So hopefully everyone can hear me all right. And so welcome to day two. We're gonna be starting with module five, machine learning. And as before, this presentation and all the material that we're providing today is licensed under the Creative Commons license. So it's share and share like concept. What we're gonna be looking at today is hidden Markov models. And this is a subject of interest more for historic reasons. It's something that is frankly a very difficult subject. And I'm kind of looking forward to maybe next year where we won't really present on it, but it's been used for more than 20 years and has played a key role in a lot of development of bioinformatics software. And so we'll talk about it. We'll see how it can be used in sort of a limited example. And then we'll reintroduce it later on in the course I think in module eight again. The challenge with hidden Markov models is that they're mathematically really, really, really difficult to understand. There's probably about two people on the planet that understand them. And the rest of us are still struggling to figure out how they really work. So this is just an outline of what we'll be doing today. We've already done our check-check I think. Everyone's got their cameras working. We'll have about an hour and a quarter where we'll talk about module five, we'll have a break. Then we'll get into a very long lecture slash lab which is module six. We've scheduled two hours for it. Hopefully it won't be that long, but it covers a lot of things and maybe that's the, I'll call it the highlight for the day. For others, perhaps the highlights will come around three o'clock and 4.45 when we talk about scikit-learn, Keras, HMM learn and a few other tools which make a lot of the coding and development of machine learning so much easier. So that's kind of a quick outline of what we'll do today. So with module five, we're gonna talk about sequence motifs because this is primarily where hidden Markov models of Sean. We'll talk about both text, regular expression comparisons as well as what's something called position-specific scoring matrices or postems to identify sequence motifs. Then we'll introduce the concept of Markov chains and hidden Markov models and how we can use HMMs to identify sequence motifs. So then we'll go through the Python code for a real HMM and then I think most of you will soon appreciate just how difficult they are. So sequence motifs are something that are identified through multiple sequence alignments. Typically they're literally thousands of sequence motifs that have been identified not only in protein sequences but also in DNA sequences. And they often align to something that is critical to binding to some functional aspect of a gene or protein. This is a sequence motif for a dead box, DEAD. It's a conserved set of four amino acids. The dead box is also a key signature for ATP dependent helicases. So many helicases have this. What I've indicated in blue below the sequence alignment is the annotation that we would use in terms of a regular expression. The first residue in this 10 residue motif could either be elucine, isoleucine, valine or methionine. So it's sort of a branch chain amino acids. And there's two of them. Then there's absolute conservation of DEAD. Then the next residue can be just about any residue. So that's put a star in there. And then the next two residues also seem to be very hydrophobic. So this is a motif, which you can do the math would probably match to many possible combinations of single sequences. And this could be used to scan using regular expressions, any protein sequence to look for this particular conserved sequence. As I said, these are found in genes and proteins, binding sites, recognition sites, secondary structure, tertiary structure, targeting sites. And it is through multiple sequence alignment that most sequence motifs have been identified, whether it's in RNA, DNA or protein. Here's some examples of signaling sites that had been identified. And these can be ER directing sequence, nuclear transport signal, signal peptidase, cleavage sites. And again, you can see where there's different characters that are used. So a dollar sign is used to indicate the end of the sequence. Stars are used to indicate wild card characters or any residue. Curly brackets are used to help define the length or span of certain residues between certain motifs. So all of those types of regular expressions, and depending on the library and the annotation that's used are allowed. Here's an example of more consistent or standard regular expressions. And sort of on the left is how the regular expression appears and then the text on the right explains how that is produced. So things in square brackets give you the different possible amino acids or bases. Question marks indicate that could be yes or no. Pluses can indicate how many times it's repeated. All kinds of variations on that. And certainly in the 1980s and early 1990s, regular expressions were how most people coded or identified sequence motifs, how they talked about them in papers and journals. But there are problems. And the fact is that a regular expression performs an exact match to a sequence. So maybe if we had isoleucine, leucine, valine, methionine, but occasionally threonine is allowed, we'd have to either add a residue or we'd have to sort of allow or use some kind of scoring matrix to say, okay, this is sort of close enough but not precise. If you're trying to build out sequence motifs and you have a large sequence alignment, you're spending a long time tabulating the different residues or bases and counting them up and deciding whether you should include them or not include them or how many spaces or gaps should be allowed or not allowed. And it's a pain because I've actually written and prepared lots of sequence motif databases and I'm as a student and it was not fun. So in fundamentally sequence motifs really don't match how proteins or enzymes work in terms of recognizing binding sites, either to DNA RNA or proteins themselves. It is fundamentally in biology is sort of a fuzzy process. So what developed in the late 80s and early 90s was a concept called a scoring matrix or a position-specific scoring matrix. And we pronounce it as possum. And so there's a little picture of a baby possum on the left. But it is similar to most things in bioinformatics. It's like a sequence scoring matrix, whether it's the blossom matrix that use in Blast or the day half matrices that are used in sequence alignments. What you do with a possum is you construct it through multiple sequence alignments. And by comparing the multiple sequence alignments you're able to calculate the frequency of conserved bases or conserved amino acids. The conservation score in each position of the possum is converted to a log odds score. It sort of converts small numbers to numbers that are sort of in the range of 0.1 to one or two. And so what you've seen below the picture of the possum is a real position-specific scoring matrix spanning about 10 bases. And on the left side, you're seeing the ACGT. These aren't frequencies. Originally they were, but they're converted to a log odds score. So you can see that things are between 0.1 and 1.2, I guess. If you're given a new sequence, and that's the one that's shown in the middle, A-T-T-T, A-G-T, A-T-C, you can go along the length of that possum and every number that's circled represents, if you want the level of conservation of that sequence or agreement of that sequence to the ideal sequence. And by adding all the numbers up, you get a total score. So 0.2 plus 0.2 plus 0.1 plus 0.2 all the way up, you get a score of 2.5. Now it turns out rather than in like in bowling where the high score wins, it's more like golf where the low score wins. So the low score with the possum gives you your best performance. So the nice thing about possums is that it allows you to do fuzzy matches. You don't have to have exact matches. So it's more powerful than regular expressions. It gives you a score to assess the quality. So just like bowling or golf, you can say whether you've done well or badly. But there is a limitation, and this has been a chronic issue for possums, is that it doesn't handle insertions or deletions. So you'll look at that sequence there, that possum that I've indicated, it's a defined length. It's 10 bases long, it's not 11, it's not nine. And in fact, there isn't a really good way to describe a possum that handles insertions or deletions. So it was, I think, a realization again in the early 90s of the limitations of possums that people started to come up with other approaches to do sequence motif analysis. So this led to, particularly, the introduction of hidden Markov models. As I said, sort of at the beginning, I hate them because they're really hard to understand. And I think you can kind of appreciate just even looking at this picture of how difficult the hidden Markov model is. It looks like there's nodes and connections. And you can say it sort of looks like a neural net, but it's not. And in fact, the way that it's diagrammed and how those connections go forward and backward is critical to the performance of a hidden Markov model. And it's technically called a probabilistic graphical model. So it means they have to have pretty good understanding of both probability of graph theory and of some fairly advanced and sophisticated mathematics. More recently, thanks to developments in the deep neural nets, most of what can be done or is being done by hidden Markov models can be done generally better and more understandably through deep neural nets. So this is why I suspect this may be the last year we'll actually teach about HMMs, but from a historical perspective, HMMs are important. So I've mentioned that HMMs have been used for a long time, particularly in speech recognition. So we talked about Alexa, Siri and Google Home. If you've used them or tried them out, they do a pretty good job with speech recognition. They initially used HMMs, I think now most of them use deep neural nets. Language translation was something, stock price prediction has been another one, musical composition, anything where there's a set of sequence or events. So music is a set of events, words, a spoken word, or sentences, a set of words and events. Time series data, so if they're looking at analyzing cardiac monitoring, seismic data to look for patterns. And in gene finding and motif finding for bioinformatics, again, viewing that a collection of sequences essentially is a sequential collection of letters occurring one after the other. And so this is what HMMs were initially designed for and I'll explain that a little bit more. HMMs initially in the world of bioinformatics were used a lot in prokaryotic and eukaryotic gene prediction. They have been used to create sequence profiles and there are now large collections of HMM models that were used both to get sequence motifs but also to classify sequences into families. HMMs have been used in multiple sequence alignment. They can be used in three-dimensional structure analysis, protein topology analysis. So the heyday of HMMs was probably through the mid-90s to I guess maybe about five or 10 years ago, but they are ubiquitous in the field of bioinformatics. They are, they're strengths so that they are statistical or probabilistic so there's lots of robust math associated with them. It, as you'll find out, allows you to come up with a pretty systematic, mathematically robust approach to estimating parameters and to calculating probabilities. It's an iterative process for improving probabilities. So when we calculate probabilities by hand typically, we measure a whole bunch of events. There might be conditional probabilities so we'll collect all of that information, run numbers through it and then we come up with estimates. Hidden Markov models use things like expectation, maximization methods to help actually improve those probability estimates. The strength primarily at least as an example we're gonna use today and look at is with sequence motifs and dealing with insertions and gaps. And as I said, with regard to things like regular expressions or more specifically to possums, that's a weakness. They can't handle insertion situations whereas Hidden Markov models can. So my point at the bottom is that Hidden Markov models are really, really difficult to understand. So I'm not expecting any of you unless you've been studying Hidden Markov models for the last two or three years to understand all of the material I'm gonna present today. But I'd like you at least to get a general appreciation of what's done in part because some of the concepts from Hidden Markov models have made their way into even the theory for neural nets. So Markov models are different than Hidden Markov models. Markov models are essentially a set of events or sequential events. Essentially a Markov model is something that depends only on the previous event. So if you're going down a pathway and there's multiple forks in the pathway where you end up is essentially a function of what you did in terms of choosing one or two directions. So it's a little bit like the path decision making in terms of a decision tree. There's an interesting historical bit of trivia here which is that Markov models were actually used to create the very first sequence scoring matrices. That was called the point, I guess the point assisted mutation matrix or PAM matrix that Margaret Dayhoff who was the founder of Biogeometrics developed in the 1960s. And so what she did was she calculated essentially a scoring matrix for very, very similar sequences. And that scoring matrix was called the PAM one matrix an assumption where there's just small mutations or small numbers pretty closely at aligned sequences. And that roughly correspond to about one million years of evolution, at least that was her estimate by multiplying the PAM one matrix 250 times. So that's one after the other, after the other. So this is matrix multiplication. She produced the PAM 250 matrix which corresponded to the expected evolution of sequences over 250 million years. Again, to produce it you had to do a multiplication in sequence. And so this was essentially a Markov process where one million years of mutation times another million years of mutation produces the PAM two matrix. It was all theoretical, but what she ended up producing actually was a scoring matrix that was amazingly useful. It was useful for more than 20 years in terms of sequence comparison alignments. And it was only improved on slightly through the development of the blossom matrix. So a Markov model, as I say, it's a set of sequences and typically there are connected by arrows or in some cases multiplication events. So the arrow represents a probability of transition. So the probability of A to B or from B to C. So the probability of B coming from A is equal to probability of the state being B and the previous state being A. In this case, B can only come from A and so the current state depends on the previous state's transition probability. If that transition probability is zero, then obviously B cannot come from A and therefore C cannot come from B. So that, as I say, is the Markov model. There are different types of Markov chains. If we have the simplest one, which is only the preceding event or preceding base or preceding amino acid, determines what's gonna follow. That's a first order Markov. A second order Markov chain depends on having, or is dependent on two other preceding events. So in the sequence that's given in the middle, you need A and T to contribute to the occurrence of G. You need T and G to contribute to the occurrence of C. Now, a Markov chain becomes a hidden Markov chain when we have the observable sequences, ATG, CATAA there, but then we have these other boxes, which are hidden effects or hidden observations that influence things. So it's sort of the puppeteer behind the curtain or the sound effects from, again, the hidden black curtain that influence those sequences. So we know that amino acid sequences are not, or even base sequences are not entirely influenced by the preceding base. They're influenced by other effects. And similarly, in terms of deciding, so there's the invisible hand of evolution that is guiding that. And so to some extent, that's what these hidden observation or hidden effects have to do. We are typically, when we're talking about hidden Markov models or Markov models, we're working in the field of conditional probability. So the probability in terms of a first order Markov model of seeing the sequence A, C, T, G, T, C is just simply the probability of A times the probability of C times the probability of T and so on. The second order Markov model of seeing the same sequence would say that the probability of A, C, T, G, C is equal to the probability of A times the probability of C given A times the probability of T given C. And then a third order would be what's shown there where we've got P given A, P of C given A, probably of T given A and C and so on. So again, if you know a little bit of probability, you can see where it can get a little complicated that it starts including Bayesian types of models. If we wanted to look at a true, this is a somewhat simpler architecture for a hidden Markov model, we talk about topologies and this is where the term graphical model. So hidden Markov models always begin with a graph or a picture. And there are certain conventions on how these pictures have to be drawn. So in the case of sequences, circles are used to indicate where there are deletions. Diamonds are used to indicate where there are insertions. Squares are used to indicate if you want the sequence. It is structured like a network. So there are arrows with directions. Some from any given node, there might be two or three or four different arrows coming in and coming out. There can also be self arrows. So something leaving and then coming back in. So those rounded arrows. And within the arrows, what we would call in neural nets, the weightings, these are called transition probabilities. Those are the edges in this network. And then the squares, diamonds and circles, they have certain probabilities as well. Those are written in the numbers there. Those are called emission probabilities. So the arrows have numbers and those are assigned values between zero and one. And the squares, diamonds and circles have probabilities. So we have different layers, different states, numbers within the nodes and numbers on the arrows for the nodes. And this topology here is a typical one that's used to handle sequence motifs because it allows for matching sequences. That's the match state. It allows for insertions and deletions. So we're gonna take an example of a hidden Markov model where we're beginning essentially from a sequence alignment. So we have five sequences here and it's a very short kind of meaningless motif, but it's at least simple to calculate. What we're showing here are sort of modestly conserved set of residues and maybe the second and maybe the set of A's at the, where the gap is. But what we've got are gaps or insertions here. And what I've written below is a regular expression which would explain this motif. And if you do the math, this motif would have about 3,600 possible valid sequences which is a huge number and probably is not terribly useful in terms of defining a sequence motif. And the fact that there's this inclusion of gaps and other challenges with the regular expression makes the regular expression kind of useless. And what it would suggest is that a hidden Markov model would be better. So we're gonna use this multiple sequence alignments to help build it out. What we do is we start calculating the frequency of from the multiple alignment, the number of A's and T's in the sequence. So we go column by column in this case. And so the first column, we can see that there's four A's and one T. So we can convert that to a probability four out of five is 0.8, one out of five is 0.2. We can do that for the second column. We get a probability of G and C, a probability of A and C. Then it gets messy because now we're dealing with insertions. And so we can go column by column, identifying the occurrence of essentially insertions and no insertions. So where we have a delta, we have in column, I guess it's four, column five, column six, we have inserts instead of the calculations done there with a number of sequences that have inserts is 0.6, number of sequences that don't have insertions is two out of five. And then column by column, we can see the probability of A's and C's and T's and G's are also given. So that's the messy part where we're dealing with the insertion. And then we go to the seventh column, we can see it's all A's, so the probability of A is one and so on with the seventh and eighth, the ninth columns. So this is how we get some initial statistics. Now we have to generate a model. And if you recall that diamonds are used for insertions, circles are for deletions and squares are used for matches. So we have to now draw out a graph. This is the graphical model for that sequence alignment which is shown in the corner there with the sort of the screenshot. And this is the graph that would explain or best explain the model through a hidden Markov approach. So we can see A and T, we can write in terms of the emission probabilities in the squares, it's 0.8 and 0.2. We have a transition probability of one going to the second column. We have a transition probability of one going to the third column. But then as we get to the fourth, fifth and sixth columns, we have this probability for essentially insertions. And so this is where we fill in the diamond with all the probabilities for A, T's and G's and C's. We also fill in the diamond for both transitions to the insertions and also for the occurrence of the first base of what we want to see, I guess. So you can see the transition and emission probabilities, 0.6, 0.4, 0.6, another 0.4. Those are all taken from the calculations that we have on that little diagram in the corner. And then we get back to the squares, which now corresponds to column seven. And we can see A has a probability of one, so that's the emission probability, transition probability of one and so on. So with that model, there's a path that we can follow. And so if we're given a sequence, let's say the sequence is ACAC dash dash ATC, we can essentially calculate the probability of its occurrence by taking the transition and emission probabilities and multiplying them all the way through. So it's an exercise in multiplication, 0.8 times one times 0.8 times one. And again, we're looking at the sequence and we're using the emission probabilities that are in each of the squares or the diamonds to come up with a value. So we do all the multiplication and we end up with a score of 0.047. We can convert that rather small number to a log odds ratio or LOD. And we can use the formula here, which allows us to convert those numbers or those probabilities and correct for both the frequency of bases. So there's four bases, so 0.25 is used for DNA, there's 20 amino acids, so one out of 20.05 is the probability for any given amino acid. And so this is the formula for log conversion. So we can convert that now to log odds values and I've put those in. And once we've converted to log odds, instead of doing multiplications, we can do additions. So the same graphical model and the same set that we saw here has again been converted to log odds. And you can see the numbers are different, but and that we simply, we add them all up. So instead of getting something at 0.047, we now get a score of 6.67 when we do our trace through with this particular sequence. So the point is that with this hidden Markov model, this graphical probabilistic model, we can calculate scores for sequences and say how good is this sequence, how well does it match to my sequence motif? Is it a high-scoring sequence motif? Is it a low-scoring sequence motif? And should it be considered as a real one? And so now it's better than the possum because we're able to handle gaps in both insertions and deletions and we're also able to handle the appearance of matching bases or amino acids. So we can take in a whole bunch, here's seven or eight different sequences and we wanna see whether any of these approximate that motif that we are postulating on. So I've put in a bunch of sequences, I calculated both through multiplication and through the law of God's calculations. And what we find out is that there's one that has a very high law of God score and that one's a very good match to our motif and then there's one in red which has a very low law of God score and that's one obviously that shouldn't be included. And then there are others that are hovering around 4.6 to 5.3 and depending on what you've chosen as your threshold or your cutoff, you could say, well, these are also probably legitimate motifs. So what we're doing in a hidden Markov model and let's say this is a very simple one. We had a very small number of sequences and so at some level we could evaluate it. If this is a real example, one where we are trying to actually have legitimate motif, trying to create a motif out of five sequences, something you shouldn't do, there's a trick called pseudo counting which has been first developed for possums that allows you to sort of fill in extra information so that you're essentially these are dummy variables but that's another thing that you could have done with this HMM. So there's an evaluation problem and when you're doing hidden Markovs, that's where I was doing all the additions and multiplications and where I had to follow up path. There's this determining which sequence to follow or a set of events to follow.  Those are paths and when you are determining a path in a sequence, you use dynamic programming and some of you may have heard of dynamic programming, it's always used in sequence alignment, it's a path finding algorithm and there's the needle and winch path finding algorithm and there's also the Viterbi path finding algorithm. So in hidden Markov models, we use the Viterbi instead of the needle and winch algorithm for dynamic programming. That's called a decoding problem. So there's an evaluation problem, a decoding problem. In situations where you don't have an alignment and this is more frequent in not only sequence motifs but in general for most hidden Markov models, you can learn the transition and emission probabilities. So in our case, because we had an alignment, we could calculate the emission and transition probabilities but if you don't have an alignment, you can have a learning algorithm, it's called the Baum-Welsch algorithm to estimate the emission and transition probabilities and so that's the learning problem. So in HMMs, you have to solve three problems, the evaluation problem, the decoding problem and if you don't have alignment information, you also have to solve the learning problem. So this is summarized here. So for evaluating, given the model parameters, calculate the probability of a particular sequence and you saw how I did that for some simple sequences back here, I just did some log odds or simple multiplications. But while it seemed simple, I still had to essentially follow a path and determine what those numbers are. There's this decoding one, which is in fact, how did I find the path and how did I get those, both include the certain hidden states, the circles and the diamonds in my calculation. And the learning problem, I didn't have to do that in the example I gave you, but if I just had the simple observations that I would have had to have estimated the emission and transition probabilities. So we're gonna take an example which is more complicated than the simple one I just gave, where we're gonna try and essentially solve or address all three problems, which is pretty standard for most hidden Markov models. Now, to do evaluation, typically we use a technique called the forward algorithm. So it's a path tracing algorithm. So it's a form of dynamic programming. In the example I gave you, it wasn't a very challenging dynamic programming when it was just followed the obvious path. So there's something that we'll call the forward algorithm. You'll see that a little later. Then the decoding problem, that's another dynamic programming algorithm. It's to find the most likely sequence of hidden states that results in the observed set of events. So it's, how do I include the insertions and deletions, the diamonds and the circles? Which path do I follow? And it is essential for HMMs involving sequence profiles. So here the word returbie a lot when people talk about sequence motifs. The one that's probably more interesting at least as it pertains to machine learning is a forward-backward algorithm. This is also what's called the Baum-Welsch. And it uses a technique called expectation maximization. So it's an optimization algorithm at some level. And it allows you to estimate the transition and emission probabilities without having, in this case, sequence alignments. It iterates, it estimates probabilities and then refines them. And so in that regard, the Baum-Welsch algorithm, you could say is an analog to say the back propagation elements that we saw in neural networks. It just, it optimizes things and it calculates error, goes back, adjust things, calculates the error. And just like in neural nets, you have this idea of going forward, backward, forward, backward. And that's why Baum-Welsch is called a forward-backward algorithm. Okay, so hopefully I haven't lost too many of you, but as I say, hidden Markov models are really complicated and I have no expectation of anyone really knowing the innards of hidden Markov models after this. But we're gonna try it or show how it would be used in bacterial DNA sequence. We've chosen bacterial DNA because bacteria have simple gene structures, simple promoter structures. Eukaryotic gene structure is really, really complicated and certainly there have been very good successes with the Eukaryotic gene analysis using hidden Markov models, but they get incredibly sophisticated and are really complicated. So we're not going to try and go from zero to 60 here. So just for people who don't know or as a reminder for people who've forgotten, promoters are sections of DNA located typically on the five prime or in the front of genes that promote the binding of other proteins to enhance transcription. Typically you'll find promoters anywhere from 30 to 200 base pairs in front of the translation start codon. So they're not immediately in front, they're kind of a little further down. They're typically associated with operons, so you don't find promoters for every single gene. You'll find promoters maybe for gene clusters. So I've illustrated there again, the sequence ATG is the typical start codon, the promoter is some random sequence up there. In particular, there's one site that's called the Prygna box, which is one that's used for transcription initiation and sequence alignments and sequence comparisons have identified this RNA polymerase site that has modestly conserved TTGAC in the minus 35 site and then a TATA T-A-A-T sequence a few bases downstream from that, about 20 bases or so. This is not 35 bases upstream of the ATG site, it's just could be anywhere up to 200 bases away, but this is a characteristic of called the Prygna box. So we're gonna be looking for promoter-like sequences, similar to the Prygna box. And what you saw with the sequence there is it's sort of a sequence motif. The conservation again is lower cases indicates it's not well conserved, upper case say these are well conserved, but this is not a great sequence in the sense of it's not a regular expression that doesn't allow fuzzy matches, doesn't really handle gaps because the gaps can be variable. So this is a sequence that's just ripe for doing hidden Markov models. So this is the workflow we've talked about in the past, instead of how do I define or how do I generate a motif from unaligned sequence data. So we define our problem, what we're gonna do is looking at promoter sequences that have been collected until identify this Prygna box. So here's a mess of sequences. And we wanna run our hidden Markov model through that and we wanna be able to see that TTGAC and TATA link with certain variable gaps in between. So we wanna see if our hidden Markov model can pick out those promoters and conserved elements within the promoter sequence. So what we're gonna do is take a set of about 50 bases. We're gonna develop a hidden Markov model with a total of 50 hidden states. And we're gonna train them on a set of sequences. We're gonna determine the emission and transition probabilities from this set of unaligned sequences using the Baum-Wilch algorithm. So that's our plan. We'll see if we can do that. So from our plan, we have to get our data set. So there is a large collection of E. coli promoter sequences, a total of about 1800 promoter sequences where there's a known transcription start site. And these ones are all collected to span about 50 bases before the transcription start site. Now, these are not aligned. So we aren't attempting to find the Pribno box through alignments. We're just simply saying, here's a mess of sequences. Here's 1800 of them. Let's use the Baum-Wilch algorithm to figure out where the patterns are. Now, the other point is that within E. coli, there's about 4,500 genes. So promoters on average, there's one promoter for every three genes. And that's just a characteristic of many bacteria because they have operons where they just need one promoter, maybe for three or four genes that are runoff in the operon. Okay, so we're gonna try programming our hidden Markov model. If we were to do this, we'd go to our colab file. In our case, obviously we're not expecting you to write this, but we've already written it for you both in the Python and in R. It's given the title HMM motif, and so you can open it up. And the general algorithm we're gonna follow is outlined here. Just like with all the other programs, we're gonna read our data. We're gonna do some encoding. It's not one hot encoding, but we are encoding the sequence data. We're gonna initialize our HMM. We're gonna write our forward algorithm for the Baum-Welsch. We're gonna write the backward algorithm for Baum-Welsch. So forward backward is another name for Baum-Welsch. And then we're gonna combine the two to create the Baum-Welsch function. Then we're gonna write the Viterbi function. So this is the dynamic programming function that I talked about. And we're gonna initialize and train the hidden Markov model by calling the two algorithms, HMM initializing and Baum-Welsch. And then we're gonna create the log probability functions. That's the, if you want the log D or log odds. And then we're gonna use the Viterbi algorithm again to do the evaluation to find those log probability measures. And they're gonna evaluate the performance of our motifs in terms of detecting or correctly detecting the promoters. So it's a fairly complicated algorithm and game probably don't have time. In fact, we don't have time to go into a lot of the details. But with most things that we've seen in machine learning, we call up NumPy and Pandas. We have the dataset reading. So we have our motif sequences in a comma separated file format. They're structured in a certain way. We're using a drop NA function to help clean up some of the data. We're looking for any, well, we're also looking for the reverse sequences as well as the forward ones. So we've read in our dataset, we're gonna now transform our features. So in this case, we're converting A, T, C and G into numbers, zero, one, two, three here. So this is a form of encoding to help simplify things. Again, we're working with the forward sequence as well as the reverse sequence. We've chosen to solve this using an HMM. As I said, in the future, we're probably gonna be using recurrent neural nets or LSTM models. But historically, this is how people would do HMMs or use them. So we're gonna initialize our parameters. We're gonna initialize the transition probabilities. We're gonna initialize the emission probabilities and we're gonna initialize the initial state probabilities. And so basically we're calling random numbers to put in random start points. And this, as I say, is what you do when you don't have an alignment. You're letting the bomb wash do your work for you. And you can see various functions like random or random.rand that help create those initial random distributions. So now we encode the forward algorithm and bomb wash uses both forward and backward. So the forward algorithm is defined here. I'm not gonna get into the details. It's pretty complicated math, but that's what it looks like. It calculates the current state to turn the probability of the next state. So this is where the Markov concept comes in. We have visible states. Those are the, if you wanna call them the match states, which are the squares. And we're then gonna calculate probably in Markov model will be in a particular state at a particular step. So this is essentially the optimization equivalent to the back propagation that we talked about in neural nets. It's fairly costly in terms of calculations. It goes as the order n squared. And there's the backward algorithm, which is the other half of the viterbi or rather the bomb wash. So consider this the equivalent to back propagation like we had in neural nets. And it's used to calculate the probability of observations given the hidden states. So we've initialized HMM. We've generated the forward algorithm. We've generated the backward algorithm. So then you have to combine the two to create the forward slash backward algorithm, which is essentially the learning algorithm. So what this is doing is it's calling. So this is the bomb Welsh function, we're creating that. But then here's where we're calculating the forward backward. Those are the calls that we're making here. And then there's some normalization, some dot products that are also calculated through the matrices that we're building out. That carries on. Again, fairly complicated math and we're not expecting anyone to understand that. But in the end, we create our transition and emission probabilities. So these are tables of transition emission probabilities for this particular hidden Markov model. So that's the learning part. And as I say, think of it as being equivalent to the back propagation algorithm, but we call it the bomb Welsh function. Then we have to create the viterbi function, which does the dynamic programming. So this is, it's used in, as we call it the decoding, also in the evaluation. And again, fairly complicated math, lots of probabilities determined through it. It's not a short program. It's calculating various maximum values. It's doing some essentially what most dynamic programming algorithms do, which is this trace back step to find the best path. So this is the viterbi algorithm. Again, we're not gonna come into details, but just trust me that it is a dynamic programming algorithm. So we've built out all the functions that are key for hidden Markov models. Now we can actually start putting the hidden Markov model together. So we've built the base, now we can put on the icing. So we start off with initializing, in the sense that we have the initializing function that we had created that's called here, the bomb Welsh function. These are highlighted sort of in blue just to show you that we're calling them. And this is where we're essentially training. So we start off with these random set of probabilities, then we go through this iterative training with the bomb Welsh. And the result is these are the probabilities that essentially come out from that training. So these are state to state transitions. So there's essentially a seven by seven matrix and then there's the emission probabilities. That's a four by seven matrix for the different bases that we're talking about. The initial probabilities and array of seven numbers. From that calculation of the transition, emission, initial probabilities, then we have to call the viterbi dynamic programming algorithm to calculate the log probabilities. And so this function calculates the log probabilities and it also has a cutoff to sort of draw the line. And through running that viterbi program, we can test our sequences. We can look at the 1800 promoter sequences along with thousands of other non promoter sequences that we also had. And then we have a cutoff that essentially says, is this a sequence that's a promoter or does it fit the promoter probability or does it not? And that's, if you recall, how we were doing our log odds evaluation where we either multiplied or added. And we said, is this above or is this below some kind of cutoff? Well, we accept it as a member of our motif or not. So this again is using the similar sort of thing. Is there a cutoff? Is it a member of the promoter motif or the priv-nobox motif or not? So a lot of work, really complicated. And this is the result. So again, we've got 1800 promoter sequences and thousands of other non promoter sequences. The confusion matrix is shown on the right. Recall that a good confusion matrix along the diagonal for prediction, matching, observed should be something on the other of 0.9 and 0.9. Instead, we're getting 0.2 and 0.7 and that are often diagonals are 0.8 and 0.3. So in some respects, this hidden Markov model is a failure. And it just underlines how complicated they are and the fact that we were sort of naive and taking just the first 50 bases because it turns out that some of the promoter motifs are outside of that 50 base scan. So at some level, it's a lot of work for nothing but at least the diagonal is not all zeros. So it is picking up promoter sequences and it highlights the fact that promoter sequences are actually pretty noisy. That the conservation of the pridinal box is actually quite poor and that the position of the pridinal box actually varies tremendously more from the zero to 50. It also highlights some of the weaknesses I think have hidden Markov models, which is A, as you've seen from the code, they're really complicated, and B, we didn't do sufficient feature engineering in this particular example to really build on what's known or some of the other components or a smarter way of assembling the data or compiling the data so that we get a slightly better performance. So I guess what I basically say is that we have an algorithm that sort of works. It's a correct hidden Markov model. It doesn't crash, but because we hadn't been careful in assembling our data and putting in a sufficient number of features, the performance is not great. Through this, we can still create sequence motifs with this trained hidden Markov model. And so there's additional code in the program to actually perform that and to propose a minus 10 box and a minus 35 box from a particular sequence. So overall, it's a big program, hundreds of lines long, it takes a long time to train, it takes a fair bit of time to run. We've also written the program in R and the performance in R and in Python is about the same. R is a little faster, but the R code is a little longer. In R, it's pure R, so we aren't using any extra functions like matrix or data reading tools like NumPy and Pandas. So whether it's in pure Python or pure R, we've had a hidden Markov model. Performance isn't great. We think there's still possibly a bug in the code, which is why it's not doing perfectly, but we've never been able to find the bug in the last year. So maybe that's just the actual performance. It is possible to use this structure, the hidden Markov model structure, where you've got the bomb wash, we've got the terby algorithm, so that you could potentially apply it to more sophisticated things, but you'd really have to understand the code. And as I say, very few people really truly understand hidden Markov models. So we also, as I say, have the R code and if you're more comfortable in R, you can run that.


Welcome to Digital Asset News, the guitar stories and crypto currency new assets and bring down a bite-sized pieces. So today interesting stories all about Cardano. So first up, Cardano prepares to welcome Singularity Net as its Ethereum contracts gets terminated on May 31st. And this is just the beginning because we're looking at ERC20 converters and different projects that were on the Ethereum blockchain, which are going to be moving over to the Cardano blockchain. And how much is really going to eat into Ethereum's dominance and what is happening. So we're going to take a look at what is going on there on top of how I believe things are actually going to move in the right direction for smart contracts as they get rolled out in a three-tiered stage. And what this really means for the Cardano ecosystem, we're going to be taking a look at a lot of those over the next coming weeks over on Dan Clips. And finally, the reason why they're doing this so delicately and in a step-by-step fashion is because of fraud and different hiccups and problems that happen in the DeFi space in general, as far as smart contracts and people losing their money. So we'll take a look at all that, but first let's take a look at what's going on the market. So before we start, as you may see, that we are in a lovely, nice demoed home here. It's one of our investment properties and we're back in Houston for a bit to get some things done over here as we turn our property around and see what we can do and all that great stuff, which is just a fantastic part of getting into investment properties, short-term rentals and things like that. So one of these days, I'll do a more in-depth video about it. I've already done one before, but this is just what we like to do and here we are. So anyhow, it doesn't really matter. This is what's going on in the market. That's what everybody cares about. So right now we're at 1.4 a trillion and like we talked about yesterday, it's going to be either it's going to go sideways, a little bit of bumps up and down. And we're going to see some different things happening as far as like, you know, just sideways action. And in my personal opinion, this is where all the money is made. All the money is made when it's boring. Everybody's like, forget it. I don't want to do anything with this. And they just kind of get out because they don't want to, it's not sexy, really, you know, glamorous as things are moving sideways. But this is when you do things like, look, if you would have invested back when I was investing in 2018, when everything dropped down 80%, you'd be loaded right now. So this is not investment advice. This is just investment opinion. I go and tell you what I've done and it's not for everybody. That's all I can tell you. But if you have the gumption, this is a better, it's probably a better term than that. But to get into this, then here is what it's all about. And these are the times that I live for actually. Going out of Bitcoin is down. Everything's down. It's just, it's all down. And it's just what it is. And you know, we've seen these dips. This would be the fourth dip and people are always asking me what's going to happen over the weekend. Like I said, I'm like, well, I don't think it's going to go on 25K, but I do think we're going to bounce up and down a little bit. It's Memorial Day weekend for Americans. So we have a three-day weekend. I don't think a lot of people are going to be doing a ton of trading in America, maybe outside, of course. But I just don't think it's going to be massively, you know, bad to like 25, 20K or something like that. People talking about, I think it's going to go bounce around. It's going to get boring. People are going to jump out because they don't really care. And people like me and you probably just sit back and go, cool. I'll just accumulate until everything takes off at the end of the year, which is what I think is going to happen. Anyhow, that's what we have in the market. Everything's red and that's what it is, except for Matic. Wow, 26% for seven days.   I, excuse me.  I don't think he knows everything about it, but he's probably got his hands into it and the price of it. So good for that. I own Matic myself a little bit. Okay. Anyhow, here's what's going on as far as Cardano. And this is what I think is going to be the next big thing. This is like the fifth time I think I've talked about this. I believe that Ethereum had its day in 2017 and all the ICOs are built on. Okay, granted. That makes sense. And then everything was going on long swimmingly. And then different things happen with the ICOs and work out so hot. A lot of them. And then we move on into the Gatsby issue and then Binance Chain came up and they have their day and a lot of things are built on that. Now I think with smart contracts being coming forth with Cardano, I just don't understand why people can look at this and go, yeah, Cardano's a ghost chain. Nothing's going to happen. I really truly believe that a lot of things are going to be built on Cardano and it's going to just explode. On top of that, people think that Ethereum is going to be the dominant force forever. It could be. I have no idea. I own both. And it's not my place to say, you know what, this is definitely going to be it. I'm just an investor. So I just hedge my bets and go from there. And I think Cardano's going to do pretty well over the next couple of months. So the first sign I can see is different projects jumping ship. Projects that were on the Ethereum blockchain, which is saying, you know what, there's an ERC-20 converter coming that's out and we're going to be doing these smart contracts. Let's just go over to Cardano because we want to go where the fees are low and people will come back and say, but you don't understand because Matic and Layer 2 Solutions and it's going to be awesome. Sure, it could be, but that's where this company wants to go. So let's take a look. Anyhow, what's happened here? Well, Singularity Net, a decentralized artificial intelligence platform, will terminate its old Ethereum contracts on the 31st of May, following a snapshot taken on the 28th of May. So if you have any Singularity Net tokens, just know that there is a process. There is a website. I have a link in the description below, SingularityNet.io, at the very top here it says AGI to AGIX Hard Fork upcoming May 28th. Don't wait, take action now and it tells you exactly what to do. So they're going to be going from Ethereum over to Cardano. So just so you know, that's what exactly is going on. And then it says here, Cardano will officially become a smart contract platform and it will take bytes out of the competitors. Thanks, we all know that. The first of the lines of test has gone live, great. And then this is the interesting part. SingularityNet to generate 1 billion AGI's on the Cardano network. So they're going to generate 1 billion the token on the Cardano network. In addition to the AGI token as a supply of 1 billion Ethereum. The entry of tokens produced in Cardano into circulation will last for 91 years and the Ethereum based AGI's will start to be considered Illigent. I think it's going to be a little faster than that. I think it's going to just go away. Look at the website, it explains it quite clearly. But just so you know, first of all, the circulating supply is 1 billion. The price right now is about 4 cents or so, it's not too much. The question might ask is what the heck is SingularityNet? Well, SingularityNet decentralized marketplace for AI, artificial intelligence. It states there's a significant gap between the people developing AI tools, researchers and academics, and the businesses that want to use them. Organizations need a more customized solution that want a single AI project can offer and research project. Oftentimes have trouble accessing a large enough data. And this is where SingularityNet closes the gaps. So here's how, there was an example that they gave because they have that. They are the ones that created the Sophia AI robot. And what they say is like, they'll put the artificial intelligence in and go, okay, let's say you want, you have a business and you want to go out there and take a look at all the different websites as far as like videos and gives and puts some kind of data input into it. Well, you're going to need some artificial intelligence to actually go to the website to actually make that happen. Artificial intelligence to actually take a look at the video, assimilate it, see what you need to know and then put that into some place. And then the third part could be any kind of like storage or whatever else. So you need three components for AI. SingularityNet gives you all those AI different types of aspects. And you can pay for those instead of having to work it off from scratch. That is the power of SingularityNet. So I think it's an interesting concept. Let's see if it all works out, but I've been in the game for quite some time and they're the ones that gave us that crazy Sophia robot. So we'll see. But to finish this article up, this was the interesting part. CEO of SingularityNet, Ben Gortzel said, we are updating our old SingularityNet platform to SingularityNet phase two. In our own words, our old platform works fine, not counting the well-known shortcomings of Ethereum Blockchain. Just his words, not mine. And there will be many improvements in phase two. One of which will be Cardano, a much more advanced blockchain. So look, these guys are at the forefront, doing some pretty ambitious things. So we'll see if it all works out. But this is just one example of projects moving from Ethereum over to Cardano and then some people say, well, that's just one.  Let's see if Cardano can pull it off. Let's see if Ethereum can actually make Ethereum 2.0 work. Because there is a big dichotomy between a programmer and what they do and a business owner and what they do. Me personally, I'm not a programmer, but I'm a business owner. I can tell you right now, if something is expensive for me to use and doesn't work too well, I'm going to the next thing. Because it's my job to make money for me, my family, and also my employees. So it's not working.  I'm here to make a bottom line and make a buck. And that's how it works. So if I have something that's going to work a little better, I'll probably go that route. Now, later on, if something happens where it's like, well, you know what, Ethereum 2.0 is good and it's released fast and there's no gas fees, I might consider coming back. But again, business, this just makes sense to me. And if it's not working, I'm out. And that's what I can really tell you. Anyhow, let me know what you think about that in the comments section. And this kind of leads me to my next point, which is about the Alonzo rollout plan. So just so you know, they've already got their test net live. Alonzo is when everything comes in as far as smart contracts. And it's going to be staggered. And I was always critical about Cardano because it takes a damn long. But in all honesty, it's great that they do these things because they can kind of test what's going on and make sure that things actually work. And they're going to go all the way from June, July, August. And then in August, it's pretty much where it's just a done deal. September is just kind of like working out a little bit of the kinks. But they're going to get the stake pool providers, which Dan, DNews, dandiedescript.com. We are part of those SPOs so you can stake your Cardano. And when they get everything involved, the first one will be just a couple of ones in June, July, pretty much all of them. And then September, it's like a hard rollout and off they go. I think it's pretty amazing they can actually hit these numbers and actually make it happen. I think it's going to work. It seems like they've been hitting their goals every time. So again, we will see. So I think it's great that they do these things to make sure things work because this is the problem that I see with projects that come out too fast and really just don't do too much testing and reviews and things like that. You get stuff that happens kind of like this. And this is what is this? Burger or Binance Smart Chain, BurgerSwap. It loses 7.2 million from a flash loan attack. And when we look at these, we just see numbers. You just see like 7.2, you're like, well, who cares about 7.2 million? Why aren't we over like 1.4 or 5 trillion dollars in a market cap? So who cares about 7.2 million? You know who cares? The people that lost that money. And this is just a prime example of just a little bit that could happen. Now, extrapolate that out to an entire large ecosystem of a large market cap and they get in a DeFi and they lose 100 million, 200 million, a half a billion dollars. That is a catastrophe. So I'm glad that Cardano is doing these types of things. And again, I was critical before, but get it now, especially because of examples like this. So this is what happened just as a recap. Around 3 a.m. on May 28th, BurgerSwap on the Binance Smart Chain encountered a flash loan attack. 7.2 million was stolen and 14 transactions. This is what's amazing to me is that hackers can like do a little bit of work. I mean, I don't know how much it takes. I'm not a hacker. But just do a little bit. Don't have to leave their house and their millionaires. So like I just saw a guy-riching movie and it was all about a bank heist. And I'm like, that's a lot of work.  And I think this is the big thing because it's just like money sitting out there. Why wouldn't these hackers do it? You need somebody to really come in and do an audit. Take a look at all the different potential pitfalls that can happen and then protect against that because this obviously was not the team. So here's what happened. Users can add liquidity and earn the project's native token, the burger. Hackers created their own fake coin. Okay. And formed the new trading pair with Burger. This was the route. Burger to fake coin to WBNB. Through Burger, back to fake coin, trading pair. Attacker re-entering BurgerSwap through fake coin. M-manipulated number of reserve zero and reserve one in the pairs contract. Causing the price to change. And just so you know, flash under a smart contract based schemes that allow the issuance of loans within a single transaction or attack. So that's the problem with smart contracts and DeFi. And it makes a lot of sense of why I was doing a lot of their due diligence. Make sure this kind of nonsense doesn't happen. And my last point is this. I do believe that if you're looking at some massive gains, this is investment opinion, not investment advice. This is what I'm doing. Take a look at the ecosystem that's happening with Cardano. Again, I think Ethereum with their ICO days and everything's being built on it and decentralized exchanges and DeFi, they get a lot locked up. But now you got somebody coming right behind and going, you know what? We can do a lot of things too. And if you want to come over to where it's faster, it's a lot cheaper. We got a lot of things going on as far as like development goes. This could be your opportunity to get into our system. And I've already interviewed the guys over at Indigo and Liquid, Charlie, which is their Oracle, and Sunday Swap and CardStarter have already reached out as far as and also Tesseract. So right now is not a good time to do like the first part of the interviews. And then I have to put them all together because it's just not a great time. I'm just busy. So I'll put this all out in Dan Clips. And these are the things that I think that as they move forward, these are the things that I'm going to get into heavily because I believe this is the next step of crypto and where things are going. And we already talked about WMT, a world mobile token, where they're doing great things over in Africa. They're doing two parts. They're giving the infrastructure as far as the solar panels and the actual mesh telecommunications pods. On top of that, they're actually doing the token. And that'll be coming out in Q3 for the token itself. And we already did a video with Mickey Watkins, a CEO. You can find over at Dan Clips. I'll also put that in. And this is a great example of doing good and doing well. So I'll probably go in pretty heavy on that one as well. So look, that's it for today. I know it was pretty Cardano heavy. I know people love Ethereum. Probably didn't like that video. But you know what? I own both. I think they could do great. I just want to hedge my bet and just talk about the things that are really coming up. And I know everybody talks about, well, there's EIP 1539. Hey, we'll see. Just like we'll see with the smart contracts with the Cardano. It could go either way, but we'll find out. Anyhow, that's it for today. If you liked the video, give it a thumbs up. That really helps out. Consider subscribing. All the things we talked about are time sensitive. And that is all. Everything is fine as far as the links will be in the description. Thanks so much. See you on the next one.


In just a moment auto light presents suspense starring Rosalind Russell How is mr. Auto light by Cornelius Wilcox is fine December evening by Cornelius fit as a fiddle hap How's yourself all set for winter yep overcoat data mothballs Yep, I storm windows up snow shovel on the back porch Well auto lights stay full battery in your car Hello, you know friend when the bottom drops right out of the thermometer You'll appreciate a dependable auto light stay full battery more than ever Why everybody ought to switch to auto light for those auto light stay full batteries are just loaded with extra features First they have an extra large liquid reserve need water only three times a year in normal car use what an extra And what's more here's the next auto light stay full battery extra. Hello? suspense Auto light and its 60,000 dealers and service stations bring you Radio's outstanding theater of thrills starting tonight Miss Rosalind Russell in Anton leaders production of the sisters a tale well Calculated to keep you in Suspense here is one. I think would be very lovely. It has a far superior lining pure silk much heavier than the others We've looked at Do you care for this one miss Haskell? Yes, that's very nice I believe I'd like to see something perhaps even a little better. Oh, of course if you will just step over this way miss Haskell Now here here is an exquisite casket something that really does honor to the departed Yes, it's beautiful. Now the interior is just the same as the last but the casket itself is a bronze solid bronze Won't that be rather heavy? Oh, yes, but not too heavy. Will they be six ball bearers? I don't know where it doesn't matter really four men can carry this very easily very Miss Haskell, I want you to notice the floral design you're all hand wrought every bit of it And oh, yes notice the seams in this casket airtight and watertight guaranteed You know, of course, how important that is. Yes. Yes But this casket in a hundred years or even 200 years will be just as strong and work just as beautiful as it Does on this stand today.  How much would this one be please this casket? Duravo by the way, Duravo for durability. We say in the trade. This casket is priced at $775 We can't bring back the departed our only solace is the knowledge that we have done them the last possible honor very well I'll take this one. Oh, I'm sure you are making a very wise choice in all my years as a mortician I've never found a family that regretted money spent on a Duravo Now, let me see. I'll give you a check. Oh That won't be necessary not immediately after the funeral will do. Oh by the way, we haven't mentioned it our Are we handling the funeral arrangements? I don't know yet.  No, I'd like you to hold it for a while, please Hold it but how long? For three weeks three weeks. I Don't understand. Who is the party the deceased? Who is the casket for? It's for me Where'd you come in? You've been Lydia. You've been gone all afternoon. I've been shopping. What did you buy? Did you get the ribbons? I asked for no, I didn't have time. Oh, I wanted some new ribbons.  You're almost 40 years old I know Lydia. I know then try to act like it. Oh hand me my sewing and light the lamp. It's getting dark. I Wonder why we have to grow old wouldn't it be wonderful if we had always stayed young like we used to be Remember one mother used to send us out to school with our ribbons matching and I dressed as matching and at the end of the day No one would even guess we were sisters because I was always so must and you were always so clean. Oh I wish we were young again. Stop talking nonsense. Ellie. It is nonsense Oh, the doorbell rang while you were out just before you came home You didn't answer us. No, you told me never to answer. I just looked out of the upstairs window Did you see who it was? Oh, yes. Yes, it was a man a rather big man He rang a long time and then he went away. He didn't see you did he? Oh, no I just peeked ever so carefully from behind the curtains and I came down here and watched him going down the walk You came downstairs. Yes, I told you never to come down those stairs when I'm not in this house It was all right, Lydia. I held on very tight to the banisters all the way And I didn't want to look down the stairwell So I didn't get dizzy and I didn't want to jump. Well, don't do it again It was just that I was lonely. I didn't think you were ever coming home Lydia you didn't tell me what you bought a Deravo what's that? What's a deravo? Don't ask so many questions Ellie Lydia I think I'll so too. I could fix up one of these old livens May I let you yes, yes, so it will be good for you. Thank you Mm-hmm Lydia. Yes, Lydia. Could I go shopping someday?  I just thought No, I suppose you're right wouldn't do Lydia sing with me, you know, I never sing There wasn't any mail today wasn't them. No, I thought perhaps it'd be a letter from David In such a long time since he's written hasn't I haven't noticed. Oh, yes He used to write every week on Tuesday, and I get the letter on Thursday But there wasn't one this week or last of the week before that Strange isn't it? But perhaps he's been busy perhaps Still he never used to be too busy to write. I Can't understand it You suppose there's some other reason what are you trying to say to me Ellie? Are you hinting perhaps? I'm keeping your mail from you. Oh, well, you certainly seem to be Why should I keep David's letters from you? But I didn't say there. I just said it was strange that David hasn't written. That's all You wouldn't keep David's letters.  That's all you sing day and night day and night same tune over and over Nova.  Yes Evening you miss Lydia Haskell. Yes Can I speak to you for a minute? I was here this afternoon. There was no at home. What is it, please? We had a call from dawn brothers the undertakers. I'm from the police department. Oh really? I don't see what the police could want with me Come in if you wish thank you sit down. Thank you And there's nothing we want miss Haskell except it's sort of unusual for a woman to order a casket for herself Unusual I've heard of many cases of that kind people who are alone in the world is no one else to look after things Yes, sure. I know only it's a little more unusual when you can name the date The undertaker said you wanted the casket held for three weeks Why three weeks? There must be some reason for it There is I'm going to die. I Shall die in three weeks or Perhaps even before There's no doubt in my mind about it. And that's why I've ordered the casket. You may call it a Premonition if you want maybe I could also call it suicide Well, that's why I'm here miss Haskell I don't know whether you know it but suicides a crime in the eyes of the state a crime for which There is no punishment. Not if it's successful. No, but there is prevention. I know I'm going to die. I feel it I have no intention of taking my own life There's no need to do so Miss Haskell this Premonition as you call it. Have you any idea what I brought it on? No Have you been speaking to anyone? No fortune tellers or anything like that? No, what makes you so sure How do you know you can trust this Premonition? I hear not an old woman I'd say you're in pretty good health a lot of good years ahead of you I have a religion not a church religion just one of my own It preaches that people go on living until they've outgrown their usefulness Then they die from one cause or another When that time comes the desire to live is gone and only desire keeps the body and soul alive and breathing Don't understand that. I'm sorry Miss Haskell do you live alone here? Yes. No relations. No housekeeper. I live alone here Very large house for a person living alone. There are three floors and far too many rooms It's on the outskirts of town. It's quiet and it gives me the privacy I've been looking for a privacy which you are invading for the first time since I moved here five years ago I'm sorry miss Haskell. I'm only doing my job I was told to look you up and find out why you bought that casket and I think we may assume your job is over I guess so but the office might ask me to drop back once in a while just to keep in touch, you know I won't be at home. Why you don't go out very much I ask the folks in town say they don't even see you more than once a week when you come I won't be at home. All right. Sorry to bother you. Good night. Night.  I don't know nor do I consider it important Why should you? Good night. 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Bye bye Cornelius friend If you knew what I know you'd switch to auto light stay full batteries right now You'd pop into your puddle jumper pour on the power and set off at a peppy pace down to your nearest auto light dealer For a splendid new auto light stay full battery the battery with all the extras Why the thought of all those extra features makes me excited exhilarated exalted Exhaustor you'll be an ex-announcer if you don't be quiet and listen to suspense And now auto light brings back to our Hollywood soundstage Miss Rosalind Russell as Lydia with Miss Loreen Tuttle as Ellie in The sisters a tale well-calculated to keep you in suspense After he'd gone I stood there in the hall thinking Perhaps I'd made a mistake Perhaps I shouldn't have gone to the morticians I have thought it would be so clever, but I hadn't thought he might become suspicious sent a policeman Then someone snooping around asking questions trying to find out things. I was so sad thinking about it I I hadn't heard her come down the stairs What are you doing down here? What are you doing sitting on the steps in the dark? Haven't I told you never to come down here at night. What do you want? I heard that man who was here Did you why did you buy the casket? Why are you going to die?   They'd send me away like they did once before The people in the town would come and find me living here and they'd send me away go up to bed Ellie Go to sleep. Oh, can I sleep? Oh?  Why do you want to die? I don't want to die. No wonder you have such a lot to live for haven't you Ellie? Yes I've been happy Lydia. You made me happy And someday when I'm well again, I'll go back home and David will be waiting for you. You know, he'll be there. You've always told me he'd be waiting and He'll see that I'm well again, and you'll take me back I'm not so old am I? David won't see me at all. He told me that that when I was well no matter how long it took he'd still see me as a young girl That's why I've been happy Just waiting for the time. I can go back to haven't you heard yet And haven't you learned it?  No I'm getting better Lydia. You know I'm getting better. Yes, of course putting bows in your hair sewing ribbons all day long Sneaking about the house at night spying on me singing the same hymn over and over and over until I think I'm going mad, too They get away from me why I thought you loved me. Why should I love you? Look what life has given me and tell me why you've always spoiled everything for me even from the time we were children How could I spoil everything? We were just like the same child Lydia twins You were I and I was you look the same. Yes. We were born the same day. Yes, and that's what it ended You were the nice one. I used to hear them say so. You were even the prettiest They said as if they could see any difference between us Well, whatever you wanted you had you smiled so beautifully and I never smiled I was the sullen one the dark cloud in the house. You made it so Lydia. We all love when your doll was broken They gave you mine when you tore your dancing dress. You took mine. You gave it to me Lydia I remember you gave it to me. You gave I've always given things to you. I've given you my whole life I even gave you David You were in love with Dave He came to her house Was it you he came to see? Oh Lydia, I didn't know You never knew No one did I Had to stand by and watch you take him from me When you had your first attack I was glad People said it was a shame, but I was glad because I knew that he could never have you Oh, yes, you were going away and be cured. He was going to wait But it wouldn't matter how long it did it took and how long he waits You'll never be cured and he'll never have you never You hate me you always hate I see it now Even when you've been taken care of me when we came to this town you didn't bring me here So I'd be cured You wanted to keep me this way man That's why you took me out of that place Because they might have made me well go upstairs And now you're going to die leave me without anyone. I will not die. Oh, Ellie Ellie, I'm sorry. We had this quarrel. I didn't mean to upset you. It's just that I'm upset myself and tired I didn't mean the things I said you bought a cast and it was only an idea I had in case anything ever happened to me you bought a cast Was it for yourself?   It's so you want to get rid of me Because you hate me.  I'll go upstairs and get to bed Can you Ellie Ellie are you awake? Ellie a deal you mustn't think anymore about what we said tonight. Do you hear? It's not so Ellie. It's just your imagination. You mustn't think about it. It will be bad for you. Are you asleep Ellie? She's not asleep. She's lying over there on the other side of the room staring at me through the dark She knows it was the truth tonight. She's going to die.  I must I must think clearly What was my plan?  It doesn't look like murder. They suspect things and it must be suicide and it must be soon Other she knows Listen She's starting again.  Oh? I wish it were over. I could go back then Back to David How quickly she's thought through that I'd go back in her place But he'll never suspect I'll be Ellie to him Ellie couldn't have me again.  She gets dizzy if she looks down into the stairwell Yes, it will be so easy in a day or two that policemen will come back to the house They'll find her and they'll think it's me the stairwell Three floors from the attic here three floors straight down.  Are you afraid of the dark? I'll light the lamp for you There dear That's better. Isn't it? Why you're shivering are you cold come Put your wrapper on we'll go down to the parlor and light of fire And I'll make a nice cup of hot milk for you. Come Ellie.  Here's your wrapper put it around your shoulders. That's a girl now get up get up now I'll carry the lamp give me your hand dear why you're cold as ice Now be careful Slowly There we are Now hold on to the banister dear That's right. I'll hold the lamp up high so you can see better It's right here dear you see Ellie you must get over that fear Look Kelly Just look down. There's nothing to frighten you Look down the stairwell Ellie. No, I'm holding you dear. I just lean over and look down you can see all the way I'm holding you It was brought to my mind of course because this is the house just here this one the next one were coming to yes She was in disease just a few days ago came in to order the casket She saw a casket.  I notified the police of course why she said she wanted me to hold a casket three weeks Then just the day before yesterday the police came back to the house here and found her lying at the bottom of the stairwell Dead, she'd been dead about two days Funny how she knew the banister up on the attic floor broke away and she fell did she have any people? No, let alone they tell me We're going to bury her tomorrow Haskell the name was Strange living all by herself here in a big three-story frame house. Yes, isn't it say Well, what is it?  Yes sort of crooning to herself some kind of Yes, oh look supposing just supposing you didn't already have an auto light stay full battery in your car What would be the first thing you'd do tomorrow morning? Eat breakfast Then what? 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Auto light means spark plugs ignition engineered resistor spark plugs Auto light means ignition system the lifeline of your car And now here again is miss rusland russell It has been a great pleasure to appear here tonight Unsuspence and I want to thank tony leader and his fine cast And especially lorenne thuddle for her splendid performance as ellie I know none of you will want to miss james cagney's appearance next week on radio's outstanding theater of thrills in a story called No escape another gripping study in suspense Miss russell and russell may currently be seen in the independent artist's production the velvet touch tonight suspense play The sisters was written by george weles with music composed by lucian morawek and conducted by led bluskin The entire production was under the direction of anton m leader in the coming weeks suspense will present such stars as ronald colman william bendix ethyl barrymore frank sanatra and many others make it a point to listen each thursday to suspense radio's outstanding theater of thrills And next thursday same time here james cagney in no escape This is the autolight suspense show Autolight salutes the automotive industry on the occasion of the observance tonight in detroit of the production of the 100 million motor vehicle Good night switch to autolight This is cbs the columbia broadcasting system