quality of my data. The problem to use a numeric value is that if your numeric value goes more than nine, zero to nine, you cannot make the difference between, if I say here my numeric value for my first basis is 32, it's three for the first one, it's two for the second, or 32 for the first one. So what we use for the quality, we encode this value, so each numeric value corresponds to a specific ASCII, let ASCII permit ASCII, sorry, ASCII sign our parameters, ASCII letters, or characters, yes, and so each characters are able to revert to the given numeric value correspond. So you won't have to do it, every software that takes this file type of file into into account will do it for you. So what this quality means, so it's called the base quality. So it's a numeric value here, Q, which is what we call a French score. A French score is minus 10 log base 10 of a given probability, it is a definition of a French score. And so in the case of the base quality, the probability that we measure here is the probability that the base that I've been called is incorrect. So the probability that you have made an error. So as it is a minus 10 log 10, the higher the numeric value is, the lower your probability of error will be. So if we take a 30 base quality, we'll have 0.1 percent chance of error. So this is how we usually represent base quality, and how when we do base quality, how we see our sequence. What we do usually, so it's a representation of for each cycle of a sequencing experiment of the best quality, a distribution among all the bases, so among all the million reads that we generate. So it's the representation of the distribution. So as Gerard mentioned, the distribution usually starts high, reads the top quantities they can do, stay stable, and when we progress along the read when we accumulate cycles, we start to have, as I said this morning, we start to have some molecules that are not in phase. So we start to accumulate molecules which are not in phase with a group. And we start to see a cluster which is less well defined, and we start to have a decrease in the quality. That's why at the end of the read, we saw a real drop down of the general distribution of the quality. Another type of, so yeah, before going to the next step, it's important to look at your quality of your data, because if you have low quality, you are more likely to see error in your read, and if you are more likely to have error in your analysis, like SNP or as we call it. Another type of analysis or QC we do on the FASTU file is to look at the positional base content. So along your reads, what are the contents of my base? So if I'm totally random, each color represents one basis, and if I'm totally random, all my reads, I should have 25%. Do you think that's fine? Yes or no? Here that's fine, because it's a graph for RNA data. So in gene, the base content is around 25 of each basis. But for world genome, I tell you if you see, for world genome, if you see 25, 25, 25, there's probably an issue, because the GC content is not the distribution of all the base in the genome. The GC content is around, I think it's 60% or the opposite. So you should expect to have one around 30 and the other around 20. So 2 bar. If you do world genome. Another type of QC you can see is do you find specific adapters? Do you find specific known sequence in your data? And what's the amount of duplicate reads you have in your data? Yes? So here, it's just because it's a common pattern you see when you do RNA. So because the way the RNA library preparation is done with Illumina, the way the fragment is shared is not fully random. And that's why we observe this pattern, this kind of pattern, because there's specific region where the DNA is shared by the entire. The DNA will be flat. The DNA will, we don't have, this type of pattern will be flat, but with two lines around 30 and two lines around 20. I don't get your question. Yeah, but you, you, I think you share for the universal structure. It's why I have to say that it's what Illumina explained on their forums about this pattern. So some people keep these bases because if you want to do, for example, a SMV calling on RNA, here you are really more error prone because you have a specific pattern and you have problems with Illumina and a lot of people when you do SMV calling will just remove the 12 first base on everything. Another type of QC we do usually on the data is to take extract randomly a set of a given number of reads here. It was 1000 read and we just blast to the NR databases and we just look what is the more important it we've got to be sure that it corresponds to what we were supposed to sequence. And it's also a good way to flag for contamination from other space. So we have all fast Q. We see we can access the quality. So when we have this kind of pattern, we don't have usually a perfect fast profile. So what we need to do is to remove data that is with lower quality or data that is not coming from originals. So what to do? We do trimming. So when we do trimming, we apply usually three steps, three actions. So the first thing to do is to remove adaptors. So adaptors you have it at each end of your DNA fragment. So if your fragment because when you do your size animation, you cannot take exactly the size. So it's kind of an interval of size. So you will have sort of fragment for sure. And so this sort of fragment when you will sequence, you can go over the end of your DNA fragment and start to sequence the adaptor. So if you catch them, you will need to remove it. The second type of cleaning we do, we start from the trip to the end of the read. We just change the quality of each basis. And if the quality is below a given threshold, so it's your choice to apply each threshold. Depending on your experiment, usually we use either 30 or 20 on what we want to keep before to be more stringent or less major. And we remove all the bases that are under this threshold. And when in a read the threshold goes up to this threshold, we start to trim. And when we have applied these two conditions, these two filters, is the size of the remaining reads is lower than the given size. We say, okay, it's not a read that I can use efficiently for my list. I will drop it. Okay. So just a quick comment. It's important when you do this type of thing to start trimming with adaptor. Because trimming the adaptor is a sequential recognition. So you have the sequence of your adaptor. So if you start by trimming, then you will start by removing bases in your adaptor. And it will be harder to find the real adaptor. So it's important to start to do adaptor, quality and background. Yes. So when we observe this kind of pattern, it's really rare when it's mature. But usually it's sometimes it occurs. For example, we have that like one and one and a half years ago. We have a problem of temperature in the room of the sequencer. And the temperature goes up. And then the emergency, we stop everything, we put the temperature on the grid temperature and we restart. And we have one cycle that the quality goes down. In these cases, what we do with specific tools, we say, don't take interact on these bases. And we turn every call as an end. So when you say that you trim, for example, from here, let's say, this number 93%. You do that for all the reads that the machine generated or only those reads where the quality was bad. On this read, one of the quality is bad. So also one thing, you have an option. Here, when I do it, usually I do it base by base. But you can do like a sliding window. Say, okay, I take the, for example, the five first last reads, the quality of the mean quality over these five reads is lower than the threshold. Then I cut these bases. Because that's the reason for the standard deviation, right? Some of your reads will have good sequences until they're very ended. Yeah, but usually you cannot be done. Because in most of the case, if you are going down, it means that you read are unfazed. A lot of sequence on your cluster are unfazed. And you cannot refazed them at the next cycle. So usually, when your quality starts to decrease, it will not become better after a few cycles. It will just become worse and worse. But it's different for every read. Yeah, it's different for every read. I think there was a question there. Since your adapter is at the end, what's the name of the adapter that you program to? Localege. So we put the, when you, the recondition is not the perfect matches. So you tolerate some error. So when you have low quality, you don't expect to have each base as an error.  So you don't expect to have those people error at the end. I think you have another question. No? Okay. And now, just to tell you that in the way we work, now to tell you the truth, no, we didn't, when we have good, when we have good quality all of our sequence, which is the norm for that it really was, now that we have this pattern, we usually have something like that, which at the end, we are around this level of 30. So in that case, we don't do anything. Because we know of an aligner that is able to catch the adapter and softly, they have also marked the part of the read as non-genomic. Which is this alignment? BWMM, the one we would use during the practical. Yeah. Does the read of quality is lower toward the end as a scenario? No, it's just because in the first cycle, the machine is not, is needed to calibrate. And especially with the older 4-cell, we need to define the cluster. Now with the new 4-cell, the new patterned 4-cell, each cluster is already prepositioned on the 4-cell. Each cluster is, the machine knows where each cluster is at the beginning. The quality starts really higher and it's almost flat. Yeah. Soft tip? So soft tip is when you align your reads, you can do many things. I know you can do many things, but it can break your read into different pieces. But it can break your reads and say, okay, these pieces, I don't find any place for these pieces anywhere in the genome. So probably it's not a genomic region. So instead of let it there, it just marks the sequence as, this sequence last, for example, 10 days, is non-genomic. So don't use it for other subsequent analyses to look for variants for everything. So it's just a kind of additional information you add on your alignment to tell you this 10 or whatever number of reads, don't use it because it's not part of the genome. So soft tipping, you keep the sequence in your reads. So you keep the sequence in your file, but you say, don't use it. Hard tipping, you cut the sequence. So many tools to do it. As we do, we will use Trimomatic, but many other tools are available. So many other tools do the same kind of job with the same efficiency. So it's really a user preference. As it's just because we use it for long and because it was really easy to handle. Because at the beginning, when we use Illumina, the Fred's Court was not encoded the same way, and it was able to really use from one to the other. But it really has no rule of thumb about what is the best one. So when we have done the cleaning of the fast queue, so we have a good set of data, the next thing is to do alignment. Before doing alignment, when you have your reads and you have cleaned your reads, you have two possible strategies. Either you do alignment mapping. So the idea is to take your read and find the best location on your reference sequence. It's important to see it's the best location. Most of the time, best would mean the true location, but not always. It's the best location based on the reference sequence. Whereas you can do assembly, where the ID and which will be developed by tarot tomorrow, and details. It's to take all the reads to try to reconstruct contentious sequence as contigs and to regenerate your own reference sequence. And after that, when you have regenerated your own reference sequence, you can either use it as if or remap relocate your read over your new reference sequence. But me, I will not go further with assembly. So as we'll see, what is the read mapping? So the read mapping is a bit challenging because you need to map million of short reads to the genome. So really a lot of tasks to do. And so you need to map. So it's kind of, you have a puzzle of three billion place and you have millions of pieces you need to place there. And so it's a it's a logic in term of computation. And also because many mapping locations could be possible for each pieces. And you don't want to only keep exact matching. Otherwise, you won't be able to extract the variant. So you need to be able to tolerate some error in your matching. So there's many algorithms but the most used now and the one that seems to perform the world is the Bureau Wheeler-Tontron algorithm. It's the one which is implemented in the BWA mapper, the one we'll use. But there's also many other tools that exist. Why we use BWMM? Because it's been shown to be one of the best mapper in terms of accuracy. The one that would perform BWA is novel line and we don't use it usually because novel line, you have some licensing, it's not totally free.  There's other good. So for example, Bota is really good as an aligner, especially when we do RNA and to do when you want to extract exact matches. So there's other and there's a lot of review about each aligners that pop up every one or two years. When we do aligner, when we do alignment, it's really important to align each line separately. For many reasons, the first one is for speed and because sometimes when you do large world genome, you have like two or three line of alignments. It's less the case now that we have the ICX because you can have really a good amount of coverage with one line. But if you still use the ICX 2005, we'll still have for like a concert, you will need to have several lanes for each sample. So you need to align your lanes separately and when you do your alignments, what you each round of alignments, you add the RG tag. So the RG tag is a way to track where you read come from because you will align to different lanes. Each lane will have a specific each read. We have a specific RG tag that will be associated with the lane where it's come from then you merge everything. And if you see a specific pattern in your final set of align reads, you are able to split your read by a lane using the RG tag and to see if the pattern is spread in every lane or if it's lane specific. If it's spread to every lane, you can say okay, that's something that seems to be biologic. If it's in one lane, probably you have an issue in that lane. It's occurred to us, we saw a set of, one sample with an increased set of mutation in genes and then we split by lane, we say okay, we have one lane which is exome or the other where a whole genome. So that could make a difference. So it's important to set your read group. So to track error, to differentiate the origin of reads in the final band, but also because many tools will not work if you don't set the read group. So when you align, you end up with a file in a format SAM or BAM as we saw this morning. So SAM, sequence alignment, sequence alignment format. So the SAM file is a text file, the BAM file is a binary version of this file. So almost nobody use it, work with the SAM file because it's so huge, so nobody work with the BAM file. And for each read, that's the type of data you have in the SAM file. So there's many fields, not all of them are monetary. So I cut from the monetary field, but you could have extra slide field at the end of the line for each sample. So the monetary field are the read name, a flag. The flag is a numerical value that you could use to describe the mapping. So if your mapping quality is bad, if you are not primary alignment, all these kind of features that you can use to describe your alignment, to give some kind of parameter for alignment, then you have your reference position. So the chromosome and the position, you have the quality score of your alignment. So it's a thread score as we see for the base quantity. So it's a probability that your read is not mapped correctly. Then you've got the cigar string. The cigar string is a representation of your alignment. So here it tells you 16M, which is a 76M, which is a 76 basis, are matched to the reference. So map could be mismatched. You could be mapped and have a mismatch. So you could have M, you could have I for insertion, D deletion, you could have S for soft clip, H for up clip. So you have all these kind of features. Then you've got the position of the mate if you are in a pair of reads. So the equal sign means that the read is mapped on the same chromosome. If it's another chromosome, you will have the number of the chromosome and the position of that chromosome and you end up with the inter-site of your data. Then you have your sequence and then you have your base quality. So now we have done the alignment. What is important to do is to refine the alignment because every alignment is not, every aligner has his trans and weakness and there's no aligner which is perfect. So we need to take this alignment and to apply some set of filter and rearrangements to make the alignment better and more suitable for the variant calling. So the first thing we do, you will already talk about that this morning, is to embed the element. Why we do that is because aligner tend to favor of creating mismatch instead of entertaining the app. So the idea is, aligning a read is just a question of penalties and score to position your reads. And for almost all aligner, creating a gap takes a lot of penalty while creating a mismatch takes not so much penalty. So when you arrive, when you have a straight of letter like that and you have an indel, sometimes quite easy when you are at the end of your reads to tolerate one, two, three, a set of number of mismatch instead of creating a gap. So usually when you see these patterns where you accumulate snippet in a really several steps in really short position, it could be a sign of an indel, of a missing indel. So there's a tool in the GTK that is basically done that and we'll do it later on. And when you realign, when you create the indel, you see that most of your variants read disappear. Another type of refinement we do is to mark duplicates. So what is the duplicates? It's when you have different reads that represent the same initial DNA fragments in your library. So you want to count only one read or one pair of reads per real DNA fragment. So where does this duplicates come from? So it could come from PCR.  So you could also have what we call optical duplicates. So it's only valid for all type of source cells. So it's when your source cell is not well loaded. And once there are some clusters that become giants because you don't put enough DNA. So there's massive amplification. So the cluster becomes really large. And when the machine is looking at it, takes the picture, you consider it as two different clusters. So it will call a two different cluster like that. And it will call optical because it's just the optics that fail. In the new set of this type of duplicates is not anymore the new type of source cell, but we have the other one. When you don't load enough your new type of flow cell, you will have molecules. If the molecule is enough long, the molecule will try to jump into an empty cluster position. So because you are adaptable here, also if there are no molecules that go there during amplification, if the molecule is long enough, it will jump and try to amplify in the other well. And you've got the sister one is when you have to close up to close and it will create like 10 of hybrid of hybrid sequence. And then so I agree usually it will be called could be called one is one of the neighbors. So how we detect them? We can detect them before mapping using camera approach. It's what the one I told you we estimate the top duplicates at the fast Q level. But most of the people use approach where we detect duplicates and we do it after mapping. So by looking where the two reads map. So you can imagine that if you have the same fragment, the data will map exactly at the same position. Another type of quality assessment refinement we do on the bar is the base work calibration. Why we do that? Because when the sequence called the base, the base quality, it's time to inflate the value of the base. And so we need to re estimate the real value. So the calculation try to know score based on specific patterns. So based on the cycle of the machine. So if we are in a good work, we should expect to see something flat for every cycle and for every type of read. But we know that there are some bias in everything. So what we do, we look at the specific dynamic context and technical context and we re establish the true value of the best quality. So when you have done that, you have so refine the quality of alignment and then you will be ready to do variant code. So what is important to at each step of this process is to look at your matrix because it's where you will find if you have a specific issue with your data. So really I encourage you to catch matrix at each step of your process. So the matrix, so to be collected at each time, usually each tool provides their own set of matrix. So it's not super complicated to get it. But you have other specific tools you can use to ask for specific additional matrix. So there are a ton and ton of matrix. The one I really look when I do a project and analysis, I look either what is my trimming value, what are my alignment rates, what are the coverage I obtain, is that fit what we are supposed to have, what are the insights, is it correspond to what the lab did. So all these kind of matrix are really important to be sure that your experiment is correct before doing the next step of the variant calling. So the variant calling tomorrow, I will give you more detail about that in module four and five. Today just to finish, just to give you a general conclusion about that, not specifically on alignment but more specifically on working with this type of data. So if you want to do, to work on NGS, you need to be really aware of the technology and the method because every technology is different, implies different assumption, different type of sequence, different so you really need to have a good knowledge of technology and methods that could be applied to these technologies. You need to know what are the error and the technical artefact you will face based on the technology you have, you have choose. Otherwise you won't be able to understand your result or to make some between something that make biology sense or not. You need to have both mathematical and informatic skills because when we do analysis, we will use HP, HPC cluster. So we need its unique environment. If you're working on Windows, on me, it's problematic. So you need to have good informatic skills and good mathematical to understand what you're doing because many of the tools do a lot of mathematics or now do more and more machine learning of this kind of statistical approach. And now the major challenge for us as BFM musicians that work on NGS data is not so much the methodology but there's still some methodology challenge which is the capacity of the compute and the storage because when you do, for example, when we do large projects of hundreds of people in cancer, it could take 3, 2, 500 terabytes of data to store and to process. So the major cost. So that's it.


As you look through the periodic table, you may have noticed that not all atomic masses are written as whole numbers. Elements can exist with slightly different numbers of neutrons. We call these isotopes of an element. It is particularly common for heavier elements, but a familiar, lighter example is chlorine. The two most common types of chlorine atom in the world around us are chlorine 35 and chlorine 37. If we took a sample of chlorine gas, we would find that it was made up of approximately 75% chlorine 35 and 25% of chlorine 37. There are other isotopes of chlorine, but these two are the most common. The relative abundance of the different isotopes, in other words how common they are, is always taken into consideration when calculating the relative atomic mass of an element. One way of visualizing this is to imagine that you have a sample of 100 naturally occurring chlorine atoms. Based on the abundance in the example already given, 75 of these would be chlorine 35 and 25 would be chlorine 37. Knowing this, we can work out the relative atomic mass. In other words, the weighted mean atomic mass. And we can do this using a formula as follows. 75 times 35 plus 25 times 37 all divided by 100 equals 35.5. And this explains why chlorine is listed as having a relative atomic mass of 35.5 in the periodic table. The relative atomic mass of an element is the weighted mean mass of an element and it is written in atomic mass units. Here's another example for you. A sample of bromine contains 50% bromine 79 and 50% bromine 81. What is its relative atomic mass? Pause the video. You may be able to work this out straight away. If not, write it down as in the chlorine example. The answer is 80. Detailed periodic tables of elements show that most relative atomic masses aren't actually whole numbers. This is all due to the naturally occurring isotopes of each element. So to recap, the relative atomic mass of an element is the weighted mean mass of the isotopes of an element. And by weighted, we mean that we are taking the relative abundance of each isotope into consideration. And this is why relative atomic masses aren't always whole numbers.


Hi, I'm Zor. Welcome to a new Zor education. We continue talking about random variables, and after the introduction to random variables, which was during the last lecture, let's talk about certain properties of random variables, and today's theme is expected value of the random variables. I do suggest you to watch this lecture from Unizor.com website instead of directly on some other like YouTube, etc., because the website contains notes to this lecture, which is very important to familiarize yourself with. Before or after the lecture doesn't really matter, but it's very important to read the notes. Okay, so back to expected value. Now before presenting this in a purely theoretical form, I would like to have a couple of examples where it would be quite obvious actually what expected value is. Okay, example number one. Okay, the game of roulette. So the game of roulette is when, well, you have a wheel with different partitions. The American version of this game has 36 numbers from 1 to 36, 0 and 00. So 38 different partitions on the wheel. And you're spinning the ball and spinning the wheel and spinning the ball. And after they stop spinning, the ball actually falls into one of these partitions. Now, you have a choice to bet on something, but we will consider only one particular version of this type of a game when you are betting on a certain number. Let's say you are betting on number 23. It doesn't really matter. So if the ball falls on the number 23, you win. If it doesn't, you lose. Well, obviously the chances to fall on the number 23, if you have 38 different partitions are very small and the chances to lose are very large. So we have to equalize it with some payoff. Now, the standard payoff is if you win, so if the ball actually falls on the number you predicted, you will have 36 times what you have bet. And let's say you bet a dollar. So you're getting 36 dollars. But if it's not 23, you are basically losing your bet, which is $1. So that's the game. Well, a random experiment is basically play the game. So what are the results of the random experiments? These are results, 38 different results. One of them is successful and one of them is not successful. Now, considering these are 38 results with presumably equal chances to occur, because the wheel is made quite correctly and the ball is round, etc., etc., so all these partitions have equal chance to occur, which means since there are 38 of these partitions, we have to assign the probability of 138 to each result. Okay. Now, what does it mean that the probability is 138 of each result? Well, it means that if you have, let's say, n different experiments where n is a really large number and the larger the better, then 138 of this will be, let's say, 23 and n 38 of this would be number one and the n 38 times will be number, let's say, 00, etc., etc., so each result of these out of these 38 will occur approximately n divided by 38 times, right? That's what it means that out of n experiments, we have 38 different results with equal chances, so approximately 138 of n results will occur with a concrete number, let's say, number 23 or another number. All right, so, which means that if we will conduct n experiments and n is relatively big, in n time, n divided by 38 times, we will win 36 dollars. Let me just change it. In all other cases, and how many all other cases, if n divided by 38 is winning, then 37 times n divided by 38. All other, they are the losing results, so you will lose $1, so you have to subtract times $1. So, what's the result of this arithmetic? Well, the result is minus n divided by 38, right? This is 36 and this is 37, so it will do minus 1n, all right? So, this is approximately the monetary result of n games, approximately, which means that the n is, as the n is increasing, it will be closer and closer to this, but not necessarily. I mean, you can play 10 games and you can win 10 times. Yes, in theory it is possible, although unlikely, but if you will go through, I know, 1 million games, more or less it will be approximately something like this. So, there are certain theorems which are basically saying there are estimating the closeness of the real results to this average result. Now, okay, so, if this is approximately the monetary result of your playing n games, then average per game would be divided by n, right? So, per game average result is this. So, if you bet $1 on a game, then average result of this game would be minus 138, which means you will lose, basically, and casino will win. And that's how casino is making money on averages. You see, if the number of people is great and everyone is playing many different games and the average per game is something like this, then as the number of people grows, the result will be closer and closer for the casino to win 138 of each dollar. Well, basically, that's an example. And what I wanted actually to say is that this average, obviously, is not necessarily something which really occurs. I mean, if you bet a dollar, you either lose a dollar or you win $36. You will never lose 138 of a dollar. But again, among many, many different games, if you average it by the number of games, that would be the result with the number of games relatively large. Now, ideally, I mean, speaking mathematically, if n tends to infinity, then the net result of the average per game would tend to minus 138. Okay, so that's this particular example. Let's consider another example. Actually, methodically, I think it's very important to explain a couple of concepts through examples first and then go to a more abstract description of what exactly we're talking about. So that's what basically I'm doing. So the second example is, all right, in the beginning of the course on probabilities, I was talking about the person Cavalier de Meure, who lived in France very, very long time ago, and he basically invented the game of dice, or one of the first people, actually, who was playing this game using certain, well, scientific approach, if you wish. So he was trying to modify the basic game, and his proposition was, let's play the following game. We will roll four dices, four dices, or we will roll one dice four times, doesn't really matter. And as a result of this experiment, we will look for the number one appearing among all these four dice. If it appears, then the Cavalier de Meure, who actually invented this particular game, would consider himself a winner. If he loses, obviously, he will pay whatever the amount he bet. So let's say again, he bet one, I shouldn't say a dollar, there were no dollars at the time, whatever the one is, one doublon or whatever. So he paid one, he bet one, and now we have four dice, and we are looking for number one to appear among these four dice. All right, how can we calculate the probability? Well, we actually talked about this particular problem during the regular lectures on probabilities. And the really convenient way to do it is, you see, one can appear on one dice or two dice and three or four or four dice. I mean, each one of these events has its own probability. It's easier to calculate the opposite probability that there are no ones, which means that the probability of not having any one on four dice is the combination of probabilities of having not one on each one of those, right? So the probability is five over six for the first dice, not to have one, right? Out of six different sides of the cube, five are not one, and only one side is one. Now, but with each of these we have five different versions for the second dice, five different sides for the second dice, and five different for the third and five different for the fourth, right? So these are number of combinations which are considered to be the non-one-containing combinations. So it's five times five times five times five, and the number of total combinations is six times six times six times six times six. So that's what actually the probability of not having dice, which is approximately zero four eight two three. Okay, so this is the probability of not having any ones on the four dives, and obviously the probability of having one, so this is not one, so the probability of having one, either one or two ones or three ones or four ones, is the opposite of this, which is one minus five six to the fourth, which is approximately zero point, zero point fifty one seventy seven. Okay, now, so here is the game, here is the probability for Cavalier de Meire to lose the game when there are no ones, and this is the probability to win the game. As you see this probability is greater than one, greater than half, so it looks like it will be willing, right, winning. So how can we calculate it in quantitative terms? Well, again, let's consider we are playing and games against Cavalier de Meire, or he's playing and games against us. Now, if these are the probabilities, probabilities of winning and losing, so he will win approximately in this number of cases. He will win his one Dublon or Louis Dorre or whatever else, and he will lose, I put the minus sign in these number of cases. So this will be, since we are playing with one Dublon only, so this would be his total average, not average, sorry, approximation of his net sum, which he will basically gain in this case after n games, right, which is equal to n times 0.0354. So this is the net amount he might approximately gain after playing n games if n is a significantly large number. So per game, excuse me, so per game, we have to divide it by n, it will be 0.0354. So this is his average win per game. It doesn't mean that he will actually win this particular amount every game, obviously not. He can either win one or lose one, not obviously this amount, but on average, if he will play a large number of games, then his average win per game would be this. So this is how I'm basically approaching the concept of expected value. I'm calculating the approximate value of winning or losing or whatever per one particular random experiment. That's the idea and that is a characterization of the random experiment itself or the game in this particular case. So if my average per game is positive, like in this particular case, then it makes sense for the person actually who play this way, like Cavalier de Meire in this case, to play the game because since on average he will be winning each game. So even if he will win something and lose something, the winning will exceed the losing, eventually, as the number of experiments goes to infinity. Doesn't mean that he will win during the first five games. He might lose actually. But again, his purpose is to make the number of games as big as possible and that's what makes actually him as a net winner. Same thing with Casino. In a previous game of roulette, which I was talking about, the Casino's purpose is to invite as many people as possible and force them to, well, encourage them, I shouldn't say force, encourage them to play as much as possible because only the numbers will give the net result for Cavalier de Meire or for Casino, the results which is close to this theoretical average. All right. So that's it for examples and now let's go to a pure theory. Now pure theory is going along exactly the same way as I was explaining in the examples. So first of all, we have to describe our random events. So this is, let's call it omega, a combination of certain elementary events, right? Now, we might have, let's say, k different elementary events. Now, in case of roulette, we have 38 different results of the experiment, elementary events, right? In case of Cavalier de Meire, we have only two basically. There is one or there is no one among these four dice. So there are only two. Now, the second thing which we need is the probabilities of these events. So let's say we know the probabilities of these elementary events. Now, in case of roulette, it was 138 per each of them. In case of the game suggested by Cavalier de Meire, when there are only two events, one was 0.51 something and another was 0.48 something. But the sum of them obviously is supposed to be equal to 1. All right. Now, next. Next is we are talking about certain random variable, which is, well, in case of our examples is a winning, basically. The amount you win. Well, okay, it depends on the elementary events, right? In case of roulette, when we have 38 different versions and we are playing on number 23, on number 23, we have number 36 as a winning. And all others had minus one because we are betting $1, right? And that would be the losing result. So in case of roulette, we would have minus one, minus one, minus one. On one particular case, we will have plus 36 and then minus one, minus one again until the end. In case of Cavalier de Meire game, we will have basically one and one. One we lose or one we win, something like this, right? Anyway, we have certain results and I will put it x1, x2, etc. xk. These are the random variable. This is random variable, which is defined on these elementary events. So I can actually say that the value of random variable on event e i is equal to x i. Where c, the grid letter c is usually used for random variable in theory of probabilities. All right. So we've got that. This is our problem. Now, question is, what's the value of this random variable per experiment if the number of experiments goes to infinity? That's what we're looking for. Our average win per number of experiments if the number of experiments is very large. I mean, that's what gives us the feeling for kind of evaluating the game. Is it worth actually to play this particular game in the casino, right? So the average value of this random variable as the number of experiments goes to infinity, that's what we are interested in. All right. So how can we evaluate it? Well, consider we have n different experiments. Now, if n is a very large number, then what are the results of these experiments? Well, approximately in n times p1 cases, the result would be e1. Approximately in n number p2 cases, the result will be e2, etc. And the n number pk cases, the result would be ek, right? Because that's what probability actually means. If we put these probabilities for these elementary events, the meaning of the probability is. So if this is 138, 138, 138, it means that if n is multiplied by the probability, it will be n divided by 38. We will have one particular result of the spinning wheel. Let's say result 23 or 0 or double zero or whatever else, right? So that's what it means. This is basically the definition of the concept of a probability. And since the results will be e1, e2, ek, the value of our random variable will be x1, x2, and xx, xxk, right? So what's the average? Well, if we have n different values of our random variable, then the sum of these divided by the total number of variables, total number of experiments, sorry, is equal to the average per experiment, right? So in n times p1 cases, my value is x1. In n times p2 cases, my value is x2, which means that if I wanted to summarize all the values which our random variable took during all these experiments, what would be my result? Well, my result would be n times p1 times x1 plus n times p2, p2 times x2 plus etc plus n times pk xk and divide it by number of experiments, right? Which is equal to, I will use the sigma sign pi xi where i from 1 to k, which means p1 x1 plus p2 x2 plus pn p3 x3 etc up to pk xk. So this is called a mathematical expectation or expected value of our random variable xi defined by this. So all we did is we calculated what's the average value of our random variable. We summarized all the values which it took during all the n experiments and n times p1 times it took value x1 etc etc, n times pk times it took the value xk and we summarized them and we divided by the number of experiments. That's average per experiment, right? That's how we calculate the average. We summarize all the values and divide it by the number of units which we have summarized, right? Basically, that's it. That's the definition. Now, does it mean that it's the right way to say, well, the random variable xi takes the average value of this? Well, that's not exactly correct. The word takes, it doesn't really necessarily take the value because as we saw, the value can be like minus 1, 38. It does not take this particular value. It takes either 1 or minus 36 or minus 1, right? But again, the average is whatever minus 1, 38. Now, the correct way is that considering we know what's the expected value of the random variable, all we can say is that if we will experiment many, many times and we will calculate the average per experiment value, then it will be close to this. And the more experiments we conduct, the closer our result, our average per experiment will be to this theoretical expected value or expectation or mathematical expectation. All right. So, next lecture I will probably devote to a couple of examples how to calculate this expected value. By the way, notice that this expected value basically lost its, well, dependency on elementary events. We don't really need elementary events. We need just the probabilities of these elementary events and the values which our random variable took if that particular experiment resulted in that particular elementary event. So, we can say slightly different. Okay, let's consider a random variable which takes the value x1 with the probability p1, x2 with probability p2, etc., and xk with probability pk. And what would be its expected value? Well, that's the formula basically. We have to summarize p1 times x1 plus p2 times x, etc. So, basically there is no elementary event involved in this particular phraseology, if you wish. All we need is the values of the random variable and the probabilities. It takes these values. And therefore, we can arrive with expected value. All right, that's it for today. I suggest you again to look at the notes which are on Unisor.com for this lecture. And that's it. Thank you very much. Good luck.


What's up? How are you guys another week over here at Frankie's free-range meat? And I just wanted to remind you guys because of the warmer weather if you do place an order try to do at least Like 10 or 12 pounds of meat because some of you guys are ordering like two beef testicles shipped to Texas Like I'm not going to send that Yeah, it's probably going to arrive cold, but Little silly little silly on the orders. I did want to start with some reviews Five stars for the chicken eggs. These eggs are amazing not one broken. We'll be buying these forever You guys hear the tape gun in the background You know, they sell these like tape machines that are pretty expensive. I think they're like a few thousand each, but Probably not worth it. We got a review for the pasture raised iberico pork lard like bacon But better like cooking eggs with bacon, but without the corn and soy pigs Now a lot of other meat companies are selling iberico pork in the USA But what they're actually doing is they're bringing in the iberian hogs and then feeding it like corn and soy and saying it's iberico pork So a lot of liars out there, but we do have legitimate Iberico pork from Spain, which is why it's pretty expensive Another review for the eggs Great shipment eggs came in perfectly no cracks whatsoever Every yolk thus far has been a dark orange color Which is a feat that the organic pasture raised eggs from my local grocery store haven't been able to achieve We got a review for the best bar best bars are the best I love the very best bars used to love the pomekin, but its meat had to be sourced elsewhere And it's now gritty yet has a mushy texture. I'll stick with the best bars from now so I Put a price reduction on the pomekin because you guys weren't as happy with it so it's like Three-quarters of the original price or a pretty hefty reduction. We should be getting new meat source for the pomekin hopefully soon but it's still you know Not necessarily something that you're eating for enjoyment. So nothing crazy going on this week No super big announces, but you know, it is crazy I'm like the only person that would ever reduce prices in the economy with what's going on We did a slight price cut on the collagen broth for you guys as well as I think some of the ground beef products So definitely check out the website if you haven't We do have some as I said new products in stock that I'm going to show you and we also have some Restocks especially the water kefir and water kefir grains. I know a lot of you guys have been asking for that We finally have both the kefir the kefir and the grains Available on frankiesforrangefoods.com. I'll show you guys the food stuff first We did get some beef sticks one box ends up showing up still have to figure out where the other one went This was actually my breakfast. I had two ounces of the bill tongue We have more of the eight ounce bags available and Something completely grand new is these granola bars more like granola bricks. I actually ate One whole one for breakfast and it's just really really delicious. It's actually more like a rice crispy treat We're selling these as these bricks for now. I kind of like a discounted price We might cut them in the future, but you know instead of having to pay like two or three dollars per bar This is a bit cheaper, but you're getting like three quarters of a pound brick of granola So the ingredients are actually really similar to the quinoa crisp except No, we're using a lot more whole oats and there's no banana in it. So it really has this like crunchy not even that chewy Rice crispy texture and it's absolutely delicious. It's all high quality organic ingredients It's not too high in fat. So it's really good for liver detox. So I'm really happy We have these granola bars on the website right now Recipes still on the works, but even these first few batches that weren't perfect. They're just so delicious. Really good I'm happy to have it is like my breakfast now. So If you guys want to try the granola bars, we have them on Frankie's for range foods calm As I said, we might like cut them up and put them in two ounce portions in the future But right now we're selling them as those bricks at a discount I would say you probably eat half of it at once, which is the equivalent of like three of our regular bars Because for me like the whole thing for breakfast was a little too much. We have Frankie's serious foods We have almost everything in stock. You know the steak seasoning here We have our salts Some plain jerky that we're almost out of actually all the jerky's we got some teriyaki jerky some salt and pepper jerky But after this we're gonna have to find someone to make it for us This is the Iberico pork lard that gentlemen was raving about regular beef tallow rag you tallow lamb tallow over there These are the bill tongs guys. I like these a lot better than the jerky. That's why we're carrying them I'm just sure to you. We got the beef sticks back in stock Honey's back in stock. We've got the orange and the wildflower which are much more aromatic if you guys have not tried these honeys The American honeys definitely do not compare and then we got a few new things. We have these Capers I might do a recipe with these but most of the time use them in like beef tartare We got the organic fig jam And we have the artichokes spread and whole artichokes back high-quality organic The meat granola with the new and improved texture is available for you guys better buy it Otherwise, I'm gonna go broke and then we have all of the cookie bars in stock the Hitomi's dark chocolate white chocolate chip We have quinoa rice crisp available as well guys all of the Bars are in stock plenty of those plenty of those quinoa crisp bars. Yeah, that was the other main thing that I discounted Because you know, I'm just trying to keep my guys busy. That's why we started making a lot of these bars I think I listed them at like 225 or 250 each for the quinoa crisp and That price for the quality of ingredients that goes into those bars is unheard of because we're using like all organic Minimally inflammatory stuff and even if you do get an organic bar from the market, it's gonna have like brown rice syrup and Like pea protein and stuff that you really don't want to be putting into your body Some really big news that I'm not ready to show you guys yet is we got a lot of products Two pallets worth to list on both Frankie's syringe foods and Frankie's naturals So I'm gonna go through these two pallets today see what was missing Maybe we'll have some of the stuff on the website next week But that's probably going to be the bulk of what next week's vlog is gonna be just me showing you guys all the New products that got in stock So we got a lot of boxes of pork bacon that we have to slice for you guys It's gonna be available on the website today. I think we sold all the prime rib We have three lonesome pieces of roast beef left those are the key for grains that I told you guys are back in stock and We should have some more water key for available On Wednesday, so tomorrow this we're gonna have some fresh ground chuck for you guys this week And you guys didn't buy the dairy this week. So it's going back to the farm to be fed to the pigs So I'm going broke again. So that's everything in the fridge this week for the most part But guys, it's tough selling the dairy and the eggs to you know, keep everything at a consistent pace So oh you guys like it. I bought new clean curtains for the freezer.  Okay So that's our first restock of this week We have a lot of chicken available guys in the new portions on the website Drumsticks thighs breasts definitely check it out. All the breasts are boneless individually portion We do have the burgers back in stock These are about Five ounces each Oregon grind ox tail 95 five lean blend we got some hanger steak here This is the newest product that we've never had before We got some lamb feet Which are I I guess kind of cute looking, you know a few little lamb feet packed up in a package I'm sure some of you guys will like these.  We got another delivery We're gonna finally have the lamb testicles back in stock and a few other things And then we should be getting all the glands and adrenals and stuff in next week. So Definitely some more me coming in and as I showed you guys those two pallets of stuff We're gonna have that's mostly the foods and the natural So we're gonna have a lot of new products available on both frankies for range foods calm and Frankie's naturals calm Which I'm very excited about but thank you guys for joining me if you go to Frank dash the phone calm You will see all of my businesses Frankie syringe me Frankie syringe foods. Hey, what's going on? Yeah, so my age back I showed up in the middle of my outro with them bad news. Hopefully I don't go completely broken this new place But we'll see we'll see, you know, I don't exactly have another 15,000 to spend You know, I would have taken out a bigger bank loan if I knew if I knew that was gonna happen, but we'll see So thank you guys for joining me Hopefully we'll do a few more videos this week and then another vlog next week with the new products But as I said guys Frank dashed upon a calm. We got the discounts on the stuff on the meat website Almost everything's in stock We're gonna have some new products on Frankie syringe foods and Frankie's naturals And then hopefully in the next month or two. We'll also have some new stuff on orange supplements and Wi-Fi shield Thanks again guys. I'll see you soon


We're going to top here dude. No, we're not online We had everybody open but nobody open here. We go. We're still cooking. We're still looking He blitzed everybody come back here. We go Put them on a tic-tac. Put them on a tic-tac back Duke


Hi everyone, Joe for jazby's casebreaks.com coming at you with 2020 Panini flawless collegiate football pick your team number eight Big thanks to All of these folks for getting into the action in this number block, which is in a separate video And this number block right here. There are two different ones also in a separate video So it works just like our serial number breaks only for a select set of teams and only for pick your team eight here on this January the 12th now We sold all but we sold a bunch of teams We didn't I don't think we sold the Broncos. I thought they were supposed to be in a number block, but whatever we're gonna We're just gonna give them away. I don't have to deal with Selling it. So here's I'm gonna copy all the all the team names right here Take out the Broncos, of course. They can't win. You need to sign some of the Broncos now If the team on top is a number block team, then I'll randomize the number block group So let's roll it. Let's randomize it five and a one. This is for the Broncos six times one two three four five Six after six times. We've got the Rams on top and the Rams are a number block team part of that chargers Detroit Tampa Bay number block group, which is right here. See chargers Tampa Bay number block group. So let's grab your names Put them in here. Let's just use the same dice roll five and a one six times one two three four Five and six in final time name on top is Adam Adam bonus team for you And put a little rooftop next to your name so you know you won that all right now Let's print and rip. Good luck Remember we marked that pick your team eight so you know it's from the same case Collegiate football Good luck everybody And we've got plenty more football in the store including some pre-orders. So check it out Jaspy's case breaks Jaspy's case breaks calm Good luck, and I think Not I think I know we're gonna go by the no there's no group rate checklist for this So that means our non-college rule I don't know why they didn't do a checklist for this but group break checklist calm doesn't have these assigned to pro teams So we're going by our non checklist or college rules So that means it'll be the current team if they're active or the team they played for the longest if they're retired We're gonna use pro football reference calm for that and for tiebreakers All right, so we'll do the cards in the box first Oh, we've got a nice one right on top to lead things off. It's a two out of five Jalen Hertz Patch and autograph. I think that's like the college football commemorative patch there anniversary patch and His autograph two out of five for the fly Eagles fly and that's gonna be for G harp There he is got the Eagles straight up and is Rewarded Congrats, man. All aboard the big hit express Fly Eagles fly that's a franchise at the crossroads as well. They're gonna get some new coaching Do they do they start this guy next year or they do they keep Carson Wentz? But if you lose Carson Wentz, it's a lot of money. That's cash sorts of craziness We've got two out of ten Cam acres for the Rams. That's another excellent patch in there And that will be for who's got the Rams in this Rams to is Adam Koperman with Rams to The Rams are gonna need him to To really get things going They want if they want a shot at beating the Packers this week. All right, there's Rams to Next up is 12 out of 15 Albert okawa Bonham Who I think is a Bronco Yep, he's a tight end for the Broncos and that's the team I gave away also going at him Yeah, flawless usually delivers with the really fun bowl patches We got it out of five Ezekiel Elliott Star swatch signatures to color jersey and on-card autograph That's probably one of the nicer Zeke autographs. I've seen And that will be for the Cowboys. That's a number block team part of that Miami group Miami Dallas KC, etc so that'll be for That'll be for John John L with two and out of fives and under get the train whistle All aboard Nice one for Dallas Put that part of the Dallas group over here We got one out of fifth or one out of 25 Notre Dame's Alan Page. I believe is a Viking I'm not mistaken as he did he only play for the Vikings Can't math that right now. He also played for the Bears, but I think he played for the Vikings the longest All right, Hall of Famer Alan Page played. Yeah played for 12 seasons with Minnesota and the last four seasons of his career with the Chicago Bears and That goes to Matt Medlin who picked up the Vikings straight up We've got LSU's Clyde Edwards. He layer nine out of 15 for KC KC is a number block team part of that Miami Dallas KC Vegas group and Nine is for Monty Monty with KC nine gets the two-color dual relic We'll see him in action this weekend in the divisional rounds. Maybe he Increases his stock there. He definitely can We've got a Five out of five relic only and what team are you associated with?  Oh with that there it is and Chad All aboard the Big Hit Express And the last card here before we get to the encased is a dual relic Levisca Chanel Junior 12 out of 25 And that will be for The Jaguars that goes as Tobias have picked up the Jags straight up here and pick your team number a 20-20 Flawless collegiate football. All right now. Let's go to the three encased cards Let's try to get the gem card first, which is I think on the left All right, there's my guy right there Henry rugs one out of 20 diamond diamond rugs Raiders Raiders one on this side right here Oliver Soria, there you go Vegas baby Vegas on the right side is gonna be Two-color patch and autograph Jerry Judy for the Broncos one out of 20 Going to Denver Adam Koperman and Denver and the final one. Yeah, that was with the bonus spot to Denver is Wow Another Bronco John Elway three out of five great signatures Not bad for a team that we gave away Adam all aboard And there you have it ladies and gentlemen Flawless collegiate football the case is closed. Thanks for watching. Thanks for breaking with us. I'm Joe We'll see you next time for the next break


Now, in a moment, we're going to talk about the emotional effects of investing in the wrong man, the man who will break your heart. This is known as your emotional marketplace. Now what is the emotional marketplace? Well, before we get into the emotional marketplace, I think it's really important to address what men look at, and that's known as the sexual marketplace. That's right, the sexual marketplace.  Well, I first heard it when Kevin Samuels was around, and then recently today I heard it from a popular YouTube psychologist, and basically the sexual marketplace is how desirable is a woman in relationship to a man's resources and how much he's willing to commit.   I know anyone who's watching this might call me this, but I think there's a lot more value to a woman than their sexual capacity within a relationship.  This is a true statement. Oftentimes, the way we approach relationship is through sex. So it's understandable how it might be viewed this way, but I think it's more important to address from a woman's perspective the emotional marketplace. Now what is the emotional marketplace? The emotional marketplace is how much a woman is going to invest emotionally before she gives her heart to a man. Now, I said her heart because we are talking about the emotions, but at the same time, we may want to factor in the physical aspects of a relationship as well. See, a woman in my my invitation for women who are watching this is to view a man from the perspective of his emotional maturity and his character. That's right. Emotional maturity and his character. You see, women oftentimes give their power away based on those resources a guy might give you and also how much commitment he may provide for you. Isn't it fascinating that the decision for commitment all rests upon a man? I mean, traditionally speaking and generally speaking as well. You see, men are the ones who ask you to be boyfriend and girlfriend. Men are the ones who do the proposing in marriages. And so women oftentimes are left waiting for a man to make a decision when it comes to commitment.  But more importantly, is he going to commit to you before you even consider that I want you to consider the emotional effects of investing in the wrong man. Let me repeat that. What are the emotional effects of investing with the wrong man? And you've already given your body to this man. So he's the wrong man. And if you keep giving your body to all the wrong man, you'll be there's this phrase that you'll be coined out there. What's your body count? What's your body count? Because you've given your physical attributes to a man before he's earned it. So what should you be considering from the emotional marketplace? Well, as I said earlier, women oftentimes give their power away. They abandon their self worth to accommodate a man through the sexual marketplace. But I'm here to invite you to look at it from a deeper perspective. And let's start with his character. That's right, his character. Does his actions consistently match his words? OK, a man that's in the sexual marketplace might do that. Is he generous and kind? Yeah, man in the sexual marketplace could be doing that. Does he communicate clearly without wanting to be right? This is where it gets kind of tricky because these men are only in it for the sexual marketplace, all they care about is their own needs being met. See, these men are oftentimes called users. They want the benefits of sex from you and they're willing to give up some resources and pretend to be committal, if you will. But oftentimes that the men who have bought into this narrative really only care about one thing and these men will break your heart later on down the road. So they don't use people. They're clear about commitment. See, a man who has emotional maturity and character, he's very clear that commitment is an important component for a relationship. He hasn't bought into the narrative that marriage is evil, if you will, or serious commitment is evil. Men with character and emotional maturity don't use people and they're very clear about commitment. They have their act together, both physically and emotionally. And they don't chase sex, drugs, or alcohol or partying as their way to soothe their emotional challenges that they might be faced with. Now, one of the most important factors for this type of man is he's healed from his past relationships. You know, we have a significant percentage of human beings that are incredibly unhealed from their past relationships. He a man who's actually fallen in love at a very young age in his life, he oftentimes is very fearful. He has walls up. He has walls up. And so he may not be able to fully commit to a relationship. The other thing is about an emotionally mature man with character is that he's introspective. He works on himself beyond his limitations, wounds, and traumas. And I don't mean he's doing Tony Robbins, rah, rah, rah, rah, rah. Let's make money, let's make money, let's make money. OK, that might seem like they're doing personal development work because that's in the genre of personal development. But I'm talking about actually healing childhood wounds and adult traumas that oftentimes cause negative patterns and limiting beliefs in their life, particularly. And their romantic life. Now, one thing about an emotionally mature man with character is he's protective and empathetic of the women he's investing in. See, he's not in it for the sexual marketplace. He's in it because there's something deeper to a relationship than just the physical attributes. And these men believe demonstrating trust is paramount in their life. And trust is, do I have this other person's best interest at heart? You see, when men are just approaching the sexual marketplace, and I know a lot. And by the way, if you're not familiar with this, I highly invest doing some YouTube searches for yourself. But I'm inviting a new conversation. I am coining emotional marketplace because ladies, you are making an emotional investment as well as a physical investment when you're sexual with someone because you can bond with the wrong guy. You can bond with the wrong guy. And I'm here to invite you to do a bit of vetting before you make a physical as well as an emotional investment with a man. Folks, hey, we just talked about a really important conversation, the emotional marketplace in comparison to the sexual marketplace. I'm here to say is the emotional investment that you make into a man can directly affect your emotional well-being. That's right, it can directly affect your emotional well-being. And so I'm here to say, before you even remotely consider someone from a dating perspective, do your homework ahead of time first, meaning get really crystal clear on who you are and what you want. And then during the process of dating, vet, vet for their emotional maturity, vet for their character. Because quite frankly, these days we're walking around with a loaded gun like this. And the minute you're with the wrong person, it's like clicking the button. And what I mean is emotionally speaking, it can be heartbreaking. And I want you to avoid heartbreak at any and all costs. Is this thinking in? Is this resonating? Please let me know if it is. Post a comment below. I'd like to hear your thoughts. As always, if you find value in this video, please hit that like button. Please share this video. Please subscribe to my channel and hit that notification bell as well. And if you want to connect with me, check out the links below to schedule a discovery call with me to find, following me at my group called Midlife Love Mastery, follow me on Instagram and all that good stuff listed below. And I'm gonna wrap up this video as I always do.  I'm gonna reach into the camera and give you a hug of love, if that's okay. I'm asking you to turn to someone, a pet, a teddy bear pillow and give it or them a hug of love because hugs are a great source of love. And let's face it, we could all use more love in our lives.