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Peter Hickey, Workshop 500: The DelayedArray Framework to Support the Analysis of Large Datasets

Peter Hickey
Senior Research Officer в The Walter and Eliza Hall Institute of Medical Research
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500: Effectively Using the DelayedArray Framework to Support the Analysis of Large Datasets

Peter Hickey (The Walter and Eliza Hall Institute of Medical Research)

8:00 AM - 8:55 AM EDT on Thursday, 30 July

WORKSHOP

This workshop will teach the fundamental concepts underlying the DelayedArray framework and related infrastructure.

It is intended for package developers who want to learn how to use the DelayedArray framework to support the analysis of large datasets, particularly through the use of on-disk data storage.

The first part of the workshop will provide an overview of the DelayedArray infrastructure and introduce computing on DelayedArray objects using delayed operations and block-processing.

The second part of the workshop will present strategies for adding support for DelayedArray to an existing package and extending the DelayedArray framework.

Students can expect a mixture of lecture and question-and-answer session to teach the fundamental concepts.

There will be plenty of examples to illustrate common design patterns for writing performant code, although we will not be writing much code during the workshop.

Moderator: Charlotte Soneson

О спикере

Peter Hickey
Senior Research Officer в The Walter and Eliza Hall Institute of Medical Research

I enjoy making sense of data and making it easier for others to do the same. I am currently a senior research officer at the Walter and Eliza Hall Institute of Medical Research where I lead the bioinformatics analysis for the Single Cell Open Research Endeavour (SCORE). With the SCORE team, I collaborate with scientists to design and analyse single-cell genomics experiments. I also develop statistical methods and software to summarise and understand genomics data, made available through Bioconductor. This site include my (very) occasional blog, along with the usual academic fare of my papers, presentations, CV (pdf), software and data.

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Alright, well everybody, my name is going to be giving a workshop on using the at the light right package to analyze large datasets the workshop. And we'll be just fine for a recording from YouTube. Just waited at the links to the recording itself, as well as the witch of material, some of the texts when playback video, so that should have screen sharing part of the presentation, due to internet connection issues and YouTube and impression of Achmed to be hard to read. So, I

suggest that you have the book for you in yet. I'm available if you can read it and I told you that follow along, you can get a CDI sevens because everything to the workshop, a couple of opportunities to sort of halfway got yourself, sorry for the certification material guys for that, 40 minutes, and then we'll come back. Check it out in a few minutes for discussions and questions. So I'm going to share my screen now and stop the video sets. Before we begin today's Workshop, we will download some tight and this is Terry for it from the experiment Hub to do this. We load the experiment, how

packaged into Ally session Once a package is loaded, we construct an experiment hub. By calling the experiment Hub function. Did I just said that we will be using in? Today's Workshop is a large single cell on a 62-7, produced by 10x genomics to find this date. Except we will query the experiment Hub with the phrase, 10 x, Brian Dieter There are a number of resources available from experiment out that match. This query, the one that we will be using in today's Workshop is this one

highlighted here? To download this resource. We access it from The Hub by talking in the name of the resource. This will download the resources from experiment Hub. This is a rather large dataset stored in the hdf5 file format. I might take a while to download. The advantage. Of using experiment Hub, to download this data set, is that once it's downloaded to your machine, subsequent close to experiment, hope we'll use the local version of the data set. That's open now would like to Statics it. Continue to download whilst We Begin the introductory material for today's Workshop.

2 / framework is led by. If I pay just one of the bike and tactical team members. the reason I'm here today presenting this Workshop is that I have been an early adopter of the Delight of a framework, using it to analyze large data, sits at The Cutting Edge of High throughput biology So I see myself as a bit of a crash test dummy for the delay, the right package with developer of packages that use and extend the delay. The right framework in particular those for analyzing DNA methylation data. At the heart of what we doing by a conductor how many Cody

destructions. One of these is the summarized experiment used to store a ride. Like that I am Associated metadata at a time at summer. Experiment is an array of values with metadata on the roads, which are the features and metadata on the columns which are out samples. We may have multiple essays, so multiple arrays of data. And we might have submitted data on the experiment as a ho, this is old encapsulated in the summarized experiment subject. Today's Workshop focuses on the SI data, the actual measurements that are the basis for our analysis. Typically days are stored as an ordinary, a,

right or Matrix. Ordinary erase a structured rows and Columns of samples. It has a Familia bass API by the software that can be extended by packages such as Matrix stats. Matrices, support Matrix algebra and a compatible with blast and light pack. And stay a C and C, plus plus accessible. So, you can write algorithms that work in these languages when necessary, and they are quite conducive to interactive data analysis. Potato getting too big for ordinary arise as an example. There's a single cell died to set published by the 10x genomics company that contains 1.3

million samples ourselves. It's One Night Trips with some 30,000, Roseau James and some 1.3 million samples. And if it's the right, it would require more than 140 GB of RAM. An example to my own work is analyzing DNA methylation data from the T. Take samples with the data would occupy more than 500. GB of memory is stored as ordinary arise. This is where the lighter a comes to the rescue for the 10x. Brian day today to set this can be stored in memory and under 200 GB of RAM. Similarly,

the jaytekz DNA methylation. Data is just over two hundred megabytes of memory and how this is done, is by keeping the s a data on disc. In these examples in an HD, avi file, that is wrapped the lighter ride, the focus of today's Workshop. Adelaide her eyes still looks and feels like an ordinary. All right. It is imperative that they use of property, so it is structured, it has a familiar IPI. We can build packages that extend upon it. We can use things like Matrix algebra. We can interact with a status. It's from say, you'll stay plus plus, using the beach, my package, in

this case, and it is even more conducive to interactive data analysis. Sodalite array refers to both the class, A package and extensible framework. And we will learn about all aspects of this in today's Workshop. As I mentioned, it is part of by conductor and develop, either they pages. And it has developed using the S4 object-oriented system like most to buy, conducta to install. You need to install the byassee manager package from kraan, and then use it to stall. Install delayed, a ride. Did you lie to write? Ecosystem is the 50 or so

packages that depend on the light array, these can be broadly broken down into use a focused or use a facing packages. Develop, a focus packages packages that uses and developers should probably know about starting with the last one, the divider, a package Implement satellite array frame with the h, d, a v, or a package extends that by allowing you to work with data stored on this skin hdf5 files, using the Delight of Ray framework The Divide Matrix. That's package, Implement several Useful broken call Sunrise,

station functions of dry rice package, which provides for working with large data sets that is compatible with the light. A right to buy a singular package allows you to perform singular value decomposition, sore, principal component, analysis of days Delight arise, A b c f. A r i n g s r a have a different Focus looking to store genotype data on disc. And accessible by the July to write framework. What's the average stay at 5 client and restful essay packages. Focus on

using remote data stores, such as an hdf5 files stored on the server and interacting with it for Adelaide, right framework? Some common by conductor packages that make you sad that the right frame would include the droplet utils package for working with 10x genomics single-celled. A data package for working with another phone is single cell gene expression data. Biscotto package which implements low-level utilities for processing. Single cell died, on the batch of the package. Which implements patch correction

algorithms, particularly for a single cell data and the BSC can benefit packages for working with DNA methylation data. finally, the beach, my package is a more developer Focus package that allows a developer to write C plus plus code to work with arbitrary types of matrices. This introductory material is Kevin Grace today tile in the workshop vignette, and I encourage you to write that in your own time will now move on to doing so, we will Begin by loading to Delight or a package into a position.

Did the lighter a package implements? The core functionality that the delay to write framework, loading thda, variety package, this package extends the Delight of a framework to allow processing of hdf5 files We will download in HD if I file from the experiment hub. We load the experimental package. And Cody experiment, Hub function. We can then query the hub for the dataset. We overusing today's Workshop. GF using the price 10x Prime data on the number of resources of which we will use

the highlighted won in today's Workshop. We will download. This resource and store the name of the resulting file in the variable. If 9 We can use functions from the rhd at 5 package to inspect. What is inside this hdf5 file. This tells us that there is a matrix with 27998 rose and some 1.3 million Collins that he's cold counts. We will now construct an HD Ava, Ray, a type of delight or a from this hdf5 file. The code is 10x. And use the HD Ava right function to specify the file. And the name of the

dataset, we wish to access. The data contained counts. On nearly 28,000, James and 1.3 million cells. This is roughly 100,000 tons more samples in a typical bolt on an icy day to sit and would be quiet / 140. Gigs of RAM. Two-story memory as a dense Matrix today. We might expect it would feel sluggish to interact with the subject but that is not the case. For example, that's Prince the entire object to screen something, which is normally a very bad idea. As you can see, this is printed a preview with the data as you might have experienced when using

other by conductor objects such as a genomic ranges or other objects, such as data, tables or tables. By now you must respect the 10x object, is no ordinary Matrix. In fact, it is an HD at 5 Matrix, which is a type of delight a, right? We can say this by looking at the class of the objects and by using the East function, to confirm that it into is indeed an HD Ava, right? The data contained in an hdf5 Matrix is actually stood on disc in the hdf. I file consequently, Stacy memory.

Do not play around with Computing on the status. It can make things easier to the first 1,000 samples. Firstly, let's compute the library sizes for these data which are the columns sounds. Secondly, suppose we want to know for each gene, the proportion of cells with nonzero expression. We can do this using standard, our commands to compute the proportion of nonzero elements. We identify how many elements in each row, a greater than 0 and divided by the number of columns in a data set. Discus, the proportion

of nonzero. Cancer. Age Jane Finally, we can compute the median expression of each gene here. We will quantify expression as can't spare a million. Kiwi normalized by the library sizes. Printing. The Camp's been building the screen again. We get the nice preview of the dataset weekend and compute the median expression of each gene using a function from The Divided Matrix steps package In particular, the median expression of each chain is given by the Romanians of the counts per million. Nytrix

Pastry examples. How about the power of the July to write, framework record that the dates are in these examples, actually live on disk, in an HD. A vile, you'll be interacting with the data and computer done. It much, as we would, as if the data were in memory, as an ordinary Matrix examples, return to ordinary a vectors. The computations for these three examples of implicit use of the three fundamental concepts in the divider, a framework operations or processing

and realization. When I discuss ancient days in Sunday time, Begin with the light operations. Look at the 10 x subset of jecht. We can say that it is a delight my tricks rather than an HD aviatrix. What has happened is that the subset in operation that we performed has degraded botanics subset object to Adelaide Matrix. The show tree function can help it. See what is change when we subset of the data. If we look at the original data, we see that the tree of

operations is simply the hdf5 date of itself if we compare it to the subset of data. We say that it now contains a delayed sub sitting operation. It's upsetting operation has been registered in what is termed, a delayed operation. Registering a delight operation does not modify the underlying data instead. The operation is recorded, and only performed when the Delight array object is realized. Tomato privations allows to change to get a multiple operations and I need the phone them as required.

He was a contrived example. Let's add one to every entry in the 10x subset. Let's look at the tree of delight operations. On this object using the show trade function. We say that in addition to the subset operation we now have delayed this operation could have, you know? Rihanna so which will explain in a moment but it basically corresponds to Adam-12 every elements of a data set. We can continue our example by the taking the logarithm of every element of a modified day to sit.

Again, we can print the tree of delight operations. Notice that this is not added an additional operation. Did you lie to write package has combines the plus-one and motivate them up, relations into a single operation. To continue this example, let's transpose the results. Again, we can Feud the set of delight operations using the show. Tree function transposing, the data has added this a poem delayed operation. Finally, let's realize a subset of the data as an ordinary array realizing the data will trigger the series after light-up relations for the

subset of requested data. She had, we realized the first five rows and first 10 columns in memory as an ordinary array. Mini common operations can be registered as tomato predictions in the interest of time. We won't go into any great detail but the workshop vignette gives comprehensive information. We now turn to another fundamental concept of the Delight of a framework. What processing, what processing address is the problem. If you have a large array and want to perform some operations on it. But anyway, the subset of the data into memory, These operations could be element wise or book wise

as an example. Suppose you wanted to compute the rose sounds of this Matrix. One way of doing this would be soloed, H row of data into memory, as a block, compute it, some and then load the next row of data into memory and continue. Similarly, if you wanted to implement a cow sounds, we could load each column of data into memory compute, the sum, and then move to the next column. Most sophisticated for processing, strategies might load multiple Columns of data into memory. For example, if we are wanting to compete to call, something's it, it may be more efficient to load

multiple Columns of data into memory and compute on those all at once, rather than constantly rating data from disk, we might also have an algorithm such as Rose. Some that requires a variable number of columns conception date. We could trade the entire nitrix is a book, however, this rather defeats the purpose of using the delay, right? Because it will load the entire data set into memory, some notion of optimal blocks and will return in two days later in the workshop. These may be sub matrices of original Matrix. That's corresponding to have the data is stored on disk

To better understand Book pricing. By using some functions that implemented to see how these work to more. Clearly Saybrook processing, an action will temporarily turn on the bass block processing. Let's now compute the column sounds of the 10 except sit object. Kia. I bet the result in invisible said that it is not printed to the screen with the first book processing. When I say that the cow sounds is implemented using black processing. In this case, Simon Says process, the data into blocks and if I buy support processing tells us that these

books are over the roads of the 10x subset sum of the most useful functions in the Delight of a package. Implement, no operations on Adelaide Matrix using clock processing. For example, we can compute the remains of the subset. This is done using pork processing. Is it lighter, right, package? Implements Road Semmes, romaine's running. Max's room means ranges and they call them lies, equivalents the delay. The right package, 07 Cummins 2 lesson, 9 functions, row, seven, awesome to

compute column and row sums of Adelaide Matrix based on a grouping variable. Matrix multiplication is also implemented using blank processing. Another useful package to know that is the Delight of Matrix that's package that implements The Matrix sets API fees, with delayed Matrix objects. It provides And 70 functions that apply to rows and Columns of delight Matrix subjects. If you've been following along with the coding examples, you might like to try out some of these functions for yourself.

as we seen many common functions of operating on July the rides at already implemented in the Delight of a package extension packages, like the right Matrix steps, and by a list of functions that can be applied to delay, the real objects, You need to implement a function that uses pork processing. The documentation on. This is a little sparse at the moment, but we will go through some simple examples in today's Workshop. Talk processing requires, 3K steps. The first is to set up what is cold and a ray grid

over the delay, the right to be processed the arrangement, specifies, the book structure will be traversed when processing the light array. And functions. You might be interested in looking at at the photo grid Photo Grid and call autogrid functions. From the / package. These functions to make automatic grits have pork processing, the finer grind control, if you are right. You may need to use the regular, I agreed or arbitrary. Wrightwood function, Oso in the lighter, a package off to setting up a theory grid. The second step is to either write or the

door light array using Theory Grid at each step. We rate a blocks worth of data into memory are the residents or sponsor, a and compute. Some statistics on it, the block, apply and book with use functions can help perform the book processing. These functions can even incorporate paralyzation by the BIOS, a parallel package. Once you computer to a book level statistics, the final step Is to combine the book level statistics to get your desired final result. The final step is generally up to you as a developer to implement as an example. That's Implement a basic

version of the cosine function. When we Define each block to be a single column dysfunctional, take in a single variable codex, which is Adelaide a ray The first step is to set up. The first step is to set up our a grid. To do this. We will use the coordinate grid function. Nicole Ortega and function automatically sets up, call them lies, grades are a delight or a Kia h block in that, crate contains one column with a data as specified by the inco arguments. The second step is to load the books of data into memory and compute the book

level statistics. We will still at work level results in the Block Level stat variable and use the block apply function to compute, the column sums of each single column of data relating to memory. So a first argument is that the right away, the second argument is a function that we want to apply once their data a loaded into memory. So disco science fiction is the ordinary face a vision of cosines. And the final argument is The Great Divide agreed that we set up in Step One. The third and final step is to combine the Block Level satistics.

In this case, it's a simple as collecting old Block, Level stats, and returning them as a bad guy. Good luck. Apply function buttons at least, which element is the cow sounds for 1 block of data. Sorry by. I'm listing, the result. We turn that into a vector. if we load out function, we can now apply a function to the 10x subset data. This might take a while. we can now compare our results to that pretend by the cosine function implemented in the divider a package

Now, it's your turn to try. Riding a basic function. That uses book processing, try, modifying, the basic cosine function to find each product. As a group of 100 columns will tentatively. You might try to implement a basic functionality using the Rogue autogrid function. See the workshop material for further suggestions. To modify a basic cosine function, to Define, h block, as a group of 100 columns. It's a simple as changing. The inco parameter to 100. If we not

load that function, we can compute the result. You probably noticed that using a grid that included. 100 Collins was much faster and agree that use a single column will return to this shortly. To create a basic Roy sounds function. It is as simple as modifying our existing function by changing the call autogrid, to be a row. Autogrid specifying that we want to operate over the rows of Adelaide Matrix and that we want to operate over 10 rows at a time. We also need to modify

the function that we apply to h block to be the rose sums function. To realize it till later. I object is to trigger the execution of the Delight of operations carried by the object and return the results as an ordinary horse Pasa, right? We can realize they died in memory or disk error in memory. We can call the as. Arrive option on it. For example, let's realize at 10 except set data, If it's something, object is an ordinary IRA. In your Explorations with the data. You

know, you noticed the tenants that contains a lot of 0 values. We might therefore up to realize the data as a spouse Matrix. We can do this using. We can do this using a sparse Matrix from The Matrix package. We can do this using a sparse Matrix from The Matrix package. in this case, the data realized is a sparse Matrix, specifically, a DJ C Matrix, Realizing in memory realizes the entire object in memory, which could require too much RAM. If the object is large enough for a large delay, the

write-up ject a preferably be realized to disc Jimmy will demonstrate by realizing to an hdf5 file. But we could also realized to another on this back end, such as a child, a b, a r, a realizing to an HD a vial. As an example, we will realize that. As an example, we will realize the data to disk has an h d. F, I file the process of realization uses. What processing, which avoids, letting the entire data set into memory, two more. Clearly stated Clearly say to block

processing action will temporarily turn on the Bose block processing. to realize that the light array as a denser, right in an hdf5 file, we will use the bright hdf5 or a function The coded realising at the light or a trick is old the Delight of operations on it. This can be saying if we can pay the tree it to light up relations on the 10x subset data said, compared to the tennis subset hdf5 data set. Prices for the taniks subset. Daidus it contains a delayed subsidy operation. Where is division that is being realized to disc does not the way we

have used to write HD at4, a function here, creates the HD, avi file, in a temporary directory, This can be controlled by the use of however, please say the workshop material for the date. I was right h d a v a r. I also allows us to control how the data is written to disk specifically, how did disaccharide chunked and compressed these topics to discuss in further detail in the workshop vignette, realization is an important topic with many subtleties. The workshop material covered, some of these in Greater detail to know about, however, is that realizing Adelaide array triggers the

execution of the accumulated Delight operations. If there are a lot of that light up relations, this can take some time, you can realize in memory as an ordinary, a right? Or a spice Matrix, what's a disc such as in an hdf5 file? Before we begin, the Q&A session will conclude with some general tips for the later. Babe, actinomyces. You cannot use the save IDs or save functions to save a copy or serialize your data. When it is an HD Ava, rayback, summarized

experiments. Instead you should use Save hdf5 summarize the experiments from the hdf. I've already packaged explained in the workshop vignette. This is because an h d a v, a r, a back summarize experiments contains falls on discs that the save IDs and say functions do not know how to serial eyes Besides hdf5 summarize experiment, is specifically designed for this purpose. Similarly, to load the data back in use the load hdf5 summarized experiments to save

hdf5. Summarized experiment will create a directory that contains a PDF file and an HD. Avi old is director, he can be moved around your computer or in date shed with collaborators who can invite her into their accession. Using the load hdf5 summarized experiment function. Once you've saved two HD Ava, Ryback summarize experiment, using dysfunction, you can proceed with you and I was just as normal. Any changes you make to the summarized experiment can quickly. Be serialized using the quick re-save version of this function. Book pricing is at the heart of March 4th of July to write

framework as a general rule. If you are and larger blocks generally means faster performance, but Hyatt Peak memory usage, using more smaller blocks will generally result in slow performance but with the benefit of lower Peak memory usage, The default block size is 100 megabytes, which can be changed with the set also block size function. Increasing the automatic block size itself in amongst the, easiest ways to speed up. Idolator a back to novices data stored on disk such as in an HD, avi file, I usually jumped into hypercube source of nitrous.

He's chunking refers to have the data at physically Stewart on disc. For example, data could be chunked on disc for a colon much as an RA is ordered by calling the ideal chunking supports whatever, Nexus passons, you need tonight to go dada. For example, if you know, you only need to process your. To buy coffee, then call them chunky and should give you the Optimal Performance. Generally you don't know what access patents you might need, or you need a combination of both row and column access. In this case, the default option of using hyper kids for the chunking, generally

offers, the best trade-off I come and confusion with the light array is the difference between the block geometry and the chunk geometry, the difference is as follows the block geometry dictates had a date at accessed, where is the chunk geometry? Dictates have a data is stored. When these two geometry, align closely than performance, using the Delight of a framework will be at his best. When working with large data, paralyzation is an attractive option for speeding up your analysis. How about paralyzation performance? Depends heavily on the choice of delight arrive. Back

in Dubai using such as an h, d a v and your computer's Hardware. Some general rules of thumb out of paralyzation is never as straightforward. As you think, I never provides as big an improvement as you heart. Generally parallel, writing to files is a bit of a no-go Zone. Where is Paulo rating from files, is sometimes, okay, it helps to break your work so I can do stages at the end of each stage. Save your outputs. For example, using the save hdf5 summarized experiment function, It really sucks have to rerun everything just to make a plug and this is good advice regardless of

whether you're using the Delight of right frame with conotton for processing large data. We've spent nearly an hour learning about the delay. The right Frame Works. Here comes the kickoff. If you don't need to use a delight array, don't use one that is if you can load your data into memory as an ordinary, a, right? Or a sparse Matrix and still compete on it, then you'll generally going to have a better time doing it that way. However, when you season an auction, when your data are too large to be stored in memory in the / framework is a powerful set of packages to help you

get your work done. is that I'd like to thank everybody that developer of delight array and the HD Avi packages in particular And to apologize to him for butchering his name. So at this presentation, I do so like to think I don't know who's developed many packages that support the wide array of objects and Mike Smith to maintains the I like today at 5 and I stay at 5, leave packages. Thank you for coming along to the witch up today and I look forward to discussing it further with you in the Q&A session. I've been looking at the Chatham Theater in any particular questions

but if anyone would like to see if I were a reading from a file within a baby out of plywood, honestly, I'm not sure, I certainly attempted rating for my stay at 5 files in parallel. And in some cases it's worked and other times it has an end Think what I would say, it's probably not a good idea, sometimes the technical reasons that I don't fully understand and I think it actually depends on how out your hdf5 so far has been sold and the particulars of their

Computing system you're working on. Sorry, I know that's not a very satisfying answer and I hope that we can develop some more clear. Guidance around that, I can have two projects. Can use a specified Amex, memory, usage, or should it be controlled by the chunk size of hdf5 in advance? Sorry, this is where the distinction between the block size and the trunk size important data, accessed of a red tights, a terrorist or disc, sorry, basically the trunk size will not influence. How much memory is you

by the block, which is how much data can be read into memory at one time. So I had to use that. You can control that Using the set water block size function or lower level utilities. I'm sorry you can specify a maximum but it's important to know that that is just controlling how much data is read into memory. It doesn't take into account, what is required to shoot on that data. For example, if you loaded night Vibes Matrix and then you want to perform a say a principal component analysis of that Matrix, That memory required to do the PCI

not affected into the block size. And so you generally don't want to loading, you don't want to have your book size to be the size of ram. You need to allow are the head for doing extra complications on the data. Curious, Sebastian status, it's any limitations. You can think about around 6 bio Banks scale data about using performance in classroom environment assumed the form. Scouts with the flavor of hard disk and it work over here if using an f s with SIM card.

It's from around 200 patients. I am particularly looking at home. Safety chain installation. Sorry, that is a set of matrices with about 200 million rows and columns for the sample. If that was a member of that would be. So I have to tear apart, but don't Discount Tire, exchange 14, episode of terabytes of data on disc. My sense is that Daddy? Performance ferry across distance and that includes how to file system setup. My experience with me when I was a party stuff.

I had a lot of support that I still struggled at times to fully understand why sitting up with another's so that's format in library, mentioned briefly in the workshop. There's a new kid on the Block for this pack arrive at a code. You may have seen a little bit about it. It'll be a witch was briefly on Wednesday fan of disappeared, but it has like a child, a day, or a package which apparently that's allows you to use a child a day to see how performance of that compares to using HD Ava, particularly, for vaginitis at San Jose State assets,

which to my understanding episode of 94.5, Hey, what's up? Sorry, hit Mountain yet. I just wanted to mention it for parallel processing. Maybe the model is like you have a reader function. The reeds are from the late already and then hands off the computer to a parallel back end and that's implemented in. I think it's in the genomic files package. There's a bunch of reduced by yield by the yield function with this is a realize Matrix probably and then passed that off. I took a function that does the computation and presumably. That sounds very promising. I think I'm one of the chance I've been

using to later, right? Only four years. Now, it's basically, since we came by to buy a conductor and the incredible job. I think it's in the area is, it was difficult to Brazen about some of how to design algorithms for, and I think as I've gained more experience and all the paperwork and more experienced, you start to recognize some of these abstractions like having a Rita, the process of data to other worlds and trying to figure out what I'm used. I'm and repeatable set of instructions will be off to the project.

Give a shout out to the the discussion of tile DB end of the developer forum. And first of all, it's there's a channel in slot for the developer Forum which has lots of interesting topics and then the specific conversation about going to say was that was in the course materials. But actually I think we failed failed to record conversations. My my plug but that forms a great place to learn about things. I will go back and watch that tonight. Anything you understand? It's nearly eleven quick and I haven't seen much of the conference this year.

What do I mean about reprising idle idle right? Sorry I worked for that rather quickly in this parking ticket names. Realizing a operations and confusing. Actual result example when you do I substitute operation or when we take a bicycle, doesn't do any competition, it just sort of a code steam idea of taking a job setting. And then when you realize the data, it actually goes through and triggers over the operations. By keeping the Directions days opportunities for do I need a ride to

simplify them sexy sample. If you have an eye tricks and you take a transfer, has been my tricks and then you take the transfer as it started. For example, divider, I can recognize that and realize that, that is an operations. If it doesn't get done it all. When we cancel that operation, now realizing it is the treatment of the operations and into memory as a write, more sparse Matrix, which means you actually can construct. The resultant memory is an ordinary are, all right? Or you can realize there was out to disk, which is used for when you have

a very large dataset because it can make you support processing. So that the whole day to sit, doesn't need to be loaded into memory for it. Once you notice due to complications example, if you had a larger right on this but you wants to compute the most at the same place sample, it was to the date the time and she's aware of everything, and then write that resulted and then read the next Address your question directly. I don't know if they's cold is outside, do not say if you have someone to take you, a question to the slack channel? Is it a

delay? The right channel is a big diet erection, which is the best place to get just more experiences of using to light a ride. But you can hear from the guy in Iron Man Has Central African to bed and I will try to answer them as best I can. Thank you.

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