So welcome all to this SIB Virtual Computational Biology Seminar Series. Today we have the pleasure to host Marcus Müller from the Podium Informatics Group, which is part of the University of Geneva and the SIB. Marcus grew up in Zurich, where he studied physics at the ETH Institute, and after some times at the Institute of Cereltical Physics at the ETH, as a researcher and teaching assistant, he moved to industry as a software engineer for several years working on data streaming, databases, image processing and code reviews. Then Marcus moved back to academia and he got his PhD in bioinformatics at the University of Geneva in the Hohenappels Group in 2003, and he worked the following four years as a group leader in the Houdi-Ebersold Institute for Molecular Systems Biology at the ETH. Since 2003, Marcus is back at the University of Geneva, and the focus of his work has shifted towards the usage of large spectral library to improve protein identification and towards statistical modeling and validation of proteomics data. So the proteomics, proteomeinformatics groups in which Marcus is now a serious scientist, is involved in developing databases and software for the benefit of the proteomics and the glycomics community. These resources are made available through the XPC portal. So today Marcus will share with us his work on mining large-scale proteomics data for protein modifications. Marcus, thank you again for accepting our invitation and the floor is yours. Thank you very much Diana. Protein modifications are central to our most cellular mechanism. To illustrate that, I'll show you this picture here from a publication by the H.A.R.T. adult in MCP in 2014.  They extracted P53 from these cells and isolated it and then they used a combination of open modification and variable modification searches to find as many modifications as possible on this P53 protein. As you can see, you can see two things. First, this was the state above here of before the publication, this is after publication, so there's a lot of things to be discovered on the PTM level. They more than doubled the number of PTMs known for this P53 protein, which is a very well researched group. On the other hand, if you have so many modifications, you can imagine the astronomical number of combinations you have and it is a different task to actually find out which of these combinations are present in the cell, which also these combinations are functional and what or which function they perform. So this is a little illustration here. These PTMs can be seen as devices that sense the environment of a protein. So you have proteins like kinases that can write on these devices, they can write the record. You have protein like phosphatases that can actually erase the record again. There is cross talk between these modifications. For example, this modification here can only be put on the specific site if the other modification is present. Then you also have competition of several writers that try to write on the same modification site and the writer that is more active as preference and will be able to write modification. As a result of all this, you get like a code, so called PTM code. One talks a lot about histone codes, there are the codes as well. And that code actually defines the function, represents somehow the state of the cell and defines the function of the protein. There's a large number of functions one can implement with this type of PTM mechanism. So you can implement switches, very robust switches, which are for example used for cell division or to start cell division. You can define amplifiers, you can define signal integrators that integrate different signals at the same time or over different time points. Mass spectrometry is, I guess, the method of choice to find the post-translational modifications. I don't think there's any other method that can do that in an unbiased way on a large scale. So very briefly in this standard shotgun mass spectrometry approach, what you do is you extract different proteins from a cell, I say it, you digest them, you separate the peptides in the LC column, you inject it to a mass spec and the most intense signals are then chosen for fragmentation. And you get thousands of these peptide-fragment fingerprints, which are then used to identify the peptide in a sequence database. Now if you have a modification on this peptide here, for example, you have three-betulation sitting on this arginine, all the fragment ion peaks that contain arginine will shift by the mass of the three-betulation and all the fragment ions that do not contain arginine will remain the same. With that, you can detect the three-betulation, you can detect the modification and you can pinpoint it with quite high accuracy on the right residue in your peptide. This is somehow a motivation for what we're doing. This is the publication from Steve Geige's lab. It's just very recently, it actually came out just briefly before our own publication, where they analyzed about a million, more than a million spectra from a cell line and they concluded that at least one third of the unassigned spectra arise from peptides with substircumetric modifications. So there's a lot of modification present in this MSMS spectra, which are usually undetected. A different approach and they use the so-called open modification search to achieve that. The different approach is, but also very interesting, if you, and this becoming more and more common, is to reuse or reanalyze existing proteomic data. For example, in this publication they make use of the fact that in a, if you have a phosphor isolation study, where you isolate for phosphates, that you usually do not only isolate for phosphates, but they usually also isolate for other molecules that contain a phosphate. In this case, it was ADP resolation and you can actually use this already measured existing data to pull out this, a lot of these ADP resolation sites and this was a very characterized modification and they could largely increase the knowledge about this modification just by reanalyzing this data. By the way, most people not analyze or not use open modification searches or similar things, do not extensively look for phosphorization modifications. The reason is simple. If you look for phosphorization modifications, you're in the situation of that picture here on the lower right. It is kind of difficult to do. It's a slow process and there's sometimes a lot of manual work involved. So why is it a slow process? This has to do with the search space. Let's assume you try to find, you have human proteins, about these 20,000 proteins. You have your fast file, which is your to use as a search space and then you digest the proteins here in silicone and you get a list of peptides. In that case, it's about 1.3 million peptides with a mass in a certain mass range here. However, if you allow a modification, let's assume we want to look for phosphorylation on serine or trionine and for oxidation or metronine and we allow only two modifications per peptide. Then the number of peptides in our search space, now each serine you have to count as either modified or not. Each metronine has to be considered as either modified or not. So the number of peptides in our search space goes up to almost 5 million. Now this is only for two modifications. If you have more modifications, it gets more complex. If you don't know at all which modifications are present in your sample, then you might have an idea just to take a database like Unimog, which lists all the potential modifications and look for those, but then it becomes prohibitive and in the search time will be too slow and you also have to deal with force positives and another effect is that if you do such a search here is from a modification search with six variable modifications that was run at the global FDR of 1%, that actually the peptides that have one modification already have a higher error of about 2.5% and the peptides with two modifications have an error of about 8%. So the more modifications you include, the more error you include as well. Now instead of configuring as it is usually the case configuring the modification you want to look for prior to your search, in our lab we use a different approach which is an open modification search approach where we actually reach the modifications directly from the sample. So we don't need any prior knowledge which modifications are present, we just use the spectra that are given to us. And we have a very special approach here which is used in some other labs as well, but it was mainly developed in our own lab and we give some justification for this approach later. At the moment I just like to describe it, so it is based on a spectrum library approach. A spectrum library is a assembly of spectra that are identified with a high significance. So we take a sample, we run a standard identification tool with no or just a few modifications. We identify that for example with Maxfont or Mascot or whatever. Then we take the identified PSMs and spectra, merge them together, so we take all the spectra to the match to the same peptide. It is the peptide with the same modification state and the same chart. And then for this PSM we calculate a consensus spectrum which usually has the better quality than an individual spectrum. We put aside the non-identified spectra and then we build this spectrum library. We'll also give more detail on this. Since you want to control the error rate in this approach, we calculate this decoy spectra as well and then we use our tool. This liberator builds a spectrum library, the liberator builds decoy spectra and MZ mod. Thus the open modification search on this spectrum library using the unidentified spectra. So how these open modification searches are based on spectral alignments and these spectrum alignments actually allow to extract the modifications directly from your data. So how do they work? They're actually very simple. Assuming you have a gravity spectrum with a given mass and you have a mass tolerance. So you assume that the modifications that you are looking for are smaller than a certain value delta M which is usually in the range of 100 to maybe 500 delta. So most of the modifications fall in this mass range. Then you have your gravity spectrum and you have a database which are either sequences or a spectra from the spectrum library and you extract all the spectra that are within this mass tolerance here. For each of these extracted spectrum you check whether actually open or modification could explain the mass difference between the gravity spectrum and the library spectrum. How do you do that? It's actually quite simple. You just take the two precursor masses so the gravity spectrum is a precursor mass of 772. The library spectrum of 692 the difference is 80 delta. Then you assume that this 80 delta is due to a modification. So you try to put the modification on each of the residues in these peptides and you shift the ions accordingly. So you do that. And if you find a residue where this shifted ions give a large overlap with the gravity spectrum, a significantly larger overlap, then you assume that you found the modification here because this explains, modification explains the difference between these two spectra and you assume that this modification this 80 delta on trionine is actually, sorry, on tyrosine is actually present in your sample and without any prior knowledge on that. No, just by comparing spectra. So the alignment we do is of course slightly different than that. I mean we work a lot on the performance to speed these things up. But in principle this is what we're doing. Then we also spend quite some time on trying to create decoy spectra that work because it's not that easy to create a decoy spectrum because it still has to be a spectrum. It still has to contain peptides somehow. It still has to have peptide fragments. Also the most of the peaks are actually not matched to peptide fragments but they also have a structure and you have to try to retain this structure as well. What you have to do is you try to create a random spectrum or a randomized spectrum that is still a spectrum. Additionally what is often the case if you randomize too much, so the randomized spectrum is actually quite similar to the original spectrum so you have to make sure that the similarity to the original spectrum is so you have to be really careful how you created this decoy spectra but I guess we found something that more or less works. We also regularly when we do these searches we check whether our decoy calculation is actually right. We do this in the following way. So we have our standard sequence search for example Xtendem. We search for a couple of modifications which are quite abundant and some of them are then also picked up by the open modification search in AnsetMod. Both the Xtendem search and the AnsetMod search are run at a forced discovery rate of 1% so there's about 1% error in these results. Now in the overlap some of the spectra will be identified by both Xtendem and AnsetMod and the disagreement between the two in this overlap region cannot be larger than 2% because 1% maximally will be wrong here. 1% will be wrong here but the disagreement can't be larger than 2%. If it's larger than 2% something is wrong. You don't know whether the FDR calculation Xtendem is wrong or the FDR calculation AnsetMod is wrong but you know something is wrong. And this is the way we actually check whether our FDR calculations are more or less okay and they seem to be more or less okay but we also have cases for example we use this mod A tool with a reverse sequence database and the reverse sequence database just doesn't work for this type of modification searches. So it pays FDR values that were quite drastically wrong. So we did a lot of these type of analysis of these open modification searches. We tried to identify modification introduced by sample processing protocols. We tried to identify modifications introduced by certain chemicals and most of the time these projects were actually quite successful and what we try to do in this work here is we try to do this type of open modification search on a very large scale. So we took a data that is very heterogeneous. This is from the quite famous publication from Pandis Lab where they try to obtain a fairly complete map of the human proteome. This was published in Nature. So they took a lot of tissues, 17 adult tissues, seven fetal tissues and some blood cells. They extracted the protein, separated them by SCS page, digested by trypsine, separated the tryptic peptides by reverse phase and obtained the MS-MS back draw in a hcd orbit trap and this resulted in about 25 million spectra. Okay this is fairly large dataset. At the time this was about one tenth of the the spectra that were available in public repository. Also interesting is that the dataset is quite heterogeneous so it's not only one cell line or one tissue, it's an assembly of different cell lines or it's only different cells and different tissues. And we wanted to find out whether open modification searches actually work and whether they're feasible for this type of first thing we did is we just want to check how long this actually takes to search this data. So we used Xtendem as a tool like very much. It is fast, it is reliable and you can configure many things with it. So we used Xtendem on the vital IT cluster and without modification this took about 40 hours. With six more variable modifications this took about 240 hours. So without modification this is feasible. You can almost do it on your own laptop. With modification it becomes a bit more difficult and especially if you have many modifications. You need to have a large cluster. The open modification search we tried this modate tool that needed it a little bit longer so that needed about 1700 hours to run on this 25 million spectra. At the time we had a quick mode which was the tool we developed before, mthend mode and we quickly saw that quick mode didn't scale. It was difficult to be deployed on the cluster and so that since we like developing software this led us to the development of a new software tool this mthend mode and mthend mode this is not yet the fully optimized version here but it performed quite well. It had about the performance of modate. Another difficulty that you have if you analyze large data in this pundit data we had about 2,200 LC-MS runs is that if you combine these different runs together that they're statistically not independent and if you calculate an FDR of 1% for each run combine the result list of 2,200 runs together what you get at the end is an FDR of maybe 20 or 30%. Just because of that one reason that in the true hits here they come they actually maybe 100,000 peptides that come from a fairly small space and they saturate fairly quickly after maybe 20 runs or so they start saturating and you can do more and more experiments but you won't find more and more true hits. The wrong hits is completely different because especially if you have modifications most of the peptides you have in your search space will never match a real peptide in your sample that's just there in the search space and if you randomly pick one of these random hits here they won't saturate there quickly because that wrong hit search space is much larger than the true hits. So they won't saturate and as a result your true hits will saturate your wrong hits won't saturate and you will force discovery rate. Okay that's a standard thing in proteomics as something you encounter all the time and you have to be careful dealing with that. Another thing is also if you calculate this is the statistical variation if you calculate the score threshold at 1% FDR for each round separately you see this threshold histogram here you see a large variation of these thresholds which introduces non-repressibility and which introduces additional noise in your data. However if you do that for all the data together you get a very clear picture and more precise threshold. So therefore it makes sense to at least my view to analyze all the data in one go and for that you need software. Now fortunately we like Scala, we like Java, unfortunately we have now this Apaches Park framework which was recently developed it came actually out of a thesis work by Matthe Tsararia and I think it's credible indeed for its thesis so I highly recommend to actually read the thesis if you want to have an introduction into Spark and the satellite projects around Spark. Now it's part of the Apache Institution so it is developed by many developers. It has several objectives so it is easy to use so it allows writing parallel and distributed code with little overhead as you will see it runs on the Java virtual machine so you can write your code in Scala, Java or Python. It has easy IO so you can easily read Hadoop files, Hadoop key value files, you can read HBase files which are very large distributed tables, you can read, you have an SQL interface that allows you to extract data from databases, you can read things from no SQL databases as well. It's very advantage compared to all the things like the Hadoop mat reduce framework is probably that it is fast and it is fast because it allows caching your data in memory so you can distribute your data on different nodes you can keep it in memory. It also has a fast serialization and it has something like mechanism to avoid stragglers these are very slow processes that sometimes happen on a very large cluster and you can just pass around them and finish them quickly.  Spark has a system to restart this job as we see and it's very configurable so you can configure your data persistency, your serialization, your data partitioning and so on. The main data structure in Spark is the so-called resilient distributed dataset or RDV and this is a read only collection so you can only read it you can't change it of immutable objects in the objects that are in RDV you can't change and this collection here is partitioned across a cluster of machine. RDV can be built in mainly following ways so you can maybe have a Java collection, you can paralyze them, turn them into an RDD, you can read an RDD directly from stable storage from your disk space, maybe a huddle file system or local disk or from a database or you can build a new RDD by transforming an old RDD. And Spark offers quite a large set of possible transformations these are reduced map you can sample from an RDD, you can show in different RDDs, you can filter an RDD, you can build the union of two RDDs or the intersections of two RDDs and so on.  This Spark has full tolerance which is very important if you work on large clusters so if one of the cluster nodes fails Spark kind of stores the transformation graph how this partition on that cluster was built and it will just rebuild this partition from scratch and deploy it on a new cluster. It also has two types of global variables these are broadcasts and accumulators broadcasts are read only variables that you distribute to the slave nodes and accumulators are variables where you can only write to or add things to but they can only be read by the master. This is a bit maybe more visual form of this RDD so you have your RDD here you read it from this you partition it each partition is sent to a slave node together with the global variable for example a broadcast variable then on each node you perform the transformations in the easy case it's a map transformation which only uses data from the same node in a more complicated case you do for example global sorting then these nodes need to exchange data which obviously then slows down the whole process and at the end you have an action and this action will collect all the data or some of the data and transfer it back to the master. So this is Spark and we use that now to build our tool so the first tool we have is this library creation tool this is liberator we store our spectra and our peptide spectrum matches in Hadoop files which can be read by Spark and turned into a spectrum RDD and the PSM RDD direct. Then we join the two RDDs you can do that with this Spark operation here so each spectrum is joined to its peptide spectrum match. Then we put aside the filter operation the unidentified spectra and keep the identified spectra we group them so we put all spectra together that belong to the same peptide spectrum same peptide mean same peptide same modification state same charge state and then we use this map function here to actually calculate the consensus spectra and to also calculate the decode spectrum. We put a lot of effort just into this part here I can't go into details for that but this most of the work actually went in here but the Spark gives you a nice framework to parallelize this code here. Then we take the non-identified spectra as described earlier and use msubnodes to identify or to the open modification search this is not the real msubnode code but the real msubnode code is actually no much more complicated than this one here you have a little bit of initialization you read your spectrum library you distribute the spectrum library on the nodes with this broadcast for example then you do the actual open modification search so you read your prairie spectra you filter them for example you don't the only one spectra with a charge larger than one and smaller than five then in this map function you do the actual open modification search on this spectrum library and the result of this open modification search are stored in this rdd and you can choose the persistence of this rdd you can tell whether you want to keep it in memory and disk for example for later use. So Spark is really I mean that's about all you have to do and it's really an easy framework. All you need to do is to make sure that these things this broadcast and this object here will be sent over the network so you have to make sure that they are serializable and obviously this all the intelligence in the open modification searches within this object here and you have to implement this intelligence as well. This is an open modification search like it would run on one single node and using Spark you can just deploy this open modification search all over. So these are some results these are just some tests we did so we also worked a little bit on the scoring. We used the classical scores that are used in proteomics within to any wonders here so we used kind of a normalized dot product score to evaluate the correlation between the 20 spectrum and the library spectrum then we have a positioning score that evaluates how well the alignment works taking the sequence information into account and we have a score that evaluates how well the aligned spectrum covers actually the sequence of the pattern. All these scores are essential they improve the results you have here the number of spectra sorted by their score and here you have the number of wrong hits so the flatter this curve is the better it is the better wrong hits number the smaller the number of wrong hits for a certain number of identified spectrum. We also have a delta score which is also quite known in proteomics it is like an A score or a score that evaluates how well the best position distates itself from the from the runner up positions and you can see that by adding this course we can improve the whole performance of MZ mod and we get actually right times. One thing that is kind of the curse of these open modification searches are these ambiguous hits so each time you do these things you fall over them there's nothing you can do to avoid them or there are actually things you can do to avoid them but most of the tools actually don't do that because these two are somehow blind. Now let's assume in your search space you have two peptides this one and this one here they only differ in this two in this aspartic acid and aspartic acid and glutamic acid here in these two positions. So the two peptides have almost the same mass so they have a mass difference of 14 delta. Now for an open modification search tool which is kind of a blind tool it is somehow the same thing whether you identify this peptide here or whether you add modulation on lysine here and identify this. Apart from that one peak that matches here there's no difference. So the open modification search tool is blind so it doesn't know for us somehow clear okay this is more likely here maybe also this belongs to a protein which is more abundant than this one here that makes things clear but for the open modification search tool these things are almost equivalent and it has to be the same. And this is actually something where spectrum libraries help as can be seen in this example here so we have again some ambiguous hits we have the true hit here this is a peptide with an oxidized metionine on myosin then Amphibnode also found this oxidized peptide here because the non-oxidized version is present in the spectrum library. And Amphibnode found this peptide here which is very very similar instead of a metionine it has a lysine and then it has to correct for the mass shift and it just adds a mass difference of 33 Alton. Now for mod A this is almost the same thing again it doesn't know that a mass of 33 Alton 0.9 Alton on lysine does not really exist it just looks for mass shift and finds this. And this is wrong in this case and Amphibnode was saved because this peptide here was not in the spectrum library so it just did not even consider it. And the reason for why Amphibnode works often better than Mod A is that it is much more likely if you have a modification the modification is much more likely to be real if the non-modified peptide is also present as simple as this. I mean there are some differences as well in sporing and all that but I guess one of the main differences is due to that. It doesn't always work for example if the wrong peptide is also in the spectrum library Amphibnode will also pick the wrong one if that gives the higher score. But in many cases you are in this opposite situation here where Amphibnode picks the right. So this is the summary of this comparison between Mod A and Amphibnode M score. The Mod A curve here is in red and Amphibnode curve in blue so the flatter these curves are the better it is. If you had a means to identify this ambiguous hit and to pick the right hit among these ambiguous hits the performance of Amphibnode would improve quite largely and those of the performance of sorry of Mod A would improve largely and those of the performance of Amphibnode. But right now we don't have this criteria to identify the right hit among the ambiguous ones and I think we should work on trying to do that and not improve other things. If you do open modification searches replace standard sequence searches the short answer is no. If you compare for a specific modification how many modifications are picked up by extend them if you configure that as a variable modification compared to mz mod for example you see that in all cases extend them finds more hits than mz mod and mod A. Just because xonem has an easier task it only has one modifications to search for whereas mz mod or mod A have the whole space of allowed modifications so that creates a lot of false positives and requires more restrictive thresholds.  However the open modification search tool makes sense if you don't know that or if you have too many of these modifications then they become useful and I think we think that mz mod is quite a good tool for that so in general it gives you more identifications than mod A on this very large dataset. So this is kind of a summary of the modifications that were picked up by all three tools you see there's about two million spectra could be matched to a modification. xonem searched for the standard modifications like phosphorylation acetylation and so on and mod A and mz mod looked for all the modifications. Each tool finds modifications the other ones don't find all of the tools were on at AFTR of one percent. It's about two million so that's quite a bit so at the end about 30 percent of your PSMs are modified PSM so that's a significant. However if you look at these modifications if you do the modification mass histograms where you just count how many times that modification mass shift is detected you will see that the vast majority of these modifications are chemical. These are the lone things like metonyne oxidation, deamidation, double oxidation, carbamidamylation, carbamino methylation. These are the things that are just there to sample processing they react with the proteins and we pick them up because these searches are quite sensitive. Here you have as a little tiny peak here phosphorylations. It looks tiny compared to this huge peak but it's actually not that tiny only mz mod alone did pick up about six thousand unique peptides that were phosphorylated which is comparable to a standard phosphorylation study where you enrich phosphor peptides and it found quite a lot of these phosphor peptides just due to the sheer volume of the data. Are these modifications these chemical modifications completely useless? You could say okay we calculate over two thousand hours just to find mainly chemical modifications. This is a recent work done by Debo Hoba and he showed actually that it includes the most abundant chemical modifications in your sequence search that you actually find some more peptides than if you do a sequence search without any modifications and since tools like mz mod or mod A give us information which are abundant chemical modifications you can extract this information configure your sequence search accordingly and research your data with these modifications and in this case this is from human sperm data. There are a lot of this project together with French groups and we could identify quite a lot of proteins that don't have experimental evidence and if you add these chemical modifications to your search it could increase the number of peptides that match to these proteins here quite significantly. So they're not completely useless these chemical modifications the question is whether you want to take into account the increase in search time and maybe other factors in order to find them. So at the end just some results briefly these are things I found with mz mod. For example you have something like oxidation of proline. You could imagine that oxidation of proline might not be the most interesting thing maybe it is not interesting but the question here was more whether oxidation of proline compared to oxidation of metadiene is actually an artifact or whether it is actually real. And the data seems to indicate that at least part of this proline oxidation is real. For example if you have this graph here you have from the x-axis the tissues on the y-axis you have the modification counts or how many times this modification was detected in a specific tissue you see the two there's no correlation between proline oxidation and metadiene oxidation. If that would be an artifact due to the amount of oxygen you have in your sample there should be at least some correlation but there's nothing. It's also quite interesting to see that the proline oxidation is very down on the cells on the single cells. Proline oxidation happens in polar gene I guess and the polar gene forms the extracellular matrix so in cells where you don't have extracellular matrix you almost have no proline oxidation. The overlap with the annotation in uniprot is very small and the main reason is that most of the oxidations we actually found was in polar gene and these are not annotated in uniprot. They only have a very small overlap but I think at least a large part of these proline oxidations might be real. Another quite important modification is citrullination on arginine. This is basically deamidation of arginine which changes the mass by one dalton and which removes the charge from arginine. So removing the charge from arginine can have a very drastic effect. It is often used in scaffold proteins like myelin, TT, polygane and so on and the removing of the charge can either condense or deconsent these large protein complexes. Recently it was also discovered that it has a function in the decondensation of chromatin so if you citrullate arginine on I think histone one the arginine or the positively charged arginine becomes neutral it attaches from this negatively charged DNA and it leads to a decondensation of the chromatin. So this can have some recent papers out on that and this can have quite a drastic effect. We found here again we have the tissues we found most of the citrullination in the spinal cord which makes sense there's a lot of myelin there and myelin is known to be citrullated. Other modifications were on TT and other structural proteins. Here this co-analysis showed that we have a lot of these structural proteins in our list of citrullated proteins. The overlap with unipot was this time a little bit better about 18 or sorry about 30% of the unipot proteins that have a citrullination annotation were also found in our sample. However we found a lot of these citrullation which were not annotated. In unipot and also quite interestingly we found a lot of citrullination on proteins annotated in unipot but on different sites. Whatever that means that you can speculate or but it needs to be verified what the meaning of that. As a last example there's another modification here this is also quite a common modification to chelination on lysine. It's a mass shift of about 100 dalton which also had a very clear spike here. It occurs both in liver and frontal cortex. Again this makes sense. We detected the liver chelination on this alcohol the hydrogenase which is a protein which is predominantly found in liver. This chelination is not annotated in unipot so there might be something new. We also found it on the albumin where it is annotated but the albumin chelination was only found in the liver and not in the other tissues. We found it in the brain as well on many of these brain proteins here and I mean one has to go through each one of them and look in detail whether these modifications actually make sense at these positions. So as conclusions open modification searches on very large datasets they are feasible and you actually get some results out of them and you can add about 40 percent of PSMs modified PSMs to a list of non-modified PSMs. If you search for specific modifications don't use open modification searches. It doesn't make sense then you just configure these as variable modifications and search that way. Our spectrum library approach has some advantages over maybe model A in terms of sensitivity and accuracy. This Apache Spark framework is really a great framework and I think it's very well suited to deploy these calculations on a cluster. Most modifications you find are chemical that's the way it is, it's not necessarily bad and there's still a lot of work needs to be done on post-processing these results. There's lots of manual validation still involved and it would be nice to automate at least part of this validation process. So at the end I just like to thank the people involved in this project. So this is especially Oliver Hoelachter who did most of the coding. He's really a great programmer and he implemented, re-implemented liberated tool, meant a dance and mod tool and he did really a great job there. Then Thibet Robin who uses now answered mod tool to look for modifications in spam data and which is a collaboration with Nexpro, especially Lili Lane and Labs in France. This is Charles Pino, Yves van der Brug, Fliga are the main people involved. Then I would also like to thank the proteome informatics group. It's a very nice group to work in and we have a lot of discussions on these subjects. Most of the people here do either databases or like comics but there's a lot of overlap between the two fields and we have a lot of comment there. Okay and I would like to thank you for your attention.


Hi everyone, Joe, for Jaspy's Case Breaks.com, coming at you with a half-case break of 2022-23 Panini Donner's Optic Basketball. Six Fox, pick your team number one all-card ship. We know what the drill is with this stuff by now. And from a fresh case, but first big thanks to this group for making it happen here on Wednesday the 12th, hump day. Second half already in the store right now if you're watching live. So if you want to get your teams before someone else does, make it happen. Melissa with Last Bot Mojo with the Sixers, 70% of the time Last Bot Mojo hits 100% of the time. Voice a little weak today, ladies and gentlemen. I think I'm still kind of recovering from the dry temperatures of my little mini vacay last week in Vegas. And I guess that and smoky casinos and a lot of debating with my cousins, drinking a lot of booze caught up with me, I think. Physically, I feel fine. The voice is a little weak today, so I'm going to have to forgive me in advance for that. Alright, one, two, three for the left side, four, five, six for the right side. Six, one, two, three, four, five, six, and then we'll use this for pick your team two. Which again is on the website right now. Kind of look like these, but you get the idea. My people will run this back tonight. Alright, let's get on with it. On card rated rookie signatures, a lot of fun parallels to chase in here. All in all, I think a very solid break and a pretty popular product from year to year. Rex was saying earlier Dodgers got Tyson Miller. I have no idea who that is from the Brewers. How do we feel about no idea who that is? But knowing the Dodgers, they don't get players just to get players. They're a very methodical group front office. They are very deliberate in what they do. Well, I mean, I guess all GMs are deliberate in what they do, but they seem to make more correct decisions than not correct decisions. So I'm sure there's a reason why they got them. And yeah, like Oliver said, they'll probably turn into an all star by next year. Yeah, I think I'm with Frank. They're calling it a cheese burger, but it's not a cheese. There's no burger element to it. It's a cheese sandwich. Yeah, 20 slices of cheese. Who's going to... I mean, I don't... I'm not terribly familiar with Thai food culture. I do eat Thai food. That's a nice Pad Thai in Vegas over the weekend. But anyway, I don't know. Is that what the people want? They're calling it the wrong thing.  It's a cheese sandwich. 20 slices. What kind of cheese? Like American cheese? Cheddar cheese? I feel like... I don't know if I could do... If I could do like an American cheese, 20 slices. We'll do top-bottom randomizers for that. Looks like American cheese. That's too much American cheese. Nikola Jovich to 149 for the heat, Kevin. If it was like cheddar cheese, I feel like I can do a decent amount of cheddar cheese. American cheese is... Is American cheese cheese? There's Le Coudage, lime green to 149. Homer Simpson spent a whole night at his kitchen table in his underwear eating 64 slices of American cheese. Homer Simpson would enjoy it. I'm sure the Simpsons might have even predicted that to happen in maybe 12 seasons ago. Rex says I love grilled cheese, but I don't like cheese that isn't melted in some fashion. I've said this before. I'll say it again. No one is going to mistake Rex for a foodie. It's a 79. Jared Jackson Jr. Paolo Bencaro the Rookies. And Vince Williams Jr. Paolo. Our first Bencaro, first of many I hope, for Nathan who won that team in the Team Giveaway pack break. Deandre Hunter to 199. And Ty Ty Washington is your rated rookie autograph. John Jackson with the Rockets won the Rockets in that Giveaway break. Tyries Maxi to 149. Lyme Green for the Sixers. And that's our first box. Next box. We've got a little summer league action on the background. Toronto, Detroit. Toronto up by three. 85-82. Two minutes left in the fourth quarter. A Grady Dick kid is looking pretty good for Toronto. I actually saw him play a little bit in a summer league game last Friday. I mean this is with the caveat that this is only summer league, right? So he's playing against other summer leagueers. But someone to keep an eye on might be next year's when 2023, 2024 products are to come out. Some names to look out for. Speaking of the Simpsons, how many of you believe are fairly accurate?   Easy to fact check. But I got to say the ones that are at least popular have to be real. Otherwise they could have been debunked. I guess just a quick scroll through any of the YouTube comments will be like nah man this is fake. You know, or whatever. I mean the ones you should believe that actually show you the episode or the season episode so you can fact check it. But I don't know. There's a lot of smart riders in that room. They've done a zillion seasons. There's probably far more that they would never get right. You know what I mean? There's the honest on Tacombo 99. But I mean is that, it's not crazy. Trump had run for office before, made overtures about running for office before. Now you put two and two together and sometimes you hit on some stuff. There's Scottie Pippa Jr. to 79. And I think these are short prints right here. There's Gary Trent Jr. for Toronto. Alan Murdock. Let's check Holmgren the rookies. There's Aaron Gordon to 99. No check that to 39. And that'll be for Tristan. New Futurama. We don't need new Futurama episodes. Is it all the original riders? There's a shy Agbaji. Did they get the bender voice back? It's for the jazz. That's going to be for David. Oh, that was our second. I was like, did we get two hours out of the box? No, that's our second box. There's the Anthony Melton with the basketball emoji print in the background. I guess. I wish they would have just left it alone. They're so smart. Can't they come up with a new show? Not that smart, I guess. Well, that's true.  There's nothing original anymore. There should be more original things. But the nostalgia machine is powerful. And, you know, most of the masses just want the familiar things. Change is bad. New things are bad. I don't want to consume new things. Like, seriously, come up with something else. Simpsons is great. I mean, Simpsons, I guess, is just a money machine now. But like... Listen, you don't think former... You don't think former Simpsons riders or Futurama riders can get together and come up with something new? Andrew, what's up? Not to my knowledge. On that crime royale. But I don't do the buying here. So who knows? We get shipments in every other day with some new stuff. So you never know when that's going to pop back onto the website. Which is why everyone should look at the website every minute of every day, jaspyscasebreaks.com. Don't miss out. I'm surprised that when things arrive. I do what you do. I check the website. When I wake up, keep refreshing throughout the day. There's Grant Williams. What's on the site? What's new? This is nice. Jail in green. For the Rockets. He's pretty good. Dominator's autograph going to John in Houston. 4799. So does everyone else. Andrew, the Kabooms are super popular, which sometimes makes getting stuff like Crown Royale back just appeal back the curtain a little bit. Sometimes it makes it difficult for us to find. Sometimes we ask our distributors and they're like, we just don't have anymore. Seth Curry to 49. Or they'll be like, yeah, we have it, but we'll sell it to you for, I don't know, 40% more or something like that. We're like, all right, man. It's nice, but it's a little much on the price point. We'll wait until it, we'll wait until maybe we get a better offer on it until we'll pass on that. A lot of things that can happen. Availability, sometimes the price point isn't right. It's Jay Nivey rated here. Josh Hart to 199. Some Keegan Murray. And some Musa Diabate to 199. They did do Disenchantment, right? How did that do? Probably not so well. Herbert Jones and Andrew Wiggins. All right. Next one. Is that the one set in like medieval times? All right. Next box. Second half in the store. It's a pick your team, so no filler yet. Pick your team before someone else does. If you're like, man, I was waiting on this team. Now's the time to get that team. Jan, what's up? You have an app called The Sport. And you're looking at our article. It stars from other sports played football, like Otani as QB. Not really about sport, it is about fantasy. You have the What If app, the speculation app. You don't need an app for that. We can do that here, Jan. You don't even have to download anything else. I can do that for you. That's a common one. Jan. Especially with soccer. It's like, oh, what if America's best athletes, what if our best American athletes played soccer instead of their respective sports? What would LeBron be like as a goalkeeper? You know? What would Odell Beckham Jr. look like as a striker? He's been there. He's done that. Roger Maynard's goal is 55%. Yeah. I mean, it's hard. The Simpsons, Futurama, Family Guy, all have such a certain character base and a formula in a sense. It's hard to really match those. I know there's a certain animation style for it, but I think people would have rather seen something a little different. If you want that Simpsons aesthetic, you can watch Simpsons or Futurama. It's Jalen Brunson to 199. I don't know. If it was like the same creative crew, but try to do something different with the animation, push the envelope a little bit, but disenchantment, at least from the trailer, I should give it a shot, but to me, it just essentially looked like the same animation that I find in Simpsons and Futurama. And I was just like, put just a different time period and that's it. Probably the same similar jokes because they are the same writers. Lori Markin will go to David H. When it's Jaden Hardy, Rookie Otto will go to Dallas. That's going to be for Adam. It's tricky, right? Yeah. Once you're making good money, writing for a show that will never be canceled like The Simpsons, it's hard to break out to do something else. Unless you truly have a vision, I suppose. Zach Levine, 48 out of 79. Bulls, Alan. This guy got a nice little contract with the Pistons. There's another Jaden Ivey. Pistons could be the next team that could be surprisingly ahead of schedule. That would be pretty cool to see. There's Andrew Nemhart. Pacers are another one of those teams too, 31 out of 99. Also the animated series, I feel like is going to get Jeremy Sohan for the Spurs. That'll be for James. It's pretty good too. I wonder if like, the animated space is hard too. It's traditionally been traditionally been a difficult space. There's not too many networks that are willing to do that. At least sort of network television kind of animated shows. Now there are plenty of kind of exciting adult swim shows that are out there. But in terms of a that's more cable, right? It's more edgier stuff. You know, an audience that's more willing to consume more challenging animation and narrative structures. But for network television I mean, essentially you're trying to make a sitcom with cartoons and cater to a broad audience and that's difficult. I'm wondering how good or bad movies and shows will be ten years from after AI gets perfected. I don't know if I ever want AI to get perfected. You know, AI rex is only as good as the information we feed it, so that means we would be perfected if AI was to be perfected, right? Right, those mainstream anime shows don't make much money either. I mean, Simpsons is kind of like SNL you know. It can just live on in perpetuity. I don't think AI will be perfected. Because it's only as good as the humans that feed it information. Why am I pulling only color? I'm setting those aside so those can get sleeved. Slightly more important cards. Everything else, all cards ship though in this great. Yeah, I mean it could gather on its own, but there's a limitation to AI. Again, it'll be only whatever information it could gather. False or not. True or not. I don't know. For now anyway, at least in our lifetimes AI is probably not going to I don't think it's going to be it's kind of like when the computer generate a character right, in a a computer generated face in a movie with live action characters you can always tell there's a word, there's a phrase for it where there's like something just feels off no matter how good it is it's Mozambique for the warriors. I think that's going to happen with like with AI generated like content. Nice Jalen Williams that's Santa Clara Jalen Williams. Ready to rookie out of four? Okay, going to the thunder. 27 out of 49. Do you think it's possible to get nuclear codes? No. You cannot. It's Jamal Murray to 49. I was listening to a an NPR interview or something like that with one of the Godfathers of AI and like those doomsday scenarios that people are like the terminator scenarios are most likely not going to happen. I think like the first sort of wave is just going to be people trying to wrap their heads around how to how to differentiate between what's a real AI what is real and what's not what's AI generated in terms of images text content you know when video content gets to that point as well all that sort of stuff so in terms of managing information I think that's going to be the huge initial challenge before we get to the next sort of disruption which would be um it's more computer programmers you know AI is going to make coding so much easier so there won't be armies of people into armies of people like coding for things a lot of that's going to be so like so streamlined so you're going to lose jobs in one sense you're going to get efficiencies in other things like robots in factories building cars it's like the same sort of thing yeah he did quit because he was scared of what he created I think the biggest fear is the um well that guy at google google was going for a military contract using their AI stuff that's one of the reasons why he quit because the google never um actually threw their hat into the ring for that but the main fear I think is how it can be purposed militarily the concern being with the right AI you know I mean the idea is you don't put human lives at risk right which is on the surface a great thing but the consequences of that is potentially for bad actors in global politics the barrier of entry to war is a lot less is easier what's the size of North Korea's military right but what if they built an AI army of robot soldiers they're barrier to entry just to put those guys into action is a lot less I mean this won't be really a thing for another 50-60 years but that's like the path that you're going down but yeah the replication of like I don't know like clear bank accounts and stuff I mean that's not the real that's not the real worry that's gonna be fine you know it's no different from a telephone scammer it's just that it's automated so you'd have to be pretty pretty lax in your own personal cyber security if you're gonna get duped into although I mean older people it's happening already yeah like Ping is saying there's some already automated automated AI voice generated calls that are happening but that's not small potatoes compared to what the potential of this could be a lot of good can happen out of this so can a lot of bad it's just another another technology related issue that we have to go in is what happened when the printing press happened there are a lot of concerns when the printing press came about when radio came about when the internet came about we just have to be smarter about how we use it 71 out of 99, Andre Drummond that's gonna go to the bulls think about the 90s and what the fears of the internet was we'll seem ridiculous now but there were genuine fears there's Kenyal Martin Jr. 199 and that my friends is that alright let's do a randomizer for this this is also a wax party break so let's do that nothing too crazy here guys so I feel like the second half I like the Jalen Williams okay that was strong I like the Jalen Green you know but I feel like there could be some really good potential for some monsters in that second half alright so now let's do the let's do it all in one dice roll so one dice roll for top bottom on those cards and then we got a wax party stuff I don't think it's that different we're talking about jumps in technology Jan broaden out the we're looking at more of a top level view and Gutenberg didn't create the printing press just to get around the church I think it's more of because the technology was available he was an inventor want to promote knowledge but not directly to get around the church which bring more power to the people let's roll it, randomize it three and a two, five times so top bottom one two three four and five so the top cards will get those and three and a two, five times for the wax party invite so good luck with that one two three four and five after five times name on top is going to be well first of all the sad name is going to be Adam appreciate you trying appreciate you getting in there will be some other opportunities keep trying, jaspyscasewrakes.com congrats to you though, J goings there you go J after five times your name is on top you got a wax party invite I'm Joe for jaspyscasewrakes.com thanks for watching, thanks for breaking with us let's get into break two, bye bye


The Ukrainian president, Vladimir Zelensky, has addressed a summit of EU leaders this evening. The European Council is meeting to consider further sanctions on Russia, but with little hope of a sixth round of measures being agreed. Hungary, in blocking a total ban on Russian oil imports with fears about the impact on its economy. Prime Minister of Luxembourg Xavier Betel is hoping they can change the minds in the meeting room. Clearly we have more tensions and differences before the Councils that in the meeting rooms. That's because we have a national audience and we have to say that we are going to fight for one thing. But at the end, we were always able, I'm nearly nine years now in this room, usually we're always able to find compromise. And over a thousand delegates have descended on Dublin for the World Potato Congress. It's taking place at the RDS in Dublin with representatives from over 60 countries taking part. Agriculture Minister Charlie McConnelogue says it's a significant event. It's the first time in the history of the World Potato Congress that has actually been hosted in Ireland and we have a tremendous tradition as we know with the potato in this country so there's tremendous symmetry there.


Welcome back. We are looking at proof of the Chinese remainder theorem. We have done two baby cases k equal to 2 and k equal to 3. These two cases were easy but they tell us how we can do the general cases. So, k equal to 2 case just to go through that orally very quickly was that we first solved for two systems of solutions x 1 congruent to 1 mod n 1 and 0 mod n 2 and x 2 congruent to 0 mod n 1 and 1 mod n 2. So, the x 1 which was 0 mod n 2 directly gave you that x 1 has to be a multiple of n 2. And so, we write it as n 2 k 1 and the first part of that system of simultaneous linear congruences would then ask you for solving for this k 1. So, we will then have a system n 2 k 1 congruent to 1 mod n 1 and we are solving for k 1 which is guaranteed because n 1 and n 2 are co-prime. Similarly, you solve for x 2 because x 2 is multiple of n 1. So, x 2 will be n 1 k 2 and then we are asking for n 1 k 2 congruent to 1 mod n 2. So, you can solve for k 2 also and once you have solutions to these very special cases of simultaneous congruences you can solve the general case by taking linear combinations of these two. We have a similar situation when we had the case for k equal to 3 x 1 was the system which was 1 mod n 1 and 0 mod all others n 2 and n 3. So, x 1 was a multiple of n 2 and 3. So, we wrote x 1 as n 2 n 3 k 1 and we called that n 2 n 3 as c 1 and then c 1 n 1 are co-prime because n 1 had no common factor with n 2 neither did it have a common factor with n 3. So, n 1 would have no common prime factor with the product n 2 n 3. So, c 1 and n 1 are co-prime and therefore, c 1 k 1 congruent to 1 mod n 1 has a solution. Similarly, x 2 was the special system where you had 1 mod n 2 and 0 mod n 1 0 mod n 3. So, x 2 should be a multiple of n 1 n 3 and then you solve for k 2 because n 2 n 3 the product which we call n 1 n 3 the product which we call c 2 is co-prime with n 2 and then similarly we do x 3 and so on. So, we are going to do the general case now. Let me just remind you with the statement of the theorem we have n 1 n 2 n k this is the case that we are now going to prove. We have a k tuple of natural numbers consisting of pair wise co-prime integers. We have a k tuple of another k tuple of natural numbers a 1 a 2 a k and we are asking for the solution to the system x congruent to a 1 mod n 1 a 2 mod n 2 a k mod n k. The uniqueness part will be seen later. So, now we are going to prove this general case. So, we now prove or we now solve the special system for each i going from 1 to up to k and the special system is x i congruent to 1 mod n i and x i congruent to 0 mod n j whenever i not equal to j. So, this was the system which we had in the last case the case k equal to 3 where we had x 1 which was 1 mod n 1 0 mod n 2 0 mod n 3 x 2 which was 1 mod n 2 0 mod n 1 0 mod n 3 and x 3 which was 1 mod n 3 but 0 mod n 1 0 mod n 2. So, similarly here we have this x i which is 1 mod n i and 0 mod n j whenever i is not equal to j. So, if we define c i to be n 1 n 2 dot dot dot n i hat dot dot dot n k. So, here the hat means we are omitting this particular number. So, what we are doing is that we are taking the product n 1 into n k and dividing by n i or to make it more precise we are looking at the product n 1 n 2 n i minus 1 n i plus 1 up to n k. We are looking at this particular product and now we observe that since n i with n j is 1 for each j not equal to i. So, c i and n i are co-prime and let us again recall what we were looking at for x i x i we wanted to be 1 mod n i and x i was 0 mod n j for each j not equal to i. So, this condition tells us that this x i is a multiple of c i because each n j wherever j is not equal to i would divide x i again for each j not equal to i and therefore x the product n j where j not equal to i divides x i but this is simply c i by our definition of c i. So, we have that x i can be written as c i times some integer k i and now we need to solve for this. So, we have c i k i congruent to 1 mod n i but this has a solution since c i and n i are co-prime. So, thus each x i can be found the general solution x equal to a 1 x 1 plus a 2 x 2 plus dot dot dot a k x k. So, if you were to look at it modulo any particular n i so mod n i if we go then x is congruent to remember mod n i each of the x i where i is not equal to j is going to give you 0. So, the only thing which survives in this is a i x i which is congruent to a i because x i is now 1 mod n i. So, this is our solution to the general system of the simultaneous linear congruences. So, once again we solved very special systems which were giving 1 mod a particular n i and 0 mod all other n j's then the solution will be a multiple of the product of these n j's and using the property that since each of the n j is co-prime to n i the product of n j's is also co-prime to n i we have a solution to that particular spatial system of congruences simultaneous congruences and then we have a general solution. So, now that we have proved the existence of a solution we go towards proving the uniqueness. What is the meaning of uniqueness before that let me write what we have done and what we are yet to do. So, thus we have proved the existence of a solution now we go towards proving uniqueness this solution modulo n which is the product of these k natural numbers. So, what is the meaning to say that we are looking at uniqueness it means that if you have two solutions suppose I have a natural number alpha which satisfies that simultaneous system of linear congruences. So, I would have alpha congruent to a 1 mod n 1 alpha congruent to a 2 mod n 2 so on up to alpha congruent to a k mod n k and suppose we have one more natural number beta satisfying the same then alpha and beta should be congruent to each other modulo n this is what we want to prove. So, let us write it. So, if alpha beta they exist in let us say natural integers meaning why only natural numbers such that alpha congruent to ai mod ni and beta also congruent to ai mod ni then alpha is congruent to beta mod n this is the statement that we are to prove this is the statement that we want to prove. So, let us see how one can prove such a statement. So, since we want to show that alpha and beta are congruent modulo n we must look at alpha minus beta and we have that alpha is congruent to ai modulo ni and beta is also congruent to ai modulo ni. So, mod each ni we are going to get that alpha minus beta is 0 and this is to say that each of the ni is going to divide the product alpha minus beta. But if ni divides alpha minus beta and we also have that ni are pair wise coprime therefore the product ni is going to divide alpha minus beta which says that n divides alpha minus beta or that we have alpha congruent to beta modulo n. So, let me make some comments about this particular statement that when you have some set of coprime elements divide an element then the whole product goes and divides it. So, how do we think about this? So, let me state that here and prove it for you. So, we now prove that if ni divide gamma for each i then product ni divides gamma since ni nj is 1 for all i not equal to j. So, this tells us that first of all you have n1 dividing gamma and therefore gamma can be written as n1 into let us say m1. Once you have written gamma as n1 m1 we consider the case that n2 divides gamma. Once you have n2 dividing gamma, gamma is n1 m1. Now each prime factor of n2 will have to divide m1 because n1 and n2 are pair wise coprime. So, all the prime factors of n2 will divide m1 with the same power. So, n2 will divide m1 and hence the product n1 n2 divides gamma and then by induction then the proof follows by induction. So, the only thing to note here is that we have the fundamental theorem of arithmetic which guarantees that the primes occurring in a factorization are unique with the powers also being uniquely determined by the integer n. That is the only thing which will give us all these solutions. So, what we have now done is we have completed the proof of the Chinese remainder theorem. We proved the existence of solution by proving the existence of solutions for a very special case of simultaneous congruences and then we also have proved the uniqueness modulo n. So, after having proved this impressive theorem, the next thing to do is to try our hand at some problems. So, we look at this particular problem to begin with. This system says that we want to solve for x congruent to 1 mod 4, x congruent to 2 mod 3 and x congruent to 3 mod 5. So, here our a1 is 1. Let us compute, let us write all our tuples. So, n2, n3, n1, n2, n3 are 4, 3 and 5 in that order and clearly we have that they are all pair wise coprime. Then we have a1, a2, a3. So, these are 1, 2 and 3 and then if you remember the proof that we had done, we had actually looked at c1, c2, c3. So, c1 was n2, n3. Therefore, this is 15. c2 was n1, n3. So, that is here 20 and c3 was n1, n2. So, that product is 4 into 3 which is 12. And then once again we observe that 4 and 15 are coprime, 3 and 20 are coprime and 5 and 12 are coprime. So, we construct 3 systems from this where we are asking for inverse of each of these inverse of each side of the CI modulo ni. So, we solve for CI, KI congruent to 1 mod ni. This is the system that we are going to now solve first. So, 15, 20 and 12 modulo 4, 3 and 5. So, the first one is the product of these two. So, 15 k1 congruent to 1 mod 4 and then we see this quite easily that here k1 has to be 3. So, x1 equal to 45. After that we look at 4 into 5 which is 20 k2 congruent to 1 mod 3 which will give us. So, remember 20 itself is congruent to 2 mod 3. So, if I multiply 20 by 2 I get 40 which is congruent to 1 mod 3. So, k2 is 2 and x2 is 40. And similarly we solve for x3 by asking for 12 k3 congruent to 1 mod 5 and then we observe that k3 is 3. So, we have x3 congruent to x3 equal to 36. We can quickly observe that each of these have the required properties that 45 is divisible by 5 and 3 and is congruent to 1 mod 4. Similarly, 40 is divisible by 5 and 4 but is congruent to 1 mod 3 and 36 is divisible by 4 and 3 and is congruent to 1 mod 5. So, let me write it here once again we have 45, 40 and 36. These are the values of x1, x2, x3 and to compute the final answer we have to simply multiply the xi by ai and compute the final answer. So, x is 1 into 45 that is simply 45 plus 2 into 40 that is 80 plus 3 into 36 which gives you 108. So, 45 plus so we have 5 plus 8 gives you 13.   But we should also go modulo. So, we should we go modulo the product of the 3 moduli which we have here. So, 4 into 3 into 5 which is 12 into 5 which is 60 and thus our answer is x is congruent to 53 mod 60. So, I will now just write 60 here and we can easily check that when we go modulo this is what we always tell all the school students that once you have computed the answer you should check it again. So, when you go modulo 4 for 53 you see that 52 goes out and what is remaining is 1. When you go mod 3 you see that 51 is subtracted and what is left is 2 and when you go modulo 5 then from 53 you subtract 50 and what you are left with is 3. So, the answer is indeed 53 mod 60. Let us do one more problem before we finish this lecture. So, this problem is similar we want to solve this system of the simultaneous linear congruences and I will now be slightly fast because you know the method already. So, we will write n1, n2 and n3 in the order 7, 9 and 4 and we have a1, a2 and a3 which are nothing but 2, 7 and 3 and then finally we need to compute c1, c2, c3. So, remember once again c1 is the product of n2, n3. So, this is now 36, c2 is the product of n1 and n3 which is 7 into 4 so that is 28 and c3 is n1, n2 which is the number 63. So, now we want to solve for xi to be ci ki congruent to 1 mod ni this is the solution. So, we need to solve for the k. So, we go to the next slide but remember we have 36, 28 and 63 as the ci so c1, c2 and c3 are 36, 28 and 63 and I want to solve for k1. So, k1 should give me the property that 36 k1 should be 1 mod 7 but 36 is already 1. So, we have that this is 1 into k1 congruent to 1 modulo 7 and therefore k1 is 1. So, I get the final answer is that k1 is 1. I will solve similarly for k2 which should have the property that 28 k2 should be congruent to 1 modulo n2 which is 9 but 28 already is 1 mod 9. So, this gives me k2 congruent to 1 mod 9 and therefore k2 is 1. So, we get k2 also to be equal to 1. We should now solve for k3 with the property that 63 k3 is congruent to 1 mod 4 but 63 is 3. So, we should solve for 3 k3 congruent to 1 mod 4 but 3 k3 the k3 should be equal to 3 because 3 into 3 is 9 which is 1 mod 4. So, k3 has to be equal to 3. So, these are the values which we obtained for k1 k2 k3 and from these we should now obtain the xi x1 x2 x3 remember x1 is c1 k1 x2 is c2 k2 and x3 is c3 k3. So, x1 is 36 into 1 therefore this is 36 x2 is 28 into 1. So, that is simply 28 and x3 is going to be 63 into 3. So, I hope you have your multiplication tables with you it gives you the number 189. So, 36, 28 and 189 these are the x1 x2 x3 36, 28 and 189 this is x1 x2 and x3 and now what we should do to compute the final answer is to take x to be summation ai xi. So, I will multiply to 36 by 2 I get 72 then 228 I multiply by 7. So, 28 into 7 28 is already 7 into 4. So, that gives us 49 into 4 and 49 into 4 is 200 minus 4 because 50 into 4 is 200. So, we get it to be 196 plus 189 into 3. So, this is the product that we have to do in our in our head 9 into 3 gives us 27. So, we have 7 and then there are 2 left and 18 threes are 54 and we add those 2 to get 567. So, the final answer here is 7 plus 6 is 13 plus 2 is 15. So, we write 5 and 1 is left 6 plus 1 is 7 plus 9 is 16 plus 7 is 23. So, we have 3 and then there are 2. So, 5 plus 2 is 7 and 1 8 8 35 this is the answer but we have to go modulo the LCM which is 9 into 7 63 into 4 63 into 4 is 252. So, we need to subtract multiples of 252 from this number we multiply 252 by 3 to get 756 after subtracting this from this we get 5 mix 15 minus 6 is 9 you have 1 here 83 minus 76 this becomes 7. So, the answer is 79 mod 252 let us just verify quickly that 79 is indeed the answer. So, when you go modulo 7 to 79 11 into 7 or 77 and what we are left with is 2 when you go modulo 9 you will remove 72 what is left is 7 and when you go modulo 4 of course 76 are removed and what is left is 3. So, we have successfully applied the Chinese reminder theorem to apply these 2 systems of linear congruences what we are going to do in the next lecture is to look at some more complicated systems and try to use Chinese remainder theorem by doing some modifications to the system. So, I hope to see you in the next lecture. Thank you.


Hello people! I'm Ginny Metherill and I am a fourth generation witch. Very exciting, I know! Today I want to look at the wonderful Neo-Pagan Wiccan Festival of Ostara, how you might celebrate it, its rites, its traditions and its rituals. So what exactly is Ostara? This is simply the spring equinox when day and night are an equal length and the world is in balance. It happens this year on Monday the 20th of March. Take note, should you wish to do some veneration at that time. And it's especially auspicious because the vernal equinox brings this moon phase to its fruition and we start with the new moon on the 21st. It also happens on a Monday which is a moon day anyway and I'm pretty sure that adds a little more oh my god this is brilliant to the whole affair. I have received several messages from varying viewers saying that Ostara is just an invention of the great Gerald Gardner who created the Neo-Paganism form of Wiccan. However they are wrong. What Gerald Gardner did was simply formalize the date of Ostara. Ostara was always a movable feast which was celebrated on the first full moon after the vernal equinox which this year as I have said happens on the 20th of March. So it was a movable feast and you'll find that the Christian religion have given the name Easter to this festival. Now he did not invent the term Ostara. The first written text that mentions Ostara that we have was produced in the very late 600s AD. Now this is in the veritable dark ages when we were quite pagan still. The venerable lead who was a monk wrote down that the Anglo-Saxon Easter is simply their version of the Germanic goddess Ostara and there are many festivals celebrated in the spring for her. So this is definitely a goddess festival. What Gerald Gardner did was simply formalize the festival of Ostara onto the spring equinox. The written information and the knowledge that we have about the festival of Ostara or Easter is very scant because this is traditional worship folklore and it was an oral tradition or a let's do it tradition you know they just got on with it there was no need to write it down. The next source of information that we have of this comes from some text from Germany. Jacob Grimm wrote about this in his German mythology of the late 1800s in the Victorian area that there was still festivals of Ostara. So we don't know but it certainly wasn't an invention of Gerald Gardner. So now I've addressed that historical note let's move on to what it actually is. The vernal equinox itself is and has been celebrated throughout our known history. For example if you check out Stonehenge it's aligned with the vernal equinox they don't build this massive temple which took them probably generations to do and align it to the vernal equinox without the vernal equinox meaning something. So traditional English folklore have Ostara as a hair-headed goddess and the tale goes as follows on the mourn of the vernal equinox a farmer walked out across his land and as he was crossing his field he saw a hair start up and dash across in front of him. When he reached the place where the hair had started up from he found a clutch of eggs.  Modern day astrologers think that the vernal equinox is actually the first day of spring however we witches know the first day of spring to be way back in the beginning of February and actually the vernal equinox is the spring high point. This is when everything is in full spring flow the green man that god of spring is stalking across the land pulling forth the prana or the vitality of the earth to produce the spring that we know and love. The sun is directly above the equator and it spreads its rays across from pole to pole. This means that the earth is balanced and in harmony with the sun so one of the traditional witchcraft pagan rituals will be to go out and witness the dawn on the morning of the vernal equinox. Open your face to the sun and let its rays bathe you understanding that the sun is bringing this dawn equally across the world from pole to pole. It is a wonderful ritual to do and I thoroughly recommend it. You can also cast some pretty powerful spells using earth magic at this time with the vernal equinox to help you. I keep repeating this word balance and this is the most important thing about the equinox. It is also about abundance and you can tip the world into your favour to bring about your fertility and if you haven't seen my fertility spell I'll put it up here for you. Do have a go at it on the 20th. It will bring about some fine results and I do know lots of people who've emailed me saying oh yeah I did your fertility spell and it was marvellous so I've now got a blur blur blur blur probably do many children now but they've got them. So have a go. How else do you celebrate Ostara? Well in the Wiccan tradition of course you have an altar, you would have a feast and you might do some sun salutation on the morning of the equinox itself. Otherwise the traditional witchcraft ways of doing this was if you were a fisherman you would walk a labyrinth. Fishmen are starting up their trade again at this time of year and so one of their traditional crafts was to go and walk a labyrinth. This is an order to ask the sea and there is a sea spirit that you can placate as the wrong word but you can ask for help form to keep their ship safe and return home with a good catch. So if you happen to be near one of these labyrinths it's a great way to celebrate Ostara by walking about its nine rounds and using it to bring yourself into balance. The other way to celebrate Ostara is of course with flowers and although I've got daffodils here because the primaries aren't out quite yet it is actually snowing and we're covered in snow at the moment because obviously I'm doing this before Ostara so it's a bit chill and I'm not even sure that I can show you the primroses that I wanted to show you because it's too cold and I don't like the cold. I'm a bit wet really when it comes to cold. I like to huddle up by the fire with a good book. Summer on the other hand has me outdoors practically at dawn. Primroses are one of the honoured flowers of spring and Ostara but if you pick primroses to bring into your house you must pick 13. If you lay 13 primroses underneath your broody hen she will lay 13 eggs which is the apparent ultimate clutch of eggs and they will all hatch. If you only put six primroses only six will hatch so you know it's worth doing the extra of 13 I think. When you bring primroses inside also make sure you bring them in increments of 13 because this is the traditional number for luck with primroses. Planting primroses and pots just outside your doorway will also help with the fay.   Primroses are most beloved by the fay and so there's all sorts of stories about if you hold primroses and look over their flower heads and you'll see the fay they are an entrance to the fairy realm and I think my March video goes into this in a bit more detail and if you haven't seen it I'll put that up here for you because it's quite interesting and there's lots of other bits of detail in fact about Ostara which I don't think I've done in this one. I can't remember. Forgive me you'll have to go and look at it. Another great way to celebrate Ostara is of course a spell for balance. Ostara is also a great day to get any relationships back into balance. You might have a relationship which is out of kilter with each other. Now I'm very concerned about the Americans work life balance. They seem to work all the time and not have enough time off for their families and this concerns me and so to take stock of this and write down what you would like that relationship to be or how you want your life work to be. Write it down on a piece of paper and then you can cast a circle. Place the piece of paper in the cast of circle and use four candles at the four directions. Light the candles and using a wand ask the sun because this is a sun spell to let these wishes come to you. It'll work. Ostara is not one of the big glamorous festivals but it is important to mark these times in our life so that we can step back and realise the blessings and the wonder that we already have. I would love to know what you think about Ostara and whether you are going to celebrate it in any way. My celebrations will mainly be having a lot to eat with my friends and family and will also be involving. Welcoming the sun at dawn with a sun salutation and realise that everybody else in the world when they greet their dawn is seeing that same point lovely. What do you think? Leave me a comment below. In the meantime don't forget my cover meeting is coming up next week just after Ostara. I think about the 22nd which is the Wednesday so if you are interested in joining that we will be doing some Ostara related witchcraft and learning a bit about how to control that for our own benefit I think. I haven't written it yet so bear with me but you can go to patreon.com forward slash a journey meryl for all the details otherwise please give me a like and subscribe because it really helps my channel and I will see you in a few days.


Getting the title millionaire is a goal that many people share Although making a million dollars is quite hard because it is the first million It is possible, but saving alone will not get you there In this video, I will share with you 13 practical ways to make a million dollars 1. Change your mindset For many people, achieving their goal of making a million dollars means brainstorming ideas that are worth the million-dollar profit Even though this technique works, it is not the smartest way to reach your million-dollar financial goal One error with this technique is that you might end up missing opportunities and doubting the potential of every single idea that comes up in your head Now, how much do you get when you repeat a ten-dollar profit process for 100,000 times? Yeah, you're right A whopping one million dollars A mass and wealth is more about your perspective and planning than it is about creating a big idea that no one has ever thought about before 2. Be mindful of debt The number one barrier preventing people from living a rich life is getting into wrong debt The word wrong is used because there are two types of debt Bad debts are those kinds of scores you incur to purchase liabilities and depreciating assets While the other kind of debt is committed to buying assets and investment many millionaires are debtors They take loans from banks and put it into investments A student loan is also classified as a good debt According to personal finance writer Candice Elliott the beauty of good debt is that it is essentially an investment just like a stock or a bond you're spending money now in the expectation of getting your money back and perhaps some profit on top of that in the future Paying off your credit card debt and other wrong debt is one of the most important investments you can make into your rich life 3. Serve a million people When you only have a few customers and your goal is to make a million dollars the only option for you is to increase your prizes and squeeze every last dollar from your customers Well, this is an unhealthy practice because soon you will lose all your customers and your business will fold up However, when you find a way to serve a more substantial amount of people the benefit is enormous If you are new in business and have only a few customers if your products or services are top-notch the feedback up referrals can cause a magnificent increase Thus, instead of serving a few people and having them pay more determine to serve a million people by serving the few at hand incredibly well 4. Self-publish a book or sell a course Let's say you get the drift about selling your product to a million people you tried it and it's working for you Do you know that many people are not aware of this information and who are seeking ways to scale their businesses? The next big thing for you to do is to teach it to them Don't worry about the competition there's enough space in the sky Besides, you are not going to be teaching them for free Thanks to Kindle, it only takes an enchanting book cover and an excellent editor to put your book up for sale You can also art for the other option selling out your experience as a course With the aid of your smartphone and an excellent video editor you will be on your way to making an additional thousand bucks 5. Control Spending When people think about millionaires they see beautiful homes and a yacht, several luxury cars first-class tickets and private jet vacations expensive pieces of jewelry just money being used to sweep the ground So, maybe a few billionaires live such lives but this is not the case of an average millionaire Millionaires understand that tiny flops in their lifestyle can drastically affect their financial future hence they value money and are conscious of every penny they make If you cannot control your spending then you should not dream of being a millionaire anytime soon Controlling your spending does not mean you should only eat ramen noodles and beans for the next year it just means that you should be prudent with your spending 6. Sell or invest in something Of course, you cannot become a millionaire by doing nothing According to Neil Roche, founder of nichepursuits.com what usually separates wealthy and successful people from those just scraping by is wealthy people have trained themselves to recognize opportunity If you want to make a million dollars you have to be swift to adopting and executing a plan when you see the financial potential For every opportunity you either sell or invest in a product or service It does not have to be something that has not been sold before you could just improve on an existing product or service 7. Cryptocurrency Crypto is like the hardest deal in the world right now Everyone wants a taste of it and some people have even gone as far as selling their homes to purchase bitcoins but while everyone is fighting to get their hands on more bitcoin the smart crypto investors are quietly making huge amounts of money by other means Many people assume that bitcoin is the only cryptocurrency in the world or at least the only one that pays for now But other smart individuals are making a serious return on their investment with ICOs Initial coin offerings Although its longevity is unpredictable one single trade-off of a profitable ICO could bring you 60% of the way to your target of making one million US dollars 8. Have multiple income streams A funny acronym that has been formulated for the word job is just overbroke Do you know that researchers have even pinpointed a statistic that millionaires on the average have not just one but seven streams of income? Although they may be known for just one thing millionaires usually engage themselves in other income generating approaches If you want to get a million dollars from just the one job you have you might have to wait for a decade before you finally become a millionaire Even with being one of the highest paid professions many medical personnel are involved in private consultancy selling courses online, etc Even though you have a booming business it is not enough to make you a million dollars in the shortest time possible Start with your active and then build your passive Hence you must embrace passive income 9. The stock market Making money in the stock market is not as glamorous as the movie The Wolf of Wall Street makes it seem Just like other ventures, there are times you lose If you are looking for an overnight method to make a million dollars then the stock market is probably not for you The trick with investing in stock is not to focus purely on the value of the stock right now but instead on its future potential value Consider those who invested $1,000 in Netflix stocks ten years ago They would have a portfolio of $50,000 which is 4 times and 20 times what would have been made from Apple stock and Disney respectively Investing in stock can make you a million dollar rich You only have to invest in the right stock and be patient 10. Employee is sponsored 401K 401K is most times referred to as free money It is a retirement account that is offered by an employer whereby an employee puts a portion of his or her pre-tax check at every period before he or she gets the chance to spend it A 401K retirement saving is more than a subtle future investment It also lowers your taxable income For example, if you earn $5,000 a month and invest $1,000 into your account you are only taxed on the remaining $4,000 The best part of a 401K saving is that your employer might even offer you a match which makes it possible to have twice your investment 11. Understand the difference between assets and liability Many people do not understand the difference between assets and liability as well as appreciating assets and depreciating assets For instance, people assume that having a big car or big house is an asset Rich dad, poor dad, Robert Kiyosaki explained that although your net worth may include non-cash producing assets like your art collection, wristwatches and golf clubs they cannot be accurately referred to as assets Those so-called assets can only be sold for only a fraction of the value that is listed in the balance sheet Yet the moment you begin to sell them, you are taxed for gains In general, if you want to make a million dollars focus on acquiring assets such as bonds, mutual funds and royalties that can generate more money and limit amass and depreciative assets 12. Stay in that small apartment Moving to a bigger and spacious apartment is always at the top of the list for many people whenever they get a financial elevation If you want to make a million dollars, you should stay in that small house One fact that a lot of people tend to ignore is that the bigger the apartment you live in the higher your expenses Bigger houses come with significant mortgage payments Experts recommend that total housing costs should require only 20-25% of your take-home pay or 28-33% of your gross salary Total housing costs include basic home service, utilities and renters insurance Except you already have way more than a million dollars you should remain in that small apartment 13. Invest in yourself The fact is that you are worth more than a million dollars The reason why you don't seem to make money is that you run around looking for bonds scheme to invest in Ignoring yourself If you want to make a million dollars then you must invest in developing your talent and being so good at it Even if your professional qualification does not earn you a million dollars your natural ability is potent enough to grant it to you Think of that thing that you are naturally endowed with Read books, learn from mentors, watch YouTube videos and just do anything that will bring out the best in you And then launch You will be shocked by how fast you can make a million dollars There is no trick for how to become a millionaire If you want to make one million dollars you have to consistently get through a series of small everyday actions and decisions