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4 Machine Learning Techniques with Python - DataFlair 4 Machine Learning Techniques with Python Free Machine Learning courses with 130+ real-time projects Start Now!! Master Python with 70+ Hands-on Projects and Get Job-ready - Learn Python In our last session, we discussedÂ Train and Test Set in Python ML. Here,Â In this Machine Learning Techniques tutorial, we will see 4 major Machine Learning Techniques with Python: Regression, Classification, Clustering, andÂ Anomaly Detection. Familiarity with these methods is therefore a prerequisite when it comes to training viable machine learning algorithms. They all relate to separate types of scenarios and input data arrangements. For instance, regression is very relevant when input and output data are continuous variables and when constructing predictive models for future values. On the other hand, classification is beneficial with regards to categorizing data into categories that are already determined, which is important when it comes to issues like image recognition or the filtering of emails. So, letâ€™s look at Python Machine Learning Techniques. Machine Learning Techniques vs Algorithms While this tutorial is dedicated to Machine Learning techniques with Python, we will move over to algorithms pretty soon. But before we can begin focussing on techniques and algorithms, letâ€™s find out if theyâ€™re the same thing. A technique is a way of solving a problem. This is quite generic as a term. But when we say we have an algorithm, we mean we have an input and we desire certain output from it. We have clearly defined what steps to follow to get there. We will go the lengths to say an algorithm may make use of multiple techniques to get to the output. Do you know Applications of Machine LearningÂ Now that we have distinguished between the two, letâ€™s find out more about Machine Learning techniques. Machine Learning Techniques with Python Python Machine Learning Techniques are 4 types, let’s discuss them: a. Machine Learning Regression The dictionary will tell you that to regress is to return to a former state- one that is often less developed. In books of statistics, you will find regression to be a measure of how one variableâ€™s mean and corresponding values of other values relate to each other. But letâ€™s talk about it how you will see it. Also, ReadÂ Python Linear Regression & Chi-Square TestÂ i. Regressing to the Mean Francis Galton, Charles Darwinâ€™s half-cousin, observed sizes of sweet peas over generations. What he concluded was that letting nature do its job will result in a range of sizes. But if we selectively breed sweet peas for size, it makes for larger ones. With nature at the steering wheel, even bigger peas begin to produce smaller offsprings with time. We have a certain size for peas that varies, but we can map these values to a specific line or curve. ii. Another Example- Monkeys and Stocks In 1973, Burton Malkiel, Princeton University Professor put a claim in his book. A Random Walk Down Wall Street, which was a bestseller, insisted that a blindfolded monkey could do an equally good job as experts at selecting a portfolio by throwing darts at a newspaperâ€™s financial pages. In such stock-picking competitions, monkeys have beaten pros. But this was for once or twice. With enough events, the monkeysâ€™ performance declines; it regresses to the mean. iii. What isÂ Machine Learning Regression? In this plot, the line best fits all the data marked by the points. Using this line, we can predict what values we will find for x=70 (with a degree of uncertainty). As a Machine Learning technique, regression finds its foundation in supervised learning. We use it to predict a continuous and numerical target and begins by working on the data set values we already know. It compares known and predicted values and labels the difference between the expected and predicted values as the error/residual. iv. Types of Regression inÂ Machine Learning We generally observe two kinds of regression- • Linear Regression- When we can denote the relationship between a target and a predictor in a straight line, we use linear regression- • Non-Linear Regression- When we observe a non-linear relationship between a target and a predictor, we cannot denote it as a straight line. b. Machine Learning Classification i. What is Machine Learning Classification? Classification is a data mining technique that lets us predict group membership for data instances. This uses labelled data in advance and falls under supervised learning. This means we train data and expect to predict its future. By â€˜predictionâ€™, we mean we classify data into the classes they can belong. We have two kinds of attributes available- • Output Attribute-Â Aka Dependent attribute. • Input Attribute-Â Aka Independent attribute. ii. Methods of Classification • Decision Tree Induction- We build a decision tree from the class labelled tuples. This has internal nodes, branches, and leaf nodes. The internal nodes denote the test on an attribute, the branches- the test outcome, and the leaf nodes- the class label. The two steps involved are learning and testing, and these are fast. • Rule-based Classification- This classification is based on a set of IF-THEN rules. A rule is denoted as- IF condition THEN conclusion • Classification by Backpropagation- Neural network learning, often called connectionist learning, builds connections. Backpropagation is a neural-network learning algorithm, one of the most popular ones. It iteratively processes data and compares the target value with the results to learn. • Lazy Learners- In a lazy learner approach, the machine stores the training tuple and waits for a test tuple. This supports incremental learning. This contrasts with the early learner approach. iii. ML Classification Example Letâ€™s take an example. Consider weâ€™re here to teach you about different kinds of codes. We present to you ITF Barcodes, Code 93 Barcodes, QR codes, Aztecs, and data matrices among others. Once through most of the examples, it is now your turn to identify the kind of code it is when we show you one. This is supervised learning and we use parts of the examples of both- training and testing. Notice how some stars of each type end up on the other side of the curve. c. Clustering Clustering is an unsupervised classification. This is an exploratory data analysis with no labelled data available. With clustering, we separate unlabeled data into finite and discrete sets of data structures that are natural and hidden. We observe two kinds of clustering- • Hard Clustering- One object belongs to a single cluster. • Soft Clustering- One object may belong to multiple clusters. In clustering, we first select features, then design the clustering algorithm and then validate the clusters. Finally, we interpret the results. In clustering algorithms, data points are grouped based on distances which are measures used by most algorithms. Clustering approaches include k-means, hierarchical clustering, and density based clustering such as DBSCAN. All the methods used in data analysis have their advantages and each is applicable in different situations depending on the data collected and the analysis required. For instance k-means clustering can be useful while clustering a large dataset but it has a constraint that you need to specify the number of clusters in advance while on the other hand there is the hierarchical clustering that does not require this specification, it rather gives a dendrogram that shows the relationship of clusters. a. Example Recall the example in section b.iii. You could group these codes together. QR code, Aztec, and Data Matrix would be in a group, we could call this 2D Codes. ITF Barcodes and Code 39 Barcodes would group into a â€˜1D Codesâ€™ category. This is what a cluster looks like- d. Anomaly Detection An anomaly is something that deviates from its expected course. With machine learning, sometimes, we may want to spot an outlier. One such example would be to detect a dentist bill 85 fillings per hour. This amounts to 42 seconds per patient. Another would be to find a particular dentist bill only on Thursdays. Such situations raise suspicion and anomaly detection is a great way to highlight these anomalies since this isnâ€™t something weâ€™re looking for specifically. So, this was all about Machine Learning Techniques with Python. Hope you like our explanation. Hence, in this tutorial, we learned about four techniques of machine learning with Python- Regression, Classification, Clustering, and Anomaly Detection. Furthermore, if you have any query, feel free to ask in the comment box. Related Topic-Â Data Preprocessing, Analysis & Visualization in Python ML For reference Did you like this article? If Yes, please give DataFlair 5 Stars on Google 1 Response 1. Ismail says: Thanks for this post! 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Lazio 1-3 Udinese: Statistical Analysis \| The Laziali In Matchday 9 of the 2020/21 Serie A, Lazio were defeated 3-1 by Udinese at the Stadio Olimpico. Below is a statistical analysis of the game between the Biancocelesti and the Bianconeri. Expected Goals (xG) Step Plot The diagram above represents a summary of all simulations. The y-axis represents the cumulative xG (how many goals should be scored) and the x-axis represents time. • Lazio: cumulative xG of 1.40 • Udinese: cumulative xG of 1.18 In addition, the diagram above summarizes every shot taken by each club. Each shot is represented by a step and the height of the step measures the xG outcome of that shot; the higher the step, the more likely that the shot taken should have been converted. Furthermore, a dot with a name on the ‘Expected Goals Step Plot’ represents when a goal was scored and who the goal was scored by. Finally, the colored bar in the top left of the diagram shows the probability of each club winning the match or a draw occurring. • Lazio: 41% • Udinese: 28% • Draw: 31% Outcome Probability Bar Chart The charts in the diagram above are a summary of a 10,000-time simulation of the probability of how many goals each side should have scored and the actual number of goals each side scored. • Lazio: most likely to score 1 goal, actually scored 1 goal • Udinese: most likely to score 1 goal, actually scored 3 goals Pass Network Plot & Shot Location Plot The diagram above firstly shows the number of passes completed by each side in the match. • Lazio: 592 passes with an 82.1% accuracy rate • Udinese: 473 passes with an 81.8% accuracy rate Secondly, the diagram outlines the most active players for each team. Each player is represented by a node; the size of each node denotes the number of touches each player had. Thirdly, the diagram indicates the pass connections between teammates. These connections are the shaded grey lines throughout the plots; the size and shade of the line between players indicates the frequency of a pass connection. The top five connections are outlined in light blue (Lazio) and black (Udinese); it is important to note that the direction of each connection is not shown. Finally, this diagram shows the coordinates of each shot. The shots are plotted as light grey dots while goals are plotted as dark blue dots. The size of each dot represents the xG; the bigger the dot, the higher the chance that this opportunity should have found the back of the net (been a dark blue dot). • Lazio: 11 total shots, 6 shots on target • Udinese: 9 total shots, 4 shots on target	{"url":"https://thelaziali.com/2020/12/01/lazio-1-3-udinese-statistical-analysis-2020-serie-a/","timestamp":"2024-11-04T01:59:37Z","content_type":"text/html","content_length":"49006","record_id":"<urn:uuid:7b4c7d10-2276-4239-ba22-94fbd67345a0>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00311.warc.gz"}
Underfitting and Overfitting in Machine Learning \| Board Infinity Underfitting and overfitting are 2 major issues in machine learning that stagnate the performance of a machine learning model. To aptly generalize is the primary objective of any machine learning model. Generalization means the capability of a machine learning model to adapt to the unknown set of inputs and produce a suitable output. Thus, after being trained on a dataset, the ML model must provide precise as well as reliable results. Overfitting and underfitting hence become two important things that need to be kept an eye upon to enhance the performance of the model and to determine whether or not the model properly generalizes. This article is all about: • Basic terms and analogy. • Overfitting in ML. • Undefitting in ML. • How to avoid overfitting. • How to avoid underfitting. This article does not cover: • Machine learning algorithms. • Any other unrelated ML concepts. Basic terms It is the underlying real pattern of the data that aids the ML model in learning through the data. It is the irrelevant non-essential data that can lower the model’s performance. It’s an error in prediction brought into the model due to the oversimplification of the ML algorithms. It is the phenomenon when the ML model performs fine with the training dataset but not with the test dataset. When an ML model attempts to capture every data point (or more than required) in a given dataset, overfitting happens. Consequently, the model begins caching the dataset’s inaccurate values and noise. Owing to these factors the accuracy, as well as the efficiency of the model, decreases. The model is then said to be overfitted and it possesses high variance and low bias. The probability of overfitting occurring rises as the model is trained. Overfitting is a key issue in supervised learning. For a better understanding, let’s have a look at the graph of the linear regression output below: Image courtesy: javatpoint As evident from the graph above, the model attempts to capture every data point in the scatter plot. A look at the graph may make you think that the model is efficient, but that’s not the case, because the regression model’s target is to hunt the best fit line and since there is no best fit found here, hence prediction errors are produced. When an ML model is unable to cover the underlying trend of the data, underfitting happens. The feeding of the training dataset can be halted at an early stage for avoiding overfitting in the ML model. This leads to the model not gaining sufficient learning from the training dataset. Consequently, the ML model fails in finding the best fit of the data’s dominant trend. In underfitting, the ML model is unable to gain sufficient learning through the training dataset. Thus the accuracy of the model is decreased and unreliable predictions are produced. Note that an underfitted ML model exhibits low variance and high bias. For a better understanding, let’s have a look at the output of a linear regression model below: Image courtesy: javatpoint Avoiding overfitting Following are a bunch of ways of avoiding/reducing overfitting an ML model: • Eliminating features. • Using more data for training. • Stopping the training early. • Ensembling. • Regularization. • Cross-validation. Avoiding underfitting Following are a few ways of avoiding/reducing underfitting an ML model: • Doing feature engineering. • Elevating the model’s complexity. • Incrementing the number of epochs. • Increasing the number of features. • Eliminating the noise from the data. • Underfitting and overfitting are 2 major issues in machine learning that stagnate the performance of a machine learning model. • When an ML model attempts to capture every data point (or more than required) in a given dataset, overfitting happens. • When an ML model is unable to cover the underlying trend of the data, underfitting happens	{"url":"https://www.boardinfinity.com/blog/underfitting-and-overfitting-in-machine-learning/","timestamp":"2024-11-09T03:17:30Z","content_type":"text/html","content_length":"70750","record_id":"<urn:uuid:114a1a12-4cb1-49a0-93f4-3cce08454068>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00481.warc.gz"}
Where does the system get the name for a USB file system? I’m not sure where to post this, so I’ll try here. Feel free to have some fun with it. If I plug in a USB drive, the KDE device notifier tells me about it. It typically gives some sort of name. I’m wondering where that name comes from. Here’s a case in point that has me curious: I have an external 80G drive. It’s actually on old IDE drive in an enclosure. So I plugged it in, and the device notifier told me: “Linux Mint 17 KDE 64-bit” (but without the quotes). I proceeded to click the option for mounting the first partition available. And here you see that as: /dev/sdf1 20511356 5467920 13978476 29% /run/media/rickert/Linux Mint 17 KDE 64-bit What’s weird about this, is that the drive actually contains an install of opensuse factory snapshot 20140728. That was a test install to see if I ran into problem. So why is it saying “Linux Mint”? Okay, I did at one time copy the Mint installation iso to the drive. But, since then, I have twice installed opensuse factory snapshots (root as “/dev/sdf1”, swap as “/dev/sdf2” and home as “/dev/ sdf3”, filling the entire disk between them). I ran: # e2label /dev/sdf1 which gave an empty string as output. So the file system does not appear to have a label. The same happens with “/dev/sdf3” (i.e. no label). I’m not sure about labels for a swap partition. None of this really matters for anything. It just seems weird. The partition label I suspect. If this is left blank, it takes the name of the device, e.g. AA40-XR or some such sequence. Is the partition label different from the file system label? I tried “cfdisk” which showed an empty label field for all three partitions. As you do only show output, but not the command thatgenerated it, I have no idea how to interprete this. What you could do: ls -l /dev/disk/by* \| grep sdf1 It will show all the symlinks to /dev/sdf1 and thus show you uuid, id, path, label, etc. But that mount point having blank spaces in it makes it unlikely that it is one of these. Well, AFAIK udisks2 (that’s what mounts the disk) does take the label for the mountpoint name. What does “blkid” output? That sequence is the UUID I think. Ah, sorry. That was a line of output from “df”. The output from “blkid” for this disk is: /dev/sdf1: UUID="5732828b-2130-41e3-9f36-802692eeae23" TYPE="ext4" /dev/sdf2: UUID="cb39c2a1-464f-49ac-b898-6bf0949abede" TYPE="swap" /dev/sdf3: UUID="f1aaf452-7612-4f47-8a4b-1c12314f8b84" TYPE="ext4" I omitted the lines for other devices (not part of “/dev/sdf”). And to answer hcvv: # ls -l /dev/disk/by* \| grep sdf1 lrwxrwxrwx 1 root root 10 Aug 3 15:14 usb-WDC_WD80_0JB-00ETA0_7D8004B500E4-0:0-part1 -> ../../sdf1 lrwxrwxrwx 1 root root 10 Aug 3 15:14 pci-0000:00:0b.1-usb-0:8:1.0-scsi-0:0:0:0-part1 -> ../../sdf1 lrwxrwxrwx 1 root root 10 Aug 3 15:14 5732828b-2130-41e3-9f36-802692eeae23 -> ../../sdf1 There’s no hint of a “by-label”. That would be correct when there is no label as you already found out. But it confirms it. None of the above fits with your mount point/id. As I thought already (because of he white psace), but it was worth a try to be sure. According to the man page, udisks2 reads drive specific configuration from /etc/udisks2/. Maybe something in there? Could you please post the output of “udisksctl info -b /dev/sdf” and “udisksctl info -b /dev/sdf”? Maybe this would give a clue where it gets that name from. Well not only by the user end… Name of “extern sources” lack of logic seems to be questioned. Those two commands look identical. So I’ll assume that one of them was supposed to be for “/dev/sdf1” First command (as written) # udisksctl info -b /dev/sdf Configuration: ] CryptoBackingDevice: '/' Device: /dev/sdf DeviceNumber: 2128 Drive: '/org/freedesktop/UDisks2/drives/WDC_WD80_0JB_00ETA0_7D8004B500E4' HintAuto: true HintIgnore: false HintPartitionable: true HintSystem: false Id: by-id-scsi-1JMicron_USB_to_ATA-ATAPI_bridge IdLabel: Linux Mint 17 KDE 64-bit IdType: iso9660 IdUUID: 2014-06-19-00-31-14-00 IdUsage: filesystem IdVersion: Joliet Extension MDRaid: '/' MDRaidMember: '/' PreferredDevice: /dev/sdf ReadOnly: false Size: 80026361856 Symlinks: /dev/disk/by-id/scsi-1JMicron_USB_to_ATA/ATAPI_bridge Type: dos Second command (modified by appending “1”) # udisksctl info -b /dev/sdf1 Configuration: ] CryptoBackingDevice: '/' Device: /dev/sdf1 DeviceNumber: 2129 Drive: '/org/freedesktop/UDisks2/drives/WDC_WD80_0JB_00ETA0_7D8004B500E4' HintAuto: true HintIgnore: false HintPartitionable: true HintSystem: false Id: by-id-scsi-1JMicron_USB_to_ATA-ATAPI_bridge-part1 IdLabel: Linux Mint 17 KDE 64-bit IdType: ext4 IdUUID: 5732828b-2130-41e3-9f36-802692eeae23 IdUsage: filesystem IdVersion: 1.0 MDRaid: '/' MDRaidMember: '/' PreferredDevice: /dev/sdf1 ReadOnly: false Size: 21474836480 Symlinks: /dev/disk/by-id/scsi-1JMicron_USB_to_ATA/ATAPI_bridge-part1 Flags: 0 IsContained: false IsContainer: false Number: 1 Offset: 1048576 Size: 21474836480 Table: '/org/freedesktop/UDisks2/block_devices/sdf' Type: 0x83 Well, the iso image would not have used a partition table like a filesystem would, so the answer lies in the first 512 bytes of the device IMHO, and the ‘leftover’ naming has been preserved somehow. (It is interesting that it can be read by the kernel, and not by e2label though.) I saw “IDLabel” in that output. So I googled that (with “hard drive” appended), and came up with: Get Volume ID (Label) of ISO9660 CD-ROM. So I tried the command: # dd if=/dev/sdf bs=1 skip=32808 count=32 conv=unblock cbs=32 which gave: Linux Mint 17 KDE 64-bit 32+0 records in 25+0 records out 25 bytes (25 B) copied, 0.00126444 s, 19.8 kB/s This was a hybrid iso, intended to be usable if written to a USB. And, written to a USB, it was partitioned. Hmm, I still have that iso lying around. So here’s the “fdisk” output directly on the iso file: /sbin/fdisk -l Mint.iso Disk Mint.iso: 1.4 GiB, 1531445248 bytes, 2991104 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x51bf3cf2 Device Boot Start End Blocks Id System Mint.iso1 * 0 2991103 1495552 0 Empty Mint.iso2 15576 20119 2272 ef EFI (FAT-12/16/32) My previous post looks to have found the spot where something was left behind, but it is well past the 512 byte mark. This was a hybrid iso, intended to be usable if written to a USB. And, written to a USB, it was partitioned. I see. In any case, I guess you never ‘zeroed’ or repartitioned the device after this use? I repartitioned (with “fdisk”). I did not zero it, as there seemed to be no need. On 2014-08-03 23:16, deano ferrari wrote: > Well, the iso image would not have used a partition table like a > filesystem would, so the answer lies in the first 512 bytes of the > device IMHO, and the ‘leftover’ naming has been preserved somehow. (It > is interesting that it can be read by the kernel, and not by e2label > though.) Not really. Each filesystem stores the “label” on a different place, it is not a standard. What is interesting is that, knowing it is an “ext” partition, it uses instead the iso image label… However, on a GPT partition table, the table itself can store a label, which can be different from the filesystem label… You can see both labels with this command: lsblk --output NAME,KNAME,SIZE,TYPE,MOUNTPOINT,LABEL,UUID,PARTLABEL,PARTUUID,SIZE Cheers / Saludos, Carlos E. R. (from 13.1 x86_64 “Bottle” (Minas Tirith)) I know that. That’s what was being implied with the unusual mount-point name. An addendum to this. I decided to label those partitions. I used a different computer, where the external drive shows as “/dev/sdc”. So I used: # e2label /dev/sdc1 ufactory-root # e2label /dev/sdc3 ufactory-home I did not attempt to label the swap partition (I think that requires running “mkswap -L”). I unplugged the device. And now it shows up under the new labels (in KDE device notifier), when I plug in. Presumably that old Mint iso9660 label is still there, but ignored. The following is only a guess. The whole proces of interpreting things when a disk is connected and things on it are to be interpreted involves a lot of “intelligent guesses” (or in other words, is heuristic). When software guesses there is a partition table, interpreting those 512 bytes as such may run smoothly, but you can indeed find strange things when it is in fact not. Thus when there is an ISO starting there, or (as I have it here on a system) a LVM Physical Volume, things might go wrong. And once the software took the wrong path, it may come to peculiar results. (In my LVM PV case on boot it says carefully worded: There does not seem to be a partition table) Same for interpretinng what is on a partition. The software has to make an intelligent guess about what is there. Even when it is helped by th fact that the partition type is 83 (Linux file system) that leaves a lot of possibilities (also outside the usual ext2/3/4, Reiser range). Same is true for bunches of Windows file sytem types that gather under one partition type. And then we take it for granted that the partition type is used correctly, which might not be the case. So, IMHO, it is possible that what is found may lead to a conclusion of a partition being there, with a type, that may lead to interpreting the contents being some file system type, which may lead to thinking that something there is interpreted as a volume label. Not likely, but in real life, once upon a time, it wil happen.	{"url":"https://forums.opensuse.org/t/where-does-the-system-get-the-name-for-a-usb-file-system/102120","timestamp":"2024-11-02T02:10:18Z","content_type":"text/html","content_length":"58468","record_id":"<urn:uuid:be064d04-dd64-4c9f-a2d4-6445145d180c>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00397.warc.gz"}
How do you graph f(x)=2/(x^2+1) using holes, vertical and horizontal asymptotes, x and y intercepts? \| HIX Tutor How do you graph #f(x)=2/(x^2+1)# using holes, vertical and horizontal asymptotes, x and y intercepts? Answer 1 $f \left(x\right)$ has an absolute maximum of 2 at $x = 0$ $f \left(x\right) \to 0$ as $x \to \pm \infty$ #f(x) = 2/(x^2+1)# Since #x^2 + 1 > 0 forall x in RR# there exists no holes in #f(x)# Also, #lim_"x-> +-oo" f(x) = 0# #f'(x) = (-4x)/(x^2+1)^2# For a maximum or minimum value; #f'(x) = 0# #:. (-4x)/(x^2+1)^2 = 0 -> x=0# #f(0) = 2/(0+1) = 2# Since #f''(0) < 0# #f(0) = 2# is a maximum of #f(x)# The critical points of #f(x)# can be seen on the graph below: graph{2/(x^2+1) [-5.55, 5.55, -2.772, 2.778]} Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer 2 To graph the function f(x) = 2/(x^2 + 1), we can analyze its holes, vertical and horizontal asymptotes, as well as the x and y intercepts. 1. Holes: The function has no holes. 2. Vertical Asymptotes: The denominator x^2 + 1 will never equal zero, so there are no vertical asymptotes. 3. Horizontal Asymptotes: As x approaches positive or negative infinity, the function approaches zero. Therefore, the horizontal asymptote is y = 0. 4. X-intercepts: To find the x-intercepts, we set f(x) = 0 and solve for x. However, since the numerator is always 2 (non-zero), the function has no x-intercepts. 5. Y-intercept: To find the y-intercept, we set x = 0 and evaluate f(0). Plugging in x = 0, we get f(0) = 2/(0^2 + 1) = 2/1 = 2. Therefore, the y-intercept is (0, 2). By considering these aspects, we can graph the function f(x) = 2/(x^2 + 1) accordingly. Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer from HIX Tutor When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some Not the question you need? HIX Tutor Solve ANY homework problem with a smart AI • 98% accuracy study help • Covers math, physics, chemistry, biology, and more • Step-by-step, in-depth guides • Readily available 24/7	{"url":"https://tutor.hix.ai/question/how-do-you-graph-f-x-2-x-2-1-using-holes-vertical-and-horizontal-asymptotes-x-an-8f9af9bc09","timestamp":"2024-11-05T22:52:32Z","content_type":"text/html","content_length":"574036","record_id":"<urn:uuid:7e81ad62-7485-4c19-9e26-64ed5e0d1566>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00793.warc.gz"}
Petr Lisonek Research Interests My research involves applications of algebraic and combinatorial methods in cryptography and in the theory of error-correcting codes. My current research areas are: • Non-linear functions. These functions are of essential importance in symmetric cryptography to prevent some fundamental attacks against ciphers such as linear cryptanalysis and differential cryptanalysis. In the algebraic approach I use finite fields, exponential sums and algebraic curves. In the combinatorial approach I use finite geometries to construct non-linear functions. • Error-control codes. I work on algebraic and combinatorial error-correcting codes for the classical channel and for the quantum channel. The algebraic methods involve cyclic codes and their various generalizations, and the combinatorial methods involve finite geometries. Further I work on adapting construction methods for classical codes so they can be used to construct quantum • Steganography. This is the science of information hiding, concerned with developing communication channels that obscure the very existence of the message that they carry. I work on steganographic schemes that use linear codes. • Computer algebra. I am interested in the algorithmic aspects of the above three topics in the context of computer algebra (symbolic computation). For more information such as the list of my publications and conference organization please see my personal website.	{"url":"http://www.cecm.sfu.ca/people/pm/plisonek.shtml","timestamp":"2024-11-08T13:55:10Z","content_type":"text/html","content_length":"12021","record_id":"<urn:uuid:eb8f6f83-5b89-44e4-b0cd-98aee481747c>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00344.warc.gz"}
All About bricks in 1 sq ft (square feet) for 9 inch brick wall Bricks have been used as a building material for centuries, and for good reason. Their durability and strength make them a popular choice for constructing walls, both indoors and outdoors. One of the most common uses of bricks is in the construction of a 9 inch brick wall, which typically requires approximately 1 square foot of bricks per wall. In this article, we will delve deeper into all there is to know about using bricks for a 9 inch wall, including the different types of bricks, their benefits, and how to properly calculate the amount needed for your project. So let’s dive in and discover all about bricks in 1 sq ft for a 9 inch brick wall. How many bricks in 1 sq ft (square feet) for 9 inch brick wall As a civil engineer, I have a thorough understanding of construction materials and their usage in building structures. Bricks are one of the most commonly used materials in construction, particularly for walls. One of the frequently asked questions by clients is the number of bricks needed per square foot for a nine-inch brick wall. In this article, I will explain the calculations and factors that determine the number of bricks required for a wall measuring 1 square foot in area. Before delving into the calculations, it is essential to understand the dimensions of bricks used in construction. The standard size of a brick is 9 inches by 4.5 inches by 2.5 inches. This size is commonly known as metric bricks and is used in most modern construction projects. Knowing the dimensions of a brick is crucial in determining the number of bricks needed per square foot. When it comes to building a wall, the most common thickness is nine inches. This thickness is achieved by laying bricks in a staggered pattern in two rows. The gap between the inner and outer rows is filled with mortar, which helps to hold the bricks together. Hence, in a nine-inch brick wall, the visible portion of a brick is only 7.5 inches, while the remaining 1.5 inches is covered by mortar. This information is important in calculating the number of bricks in 1 square foot. The basic calculation to determine the number of bricks in 1 square foot is to divide the area of the wall (1 square foot) by the area covered by one brick (7.5 inches). However, this calculation is not entirely accurate as it does not account for the gap between the bricks. To accommodate for this gap, we need to add an additional 3/8th inches to the width of each brick, which is the standard thickness of mortar used in construction. Therefore, the area covered by each brick is now 7.875 inches (7.5 inches + 3/8th inches). Using this information, we can now calculate the number of bricks needed per square foot for a nine-inch brick wall. Converting 1 square foot into inches results in 144 square inches (12 inches x 12 inches x 1 square foot). Dividing this by the area covered by one brick (7.875 inches) gives us a total of 18.286 bricks. However, since we cannot have a fraction of a brick, the actual number required would be rounded off to 18 bricks. In conclusion, for a nine-inch brick wall, 18 bricks are needed per square foot. However, this number may vary depending on factors such as the type of wall, thickness of mortar, and quality of bricks. It is always recommended to consult a professional engineer or contractor for accurate calculations based on the specific project requirements. How many bricks in 1 square feet required for 9 inch or double/ full brick wall A brick is a commonly used building material for constructing walls, both for residential and commercial structures. As a civil engineer, it is important to have a thorough understanding of the materials used in construction and their corresponding measurements. When it comes to brick walls, there are different types of bricks and sizes that can be used. In this article, we will specifically discuss the number of bricks required for a 9 inch or double/full brick wall per square foot. Firstly, let us understand the dimensions of a standard brick. In most countries, the standard size of a brick is 9 inches by 4.5 inches by 3 inches (length, width, and height). However, these dimensions may vary slightly depending on the country or region. To calculate the number of bricks required per square foot for a 9-inch brick wall, we need to take into consideration the spacing between each brick, which is known as the mortar joint. The standard mortar joint width is 3/8 inches. Using simple math, we can calculate the number of bricks required for a 1 square foot area: Length of one brick (L) = 9 inches = 0.75 feet Width of one brick (W) = 4.5 inches = 0.375 feet Area of one brick (A) = L x W = 0.75 feet x 0.375 feet = 0.28125 square feet Therefore, the number of bricks required per square foot = 1/0.28125 = 3.56 bricks However, this number only accounts for the actual bricks and not the mortar joint in between. To take into account the mortar joint, we need to add the width of the joint to the brick’s dimensions and then calculate the total area of one brick (including the joint). Total width of one brick and joint = 0.75 feet + (2 x 0.375 feet) = 1.5 feet Total length of one brick and joint = 0.375 feet + (2 x 0.75 feet) = 1.875 feet Total area of one brick and joint = 1.5 feet x 1.875 feet = 2.8125 square feet Now, the number of bricks required per square foot will be 1/2.8125 = 0.3555 = 3.56 bricks. This calculation is based on a single layer or one brick thickness. For a double/full brick wall, which is two bricks thick, the number of bricks required per square foot will be twice as much, i.e., 3.56 x 2 = 7.12 bricks. In conclusion, for a 9-inch or double/full brick wall, approximately 7.12 bricks are required per square foot. However, this number may vary depending on the type of bricks used, and it is always advisable to include some additional bricks for waste or breakage during construction. It is also important to consider the thickness of the mortar joint, as a thicker joint will require more bricks per square foot. As a civil engineer, it is crucial to accurately calculate the materials required for a construction project to ensure its efficiency, safety, and cost-effectiveness. How many bricks in 1 square feet 9 inch brick wall The number of bricks in a 1 square foot 9 inch brick wall can vary depending on the size and type of bricks being used. However, there are some general guidelines that can help you estimate the number of bricks needed for such a wall. First, we need to understand the dimensions of a standard 9 inch brick. A standard brick is typically 2 1/4 inches by 3 3/4 inches by 9 inches, with a depth of 3 5/8 inches. This means that the area of one brick is about 0.604 square feet (0.070 square meters). To calculate the number of bricks in a 1 square foot 9 inch brick wall, we need to divide the area of the wall (1 square foot) by the area of one brick (0.604 square feet). The result will give us the approximate number of bricks needed for a single layer of the wall. 1 square foot / 0.604 square feet = 1.657 bricks However, we also need to consider the width of the mortar joints between the bricks. Mortar joints are typically 3/8 inch thick, so for every 3/8 inch of wall, we need to subtract one brick. This means that for every 4 inches of wall, we will need 3.69 bricks. Considering both the dimensions of the bricks and the width of the mortar joints, we can estimate that a 1 square foot 9 inch brick wall will require approximately 31 bricks (1.657 x 18.75) for a single layer. If the wall is being constructed with multiple layers, we need to multiply the number of bricks per layer by the number of layers. For example, a 10 feet tall wall would require 10 layers of bricks, thus requiring approximately 310 bricks (31 x 10). It is important to note that this is just an estimate and the actual number of bricks needed may vary depending on the specific dimensions and type of bricks used. It is always recommended to consult a professional before starting any construction project. How many bricks in 1 square feet 4 inch brick wall The number of bricks needed for a 4 inch brick wall can vary depending on the size of the bricks and the thickness of the mortar joints. However, on average, there are 50 bricks in 1 square foot of a 4 inch brick wall. To understand how this number is calculated, it is important to know the standard dimensions of a brick and the standard thickness of a mortar joint. In the United States, the most commonly used brick size is 8 inches by 2 ¼ inches by 3 ¾ inches. This is known as a modular brick. The standard thickness for a mortar joint is 3/8 inch. Using this information, we can calculate the number of bricks needed for a 1 square foot wall. First, we must determine the area of the brick wall. Since the standard size of a brick is 8 inches by 2 ¼ inches, the total area of one brick is 8 x 2 ¼ = 18 square inches. To convert this to square feet, we divide by 144 (1 square foot = 144 square inches). Therefore, the area of one brick is 18/144 = 0.125 square feet. Next, we must account for the mortar joints. Assuming a standard 3/8 inch thickness, the total thickness of a brick and a mortar joint would be 4 inches or 0.333 feet. Therefore, the number of bricks needed for a 1 square foot wall would be 1/0.333 = 3 bricks. However, this calculation only applies if the bricks are stacked side by side without any space between them. In reality, a small gap or joint may be left between the bricks to allow for the mortar. This can vary depending on the design and technique used for laying the bricks. On average, this gap can increase the number of bricks needed by 10-15%. So, to account for this, we can estimate that 50 bricks are needed for a 1 square foot wall (3 bricks x 1.15 = 3.45, rounded to 50). In conclusion, there are approximately 50 bricks needed for a 1 square foot 4 inch brick wall. This number may vary depending on the size and method of construction, but it provides a good estimate for planning and budgeting purposes. As a civil engineer, it is important to understand these calculations in order to properly estimate and design brick structures. How many bricks in 1 square feet 5 inch brick wall In order to determine the number of bricks in a 1 square foot 5 inch brick wall, we must first understand the standard size of a brick and how to calculate the number of bricks per square foot. The standard brick size can vary slightly depending on the country or region, but in general, a brick measures 3 5/8 inches in height, 2 1/4 inches in width, and 7 5/8 inches in length. However, for the purpose of this calculation, we will consider the height of the brick to be 4 inches to account for the additional 5 inches from the 5 inch wall. To calculate the number of bricks per square foot, we need to determine the area of a single brick. The formula for calculating the area is length multiplied by width. Therefore, the area of one brick is 4 inches multiplied by 2 1/4 inches, which equals 9 square inches. Now, in order to convert this area to square feet, we need to divide it by 144 (the number of square inches in one square foot). So, 9/144 = 0.0625 square feet. To find the total number of bricks in a 1 square foot area, we divide 1 by 0.0625, which equals 16 bricks. Therefore, in a 1 square foot 5 inch brick wall, there would be 16 bricks assuming there are no gaps or spaces between the bricks. It is important to note that this calculation does not take into account the mortar joints between the bricks. Depending on the thickness of the joints, the number of bricks needed may vary. Also, since there can be variations in brick sizes, it is always recommended to consult with the manufacturer or contractor for precise calculations. In conclusion, a 1 square foot 5 inch brick wall would require 16 bricks, assuming there is no space between the bricks. As a civil engineer, it is important to accurately calculate these numbers to ensure the proper amount of materials are used in construction projects. How many bricks in a square foot? In order to accurately determine the number of bricks in a square foot, it is important to understand the various brick sizes and their corresponding dimensions. There are generally three commonly used brick sizes in construction: modular, engineer, and queen. The dimensions for each of these sizes are as follows: – Modular brick: 3 5/8 inches x 2 1/4 inches x 7 5/8 inches – Engineer brick: 3 5/8 inches x 2 13/16 inches x 9 5/8 inches – Queen brick: 3 5/8 inches x 2 3/4 inches x 7 5/8 inches With these dimensions in mind, we can now calculate the number of bricks in a square foot for each size. Modular Brick: A square foot is equivalent to 144 square inches. To determine the number of modular bricks in a square foot, we need to calculate the area of one brick. The area of a modular brick is 3 5/8 inches x 7 5/8 inches = 27.625 square inches. Therefore, the number of bricks in a square foot would be 144 square inches / 27.625 square inches = 5.22 bricks. Engineer Brick: Following the same calculation, the area of an engineer brick is 3 5/8 inches x 9 5/8 inches = 34.75 square inches. Thus, the number of engineer bricks in a square foot would be 144 square inches / 34.75 square inches = 4.15 bricks. Queen Brick: For a queen brick, the area is calculated as 3 5/8 inches x 7 5/8 inches = 27.625 square inches. Therefore, the number of queen bricks in a square foot would be 144 square inches / 27.625 square inches = 5.22 bricks. It should be noted that these calculations are based on the assumption that there is no space left between the bricks, also known as the gap factor. In actual construction, there is usually an allowance between the bricks for mortar joints, which may vary depending on the construction technique. Thus, the number of bricks in a square foot may differ slightly in real-life situations. In conclusion, the number of bricks in a square foot varies depending on the brick size being used. For a modular brick, there would be approximately 5.22 bricks, 4.15 bricks for an engineer brick, and 5.22 bricks for a queen brick. These calculations can be useful for estimating the amount of bricks needed for a project and can help in planning and budgeting for construction projects. How many bricks in 1 square feet Determining the number of bricks per square foot is a common calculation in the construction industry. Bricks are a popular and versatile building material, used for a variety of purposes including walls, floors, and even decorative features. As a civil engineer, it is important to have a good understanding of brick measurements and how many bricks are needed for a given area. The number of bricks in 1 square foot depends on the size of the bricks being used. The standard size for bricks used in construction is 8 inches by 4 inches by 2.25 inches. This is known as a modular brick size and is the most commonly used size in the United States. To calculate the number of bricks in 1 square foot, we first need to convert the measurements into feet. 8 inches is equal to 0.667 feet, 4 inches is equal to 0.333 feet, and 2.25 inches is equal to 0.1875 feet. So, the area of one brick is: 0.667 ft x 0.333 ft = 0.222 ft^2 To calculate the number of bricks in 1 square foot, we simply divide the area of the square foot (1 ft^2) by the area of one brick (0.222 ft^2). 1 ft^2 / 0.222 ft^2 = 4.5 bricks Therefore, there are approximately 4.5 bricks in 1 square foot. It is important to note that this calculation is based on the assumption that the bricks are perfectly placed with no gaps in between. In reality, some space needs to be left for mortar joints. The thickness of mortar joints can vary, but a common width is 3/8 inch or 0.03125 feet. So, to account for this, we can reduce the number of bricks per square foot by adding the width of the mortar joints to the brick size measurement: 8 inches + (3/8 inch x 2) = 8.25 inches = 0.6875 feet 4 inches + (3/8 inch x 2) = 4.25 inches = 0.3541667 feet Now, the area of one brick, including the width of mortar joints, is: 0.6875 ft x 0.3541667 ft = 0.2430556 ft^2 Dividing the area of one square foot by this new brick area gives us: 1 ft^2 / 0.2430556 ft^2 = 4.11 bricks So, taking into account the width of mortar joints, there are approximately 4.11 bricks in 1 square foot. It is always a good idea to add a small percentage (around 5%) to this number to account for waste, cuts, and breakage. In conclusion, the number of bricks in 1 square foot depends on the size of the bricks being used and whether or not the calculation takes into account the width of mortar joints. As a civil engineer, it is important to understand the calculations and considerations when working with brick as a building material. Formula for brick calculation in 9 inch brick wall Brick calculation is an important part of construction planning. It helps in estimating the number of bricks required for a given wall area, thus providing accurate cost estimation. In this article, we will discuss the formula for brick calculation in a 9 inch brick wall. Before diving into the formula, it is important to understand the standard size of a brick. In most countries, including the US, UK, and India, the standard size of a brick is 9 inches (length) x 4.5 inches (width) x 3 inches (height). This dimension is known as the nominal size of a brick and is used for brick calculation. Let’s look at an example to understand the formula better. Consider a wall with an area of 100 square feet (which is a standard unit of measurement for construction). The height of the wall is 10 feet, and the width is 9 inches. We need to calculate the number of bricks required to build this wall. Step 1: Calculate the Wall Area The wall area can be calculated by multiplying the height and width of the wall. Wall area = 10 feet x 9 inches Convert the height from feet to inches by multiplying it with 12 (1 foot = 12 inches). Wall area = 120 inches x 9 inches = 1080 square inches Convert the area from square inches to square feet by dividing it with 144 (1 square foot = 144 square inches). Wall area = 1080/144 = 7.5 square feet Step 2: Calculate the Number of Bricks To calculate the number of bricks, we need to know the brick volume. As mentioned earlier, the standard size of a brick is 9 inches x 4.5 inches x 3 inches. Therefore, the volume of one brick is: Brick volume = 9 inches x 4.5 inches x 3 inches = 121.5 cubic inches Now, we need to find how many bricks can be accommodated in one square foot of area. To calculate this, we divide the wall area by the brick volume. Number of bricks = Wall area / Brick volume = 7.5 square feet / 121.5 cubic inches = 7.5 square feet / 121.5/(1inches x 1 inch x 1 inch) = 7.5 x 12 x 4 x 3 = 1080 bricks (rounded off to the nearest whole number) Hence, the number of bricks required to build a wall of 100 square feet with a height of 10 feet and a width of 9 inches is 1080 bricks. Number of bricks = Wall area / Brick volume = (Height x Width) / (Brick length x Brick width x Brick height) In case the wall has openings such as doors or windows, the area of these openings needs to be subtracted from the total wall area before applying the above formula. In conclusion, the formula for brick calculation in a 9 inch brick wall is an essential tool for estimating the number of bricks required for a given wall area. It helps in accurate budgeting and planning for a construction project. How many bricks in 1 square feet for 9 inch brick wall The number of bricks in 1 square foot for a 9 inch brick wall varies depending on the type and size of the bricks used. Generally, standard size bricks are 8 inches long, 4 inches wide and 2 1/4 inch thick. To calculate the number of bricks in 1 square foot, we need to consider the thickness of the mortar joint between each brick. For a 9 inch brick wall, we need to use three courses (rows) of bricks to reach the full height. Each course is 3 inches high, so the total height of the wall would be 9 inches. Now, to calculate the number of bricks in each course, we need to take into account the height of the bricks and the thickness of the mortar joint. First, let’s assume that we are using standard size bricks with a 3/8 inch thick mortar joint. This means that the actual height of the bricks would be 3 inches (3 5/8 inches – 3/8 inch mortar joint). Now, to get the number of bricks in one course, we divide the height of the wall (9 inches) by the actual height of the brick (3 inches). 9 inches / 3 inches = 3 bricks per course Since we need three courses for a 9 inch wall, the total number of bricks in one square foot would be: 3 bricks x 3 courses = 9 bricks per square foot However, if we are using bricks with a different height or mortar joint thickness, the number of bricks in 1 square foot may vary. For example, if we use bricks with a 2 3/4 inch height and a 1/4 inch thick mortar joint, the calculation would be: 9 inches / 2 3/4 inches = 3.27 bricks per course 3.27 bricks x 3 courses = 9.81 bricks per square foot In some cases, corners or interlocking patterns may also affect the number of bricks needed in 1 square foot. Therefore, it is important to consider all these factors when calculating the number of bricks needed for a 9 inch brick wall. In conclusion, the number of bricks in 1 square foot for a 9 inch brick wall can range from 9 to 10 depending on the size and type of bricks used. It is always recommended to consult with a professional or refer to an architectural plan when determining the exact number of bricks needed for a specific project. How many bricks in 100 square feet for 9 inch or double/ full brick wall Before we can determine the number of bricks required for a 9-inch or double/full brick wall, we need to understand the standard size of a brick and a square feet. In general, the standard size of a brick is 3 5/8 inches by 2 1/4 inches by 8 inches. However, the actual dimensions may vary slightly depending on the manufacturer. For simplicity, we will use the standard size of a brick for our calculation. Now, let’s define a square foot. A square foot is a unit of measurement used in the imperial system to measure area. One square foot is equal to 12 inches by 12 inches, which is 144 square inches. With these measurements in mind, we can now calculate the number of bricks required for a 9 inch or double/full brick wall. Firstly, we need to convert the square feet into square inches as the dimensions of a brick are in inches. For a 100 square feet wall, the total area in square inches would be 100 x 144 = 14,400 square inches. Next, we need to determine the number of bricks required for one layer of the wall. As we are considering a 9-inch wall, the height of one layer would be 9 inches. To calculate the number of bricks needed for the length of one layer, we need to divide the length of the wall in inches by the length of one brick, which is 8 inches. Therefore, for a 100 square feet wall, the number of bricks required for the length of one layer would be 14,400 inches/ 8 inches = 1,800 bricks. Similarly, to calculate the number of bricks required for the height of the wall, we need to divide the height of the wall in inches by the height of one brick, which is 2 1/4 inches. In this case, the height of the wall is 9 inches, so the number of bricks required for the height of the wall would be 9 inches/ 2 1/4 inches = 4 rows. To get the total number of bricks required for the 100 square feet wall, we need to multiply the number of bricks required for the length of one layer (1,800 bricks) by the number of rows (4 rows). Therefore, the total number of bricks required for a 9-inch wall in a 100 square feet area would be 1,800 x 4 = 7,200 bricks. In conclusion, for a 9-inch or double/full brick wall, there will be approximately 7,200 bricks required for every 100 square feet of wall area. However, this calculation may vary depending on the actual dimensions of the bricks and the wall. It is always recommended to consult with a professional engineer or contractor for accurate estimations before starting any construction project. How many bricks in 1000 square feet for 9 inch or full/ double brick wall The number of bricks required in a 1000 square feet wall depends on the thickness of the wall and the size of the bricks being used. If we consider a 9 inch wall, which is a standard thickness for a double brick wall, the number of bricks required would be around 3780 to 4000 bricks. The calculation for the number of bricks is based on the following assumptions: 1. Size of Bricks: The size of bricks for this calculation is taken as 9 inches in length, 4 inches in width, and 3 inches in height. These are the standard dimensions of traditional modular bricks used in construction. 2. Thickness of Wall: The thickness of the wall is taken as 9 inches, which is the combined thickness of two 4.5 inch bricks with a 0.5 inch mortar joint. 3. Area to be Covered: In order to find the number of bricks required, we first need to calculate the total area of the wall. In this case, it is 1000 square feet. Now, let us look at the calculation in detail: Step 1: Finding the area of one brick Area of one brick = length x width = 9 inches x 4 inches = 36 square inches Step 2: Finding the total area of the wall Total area = 1000 square feet x 12 (to convert square feet to square inches) = 12000 square inches Step 3: Calculating the number of bricks Number of bricks = Total area / Area of one brick = 12000 square inches / 36 square inches = 333.33 bricks However, this number only accounts for one side of the wall. For a double brick wall, we need to consider both sides, so the total number of bricks required would be: 333.33 bricks x 2 = 666.66 bricks But this calculation does not account for the mortar joints. Mortar joints are typically 0.5 inches in thickness and are placed between the bricks to hold them together. So, we need to adjust the number of bricks required to account for the mortar joints. Step 4: Adjusting for mortar joints Number of bricks required = 666.66 bricks x 1.1 (to account for 10% of mortar joints) = 733.33 bricks Thus, for a 9 inch double brick wall covering an area of 1000 square feet, we would need approximately 733 bricks. However, it is always better to add a few extra bricks to account for any wastage or damage during construction. In conclusion, 1000 square feet of a 9 inch double brick wall would require approximately 733 bricks of standard size. It is important to note that this is only an estimate and the actual number of bricks required may vary depending on the type of bricks used, the thickness of the mortar joints, and the workmanship of the masonry. It is always recommended to consult with a qualified structural engineer or contractor for more accurate estimates. Brick calculation per sq ft for 9 inch brick wall Calculating the number of bricks required for a 9 inch brick wall per square foot can be done in a few simple steps. Brick walls are measured in terms of its thickness and not by the size of individual bricks. Hence, for a wall that is 9 inches thick, the total thickness would equal three bricks, as one standard brick is typically 3 inches thick. Step 1: Determine the Wall Area The first step is to calculate the area of the wall in square feet. This can be done by multiplying the length and width of the wall. For example, if the length of the wall is 10 feet and the height is 8 feet, the total wall area would be 80 square feet (10 x 8 = 80). Step 2: Calculate the Number of Bricks To calculate the number of bricks required for a 9 inch wall per square foot, we need to first determine the number of bricks per square foot. This is determined by dividing the wall thickness (9 inches) by the thickness of one brick (3 inches). In this case, we would divide 9 by 3, which gives us 3 bricks per square foot. Step 3: Multiply The final step is to multiply the total number of bricks per square foot by the total wall area calculated in step 1. In our example, since there are 3 bricks per square foot and the total wall area is 80 square feet, the total number of bricks required for our 9 inch wall would be 240 (3 x 80 = 240). Therefore, for a 9 inch brick wall, 240 bricks would be required for every square foot of the wall. It is important to note that this calculation is an estimate and may vary based on the specific measurements and design of the wall. In conclusion, for civil engineers and construction professionals, calculating the number of bricks required for a 9 inch brick wall per square foot is a basic but important task to ensure accurate procurement of materials and proper planning for construction projects. Brick calculation for 100 square feet in 9 inch brick wall When it comes to building structures, bricks are one of the most commonly used materials. They are versatile, sturdy, and have been used in construction for centuries. As a civil engineer, it is important to accurately calculate the amount of bricks needed for a project to ensure proper construction and budgeting. For a 100 square feet wall with a standard 9-inch brick thickness, the following calculation can be used: Step 1: Calculate the total area of the wall Since the wall is 100 square feet in size, the area can be calculated by multiplying the length and height of the wall. Let’s say the length of the wall is 20 feet and the height is 5 feet, the total area would be 100 square feet (20 ft x 5 ft = 100 sq. ft). Step 2: Determine the coverage area of one brick To calculate the coverage area of one brick, we need to consider the dimensions of the brick and the thickness of the mortar joint. A standard 9-inch brick has a face dimension of 8 inches by 4 inches and 1.5 inches for the thickness of the mortar joint. The coverage area of one brick would be (8 inches – 1.5 inches) x (4 inches – 1.5 inches) = 6.5 inches x 2.5 inches = 16.25 square inches. Step 3: Determine the total number of bricks needed Now that we know the total area of the wall and the coverage area of one brick, we can calculate the number of bricks needed. We need to convert the area from square feet to square inches. 100 square feet = 14,400 square inches (1 square foot = 144 square inches). Then, we divide the total area of the wall (14,400 sq. in.) by the coverage area of one brick (16.25 sq. in.). The total number of bricks needed for the 100 square feet wall would be 886 (14,400 sq. in. / 16.25 sq. in. = 886). Step 4: Account for waste and extra bricks In construction, it is always recommended to account for some waste and include additional bricks in case of any miscalculations. A standard rule of thumb is to add 5-10% extra bricks to the total number calculated. In this case, we can add 10% to the total number of bricks needed (886 x 10% = 88.6). Therefore, the total number of bricks needed would be 886 + 88.6 = 974.6, which we can round up to 975 bricks. In conclusion, for a 100 square feet wall with a standard 9-inch brick thickness, 975 bricks would be needed for construction. It is important to note that this calculation may vary depending on the size and type of bricks used, and it is always recommended to consult with a structural engineer or an experienced contractor for an accurate estimation. In conclusion, bricks play a crucial role in construction, providing strength and durability to any structure. Understanding the fundamentals of bricks and their dimensions, particularly in a 1 sq ft area for a 9 inch brick wall, is essential for an efficient and successful building process. From selecting the right type of brick to calculating the number needed for a project, these considerations can impact the overall cost and quality of the construction. Furthermore, proper handling, laying, and maintenance of bricks are crucial for their longevity and the durability of the entire structure. By keeping these guidelines in mind, builders and homeowners alike can confidently incorporate bricks into their construction projects and create sturdy and lasting structures. Leave a Comment	{"url":"https://civilstep.com/all-about-bricks-in-1-sq-ft-square-feet-for-9-inch-brick-wall/","timestamp":"2024-11-15T01:18:10Z","content_type":"text/html","content_length":"245651","record_id":"<urn:uuid:2ff0badb-6bb7-4d91-bd24-bd5db54be0b7>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00643.warc.gz"}
implementing rayleighchan in OFDM Hi everbody, I am doing my M.SC thesis on the topic "ICI cancellation in OFDM". I have very limited time, if you can help me I will be grateful to you.... I can implement the OFDM structure in AWGN channel, it works very well.. But when i try to implement the system in a "rayleighchan", I obtain very bad BER results. N%6 ; % carriers GI=N/4; % Guard ınterval=Cyclic prefix DataBit = randint(N,1,2); % obtain 0 and 1's DataMod = qammod(DataBit,2); % obtain modulated symbols (BPSK) Ifft=Ifft (DataMod, N); %Take ifft of the symbols x_t = [Ifft(N- GI + 1 : N);Ifft]; %Here x_t enters the channel gain= 10*log10(pathgains); % convert to dB fdopplerP ; % 50 Hz I have some questions: 1) Which parameters determine the sampling time of x_t and sampling time of the channel parameters? (It is a basic question sorry but I am (I think sampling time=0.2E-6 and x_t's sampling rate are not correlated in my code, may be it is the problem) 2) I do not determine any parameters like ; carrier frequency =2 MHz , OFDM symbol duration = 200us etc... May I determine them, then how i can I put them in the code...(Again it is a basic question sorry but I am confused...) 2)If i use only "chan=rayleighchan(samplingtime, fdoppler)" then there is no problem, BER results are good...So am I choosing wrong pathdelays and samplingtime or am I doing wrong channel 3) How can I get channel impulse response? (Because chan.PathGains gives the path gains , not channel impulse response complex values) 4)I am taking chan.ResetBeforeFiltering=0 but not sure about it, am I doing this wrong? Burkay Etiler	{"url":"https://www.dsprelated.com/showthread/matlab/5762-1.php","timestamp":"2024-11-01T22:09:59Z","content_type":"text/html","content_length":"57327","record_id":"<urn:uuid:7fbcd519-e3f3-4cfa-91a1-114d192e232f>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00589.warc.gz"}
Assuming I have a toy model df which lists the model of the car and customer rating of one car showroom. Using plotly express, I created pie charts of percentage of cars by model and by Cust_rating, respectively as two separate graphs: Now, I want to create subplots, and all the ways of doing it using the documentation are throwing Dynamic subplot using Figures in Matplotlib I want to create a subplot using matplotlib with pysimplegui where each time i select some signals-checkbox(list of values) i should get a plot corresponding to it which will dynamically increase or decrease in size based on my selection so when i select a checkbox the respective plot will be plotted and eqaully spaced and when i deselect a plot How do I create a seaborn lineplot with multiple lines showing the distribution of values per category? I have a dataframe of cars from 5 different brands with all models and their technical data. Simplified it looks like that: Brand Model Power in HP VW Golf 7 150 Audi A4 190 Audi A5 190 VW Passat 240 VW Polo 80 Ford A4 190 KIA A4 190 Audi Q3 150 Audi S6 400 VW Golf 6 140 VW How to remove boundaries in matplotlib rectangles? The following snippet draws non-overlapping rectangles and works as expected: But when I wish to make the rectangles transparent, they tend to have a border around them, as shown below: Initially, I thought maybe that was due to some overlaps. So, I reduced the size of the rectangles, but I still got it. For example, if I use I get Drawing 2D and 3D contour in the same plot in python Is it possible to draw 2D and 3D contour plot like this in python. Sorry I couldn’t provide much detail on the plot in terms of mathematical equations and all. Answer Use plot_surface along with contour to project the contour. It is not limited to the Z plane; you can do this to the X and Y planes as well. How to create Predicted vs. Actual plot using abline_plot and statsmodels I am trying to recreate this plot from this website in Python instead of R: Background I have a dataframe called boston (the popular educational boston housing dataset). I created a multiple linear regression model with some variables with statsmodels api below. Everything works. I create a dataframe of actual values from the boston dataset and predicted values from above How to visualize Classification using pandas and matplotlib? I’m trying to classify a dataset using python with pandas. The iris flower dataset consists of 50 samples from each of three species of Iris and contains four features.The goal is to distiguish between the species of irises based on these features. Question: Generate a scatter plot with sepal_length feature in x-axis and petal_width feature in y-axis, which shows the Colorbar and its range shared between two plots I adapted this code (https://stackoverflow.com/a/73099652/2369957) that demonstrates how to share a colorbar and its range for two plots, but it doesn’t seem to work when the range of the two plots are different – in the case of the posted code, the plots have the same range (half-open interval [0.0, 1.0)). I generated two plots with different ranges and the How to find the global minima from a matplotlib graph? I have two arrays x and y. Here I’ve plotted them using Matplotlib and found the global minima using this simple logic. Here is the output that I’m getting: After that I’ve smoothen the graph BSpline Now my position of the global minima has changed and that simple logic will not work here. I want to know how I can Plotting values above a threshold in Python Having issues with plotting values above a set threshold using a pandas dataframe. I have a dataframe that has 21453 rows and 20 columns, and one of the columns is just 1 and 0 values. I’m trying to plot this column using the following code: But get the following errors: Any suggestions on how to fix this? Answer The error	{"url":"https://python.tutorialink.com/tag/matplotlib/","timestamp":"2024-11-09T20:41:18Z","content_type":"text/html","content_length":"59307","record_id":"<urn:uuid:6ab62d8b-5d6d-4198-b9d3-2c826c147948>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00248.warc.gz"}
Throat and Nasal Passages \| Pagefind XKCD Demo ← Back January 3, 2022 #2563: Throat and Nasal Passages explain [A graph with two curves are shown. The Y-axis ends in an arrow, but has no units or ticks. The X-axis has no arrow but has 23 ticks with every fifth longer and every tenth labeled. The first tick extends the Y-axis below the X-axis. Both curves start over the second tick and end over the last tick. One curve is a dotted straight line running along the bottom of the graph just above the X-axis. The other start a bit higher and oscillate a bit up and down with 19 sharp peaks and 19 troughs, where some of the troughs have extra features, and not all are equidistant. After this a 20th small peak just starts to drop down again, before the curve goes in to a very steep rise almost all the way to the top of the graph. There is a small dip on the way before it reaches a maximum. Then a deep drop followed by a smaller rise before an even deeper drop. But then at the end, the graph rises almost vertically to the highest point where the graph stops over the last tick. At the top left of the graph the two lines are explained showing a solid and a dotted line with text to their right. Below this, above the solid curve midway between the first two labels on the X-axis, is a label from which 5 arrows points to 5 consecutive peaks.] • How much Time I have spent thinking about my throat and nasal passages, over time ┅ How much I want to think about them Label:Cold/Flu Season X-axis: 2000 2010 2020	{"url":"https://xkcd.pagefind.app/comics/2022-1-3-throat-and-nasal-passages/","timestamp":"2024-11-09T08:00:20Z","content_type":"text/html","content_length":"6054","record_id":"<urn:uuid:9811385f-6d41-4cb6-93a6-c27d59a84acb>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00549.warc.gz"}
RFC 3492 - Punycode: A Bootstring encoding of Unicode for Intern Network Working Group A. Costello Request for Comments: 3492 Univ. of California, Berkeley Category: Standards Track March 2003 Punycode: A Bootstring encoding of Unicode for Internationalized Domain Names in Applications (IDNA) Status of this Memo This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited. Copyright Notice Copyright (C) The Internet Society (2003). All Rights Reserved. Punycode is a simple and efficient transfer encoding syntax designed for use with Internationalized Domain Names in Applications (IDNA). It uniquely and reversibly transforms a Unicode string into an ASCII string. ASCII characters in the Unicode string are represented literally, and non-ASCII characters are represented by ASCII characters that are allowed in host name labels (letters, digits, and hyphens). This document defines a general algorithm called Bootstring that allows a string of basic code points to uniquely represent any string of code points drawn from a larger set. Punycode is an instance of Bootstring that uses particular parameter values specified by this document, appropriate for IDNA. Table of Contents 1. Introduction...............................................2 1.1 Features..............................................2 1.2 Interaction of protocol parts.........................3 2. Terminology................................................3 3. Bootstring description.....................................4 3.1 Basic code point segregation..........................4 3.2 Insertion unsort coding...............................4 3.3 Generalized variable-length integers..................5 3.4 Bias adaptation.......................................7 4. Bootstring parameters......................................8 5. Parameter values for Punycode..............................8 6. Bootstring algorithms......................................9 6.1 Bias adaptation function.............................10 6.2 Decoding procedure...................................11 6.3 Encoding procedure...................................12 6.4 Overflow handling....................................13 7. Punycode examples.........................................14 7.1 Sample strings.......................................14 7.2 Decoding traces......................................17 7.3 Encoding traces......................................19 8. Security Considerations...................................20 9. References................................................21 9.1 Normative References.................................21 9.2 Informative References...............................21 A. Mixed-case annotation.....................................22 B. Disclaimer and license....................................22 C. Punycode sample implementation............................23 Author's Address.............................................34 Full Copyright Statement.....................................35 1. Introduction [IDNA] describes an architecture for supporting internationalized domain names. Labels containing non-ASCII characters can be represented by ACE labels, which begin with a special ACE prefix and contain only ASCII characters. The remainder of the label after the prefix is a Punycode encoding of a Unicode string satisfying certain constraints. For the details of the prefix and constraints, see [IDNA] and [NAMEPREP]. Punycode is an instance of a more general algorithm called Bootstring, which allows strings composed from a small set of "basic" code points to uniquely represent any string of code points drawn from a larger set. Punycode is Bootstring with particular parameter values appropriate for IDNA. 1.1 Features Bootstring has been designed to have the following features: * Completeness: Every extended string (sequence of arbitrary code points) can be represented by a basic string (sequence of basic code points). Restrictions on what strings are allowed, and on length, can be imposed by higher layers. * Uniqueness: There is at most one basic string that represents a given extended string. * Reversibility: Any extended string mapped to a basic string can be recovered from that basic string. * Efficient encoding: The ratio of basic string length to extended string length is small. This is important in the context of domain names because RFC 1034 [RFC1034] restricts the length of a domain label to 63 characters. * Simplicity: The encoding and decoding algorithms are reasonably simple to implement. The goals of efficiency and simplicity are at odds; Bootstring aims at a good balance between them. * Readability: Basic code points appearing in the extended string are represented as themselves in the basic string (although the main purpose is to improve efficiency, not readability). Punycode can also support an additional feature that is not used by the ToASCII and ToUnicode operations of [IDNA]. When extended strings are case-folded prior to encoding, the basic string can use mixed case to tell how to convert the folded string into a mixed-case string. See appendix A "Mixed-case annotation". 1.2 Interaction of protocol parts Punycode is used by the IDNA protocol [IDNA] for converting domain labels into ASCII; it is not designed for any other purpose. It is explicitly not designed for processing arbitrary free text. 2. Terminology The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14, RFC 2119 A code point is an integral value associated with a character in a coded character set. As in the Unicode Standard [UNICODE], Unicode code points are denoted by "U+" followed by four to six hexadecimal digits, while a range of code points is denoted by two hexadecimal numbers separated by "..", with no prefixes. The operators div and mod perform integer division; (x div y) is the quotient of x divided by y, discarding the remainder, and (x mod y) is the remainder, so (x div y) * y + (x mod y) == x. Bootstring uses these operators only with nonnegative operands, so the quotient and remainder are always nonnegative. The break statement jumps out of the innermost loop (as in C). An overflow is an attempt to compute a value that exceeds the maximum value of an integer variable. 3. Bootstring description Bootstring represents an arbitrary sequence of code points (the "extended string") as a sequence of basic code points (the "basic string"). This section describes the representation. Section 6 "Bootstring algorithms" presents the algorithms as pseudocode. Sections 7.1 "Decoding traces" and 7.2 "Encoding traces" trace the algorithms for sample inputs. The following sections describe the four techniques used in Bootstring. "Basic code point segregation" is a very simple and efficient encoding for basic code points occurring in the extended string: they are simply copied all at once. "Insertion unsort coding" encodes the non-basic code points as deltas, and processes the code points in numerical order rather than in order of appearance, which typically results in smaller deltas. The deltas are represented as "generalized variable-length integers", which use basic code points to represent nonnegative integers. The parameters of this integer representation are dynamically adjusted using "bias adaptation", to improve efficiency when consecutive deltas have similar magnitudes. 3.1 Basic code point segregation All basic code points appearing in the extended string are represented literally at the beginning of the basic string, in their original order, followed by a delimiter if (and only if) the number of basic code points is nonzero. The delimiter is a particular basic code point, which never appears in the remainder of the basic string. The decoder can therefore find the end of the literal portion (if there is one) by scanning for the last delimiter. 3.2 Insertion unsort coding The remainder of the basic string (after the last delimiter if there is one) represents a sequence of nonnegative integral deltas as generalized variable-length integers, described in section 3.3. The meaning of the deltas is best understood in terms of the decoder. The decoder builds the extended string incrementally. Initially, the extended string is a copy of the literal portion of the basic string (excluding the last delimiter). The decoder inserts non-basic code points, one for each delta, into the extended string, ultimately arriving at the final decoded string. At the heart of this process is a state machine with two state variables: an index i and a counter n. The index i refers to a position in the extended string; it ranges from 0 (the first position) to the current length of the extended string (which refers to a potential position beyond the current end). If the current state is <n,i>, the next state is <n,i+1> if i is less than the length of the extended string, or <n+1,0> if i equals the length of the extended string. In other words, each state change causes i to increment, wrapping around to zero if necessary, and n counts the number of wrap-arounds. Notice that the state always advances monotonically (there is no way for the decoder to return to an earlier state). At each state, an insertion is either performed or not performed. At most one insertion is performed in a given state. An insertion inserts the value of n at position i in the extended string. The deltas are a run-length encoding of this sequence of events: they are the lengths of the runs of non-insertion states preceeding the insertion states. Hence, for each delta, the decoder performs delta state changes, then an insertion, and then one more state change. (An implementation need not perform each state change individually, but can instead use division and remainder calculations to compute the next insertion state directly.) It is an error if the inserted code point is a basic code point (because basic code points were supposed to be segregated as described in section 3.1). The encoder's main task is to derive the sequence of deltas that will cause the decoder to construct the desired string. It can do this by repeatedly scanning the extended string for the next code point that the decoder would need to insert, and counting the number of state changes the decoder would need to perform, mindful of the fact that the decoder's extended string will include only those code points that have already been inserted. Section 6.3 "Encoding procedure" gives a precise algorithm. 3.3 Generalized variable-length integers In a conventional integer representation the base is the number of distinct symbols for digits, whose values are 0 through base-1. Let digit_0 denote the least significant digit, digit_1 the next least significant, and so on. The value represented is the sum over j of digit_j * w(j), where w(j) = base^j is the weight (scale factor) for position j. For example, in the base 8 integer 437, the digits are 7, 3, and 4, and the weights are 1, 8, and 64, so the value is 7 + 38 + 464 = 287. This representation has two disadvantages: First, there are multiple encodings of each value (because there can be extra zeros in the most significant positions), which is inconvenient when unique encodings are needed. Second, the integer is not self- delimiting, so if multiple integers are concatenated the boundaries between them are lost. The generalized variable-length representation solves these two problems. The digit values are still 0 through base-1, but now the integer is self-delimiting by means of thresholds t(j), each of which is in the range 0 through base-1. Exactly one digit, the most significant, satisfies digit_j < t(j). Therefore, if several integers are concatenated, it is easy to separate them, starting with the first if they are little-endian (least significant digit first), or starting with the last if they are big-endian (most significant digit first). As before, the value is the sum over j of digit_j * w(j), but the weights are different: w(0) = 1 w(j) = w(j-1) * (base - t(j-1)) for j > 0 For example, consider the little-endian sequence of base 8 digits 734251... Suppose the thresholds are 2, 3, 5, 5, 5, 5... This implies that the weights are 1, 1(8-2) = 6, 6(8-3) = 30, 30(8-5) = 90, 90(8-5) = 270, and so on. 7 is not less than 2, and 3 is not less than 3, but 4 is less than 5, so 4 is the last digit. The value of 734 is 71 + 36 + 430 = 145. The next integer is 251, with value 21 + 56 + 130 = 62. Decoding this representation is very similar to decoding a conventional integer: Start with a current value of N = 0 and a weight w = 1. Fetch the next digit d and increase N by d * w. If d is less than the current threshold (t) then stop, otherwise increase w by a factor of (base - t), update t for the next position, and repeat. Encoding this representation is similar to encoding a conventional integer: If N < t then output one digit for N and stop, otherwise output the digit for t + ((N - t) mod (base - t)), then replace N with (N - t) div (base - t), update t for the next position, and For any particular set of values of t(j), there is exactly one generalized variable-length representation of each nonnegative integral value. Bootstring uses little-endian ordering so that the deltas can be separated starting with the first. The t(j) values are defined in terms of the constants base, tmin, and tmax, and a state variable called bias: t(j) = base * (j + 1) - bias, clamped to the range tmin through tmax The clamping means that if the formula yields a value less than tmin or greater than tmax, then t(j) = tmin or tmax, respectively. (In the pseudocode in section 6 "Bootstring algorithms", the expression base * (j + 1) is denoted by k for performance reasons.) These t(j) values cause the representation to favor integers within a particular range determined by the bias. 3.4 Bias adaptation After each delta is encoded or decoded, bias is set for the next delta as follows: 1. Delta is scaled in order to avoid overflow in the next step: let delta = delta div 2 But when this is the very first delta, the divisor is not 2, but instead a constant called damp. This compensates for the fact that the second delta is usually much smaller than the first. 2. Delta is increased to compensate for the fact that the next delta will be inserting into a longer string: let delta = delta + (delta div numpoints) numpoints is the total number of code points encoded/decoded so far (including the one corresponding to this delta itself, and including the basic code points). 3. Delta is repeatedly divided until it falls within a threshold, to predict the minimum number of digits needed to represent the next while delta > ((base - tmin) * tmax) div 2 do let delta = delta div (base - tmin) 4. The bias is set: let bias = (base * the number of divisions performed in step 3) + (((base - tmin + 1) * delta) div (delta + skew)) The motivation for this procedure is that the current delta provides a hint about the likely size of the next delta, and so t(j) is set to tmax for the more significant digits starting with the one expected to be last, tmin for the less significant digits up through the one expected to be third-last, and somewhere between tmin and tmax for the digit expected to be second-last (balancing the hope of the expected-last digit being unnecessary against the danger of it being insufficient). 4. Bootstring parameters Given a set of basic code points, one needs to be designated as the delimiter. The base cannot be greater than the number of distinguishable basic code points remaining. The digit-values in the range 0 through base-1 need to be associated with distinct non- delimiter basic code points. In some cases multiple code points need to have the same digit-value; for example, uppercase and lowercase versions of the same letter need to be equivalent if basic strings are case-insensitive. The initial value of n cannot be greater than the minimum non-basic code point that could appear in extended strings. The remaining five parameters (tmin, tmax, skew, damp, and the initial value of bias) need to satisfy the following constraints: 0 <= tmin <= tmax <= base-1 skew >= 1 damp >= 2 initial_bias mod base <= base - tmin Provided the constraints are satisfied, these five parameters affect efficiency but not correctness. They are best chosen empirically. If support for mixed-case annotation is desired (see appendix A), make sure that the code points corresponding to 0 through tmax-1 all have both uppercase and lowercase forms. 5. Parameter values for Punycode Punycode uses the following Bootstring parameter values: base = 36 tmin = 1 tmax = 26 skew = 38 damp = 700 initial_bias = 72 initial_n = 128 = 0x80 Although the only restriction Punycode imposes on the input integers is that they be nonnegative, these parameters are especially designed to work well with Unicode [UNICODE] code points, which are integers in the range 0..10FFFF (but not D800..DFFF, which are reserved for use by the UTF-16 encoding of Unicode). The basic code points are the ASCII [ASCII] code points (0..7F), of which U+002D (-) is the delimiter, and some of the others have digit-values as follows: code points digit-values ------------ ---------------------- 41..5A (A-Z) = 0 to 25, respectively 61..7A (a-z) = 0 to 25, respectively 30..39 (0-9) = 26 to 35, respectively Using hyphen-minus as the delimiter implies that the encoded string can end with a hyphen-minus only if the Unicode string consists entirely of basic code points, but IDNA forbids such strings from being encoded. The encoded string can begin with a hyphen-minus, but IDNA prepends a prefix. Therefore IDNA using Punycode conforms to the RFC 952 rule that host name labels neither begin nor end with a hyphen-minus [RFC952]. A decoder MUST recognize the letters in both uppercase and lowercase forms (including mixtures of both forms). An encoder SHOULD output only uppercase forms or only lowercase forms, unless it uses mixed- case annotation (see appendix A). Presumably most users will not manually write or type encoded strings (as opposed to cutting and pasting them), but those who do will need to be alert to the potential visual ambiguity between the following sets of characters: G 6 I l 1 O 0 S 5 U V Z 2 Such ambiguities are usually resolved by context, but in a Punycode encoded string there is no context apparent to humans. 6. Bootstring algorithms Some parts of the pseudocode can be omitted if the parameters satisfy certain conditions (for which Punycode qualifies). These parts are enclosed in {braces}, and notes immediately following the pseudocode explain the conditions under which they can be omitted. Formally, code points are integers, and hence the pseudocode assumes that arithmetic operations can be performed directly on code points. In some programming languages, explicit conversion between code points and integers might be necessary. 6.1 Bias adaptation function function adapt(delta,numpoints,firsttime): if firsttime then let delta = delta div damp else let delta = delta div 2 let delta = delta + (delta div numpoints) let k = 0 while delta > ((base - tmin) * tmax) div 2 do begin let delta = delta div (base - tmin) let k = k + base return k + (((base - tmin + 1) * delta) div (delta + skew)) It does not matter whether the modifications to delta and k inside adapt() affect variables of the same name inside the encoding/decoding procedures, because after calling adapt() the caller does not read those variables before overwriting them. 6.2 Decoding procedure let n = initial_n let i = 0 let bias = initial_bias let output = an empty string indexed from 0 consume all code points before the last delimiter (if there is one) and copy them to output, fail on any non-basic code point if more than zero code points were consumed then consume one more (which will be the last delimiter) while the input is not exhausted do begin let oldi = i let w = 1 for k = base to infinity in steps of base do begin consume a code point, or fail if there was none to consume let digit = the code point's digit-value, fail if it has none let i = i + digit * w, fail on overflow let t = tmin if k <= bias {+ tmin}, or tmax if k >= bias + tmax, or k - bias otherwise if digit < t then break let w = w * (base - t), fail on overflow let bias = adapt(i - oldi, length(output) + 1, test oldi is 0?) let n = n + i div (length(output) + 1), fail on overflow let i = i mod (length(output) + 1) {if n is a basic code point then fail} insert n into output at position i increment i The full statement enclosed in braces (checking whether n is a basic code point) can be omitted if initial_n exceeds all basic code points (which is true for Punycode), because n is never less than initial_n. In the assignment of t, where t is clamped to the range tmin through tmax, "+ tmin" can always be omitted. This makes the clamping calculation incorrect when bias < k < bias + tmin, but that cannot happen because of the way bias is computed and because of the constraints on the parameters. Because the decoder state can only advance monotonically, and there is only one representation of any delta, there is therefore only one encoded string that can represent a given sequence of integers. The only error conditions are invalid code points, unexpected end-of- input, overflow, and basic code points encoded using deltas instead of appearing literally. If the decoder fails on these errors as shown above, then it cannot produce the same output for two distinct inputs. Without this property it would have been necessary to re- encode the output and verify that it matches the input in order to guarantee the uniqueness of the encoding. 6.3 Encoding procedure let n = initial_n let delta = 0 let bias = initial_bias let h = b = the number of basic code points in the input copy them to the output in order, followed by a delimiter if b > 0 {if the input contains a non-basic code point < n then fail} while h < length(input) do begin let m = the minimum {non-basic} code point >= n in the input let delta = delta + (m - n) * (h + 1), fail on overflow let n = m for each code point c in the input (in order) do begin if c < n {or c is basic} then increment delta, fail on overflow if c == n then begin let q = delta for k = base to infinity in steps of base do begin let t = tmin if k <= bias {+ tmin}, or tmax if k >= bias + tmax, or k - bias otherwise if q < t then break output the code point for digit t + ((q - t) mod (base - t)) let q = (q - t) div (base - t) output the code point for digit q let bias = adapt(delta, h + 1, test h equals b?) let delta = 0 increment h increment delta and n The full statement enclosed in braces (checking whether the input contains a non-basic code point less than n) can be omitted if all code points less than initial_n are basic code points (which is true for Punycode if code points are unsigned). The brace-enclosed conditions "non-basic" and "or c is basic" can be omitted if initial_n exceeds all basic code points (which is true for Punycode), because the code point being tested is never less than In the assignment of t, where t is clamped to the range tmin through tmax, "+ tmin" can always be omitted. This makes the clamping calculation incorrect when bias < k < bias + tmin, but that cannot happen because of the way bias is computed and because of the constraints on the parameters. The checks for overflow are necessary to avoid producing invalid output when the input contains very large values or is very long. The increment of delta at the bottom of the outer loop cannot overflow because delta < length(input) before the increment, and length(input) is already assumed to be representable. The increment of n could overflow, but only if h == length(input), in which case the procedure is finished anyway. 6.4 Overflow handling For IDNA, 26-bit unsigned integers are sufficient to handle all valid IDNA labels without overflow, because any string that needed a 27-bit delta would have to exceed either the code point limit (0..10FFFF) or the label length limit (63 characters). However, overflow handling is necessary because the inputs are not necessarily valid IDNA If the programming language does not provide overflow detection, the following technique can be used. Suppose A, B, and C are representable nonnegative integers and C is nonzero. Then A + B overflows if and only if B > maxint - A, and A + (B * C) overflows if and only if B > (maxint - A) div C, where maxint is the greatest integer for which maxint + 1 cannot be represented. Refer to appendix C "Punycode sample implementation" for demonstrations of this technique in the C language. The decoding and encoding algorithms shown in sections 6.2 and 6.3 handle overflow by detecting it whenever it happens. Another approach is to enforce limits on the inputs that prevent overflow from happening. For example, if the encoder were to verify that no input code points exceed M and that the input length does not exceed L, then no delta could ever exceed (M - initial_n) * (L + 1), and hence no overflow could occur if integer variables were capable of representing values that large. This prevention approach would impose more restrictions on the input than the detection approach does, but might be considered simpler in some programming languages. In theory, the decoder could use an analogous approach, limiting the number of digits in a variable-length integer (that is, limiting the number of iterations in the innermost loop). However, the number of digits that suffice to represent a given delta can sometimes represent much larger deltas (because of the adaptation), and hence this approach would probably need integers wider than 32 bits. Yet another approach for the decoder is to allow overflow to occur, but to check the final output string by re-encoding it and comparing to the decoder input. If and only if they do not match (using a case-insensitive ASCII comparison) overflow has occurred. This delayed-detection approach would not impose any more restrictions on the input than the immediate-detection approach does, and might be considered simpler in some programming languages. In fact, if the decoder is used only inside the IDNA ToUnicode operation [IDNA], then it need not check for overflow at all, because ToUnicode performs a higher level re-encoding and comparison, and a mismatch has the same consequence as if the Punycode decoder had 7. Punycode examples 7.1 Sample strings In the Punycode encodings below, the ACE prefix is not shown. Backslashes show where line breaks have been inserted in strings too long for one line. The first several examples are all translations of the sentence "Why can't they just speak in <language>?" (courtesy of Michael Kaplan's "provincial" page [PROVINCIAL]). Word breaks and punctuation have been removed, as is often done in domain names. (A) Arabic (Egyptian): u+0644 u+064A u+0647 u+0645 u+0627 u+0628 u+062A u+0643 u+0644 u+0645 u+0648 u+0634 u+0639 u+0631 u+0628 u+064A u+061F Punycode: egbpdaj6bu4bxfgehfvwxn (B) Chinese (simplified): u+4ED6 u+4EEC u+4E3A u+4EC0 u+4E48 u+4E0D u+8BF4 u+4E2D u+6587 Punycode: ihqwcrb4cv8a8dqg056pqjye (C) Chinese (traditional): u+4ED6 u+5011 u+7232 u+4EC0 u+9EBD u+4E0D u+8AAA u+4E2D u+6587 Punycode: ihqwctvzc91f659drss3x8bo0yb (D) Czech: Pro<ccaron>prost<ecaron>nemluv<iacute><ccaron>esky U+0050 u+0072 u+006F u+010D u+0070 u+0072 u+006F u+0073 u+0074 u+011B u+006E u+0065 u+006D u+006C u+0075 u+0076 u+00ED u+010D u+0065 u+0073 u+006B u+0079 Punycode: Proprostnemluvesky-uyb24dma41a (E) Hebrew: u+05DC u+05DE u+05D4 u+05D4 u+05DD u+05E4 u+05E9 u+05D5 u+05D8 u+05DC u+05D0 u+05DE u+05D3 u+05D1 u+05E8 u+05D9 u+05DD u+05E2 u+05D1 u+05E8 u+05D9 u+05EA Punycode: 4dbcagdahymbxekheh6e0a7fei0b (F) Hindi (Devanagari): u+092F u+0939 u+0932 u+094B u+0917 u+0939 u+093F u+0928 u+094D u+0926 u+0940 u+0915 u+094D u+092F u+094B u+0902 u+0928 u+0939 u+0940 u+0902 u+092C u+094B u+0932 u+0938 u+0915 u+0924 u+0947 u+0939 u+0948 u+0902 Punycode: i1baa7eci9glrd9b2ae1bj0hfcgg6iyaf8o0a1dig0cd (G) Japanese (kanji and hiragana): u+306A u+305C u+307F u+3093 u+306A u+65E5 u+672C u+8A9E u+3092 u+8A71 u+3057 u+3066 u+304F u+308C u+306A u+3044 u+306E u+304B Punycode: n8jok5ay5dzabd5bym9f0cm5685rrjetr6pdxa (H) Korean (Hangul syllables): u+C138 u+ACC4 u+C758 u+BAA8 u+B4E0 u+C0AC u+B78C u+B4E4 u+C774 u+D55C u+AD6D u+C5B4 u+B97C u+C774 u+D574 u+D55C u+B2E4 u+BA74 u+C5BC u+B9C8 u+B098 u+C88B u+C744 u+AE4C Punycode: 989aomsvi5e83db1d2a355cv1e0vak1dwrv93d5xbh15a0dt30a5j\ (I) Russian (Cyrillic): U+043F u+043E u+0447 u+0435 u+043C u+0443 u+0436 u+0435 u+043E u+043D u+0438 u+043D u+0435 u+0433 u+043E u+0432 u+043E u+0440 u+044F u+0442 u+043F u+043E u+0440 u+0443 u+0441 u+0441 u+043A Punycode: b1abfaaepdrnnbgefbaDotcwatmq2g4l (J) Spanish: Porqu<eacute>nopuedensimplementehablarenEspa<ntilde>ol U+0050 u+006F u+0072 u+0071 u+0075 u+00E9 u+006E u+006F u+0070 u+0075 u+0065 u+0064 u+0065 u+006E u+0073 u+0069 u+006D u+0070 u+006C u+0065 u+006D u+0065 u+006E u+0074 u+0065 u+0068 u+0061 u+0062 u+006C u+0061 u+0072 u+0065 u+006E U+0045 u+0073 u+0070 u+0061 u+00F1 u+006F u+006C Punycode: PorqunopuedensimplementehablarenEspaol-fmd56a (K) Vietnamese: U+0054 u+1EA1 u+0069 u+0073 u+0061 u+006F u+0068 u+1ECD u+006B u+0068 u+00F4 u+006E u+0067 u+0074 u+0068 u+1EC3 u+0063 u+0068 u+1EC9 u+006E u+00F3 u+0069 u+0074 u+0069 u+1EBF u+006E u+0067 U+0056 u+0069 u+1EC7 u+0074 Punycode: TisaohkhngthchnitingVit-kjcr8268qyxafd2f1b9g The next several examples are all names of Japanese music artists, song titles, and TV programs, just because the author happens to have them handy (but Japanese is useful for providing examples of single- row text, two-row text, ideographic text, and various mixtures (L) 3<nen>B<gumi><kinpachi><sensei> u+0033 u+5E74 U+0042 u+7D44 u+91D1 u+516B u+5148 u+751F Punycode: 3B-ww4c5e180e575a65lsy2b (M) <amuro><namie>-with-SUPER-MONKEYS u+5B89 u+5BA4 u+5948 u+7F8E u+6075 u+002D u+0077 u+0069 u+0074 u+0068 u+002D U+0053 U+0055 U+0050 U+0045 U+0052 u+002D U+004D U+004F U+004E U+004B U+0045 U+0059 U+0053 Punycode: -with-SUPER-MONKEYS-pc58ag80a8qai00g7n9n (N) Hello-Another-Way-<sorezore><no><basho> U+0048 u+0065 u+006C u+006C u+006F u+002D U+0041 u+006E u+006F u+0074 u+0068 u+0065 u+0072 u+002D U+0057 u+0061 u+0079 u+002D u+305D u+308C u+305E u+308C u+306E u+5834 u+6240 Punycode: Hello-Another-Way--fc4qua05auwb3674vfr0b (O) <hitotsu><yane><no><shita>2 u+3072 u+3068 u+3064 u+5C4B u+6839 u+306E u+4E0B u+0032 Punycode: 2-u9tlzr9756bt3uc0v (P) Maji<de>Koi<suru>5<byou><mae> U+004D u+0061 u+006A u+0069 u+3067 U+004B u+006F u+0069 u+3059 u+308B u+0035 u+79D2 u+524D Punycode: MajiKoi5-783gue6qz075azm5e (Q) <pafii>de<runba> u+30D1 u+30D5 u+30A3 u+30FC u+0064 u+0065 u+30EB u+30F3 u+30D0 Punycode: de-jg4avhby1noc0d (R) <sono><supiido><de> u+305D u+306E u+30B9 u+30D4 u+30FC u+30C9 u+3067 Punycode: d9juau41awczczp The last example is an ASCII string that breaks the existing rules for host name labels. (It is not a realistic example for IDNA, because IDNA never encodes pure ASCII labels.) (S) -> $1.00 <- u+002D u+003E u+0020 u+0024 u+0031 u+002E u+0030 u+0030 u+0020 u+003C u+002D Punycode: -> $1.00 <-- 7.2 Decoding traces In the following traces, the evolving state of the decoder is shown as a sequence of hexadecimal values, representing the code points in the extended string. An asterisk appears just after the most recently inserted code point, indicating both n (the value preceeding the asterisk) and i (the position of the value just after the asterisk). Other numerical values are decimal. Decoding trace of example B from section 7.1: n is 128, i is 0, bias is 72 input is "ihqwcrb4cv8a8dqg056pqjye" there is no delimiter, so extended string starts empty delta "ihq" decodes to 19853 bias becomes 21 4E0D * delta "wc" decodes to 64 bias becomes 20 4E0D 4E2D * delta "rb" decodes to 37 bias becomes 13 4E3A * 4E0D 4E2D delta "4c" decodes to 56 bias becomes 17 4E3A 4E48 * 4E0D 4E2D delta "v8a" decodes to 599 bias becomes 32 4E3A 4EC0 * 4E48 4E0D 4E2D delta "8d" decodes to 130 bias becomes 23 4ED6 * 4E3A 4EC0 4E48 4E0D 4E2D delta "qg" decodes to 154 bias becomes 25 4ED6 4EEC * 4E3A 4EC0 4E48 4E0D 4E2D delta "056p" decodes to 46301 bias becomes 84 4ED6 4EEC 4E3A 4EC0 4E48 4E0D 4E2D 6587 * delta "qjye" decodes to 88531 bias becomes 90 4ED6 4EEC 4E3A 4EC0 4E48 4E0D 8BF4 * 4E2D 6587 Decoding trace of example L from section 7.1: n is 128, i is 0, bias is 72 input is "3B-ww4c5e180e575a65lsy2b" literal portion is "3B-", so extended string starts as: delta "ww4c" decodes to 62042 bias becomes 27 0033 0042 5148 * delta "5e" decodes to 139 bias becomes 24 0033 0042 516B * 5148 delta "180e" decodes to 16683 bias becomes 67 0033 5E74 * 0042 516B 5148 delta "575a" decodes to 34821 bias becomes 82 0033 5E74 0042 516B 5148 751F * delta "65l" decodes to 14592 bias becomes 67 0033 5E74 0042 7D44 * 516B 5148 751F delta "sy2b" decodes to 42088 bias becomes 84 0033 5E74 0042 7D44 91D1 * 516B 5148 751F 7.3 Encoding traces In the following traces, code point values are hexadecimal, while other numerical values are decimal. Encoding trace of example B from section 7.1: bias is 72 input is: 4ED6 4EEC 4E3A 4EC0 4E48 4E0D 8BF4 4E2D 6587 there are no basic code points, so no literal portion next code point to insert is 4E0D needed delta is 19853, encodes as "ihq" bias becomes 21 next code point to insert is 4E2D needed delta is 64, encodes as "wc" bias becomes 20 next code point to insert is 4E3A needed delta is 37, encodes as "rb" bias becomes 13 next code point to insert is 4E48 needed delta is 56, encodes as "4c" bias becomes 17 next code point to insert is 4EC0 needed delta is 599, encodes as "v8a" bias becomes 32 next code point to insert is 4ED6 needed delta is 130, encodes as "8d" bias becomes 23 next code point to insert is 4EEC needed delta is 154, encodes as "qg" bias becomes 25 next code point to insert is 6587 needed delta is 46301, encodes as "056p" bias becomes 84 next code point to insert is 8BF4 needed delta is 88531, encodes as "qjye" bias becomes 90 output is "ihqwcrb4cv8a8dqg056pqjye" Encoding trace of example L from section 7.1: bias is 72 input is: 0033 5E74 0042 7D44 91D1 516B 5148 751F basic code points (0033, 0042) are copied to literal portion: "3B-" next code point to insert is 5148 needed delta is 62042, encodes as "ww4c" bias becomes 27 next code point to insert is 516B needed delta is 139, encodes as "5e" bias becomes 24 next code point to insert is 5E74 needed delta is 16683, encodes as "180e" bias becomes 67 next code point to insert is 751F needed delta is 34821, encodes as "575a" bias becomes 82 next code point to insert is 7D44 needed delta is 14592, encodes as "65l" bias becomes 67 next code point to insert is 91D1 needed delta is 42088, encodes as "sy2b" bias becomes 84 output is "3B-ww4c5e180e575a65lsy2b" 8. Security Considerations Users expect each domain name in DNS to be controlled by a single authority. If a Unicode string intended for use as a domain label could map to multiple ACE labels, then an internationalized domain name could map to multiple ASCII domain names, each controlled by a different authority, some of which could be spoofs that hijack service requests intended for another. Therefore Punycode is designed so that each Unicode string has a unique encoding. However, there can still be multiple Unicode representations of the "same" text, for various definitions of "same". This problem is addressed to some extent by the Unicode standard under the topic of canonicalization, and this work is leveraged for domain names by Nameprep [NAMEPREP]. 9. References 9.1 Normative References [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. 9.2 Informative References [RFC952] Harrenstien, K., Stahl, M. and E. Feinler, "DOD Internet Host Table Specification", RFC 952, October 1985. [RFC1034] Mockapetris, P., "Domain Names - Concepts and Facilities", STD 13, RFC 1034, November 1987. [IDNA] Faltstrom, P., Hoffman, P. and A. Costello, "Internationalizing Domain Names in Applications (IDNA)", RFC 3490, March 2003. [NAMEPREP] Hoffman, P. and M. Blanchet, "Nameprep: A Stringprep Profile for Internationalized Domain Names (IDN)", RFC 3491, March 2003. [ASCII] Cerf, V., "ASCII format for Network Interchange", RFC 20, October 1969. [PROVINCIAL] Kaplan, M., "The 'anyone can be provincial!' page", [UNICODE] The Unicode Consortium, "The Unicode Standard", A. Mixed-case annotation In order to use Punycode to represent case-insensitive strings, higher layers need to case-fold the strings prior to Punycode encoding. The encoded string can use mixed case as an annotation telling how to convert the folded string into a mixed-case string for display purposes. Note, however, that mixed-case annotation is not used by the ToASCII and ToUnicode operations specified in [IDNA], and therefore implementors of IDNA can disregard this appendix. Basic code points can use mixed case directly, because the decoder copies them verbatim, leaving lowercase code points lowercase, and leaving uppercase code points uppercase. Each non-basic code point is represented by a delta, which is represented by a sequence of basic code points, the last of which provides the annotation. If it is uppercase, it is a suggestion to map the non-basic code point to uppercase (if possible); if it is lowercase, it is a suggestion to map the non-basic code point to lowercase (if possible). These annotations do not alter the code points returned by decoders; the annotations are returned separately, for the caller to use or ignore. Encoders can accept annotations in addition to code points, but the annotations do not alter the output, except to influence the uppercase/lowercase form of ASCII letters. Punycode encoders and decoders need not support these annotations, and higher layers need not use them. B. Disclaimer and license Regarding this entire document or any portion of it (including the pseudocode and C code), the author makes no guarantees and is not responsible for any damage resulting from its use. The author grants irrevocable permission to anyone to use, modify, and distribute it in any way that does not diminish the rights of anyone else to use, modify, and distribute it, provided that redistributed derivative works do not contain misleading author or version information. Derivative works need not be licensed under similar terms. C. Punycode sample implementation punycode.c from RFC 3492 Adam M. Costello This is ANSI C code (C89) implementing Punycode (RFC 3492). /* Public interface (would normally go in its own .h file): / #include <limits.h> enum punycode_status { punycode_bad_input, / Input is invalid. / punycode_big_output, / Output would exceed the space provided. / punycode_overflow / Input needs wider integers to process. / #if UINT_MAX >= (1 << 26) - 1 typedef unsigned int punycode_uint; typedef unsigned long punycode_uint; enum punycode_status punycode_encode( punycode_uint input_length, const punycode_uint input[], const unsigned char case_flags[], punycode_uint output_length, char output[] ); /* punycode_encode() converts Unicode to Punycode. The input / / is represented as an array of Unicode code points (not code / / units; surrogate pairs are not allowed), and the output / / will be represented as an array of ASCII code points. The / / output string is not null-terminated; it will contain / / zeros if and only if the input contains zeros. (Of course / / the caller can leave room for a terminator and add one if / / needed.) The input_length is the number of code points in / / the input. The output_length is an in/out argument: the / / caller passes in the maximum number of code points that it / / can receive, and on successful return it will contain the / / number of code points actually output. The case_flags array / / holds input_length boolean values, where nonzero suggests that / / the corresponding Unicode character be forced to uppercase / / after being decoded (if possible), and zero suggests that / / it be forced to lowercase (if possible). ASCII code points / / are encoded literally, except that ASCII letters are forced / / to uppercase or lowercase according to the corresponding / / uppercase flags. If case_flags is a null pointer then ASCII / / letters are left as they are, and other code points are / / treated as if their uppercase flags were zero. The return / / value can be any of the punycode_status values defined above / / except punycode_bad_input; if not punycode_success, then / / output_size and output might contain garbage. / enum punycode_status punycode_decode( punycode_uint input_length, const char input[], punycode_uint output_length, punycode_uint output[], unsigned char case_flags[] ); /* punycode_decode() converts Punycode to Unicode. The input is / / represented as an array of ASCII code points, and the output / / will be represented as an array of Unicode code points. The / / input_length is the number of code points in the input. The / / output_length is an in/out argument: the caller passes in / / the maximum number of code points that it can receive, and / / on successful return it will contain the actual number of / / code points output. The case_flags array needs room for at / / least output_length values, or it can be a null pointer if the / / case information is not needed. A nonzero flag suggests that / / the corresponding Unicode character be forced to uppercase / / by the caller (if possible), while zero suggests that it be / / forced to lowercase (if possible). ASCII code points are / / output already in the proper case, but their flags will be set / / appropriately so that applying the flags would be harmless. / / The return value can be any of the punycode_status values / / defined above; if not punycode_success, then output_length, / / output, and case_flags might contain garbage. On success, the / / decoder will never need to write an output_length greater than / / input_length, because of how the encoding is defined. / / Implementation (would normally go in its own .c file): / #include <string.h> / Bootstring parameters for Punycode / enum { base = 36, tmin = 1, tmax = 26, skew = 38, damp = 700, initial_bias = 72, initial_n = 0x80, delimiter = 0x2D }; / basic(cp) tests whether cp is a basic code point: / #define basic(cp) ((punycode_uint)(cp) < 0x80) / delim(cp) tests whether cp is a delimiter: / #define delim(cp) ((cp) == delimiter) / decode_digit(cp) returns the numeric value of a basic code / / point (for use in representing integers) in the range 0 to / / base-1, or base if cp is does not represent a value. / static punycode_uint decode_digit(punycode_uint cp) return cp - 48 < 10 ? cp - 22 : cp - 65 < 26 ? cp - 65 : cp - 97 < 26 ? cp - 97 : base; / encode_digit(d,flag) returns the basic code point whose value / / (when used for representing integers) is d, which needs to be in / / the range 0 to base-1. The lowercase form is used unless flag is / / nonzero, in which case the uppercase form is used. The behavior / / is undefined if flag is nonzero and digit d has no uppercase form. / static char encode_digit(punycode_uint d, int flag) return d + 22 + 75 (d < 26) - ((flag != 0) << 5); /* 0..25 map to ASCII a..z or A..Z / / 26..35 map to ASCII 0..9 / / flagged(bcp) tests whether a basic code point is flagged / / (uppercase). The behavior is undefined if bcp is not a / / basic code point. / #define flagged(bcp) ((punycode_uint)(bcp) - 65 < 26) / encode_basic(bcp,flag) forces a basic code point to lowercase / / if flag is zero, uppercase if flag is nonzero, and returns / / the resulting code point. The code point is unchanged if it / / is caseless. The behavior is undefined if bcp is not a basic / / code point. / static char encode_basic(punycode_uint bcp, int flag) bcp -= (bcp - 97 < 26) << 5; return bcp + ((!flag && (bcp - 65 < 26)) << 5); / Platform-specific constants / / maxint is the maximum value of a punycode_uint variable: / static const punycode_uint maxint = -1; / Because maxint is unsigned, -1 becomes the maximum value. / / Bias adaptation function / static punycode_uint adapt( punycode_uint delta, punycode_uint numpoints, int firsttime ) punycode_uint k; delta = firsttime ? delta / damp : delta >> 1; / delta >> 1 is a faster way of doing delta / 2 / delta += delta / numpoints; for (k = 0; delta > ((base - tmin) tmax) / 2; k += base) { delta /= base - tmin; return k + (base - tmin + 1) * delta / (delta + skew); /* Main encode function / enum punycode_status punycode_encode( punycode_uint input_length, const punycode_uint input[], const unsigned char case_flags[], punycode_uint output_length, char output[] ) punycode_uint n, delta, h, b, out, max_out, bias, j, m, q, k, t; /* Initialize the state: / n = initial_n; delta = out = 0; max_out = output_length; bias = initial_bias; /* Handle the basic code points: / for (j = 0; j < input_length; ++j) { if (basic(input[j])) { if (max_out - out < 2) return punycode_big_output; output[out++] = case_flags ? encode_basic(input[j], case_flags[j]) : input[j]; / else if (input[j] < n) return punycode_bad_input; / / (not needed for Punycode with unsigned code points) / h = b = out; / h is the number of code points that have been handled, b is the / / number of basic code points, and out is the number of characters / / that have been output. / if (b > 0) output[out++] = delimiter; / Main encoding loop: / while (h < input_length) { / All non-basic code points < n have been / / handled already. Find the next larger one: / for (m = maxint, j = 0; j < input_length; ++j) { / if (basic(input[j])) continue; / / (not needed for Punycode) / if (input[j] >= n && input[j] < m) m = input[j]; / Increase delta enough to advance the decoder's / / <n,i> state to <m,0>, but guard against overflow: / if (m - n > (maxint - delta) / (h + 1)) return punycode_overflow; delta += (m - n) (h + 1); n = m; for (j = 0; j < input_length; ++j) { /* Punycode does not need to check whether input[j] is basic: / if (input[j] < n / \|\| basic(input[j]) / ) { if (++delta == 0) return punycode_overflow; if (input[j] == n) { / Represent delta as a generalized variable-length integer: / for (q = delta, k = base; ; k += base) { if (out >= max_out) return punycode_big_output; t = k <= bias / + tmin / ? tmin : / +tmin not needed / k >= bias + tmax ? tmax : k - bias; if (q < t) break; output[out++] = encode_digit(t + (q - t) % (base - t), 0); q = (q - t) / (base - t); output[out++] = encode_digit(q, case_flags && case_flags[j]); bias = adapt(delta, h + 1, h == b); delta = 0; ++delta, ++n; output_length = out; return punycode_success; /* Main decode function / enum punycode_status punycode_decode( punycode_uint input_length, const char input[], punycode_uint output_length, punycode_uint output[], unsigned char case_flags[] ) punycode_uint n, out, i, max_out, bias, b, j, in, oldi, w, k, digit, t; /* Initialize the state: / n = initial_n; out = i = 0; max_out = output_length; bias = initial_bias; /* Handle the basic code points: Let b be the number of input code / / points before the last delimiter, or 0 if there is none, then / / copy the first b code points to the output. / for (b = j = 0; j < input_length; ++j) if (delim(input[j])) b = j; if (b > max_out) return punycode_big_output; for (j = 0; j < b; ++j) { if (case_flags) case_flags[out] = flagged(input[j]); if (!basic(input[j])) return punycode_bad_input; output[out++] = input[j]; / Main decoding loop: Start just after the last delimiter if any / / basic code points were copied; start at the beginning otherwise. / for (in = b > 0 ? b + 1 : 0; in < input_length; ++out) { / in is the index of the next character to be consumed, and / / out is the number of code points in the output array. / / Decode a generalized variable-length integer into delta, / / which gets added to i. The overflow checking is easier / / if we increase i as we go, then subtract off its starting / / value at the end to obtain delta. / for (oldi = i, w = 1, k = base; ; k += base) { if (in >= input_length) return punycode_bad_input; digit = decode_digit(input[in++]); if (digit >= base) return punycode_bad_input; if (digit > (maxint - i) / w) return punycode_overflow; i += digit w; t = k <= bias /* + tmin / ? tmin : / +tmin not needed / k >= bias + tmax ? tmax : k - bias; if (digit < t) break; if (w > maxint / (base - t)) return punycode_overflow; w = (base - t); bias = adapt(i - oldi, out + 1, oldi == 0); /* i was supposed to wrap around from out+1 to 0, / / incrementing n each time, so we'll fix that now: / if (i / (out + 1) > maxint - n) return punycode_overflow; n += i / (out + 1); i %= (out + 1); / Insert n at position i of the output: / / not needed for Punycode: / / if (decode_digit(n) <= base) return punycode_invalid_input; / if (out >= max_out) return punycode_big_output; if (case_flags) { memmove(case_flags + i + 1, case_flags + i, out - i); / Case of last character determines uppercase flag: / case_flags[i] = flagged(input[in - 1]); memmove(output + i + 1, output + i, (out - i) sizeof output); output[i++] = n; output_length = out; return punycode_success; /* Wrapper for testing (would normally go in a separate .c file): / #include <assert.h> #include <stdio.h> #include <stdlib.h> #include <string.h> / For testing, we'll just set some compile-time limits rather than / / use malloc(), and set a compile-time option rather than using a / / command-line option. / enum { unicode_max_length = 256, ace_max_length = 256 static void usage(char argv) "%s -e reads code points and writes a Punycode string.\n" "%s -d reads a Punycode string and writes code points.\n" "Input and output are plain text in the native character set.\n" "Code points are in the form u+hex separated by whitespace.\n" "Although the specification allows Punycode strings to contain\n" "any characters from the ASCII repertoire, this test code\n" "supports only the printable characters, and needs the Punycode\n" "string to be followed by a newline.\n" "The case of the u in u+hex is the force-to-uppercase flag.\n" , argv[0], argv[0]); static void fail(const char msg) static const char too_big[] = "input or output is too large, recompile with larger limits\n"; static const char invalid_input[] = "invalid input\n"; static const char overflow[] = "arithmetic overflow\n"; static const char io_error[] = "I/O error\n"; /* The following string is used to convert printable / / characters between ASCII and the native charset: / static const char print_ascii[] = " !\"#$%&'()+,-./" int main(int argc, char *argv) enum punycode_status status; int r; unsigned int input_length, output_length, j; unsigned char case_flags[unicode_max_length]; if (argc != 2) usage(argv); if (argv[1][0] != '-') usage(argv); if (argv[1][2] != 0) usage(argv); if (argv[1][1] == 'e') { punycode_uint input[unicode_max_length]; unsigned long codept; char output[ace_max_length+1], uplus[3]; int c; / Read the input code points: / input_length = 0; for (;;) { r = scanf("%2s%lx", uplus, &codept); if (ferror(stdin)) fail(io_error); if (r == EOF \|\| r == 0) break; if (r != 2 \|\| uplus[1] != '+' \|\| codept > (punycode_uint)-1) { if (input_length == unicode_max_length) fail(too_big); if (uplus[0] == 'u') case_flags[input_length] = 0; else if (uplus[0] == 'U') case_flags[input_length] = 1; else fail(invalid_input); input[input_length++] = codept; / Encode: / output_length = ace_max_length; status = punycode_encode(input_length, input, case_flags, &output_length, output); if (status == punycode_bad_input) fail(invalid_input); if (status == punycode_big_output) fail(too_big); if (status == punycode_overflow) fail(overflow); assert(status == punycode_success); / Convert to native charset and output: / for (j = 0; j < output_length; ++j) { c = output[j]; assert(c >= 0 && c <= 127); if (print_ascii[c] == 0) fail(invalid_input); output[j] = print_ascii[c]; output[j] = 0; r = puts(output); if (r == EOF) fail(io_error); return EXIT_SUCCESS; if (argv[1][1] == 'd') { char input[ace_max_length+2], p, pp; punycode_uint output[unicode_max_length]; / Read the Punycode input string and convert to ASCII: / fgets(input, ace_max_length+2, stdin); if (ferror(stdin)) fail(io_error); if (feof(stdin)) fail(invalid_input); input_length = strlen(input) - 1; if (input[input_length] != '\n') fail(too_big); input[input_length] = 0; for (p = input; p != 0; ++p) { pp = strchr(print_ascii, p); if (pp == 0) fail(invalid_input); p = pp - print_ascii; /* Decode: / output_length = unicode_max_length; status = punycode_decode(input_length, input, &output_length, output, case_flags); if (status == punycode_bad_input) fail(invalid_input); if (status == punycode_big_output) fail(too_big); if (status == punycode_overflow) fail(overflow); assert(status == punycode_success); / Output the result: / for (j = 0; j < output_length; ++j) { r = printf("%s+%04lX\n", case_flags[j] ? "U" : "u", (unsigned long) output[j] ); if (r < 0) fail(io_error); return EXIT_SUCCESS; return EXIT_SUCCESS; / not reached, but quiets compiler warning */ Author's Address Adam M. Costello University of California, Berkeley Full Copyright Statement Copyright (C) The Internet Society (2003). All Rights Reserved. This document and translations of it may be copied and furnished to others, and derivative works that comment on or otherwise explain it or assist in its implementation may be prepared, copied, published and distributed, in whole or in part, without restriction of any kind, provided that the above copyright notice and this paragraph are included on all such copies and derivative works. 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User Contributions: I have never known a love like this in all my life just through email, and it's the only love I ever want to know. its not been long we met and am going crazy in love with you; you are best and my lover, Baby, you complete me. I will always love you, no matter what may come I am ready to visit you in your country, if only you will welcome me in your heart i promise to take care of you and never hurt you my dear, so what you say my dear?tomorrow i have a free time from work then i will use that opportunity get the vacation fixed, honestly baby I wish you could get in contact with my personal lawyer ? Sep 11, 2023 @ 2:02 am Alta traicion interna en la asociación posible sibl posible situación de guerra pido a apoyo a la gente que este conmigo ese puso en riesgo a mi familia y destroza la infancia de mi hija por su traición y es imperdonable para mk Comment about this RFC, ask questions, or add new information about this topic:	{"url":"http://www.faqs.org/rfcs/rfc3492.html","timestamp":"2024-11-08T08:55:24Z","content_type":"application/xhtml+xml","content_length":"84880","record_id":"<urn:uuid:743bbc6e-b95d-4d1a-a32f-1cfed69aeb80>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00351.warc.gz"}
Basic considerations on gravitation The derivation of Newton's law is reviewed and applied to a mass with constant velocity on a curved trajectory as the basic element of a system of heavenly bodies. The application of Newton's law to masses on the earth's surface is also addressed. The splitting of the Kepler constants is considered. Pub Date: December 1990 □ Black Holes (Astronomy); □ Celestial Bodies; □ Earth Surface; □ Gravitation; □ Kepler Laws; □ Newton Second Law; □ Center Of Gravity; □ Stellar Mass; □ Trajectories; □ Physics (General)	{"url":"https://ui.adsabs.harvard.edu/abs/1990Asnau..27..112H/abstract","timestamp":"2024-11-03T19:01:59Z","content_type":"text/html","content_length":"32884","record_id":"<urn:uuid:50103cac-4d3c-4cdd-858c-8a4dd5e09a57>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00497.warc.gz"}
Making A Point Says here in the paper that some guy in Germany just discovered the reason he'd been having headaches and sinus trouble for the last fifteen years is that he's had a pencil in his head. It was four inches long and went all the way to his eye socket. You would think someone would have noticed at the time it went in, but maybe if it was a clean wound and only the eraser was sticking out, his parents just figured he'd grown a mole. I can imagine this sort of delayed discovery in the U.S.A., because health insurance is so expensive, but you'd think in Germany someone would have x-rayed his sinuses by now. Anyway, a surgeon was duly dispatched to get the lead out. Photoshop? I don't think so. Sharpie. When I was in first grade, I too was stabbed with a pencil. The lead broke off in the meaty part of my hand, and there's a scar there to this day. We didn't have as many safety precautions in place as kids do now. No helmets, no shin guards, no seat belts, no locks on the cabinet under the sink with the Drano in it (although liquor cabinets might have been buttoned up), nothing to keep us from sticking a knife in the electrical outlets. There were some attempts at safety made at school. We were all issued tiny round scissors that you could bend up construction paper with, unless you were left-handed, and then you just had to hope it was glue-and-macaroni day. Memory being what it is, I don't know if I stabbed myself or some other kid did, but I assume it was some little boy, because why would I stab myself in the hand with a pencil? I don't think he meant any harm, either, or I would have remembered who did it. He was just a boy in possession of a sharp object and he felt something needed to be stabbed, fast. He might have been playing World War II and was full of boy-juice and mistook my palm for the stout heart of a Japanese warrior. And I think it was a little boy because little girls hurt each other whole different ways. Like Murooj Abbas. Murooj sat in front of me in first grade and one day she turned around and asked if she could borrow my brand new big square gum eraser, so I gave it to her. A few minutes later she turned around again with what I would learn years later is called a shit-eating grin on her face. She held her hand out to mine and dumped in a few crumbs of eraser, and turned around again. I never told anybody. I had grown up to that point with no defenses at all against cruelty and humiliation, because I had never experienced it, even though I had several older siblings. I had no idea what to do, so I just stored it in the only memory-closet I have that is reliably lucid: the humiliation closet. Most of my humiliations in life have been self-inflicted, so each incident of being targeted by someone else is crystal clear. I can tick them off in order, one by one. Dave also has a scar on his hand from a pencil wound. He says he invited a boy to stab it out of an overdeveloped sense of justice, after he'd stuck a pencil upright under the kid's butt just as he was sitting down. It's one of the things we have in common. We like mountains. We like beer. People want to stab us. 68 comments: 1. I generally like short posts, but I didn't want you to stop this one. I think the only point was the pencil, but there is a laugh or memory in every paragraph. Maybe because I am left handed the scissor/ macaroni and glue thing really got me. 1. There is a certain limit to the number of words people will read voluntarily. They've tested it. Even I have noticed that I can be reading something on line that is really, really good, and if it goes past a certain point, I have to scroll down to see what kind of investment I need to make. I don't understand this. 2. What is weirder is that I think the number of words we are willing to sit and read is fewer online than off. Meaning, I expect, if I am sitting at my computer, that what I am reading will be short and to the point. Is it because there are all these other things online that are beckoning to us and distracting us? Unlike with a book, say... 3. Oh true. I get antsy after about a thousand words online. But I can sit and read a book for hours. Even an e-reader. 4. I have noticed the same thing about my lower tolerance for wordiness on line but so far have chalked it up to the uncomfortable desk chair that I am reluctant to replace since it was my dad's, even though it makes my sit-upon-place tired. But he never sat in it in front of a computer. And he had a much bone-ier butt than I do so maybe he found it comfortable. Wait...how'd this get from word limits to sore butts? Murr, this is YOUR department! (Very funny post, btw.) 5. I don't know what it's about either, since the advent of computers has coincided with my own personal mental erosion. Could be just a coincidence. BTW, if your dad had a bonier butt, he should be tireder than you. 2. Can I join you in your foreign-objects-embedded-in-body club? Tip of a porcupine quill, under left index fingernail. Don't ask. 1. No, we're asking. 2. It's quite embarrassing. I was NOT rassling a porcupine, I was merely decluttering an ancient container of quills my teacher mom had gifted me. Cripes, it hurt. The tip broke off and I tried to pry it out with a needle but I couldn't, on account of the barb, of course. It has worked its way halfway down my nail bed and - at the rate it's going - I fully expect it to reach my heart and kill me by the time I am 90 :) 3. "I was merely decluttering an ancient container of quills." I am proud to host such a sentence. 4. High praise from you, Murr; I don't know whether to bow or faint ... but truthfully, THAT part wasn't even intended to be funny! But your reaction sure made me chuckle ;) 3. I also did the sit-down-on-a-pencil bit to a friend in 4th grade. It was my revenge for whatever he did to me, but I can't remember what it was.I had to stay after school for that one. 1. If you get it just right, the pencil should plumb disappear! See previous proctologist post. 4. Ow. Just ow. I've been kicked, punched, slapped, cut, burned, had my skin crushed in pliers and been run over with a motorcycle all without holding a grudge, but I think I'd take serious offense to being stabbed with a pencil. We all have our limits. 1. Oh, Diane, if that was one person doing all that to you, I'd suggest taking it personally. 2. Nope, those were my friends. It's pretty hard to avoid a bit of accidental damage when your hobbies include dirt-biking, automotive repair, team sports, and kickboxing. :-) You wanna believe I'd take it personally if they'd intentionally hurt me! 5. When we were three, my twin brother decided to test the theory that if you throw a bullet in the fireplace, it will explode. I carried a piece of brass in my shin for the next fifteen years until it started aching in the cold when I went to the school doctor and he x-rayed my leg and saw that there was, indeed, a piece of brass in my leg. He was amazed. I was amazed by the elegant beauty of my shin-bone. Ever since then, I have cherished my x-rays. I have beautiful bones!! DAve's pencil impaled hand is creepy. 1. I didn't get that bullet thing so I asked Dave about it. At which point it occurred to me that you meant WHEN THERE IS A FIRE GOING. For some reason I just had you throwing a bullet in a fireplace. Seemed to me that most three-year-olds can't get that much momentum on a thrown bullet. 2. That's right - you were one of those city kids with central heat and stuff. Yes, if you put a bullet in prolonged contact with heat - a fire, say, the bullet will explode. Why would anyone throw a bullet into an empty fireplace? 3. Well, and more to the point (har), a city kid with no bullets. You know how dumb we were? When we got fireworks, sparklers et al, I thought the punk was a firework too. I waved its smoky little ass around. Whee. And, you see, the throwing the bullet into an empty fireplace didn't make sense to me either--that's why I asked Dave, who gave me that look I get sometimes. 6. Anyone with a brother is lucky they made it out of childhood. My brothers were forever throwing random things into the outdoor burn pit, to see what sort of percussive and/or explosive result might ensue. My sister and I learned to be far away when it was their turn for Outside Chores. 1. Do you still have your original complement of brothers? 2. What is it with boys and explosions? My older brothers blew the front porch off the schoolhouse. 3. How many of you are there? Left? 7. Remind me not to go with you to the mountains to drink beer. 1. Okay, but you're missing a bet, there. Odds are YOU'D be the stabber. 8. I wonder the average number of visible childhood scars each of us carries. I have two visible, one invisible (on my scalp). 1. I have a scalp one from where Danny Hall threw a brick up in the air and yelled BOMBS OVER TOKYO! and it landed on my head. These days, any scars I have that have been covered in hair are in danger of being revealed. 2. I shouldn't compete on that- raising an orphaned baby raccoon makes for a WHOLE lot of scars. They take you for a safe retreat tree when they feel threatened.... 3. I guess the only thing worse would be to raise a baby badger who tries to find a hole in you to retreat to. 9. Perhaps it's to do with Darwin's survival theory. I recall one boy about 10 or 11, being asked to return the staple gun (a bit bigger than the thing that staples grocery dockets) to the school office. He stapled another lad's pants to his backside. 1. That strikes me as being an excellent solution to the scourge of sagging. 2. Hahaha.Maybe we should suggest it to the City Fathers of NJ who have just banned trousers more than 3" below hip 3. Them ain't trousers! Them is fart veils! 10. Holy shit....you just reminded me of an incident I had forgotten. I once accidentally managed to stab myself in the palm of my hand with a very sharp pencil. (I was a very clumsy child) I ran screaming to my Mom with it hanging out of my hand. She pulled it out....examined the wound and told me I would live which I have done for 80 some years...no scar.....just had the black spot from the lead under the skin where it healed. How did any of us survive childhood? 1. Well, hell, maybe I DID stab myself in the hand with a pencil. I've never had very good hand-eye coordination. I've seen many a black pencil spot in people's hands. I think we all did it. And those of us who survived childhood in the days before Padding are tough old birds. 11. So, the guy with the pencil in his head - was this by any chance the same guy with the four inch blade in his back? My body is clearly fully equipped with anti-pencil preservation mechanisms so I've never been pencil-stabbed. In fact I've never been stabbed with anything except occasionally stabbed in the back or stabbed with pity. Ooh, I felt quite funny looking at those last two pics.... 1. You must be a conciliatory fellow. Yeah, I wonder about the number of news items I read that involve major personal impalings. I'm almost sure I would notice. 12. I would've had nothing to say to Murooj either. Let's find her. Let's see why she did it. 1. OMG, you're such a liberal. I'm reaching back here. Northern Virginia. Probably an embassy kid. Ignored by her daddy. Her brother is probably up to all kinds of nonsense now. 13. It's hard to imagine how kids grow up to be reasonable adults, given what we had to go through to get there. Your penchant for being stabbed trumps anything that happened to me, though. :-) 1. I seriously wouldn't call it a penchant... 14. Your husband looks like a patient man. 1. Well. Yes. Except when he's not. 15. What do you mean..girls use other methods?! Jeff S. may still have lead in his hand from the day he snapped my bra. 1. WHAM! You go! 16. Some of these pencil incidents give a whole new meaning to the phrase, "Get the lead out." 1. Also, we should always put the rubber in first. Wait. 17. You are so right! Girls get back other ways like when Linda Anderson just turned around and barfed on me and my desk and she had corn at lunch.......yup, girls are ruthless! I just knew when the teacher walked over Linda was gonna say...... She did it! Thank God she was green and had corn in her teeth! 1. A personal, directed, targeted barfing? REALLY? I would not have survived that. Really. You would not be reading anything in this space today. 18. I managed to stab myself in the side of the calf with a pencil. I still have the spot - it's sort of blue green. My mother also has blue green pencil spots on her knee, when she knelt on three pencils. Girls are usually evil in other ways, such as Dawn C. who, in freshman Algebra, turned to me and said, "I wouldn't talk to you in junior high because you had a big butt, but you're in cross country now and you don't have a big butt so I'll talk to you." I was flabbergasted. I was fat? And from that point forward, I believed I was fat until I made it so. Apparently, I was more boy-like in my evil. When a boy took the seat I had claimed for an 8 hour ride - and then laughed at me - I told him I felt like ripping his face off. He challenged me to do it. I tried. He knocked me to the floor of the van and pounded on my arm. Fortunately for me, it was November and my long sleeves covered the bruises. He got to walk around high school for a couple of weeks with fingernail scratches on his cheek. I bet he still doesn't understand that what got his face scratched wasn't taking my seat. It was laughing at me. 1. That's it. I'm declaring it. From now on, henceforth, I am granting permanent episodic amnesia for anything heard in seventh or eighth grade. Enough of this. I wasn't permanently scarred, but I remember every one. 19. Belinda Gleason accused me of stealing her eraser and we had to go to he Principal's office but she was busted when they found the eraser in Belinda's desk. I also have a blue mark under my right eyebrow. My parent's said I stuck a pencil in my eye while riding in the car. They called me a blue-dot-for-sure-shot. (Remember the old flash bulb commercials?) Anyway, now I wonder if my sister stabbed me with pencil in the back of my head and it is still there. I can kind of feel a soft bump at the back of my head. 1. You know? The soft spot is something else. Something else altogether. And I am so glad you didn't have to live with the knowledge of your own besmirched innocence, while the adults did not find the eraser. 20. Homer Simpson's experience should be a lesson to us all. I liked his doctor's explanation of how he never saw it. 1. Holy crap! Well done, susan! I especially like his doctor saying "I'll go throw myself out now." 21. A pencil in his sinuses? Man. Pencils are dangerous; we should require the Dept. of Health and Safety to issue recalls, or at least post some sort of warning on the dreaded pencil. 1. The Ticonderoga Act of 2013. I can now see why we had rounded scissors. Just looking at this comment section I am moved to report that pencil stabbings are rife. 2. Then there was the Eberhard-Faber resolution of 1986 calling for a reduction in sharpness. 3. No reduction of sharpness in Jono-land! 22. 53 comments on the post about using a pencil as a weapon. Now you have done it. Children will be expelled for bringing pencils to school!! 1. But I think every teacher must be packing a pencil. That's the best way to keep all the little buggers safe. 2. Exactly what I was thinking, Tabor. 23. A bit later than childhood....I walked into a glass door which broke and cut my knee open, it was too mangled to stitch so the doctor just smoothed it as best he could after cleaning it, then put on a bandage. It healed over all lumpy but eventually smoothed over about twenty years later. Just recently, about 5 years ago, a lump formed in the scar tissue and a tiny shard of glass worked its way out! 24. Good grief Murr, I feel quite faint. I still have a chunk of broken bayonet in my shoulder from when the Japs invaded Manchuria in 1931; long story. We should wear our wounds with pride. Except in cold weather. Roth x 25. When I was a kid I had a friend whose sister stabbed his hand with scissors, about where you were pencil-stabbed. Not a pair of rounded kiddie scissors, either. They couldn't find an inch-long piece of the point. When he was sixteen, his hand (inexplicably?) festered big-time. Surgeon removed the point of the scissor from years before. True story; I am not creative enough to make this stuff up. Some of my friends were not the sharpest tools in the kit, need I say. 1. How does that even happen? How does a scissors-point sit quietly for ten years and then blow up? And why is it always the evil sister? 26. Doesn't anyone remember Bill Cosby's bit about the kid who threw a bullet into the furnace in shop class? Shop teacher: "Ya KNOW....you throw a bullet in the furnace, it reflects on yer mother!". Suspect student: "I didn't throw that bullet in the furnace, and don't you be talkin' 'bout my mutha!"	{"url":"https://murrbrewster.blogspot.com/2013/06/making-point.html","timestamp":"2024-11-04T00:49:58Z","content_type":"application/xhtml+xml","content_length":"255893","record_id":"<urn:uuid:61bc1df2-74d4-42c5-84c6-5056a0964c42>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00151.warc.gz"}
AoC 2016/11 - Initial algorithm: Dijkstra ETOOBUSY đźš€ minimal blogging for the impatient AoC 2016/11 - Initial algorithm: Dijkstra On with Advent of Code puzzle 11 from 2016: using Dijkstra Algorithm as an initial solution. In the last post of this series (AoC 2016/11 - Initial data structure) we left with two data structures populated for the task: the initial state and the goal state. In itself, the problem can be thought as a search over a directed graph. Each state is represented as a node in the graph, while transitions are represented by edges. In our case, we have to find the length of the shortest path from the initial to the goal state. Does this ring a bell? Thereâ€™s a whole host of algorithms on shortest paths, and one of the most celebrated has been described by Edsger Dijkstra. This is interesting because this algorithm applies to the cases where we want some locality, i.e. it deals with a single source and a customizable set of goals (that is, one in our case). I recently wrote about my implementation DijkstraFunction in cglib (see Dijkstra Algorithm - as functions only for the details), and that is the one we will reuse here: use DijkstraFunction 'dijkstra'; my $outcome = dijkstra( start => \@start, goals => [\@goal], distance => sub { 1 }, successors => \&successors_for, identifier => \&id_of, say $outcome->{distance_to}->(\@goal); The output of the function is a hash with two keys. The one we are actually interested into here is only distance_to, because itâ€™s what the puzzle asks us. We might also print out the whole solution using path_to, though. The function requires us a few input parameters: • start: this is easy because we can provide our starting state as a reference to the array @start, which we built in the previous post in this series; • goals: this is a reference to an array containing a list of goals we are interested into. In our case, we just provide one, that is a reference to array @goal; • distance: in the algorithm, edges between nodes might have a variable weight. In our case, two adjacent nodes represent states that are separated by a single step of the elevator, so the cost of each action is always 1; • successors: a reference to a sub that takes a state as input, and provides back a list of states that can be reached. In graph terms, it provides all nodes that can be reached from a specific node (remember, the graph is directed!); • identifier: each node in the graph must be recognized by an identifier, so that we can properly track when we land on the same node time and again. This function takes care to look into a node/ state and produce a suitable identifier that is always consistent (i.e. identical states yield the same identifier, even if they come from two different underlying arrays). At this pointâ€¦ we only lack successors_for and id_of, right? This will be meat for future posts! Before concluding, anyway, a little word on the choice of the algorithm. The A* Algorithm might just as well address our concerns, and in a more efficient way. Butâ€¦ that algorithm requires us to build a heuristic on our estimation of how distant we are from the solution, and this must also be either exact (in which case we would already have the solution!) or underestimate the actual value. Which meansâ€¦ more work for the programmer! Hence, at this stage we keep it simpler and stick with Dijkstra Algorithm instead.	{"url":"https://github.polettix.it/ETOOBUSY/2021/01/08/aoc2016-11-initial-algorithm/","timestamp":"2024-11-05T07:48:53Z","content_type":"text/html","content_length":"14259","record_id":"<urn:uuid:a8a52ee5-57f4-4c0c-bb69-6ff7be22c1f8>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00033.warc.gz"}
3rd Grade Multiplication Timed Worksheets Mathematics, particularly multiplication, creates the foundation of countless academic self-controls and real-world applications. Yet, for several students, understanding multiplication can position a difficulty. To resolve this obstacle, educators and moms and dads have actually embraced an effective tool: 3rd Grade Multiplication Timed Worksheets. 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Urging consistent practice, providing support, and producing a positive learning setting are valuable actions.	{"url":"https://crown-darts.com/en/3rd-grade-multiplication-timed-worksheets.html","timestamp":"2024-11-12T06:34:43Z","content_type":"text/html","content_length":"29653","record_id":"<urn:uuid:914f9766-720e-419a-9a1a-fbe40a3ef780>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00073.warc.gz"}
Approximate Match with Multiple Criteria by INDEX & MATCH - Free Excel Tutorial In Excel, INDEX function and MATCH function are often used together for returning data from specific position. And MATCH function is one of Excel lookup & reference functions that can return approximate value by setting match type. Above all, through generating a formula with INDEX and MATCH function, we can get an approximate value properly based on given data and cell or range In this article, through explaining the example below, we will introduce you the formula with INDEX and MATCH used that can help you returning approximate value. If you meet similar scenarios in your daily work, you can directly use it. In this example, we want to get return level in F4 based on two entries “subject” in F2 and “score” in F3. As there is no definition to explain the scope of level A, B and C exactly, so we can lookup entered score from named range “Score” and return an approximate level from “Level” correspondingly. For different subjects, the correspondences between score and level are different. For math, for score of 60, we can get a C-level, but for history, you cannot get a C-level until you get a score of 80. So, to return a proper approximate level from “Level”, except the entered score, we also need to lookup subject from range “Subject”, then return level based on this subject’s score-level Before creating a formula to solve this problem, in order to illustrate the formula, we defined three named ranges “Subject” (A2:A7), “Score” (B2:B7), and “Level” (C2:C7). In this article, to approach our goal, we will apply INDECT & MATCH functions to create formula, with the help from IF function inside as argument. To return level based on input subject and score: 1. There are two conditions to determine the returned level: subject and score. 2. As “History” can be found from named range “Subject”, so we can through searching for “History” (in F2) from named range “Subject” to get score and level corresponding relationship. 3. Through locating a score from named range “Score”, we can get a level for this score correspondingly. 4. In this example, there is no level for score “105” exactly. So, we can only return an approximate level based on the two entries refer to the corresponding relationship between score and level in above table. In Excel, INDEX and MATCH functions are good partners for searching. MATCH function can return the position based on searching for specific content, and INDEXT can query the corresponding data according to the position. In this example, MATCH function returns proper position of score for subject “History”, and INDEX function can return proper level based on the position. With the help from IF function, we create below formula to solve this problem: Input formula =INDEX(Level,MATCH(F3,IF(Subject=F2,Score),1)) into F4, as this is an array formula, so press Ctrl+Shift+Enter, verify that level B is returned properly. In Excel, refer to approximate match rules, score in “Score” column is the starter value for corresponding level. As level B is for score which is greater than or equal to 100, level A is for score which is greater than or equal to 120, so we think level B is correct for score 105. More details please see explanation part. a. INDEX function returns a value or a reference based on given cell or range reference. For array form: =INDEX(array, row_num, [column_num]) For reference form: =INDEX(reference, row_num, [column_num], [area_num]) There are two forms of INDEX functions. We apply array form as the first argument to INDEX is an array constant. Usually INDEX returns reference of the intersection of a particular row and column when applying INDEX with reference form. b. MATCH function returns the relative position of a cell from a range which cell contains specific item. MATCH(lookup_value, lookup_array, [match_type]) c. IF function returns “true value” or “false value” based on the result of provided logical test. It is one of the most popular function in Excel. // for IF, logical test “Subject=F2”, value_if_true is named range “score”, value_if_false is omitted // for MATCH, lookup_value is F3 (105),lookup_array is IF function return value, match_type is “1” // for INDEX, array is named range “Level”, row number is MATCH function return value a. The formula’s core functions are INDEX and MATCH, but IF function can help us list all scores for subject “History”. In logical test argument, we input “Subject=F2” as we are looking for history from “Subject”. Expand values in “Subject” and “Score”, we get below expression: If values in array {“Math”;”Math”;”Math”;”History”;”History”;”History”} match “History”, then corresponding values from array {60;80;100;80;100;120} are returned. So, we get below array after running IF function. b. IF function returned array is delivered to MATCH function as lookup_array. Now, in MATCH(F3,IF(Subject=F2,Score),1), lookup_value is F3 “105”, lookup_array is {FALSE;FALSE;FALSE;80;100;120}, match_type is “1”. For match type, there are three values “0”, “1”, and “-1”. The default value is “1”. If we set match type as “1”, Match function finds out all values that are less than or equal to lookup_value from lookup_array, and returns the largest one among them. In this example, as lookup_value is 105, so from lookup_array only 80 and 100 meet the rule, 100 is larger than 80, so the relative position of cell B6 which contains “100” for subject history is returned from MATCH function. In named range “Score” (B2:B7), “100” is saved in B6, so the relative row number is 5 (the first value is started in row2). c. “5” is delivered to INDEX as row number. INDEX(Level,5) // row number is 5 for “100” Expand values in “Level”, INDEX returns “B” finally. returns “B” Related Functions • Excel INDEX function The Excel INDEX function returns a value from a table based on the index (row number and column number)The INDEX function is a build-in function in Microsoft Excel and it is categorized as a Lookup and Reference Function.The syntax of the INDEX function is as below:= INDEX (array, row_num,[column_num])… • Excel MATCH function The Excel MATCH function search a value in an array and returns the position of that item.The MATCH function is a build-in function in Microsoft Excel and it is categorized as a Lookup and Reference Function.The syntax of the MATCH function is as below:= MATCH (lookup_value, lookup_array, [match_type])…. • Excel IF function The Excel IF function perform a logical test to return one value if the condition is TRUE and return another value if the condition is FALSE. 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php require("/home/jeffery/public_html/astro/star/parallax_trigonometry.html");?> d(parsecs) = _____________ , where θ is the observed parallax measured in the unit the arcsecond ('') = 1/3600°, r is the baseline distance measured in the unit the astronomical unit (AU) = 1.495978707001011 m (exact), d is the distance to be determined in the unit the parsec (pc) = 648000/π AU (exact), and the formula is a small-angle approximation formula that is valid for the specified units. 1 parsec = 648000/π AU = 206264.806 ... AU = (3.085 677 581 491 367 ...)10*16 m = 3.261563777 ... lyr ≅ 3.26 lyr ≅ 3 lyr (see Wikipedia: parsec (pc) = 648000/π AU (exact); Wikipedia: astronomical unit (AU) = 1.4959787070010*11 m (exact), Wikipedia: light-year (ly) = 9.46073047258080010**15 m (exact)). Parsecs originally became the distance units of choice in astronomy because they are the distance units the above formula gives: 1 AU / 1 arcsecond = 1 parsec. The parsec is, in fact, a good natural unit for interstellar distances since nearest neighbor stars are typically of order a parsec apart. The light-year is a secondary natural unit for interstellar distances. In fact, the light-year would have been a better choice for the primary natural unit since it gives the lookback time immediately: an astronomical object X light-years away is seen as it was X years ago (more exactly X Julian years ago; the Julian year = 365.25 days exactly by definition). But the dead hand of the past weighs on us. Credit/Permission: © David Jeffery, 2004 / Own work. Image link: Itself. Local file: local link: parallax_trigonometry.html. File: Star file: parallax_trigonometry.html.	{"url":"https://www.physics.unlv.edu/~jeffery/astro/star/parallax_trigonometry.html","timestamp":"2024-11-15T04:19:15Z","content_type":"text/html","content_length":"8385","record_id":"<urn:uuid:0edd0a26-25bd-4a17-a9ce-6da1ea2b892a>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00829.warc.gz"}
Annals of Computer Science and Information Systems Predictive and Descriptive Analysis for Heart Disease Diagnosis František Babič, Jaroslav Olejár, Zuzana Vantová, Ján Paralič DOI: http://dx.doi.org/10.15439/2017F219 Citation: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 11, pages 155–163 (2017) Abstract. The heart disease describes a range of conditions affecting our heart. It can include blood vessel diseases such as coronary artery disease, heart rhythm problems or and heart defects. In addition, this term is often used for cardiovascular disease, i.e. narrowed or blocked blood vessels leading to a heart attack, chest pain or stroke. In our work, we analyzed three available datasets focused on heart diseases: Heart Disease Database, South African Heart Disease, Z-Alizadeh Sani Dataset and, Cardiac Dataset. For this purpose, we focused on two directions: predictive analysis based on Decision trees, Na\"{\i}ve Bayes, Support Vector Machine and Neural networks; descriptive analysis based on association and decision rules. Our results are plausible, in some cases comparable or better as in other related works. 1. P. Chapman, J. Clinton, R. Kerber, T. Khabaza, T. Reinartz, C. Shearer, and R. Wirth: “CRISP-DM 1.0 Step-by-Step Data Mining Guide”, 2000. 2. C. Shearer, “The CRISP-DM Model: The New Blueprint for Data Mining”, Journal of Data Ware-housing, vol. 5, no. 4, 2000, pp. 13–22. 3. K.S. Murthy, “Automatic construction of decision tress from data: A multidisciplinary survey”, Data Mining and Knowledge Discovery, 1997, pp. 345–389, http://dx.doi.org/10.1007/s10618-016-0460-3. 4. J. R. Quinlan, “C4.5: Programs for Machine Learning”, Morgan Kaufmann Publishers, 1993, http://dx.doi.org/10.1007/BF00993309. 5. N. Patil, R. Lathi, and V. Chitre, “Comparison of C5.0 & CART Classification algorithms using pruning technique”, International Journal of Engineering Research & Technology, vol. 1, no. 4, 2012, pp. 1–5. 6. T. Hothorn, K. Hornik, and A. Zeileis, “Unbiased recursive partitioning: A conditional inference framework”, Journal of Computational and Graphical Statistics, vol. 15, no. 3, 2006, pp. 651–674, 7. L. Breiman, J.H. Friedman, R.A. Olshen, Ch.J. Stone, “Classification and Regression Trees”, 1999, CRC Press, http://dx.doi.org/10.1002/cyto.990080516. 8. D. J Hand, K. Yu, “Idiot's Bayes-not so stupid after all?”, International Statistical Review, vol. 69, no. 3, 2001, pp. 385–399. http://dx.doi.org/10.2307/1403452 9. C. Cortes, V. Vapnik, "Support-vector networks", Machine Learning, vol. 20, no. 3, 1995, pp. 273–297, http://dx.doi.org/10.1007/BF00994018. 10. K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Networks, vol. 4, 1991, pp. 251–257, http://dx.doi.org/10.1016/0893-6080(91)90009-T. 11. R. Agrawal, R. Srikant, “Fast Algorithms for Mining Association Rules in Large Data-bases”, Proceedings of the 20th International Conference on Very Large Data Bases, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1994, pp 487-499. 12. J. Hipp, U. Güntzer, and G. Nakhaeizadeh, “Algorithms for Association Rule Mining &Mdash; a General Survey and Comparison”, SIGKDD Explor Newsl 2, 2000, pp. 58–64, http://dx.doi.org/10.1145/ 13. R. Agrawal, T. Imieliński, and A. Swami, “Mining Association Rules Between Sets of Items in Large Databases”, Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data, ACM, New York, NY, USA, 1993, pp. 207–216, http://dx.doi.org/10.1145/170035.170072. 14. B. Shahbaba, “Biostatistics with R: An Introduction to Statistics through Biological Data”, 2012, Springer, http://dx.doi.org/10.1007/978-1-4614-1302-8. 15. J. E. Rossouw, J. du Plessis, A. Benade, P. Jordaan, J. Kotze, and P. Jooste, “Coronary risk factor screening in three rural communities”, South African Medical Journal, vol. 64, 1983, pp. 16. R. Kreuger, “ST Segment”, ECGpedia. 17. R. Alizadehsani, M. J. Hosseini, Z. A. Sani, A. Gandeharioun, and R. Boghrati, “Diagnosis of Coronary Artery Disease Using Cost-Sensitive Algorithms”, IEEE 12th International Conference on Data Mining Workshop, 2012, pp. 9–16, http://dx.doi.org/10.1109/ICDMW.2012.29. 18. R. El-Bialy, M. A. Salamay, O. H. Karam, and M. E. Khalifa, "Feature Analysis of Coronary Artery Heart Disease Data Sets", Procedia Computer Science, ICCMIT 2015, vol. 65, pp. 459–468, http:// 19. L. Verma, S. Srivastaa, and P.C. Negi, "A Hybrid Data Mining Model to Predict Coronary Artery Disease Cases Using Non-Invasive Clinical Data", Journal of Medical Systems, vol. 40, no. 178, 2016, 20. R. Alizadehsani, J. Habibi, M. J. Hosseini, H. Mashayekhi, R. Boghrati, A. Ghandeharioun, B. Bahadorian, and Z. A. Sani, "A data mining approach for diagnosis of coronary artery disease", Computer Methods and Programs in Biomedicine, vol. 111, no. 1, 2013, pp. 52-61, http://dx.doi.org/10.1016/j.cmpb.2013.03.004. 21. Ch. Yadav, S. Lade, and M. Suman, "Predictive Analysis for the Diagnosis of Coronary Artery Disease using Association Rule Mining", International Journal of Computer Applications, vol. 87, no. 4, 2014, pp. 9-13. 22. S. S. Shapiro, M. B. Wilk, "An analysis of variance test for normality (complete samples)", Biometrika, vol. 52, no. 3–4, 1965, pp. 591–611, http://dx.doi.org/10.1093/biomet/52.3-4.591. 23. B. L. Welch, "On the Comparison of Several Mean Values: An Alternative Approach", Biometrika, vol. 38, 1951, pp. 330–336, http://dx.doi.org/10.2307/2332579. 24. K. Pearson, Karl, "On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling", Philosophical Magazine Series 5, vol. 50, no. 302, 1900, pp. 157–175, http://dx.doi.org/10.1080/14786440009463897. 25. R. A. Fisher, "On the interpretation of χ2 from contingency tables, and the calculation of P", Journal of the Royal Statistical Society, vol. 85, no. 1,1922, pp. 87–94, http://dx.doi.org/10.2307/ 26. G. E. Batista, M.C. Monard, "A Study of K-Nearest Neighbour as an Imputation Method", In Proceedings of Soft Computing Systems: Design, Management and Applications, IOS Press, 2002, pp. 251-260, 27. Y. Dong, Ch-Y. J. Peng, "Principled missing data methods for researchers", Springerplus, vol. 2, vol. 222, 2013, http://dx.doi.org/ 10.1186/2193-1801-2-222. 28. D. Freedman, "Statistical Models: Theory and Practice. Cambridge", New York: Cambridge University Press, 2009, http://dx.doi.org/10.1017/CBO9780511815867. 29. H. B. Mann, D. R. Whitney, "On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other", Annals of Mathematical Statistics, vol. 18, no. 1, 1947, pp. 50–60, http:// 30. P. Drotár, Z. Smékal, “Comparative Study of Machine Learning Techniques for Supervised Classification of Biomedical Data”, Acta Electrotechnica et Informatica, vol. 14, no. 3, 2014, pp. 5-10,	{"url":"https://annals-csis.org/Volume_11/drp/219.html","timestamp":"2024-11-08T15:18:33Z","content_type":"text/html","content_length":"13109","record_id":"<urn:uuid:31b9aebe-5c9c-444e-94e5-cd86881d8c45>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00235.warc.gz"}
20 000 Mortgage Payment Assuming you have a 20% down payment ($4,), your total mortgage on a $20, home would be $16, For a year fixed mortgage with a % interest rate. Use our mortgage calculator to get an idea of your monthly payment by adjusting the interest rate, down payment, home price and more. How much is the monthly payment for a 20, over 15 years? Browse the table below to view monthly payments based on interest rate. Monthly Mortgage Payment for. This calculates the monthly payment of a $20k mortgage based on the amount of the loan, interest rate, and the loan length. It assumes a fixed rate mortgage. How a Larger Down Payment Impacts Mortgage Payments*. Percentage, Down Payment, Home Price, Principal & Interest. 20%, $40,, $,, $ The size of your down payment can affect your interest rate—lenders typically offer lower rates if you make a larger down payment. (Default setting = 20%.) Loan. For conventional loans, paying at least a 20% down payment when purchasing a home removes the need for Private Mortgage Insurance (PMI) payments, which are. Calculate what your mortgage payment could be. Find out how changing your payment frequency and making prepayments can save you money. Payment FrequencyMonthly. Weekly; Biweekly; Semi-Monthly; Monthly. Interest Rate. 0; ; ; ; ; %. Amortization. 1; 5; 10; 15; 20; 5. Some loans, like VA loans and some USDA loans allow zero down. Although it's a myth that a 20% down payment is required to obtain a loan, keep in mind that the. Your rate of % will last for the first 2 years of your mortgage (the 'initial period'). After that, you'll switch to the lender's standard variable rate . Free online mortgage calculator specifically customized for use in Canada including amortization tables and the respective graphs. Use MoneySuperMarket's mortgage calculator to learn how much you could borrow, how large a deposit you will need, and if you are overpaying. Find out here. Use this mortgage calculator to estimate your monthly mortgage payments. Optionally provide your Taxes, Insurance, PMI and HOA fees to calculate a complete. A mortgage calculator that estimates monthly home loan payment While a 20% down payment will probably get you the best interest rates and. But if you don't have 20%, you can put down as little as %, or in some cases 0%. FHA loan: These loans are backed by the Federal Housing Administration. Free mortgage calculator to find monthly payment, total home ownership cost, and amortization schedule with options for taxes, PMI, HOA, and early payoff. Use our mortgage payment calculator to estimate how much your payments could be. Calculate interest rates, amortization & how much home you could afford. Determine what you could pay each month by using this mortgage calculator to calculate estimated monthly payments and rate options for a variety of loan. Calculate your mortgage payments. Discover our tool to calculate how much your payment will be. Make an appointment. Not sure how much mortgage you can afford? Use the calculator to discover how much you can borrow and what your monthly payments will be. Our Mortgage payment calculator can help determine your monthly payment and options to save more on mortgages. Visit Scotiabank online tool today! Use this calculator to calculate the monthly payment of a loan. It can be used for a car loan, mortgage, student debt, boat, motorcycle, credit cards, etc. Estimated monthly payment and APR example: A $, loan amount with a year term at an interest rate of % with a down-payment of 20% would result in. The interest-only mortgage payment calculator shows what your monthly mortgage payment would be by factoring in your interest-only loan term, interest rate and. Use this calculator to calculate the monthly payment of a 20k loan. It can be used for a car loan, mortgage, student debt, boat, motorcycle, credit cards, etc. Avoid private mortgage insurance: When you put at least 20% down on a conventional loan — or 20% home equity on a refinance — you can avoid paying monthly. A mortgage for £ repaid over 30 years will cost you £ per calendar month and cost you a total of £ This means that during the repayment of. A mortgage payment calculator takes into account factors including home price, down payment, loan term and loan interest rate in order to determine how much. Small Personal Loans With Collateral \| Hot Ev Stocks To Buy	{"url":"https://7746213.ru/recently-added/20-000-mortgage-payment.php","timestamp":"2024-11-06T15:42:24Z","content_type":"text/html","content_length":"10762","record_id":"<urn:uuid:c631ec9d-3bbb-4b74-95e7-d74a8fc3d679>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00475.warc.gz"}
Is it possible to define (or assume) a general positive function? Is it possible to define (or assume) a general positive function? Is it possible to assume a positive function when doing simplifications? (like Simplify[expr,a[t]>0] in Mathematica) To be explicit, I have # output: abs(a(t)) # changing to assume(a(t)>0) still doesn't work, and results in a DeprecationWarning a = function('a',var('t')) This is to be compared to variable case (where works): # output: t I could do a replacement to subs_expr abs(a(t)) into a(t). But is there a simple and elegant resolution? Thank you!	{"url":"https://ask.sagemath.org/question/8558/is-it-possible-to-define-or-assume-a-general-positive-function/","timestamp":"2024-11-13T19:48:58Z","content_type":"application/xhtml+xml","content_length":"48848","record_id":"<urn:uuid:a7a383f0-8755-458b-97fb-6d31642f0107>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00562.warc.gz"}
Monte Carlo One of the most efficient ways to solve really complicated problems in computer science is to repeat a bunch of random trials that simulate something in the real-world, then combine all of the results of those trials to create a solution. For example, using artificial intelligence, computers can now routinely win against the best human players in the world in classic games such as Go and chess by mentally playing different moves, then estimating a large number of future outcomes to see which leads to wins the most frequently. Ongoing research here at Oberlin is developing similar methods that could be used by robots to decide how to put out wildfires to protect people and property from natural disasters. This type of solution is called a Monte Carlo method, which we will explore in this problem. Calculating Pi using Darts One of the most famous numbers in the world is the number pi ($\pi = 3.14159265&mldr;$), which has important applications in geometry, architecture, graphic design, and even baking (no pun intended). The number $\pi$ is irrational, meaning that it cannot be expressed as a simple fraction and it has an infinite number of values after the decimal point. This makes calculating the exact value of $\ pi$ difficult&mldr;in fact it’s impossible in finite time! We can, however, estimate the value of $\pi$ to some precision. In the monte.py program, we will calculate an approximate value of $\pi$ by randomly throwing darts at a dartboard. How does that help us?!? Imagine that we have a circular dartboard in front of a square part of the wall, similar to the picture below. Say that the width of the square part of the wall (also the diameter of the circle of the dartboard) is equal to $w$. Then geometry tells us that the total area of the square part of wall is $w^2$, and the total area of the dartboard is $\pi \times ($circle’s radius$)^2 = \pi \times (\frac{w}{2})^2 = \frac{\pi \times w^2}{4}$. That means that the dartboard takes up $\frac{\pi}{4}$ of the area of the wall behind it. How does this help us calculate $\pi$? Imagine now that you are blindfolded and throw n darts at the wall. Without being able to see anything, your darts would land randomly all over on the dartboard and on the wall around it. Now, if you count how many darts land on the dartboard (yay, you got kind of close) and divide that by the number of darts you threw, you have a good approximation of the fraction of the wall taken up by the dartboard. Which we already said above is equal to $\frac{\pi}{4}$. So, with a little bit of algebra, multiplying 4 by the number of darts that hit the dart board and dividing by the number of darts you threw gives us an answer that is close to $\pi$. Indeed, the more darts you throw, the better your approximation becomes, and the closer your answer is to $\ Implementing our Experiment Let’s put the experiment above into algorithm form. 1. Draw an image for the square part of the wall and a circle in front of that square. This is the dartboard. Set the width w and diameter of the circle to 400. 2. Ask the user for a number, n, of darts to throw. 3. Throw that number of darts. 1. We pick a random location (randX, randY) on the square where the dart should land. 2. We draw a small circle on the location where the dart landed to visualize its throw. 3. We calculate whether the dart landed on the dartboard or not. If it did, we increase a count called hits. 4. We multiply 4 with the number of hits and divide by the number, n, of darts thrown to calculate the value of $\pi$ 4. Save your picture of the dartboard and darts. picture.save_picture("pi_darts.png") should be the last line in your code. Randomly Throwing Darts To calculate a random location where the dart lands, we will use the random module in Python. To use the random module, add the following line to the top of your program: import random You can get a random integer between 0 and w with the following line. randX = random.randrange(w) # returns an integer in [0,w-1] Since the square has width w, you can think about this number randX representing a random x-coordinate where the dart lands. Repeating that line of code to create a variable randY gives us a random y-coordinate for the dart to land. To display the dart throw, we can draw a small circle centered at the (randX, randY) point that was just randomly chosen (please use a color that can be seen on top of the color you choose for your dartboard). Deciding if a Dart Hits the Dartboard Once we know the location of a dart, the next question is: did this dart land on the dartboard? This sounds like a conditional, so we can use an if statement here! If the diameter of the dartboard is w = 400, then its radius is 200, meaning that any location within 200 pixels of the center of the dartboard is part of the dartboard, and any location farther away lands on the wall. We can calculate the distance using this formula: $$ dist = \sqrt{(randX - centerX)^2 + (randY - centerY)^2} $$ where for us, centerX = 200 and centerY = 200 since the dartboard is in the middle of the wall. The math module in Python provides us with the square root function needed to calculate distance. Like the random module, we can use the math module by adding the following line to the top of your import math Then, we can use: dist = math.sqrt(equation) to calculate the distance dist, where equation is the equation inside the square root described above. Finally, an if statement checks if the dart hits the dartboard. if dist < 200: hits = hits + 1 Remember to periodically commit and push your changes! Example Outputs This program approximates the value of π by simulating the random placement of darts thrown onto a round target on a square wall. How many darts do you want to throw? 1 The approximation of π after 1 iterations is 4.0 This program approximates the value of π by simulating the random placement of darts thrown onto a round target on a square wall. How many darts do you want to throw? 100 The approximation of π after 100 iterations is 3.2 This program approximates the value of π by simulating the random placement of darts thrown onto a round target on a square wall. How many darts do you want to throw? 1000 The approximation of π after 1000 iterations is 3.092 Accuracy vs Number of Darts If you only throw a small number of darts (< 100), your approximation of $\pi$ might be closer to 4 than 3.14159265… The more darts you throw, the closer your answer should get to the actual value of π. Of course, we are relying on randomness here, so bad luck could result in a large number of darts still giving an estimate that isn’t close, or good luck could result in a close estimate with only a few darts. Running your program over and over should give different answers, even for the same number of darts.	{"url":"https://cs.oberlin.edu/~cs150/lab-3/part-2/","timestamp":"2024-11-08T02:37:59Z","content_type":"text/html","content_length":"23759","record_id":"<urn:uuid:f6fe652a-78c1-48db-8d71-64ec51959660>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00814.warc.gz"}
How to Sort a 2D Array in Java Sorting a 2D array in Java Sorting a 2D array is a common task in Java programming. 2D arrays are used to store data in a rectangular grid, and sorting them can be useful for organizing data or performing analysis. There are a few different ways to sort a 2D array in Java, and the best method to use depends on the specific data and the requirements of the application. In this article, we will discuss the different methods for sorting a 2D array in Java, and we will provide examples of how to use each method. We will also discuss the time and space complexity of each method, so that you can choose the most efficient method for your needs. By the end of this article, you will be able to sort 2D arrays in Java with confidence. You will also understand the different sorting algorithms and how to choose the best one for your application. Column 1 Column 2 Column 3 Header 1 Data 1 Data 2 Header 2 Data 3 Data 4 Header 3 Data 5 Data 6 Here is the same table, but with data specific to sorting a 2-dimensional array in Java: Algorithm Time Complexity Space Complexity Bubble Sort O(n^2) O(1) Selection Sort O(n^2) O(1) Insertion Sort O(n^2) O(1) Merge Sort O(n log n) O(n) Quick Sort O(n log n) O(log n) Overview of 2D Arrays in Java A 2D array is a data structure that stores data in a two-dimensional table. Each element of a 2D array is accessed using two indices: the row index and the column index. For example, the following 2D array stores 9 integers: [[1, 2, 3], [4, 5, 6], [7, 8, 9]] The first index represents the row, and the second index represents the column. So, the element at row 0 and column 0 is 1, the element at row 1 and column 1 is 5, and so on. 2D arrays are used to store data that has a natural two-dimensional structure, such as images, spreadsheets, and games. How to create a 2D array in Java To create a 2D array in Java, you can use the following syntax: int[][] array = new int[rows][columns]; where `rows` is the number of rows in the array and `columns` is the number of columns in the array. For example, the following code creates a 2D array with 3 rows and 4 columns: int[][] array = new int[3][4]; Accessing elements of a 2D array To access an element of a 2D array, you can use the following syntax: where `row` is the row index and `column` is the column index. For example, the following code accesses the element at row 0 and column 0 of the array `array`: int element = array[0][0]; Sorting a 2D array Sorting a 2D array means arranging the elements in the array in a specific order. There are many different sorting algorithms that can be used to sort a 2D array. One of the simplest sorting algorithms is bubble sort. Bubble sort works by repeatedly comparing adjacent elements in the array and swapping them if they are in the wrong order. The following code shows how to sort a 2D array using bubble sort: public static void bubbleSort(int[][] array) { for (int i = 0; i < array.length; i++) { for (int j = 0; j < array[i].length - 1; j++) { if (array[i][j] > array[i][j + 1]) { int temp = array[i][j]; array[i][j] = array[i][j + 1]; array[i][j + 1] = temp; Bubble Sort for 2D Arrays Bubble sort is a simple sorting algorithm that works by repeatedly comparing adjacent elements in the array and swapping them if they are in the wrong order. The following is the pseudocode for bubble sort for 2D arrays: for (int i = 0; i < array.length; i++) { for (int j = 0; j < array[i].length - 1; j++) { if (array[i][j] > array[i][j + 1]) { int temp = array[i][j]; array[i][j] = array[i][j + 1]; array[i][j + 1] = temp; Overview of bubble sort Bubble sort is a simple sorting algorithm that works by repeatedly comparing adjacent elements in the array and swapping them if they are in the wrong order. Bubble sort is an in-place sorting algorithm, which means that it does not require any extra space to sort the array. Bubble sort is a stable sorting algorithm, which means that the order of equal elements in the array is preserved after sorting. Bubble sort algorithm for 2D arrays The bubble sort algorithm for 2D arrays works by repeatedly comparing adjacent elements in the array and swapping them if they are in the wrong order. The algorithm works by iterating through the array row by row, and then comparing each element in a row with the element to its right. If the element on 3. Selection Sort for 2D Arrays Overview of Selection Sort Selection sort is a simple sorting algorithm that works by repeatedly finding the smallest element in an array and swapping it with the first unsorted element. This process is repeated until the entire array is sorted. Selection sort is a comparison sort, meaning that it only compares elements to each other to determine their order. This makes it a very efficient sorting algorithm for small arrays. However, as the size of the array increases, the number of comparisons required by selection sort also increases, making it a less efficient sorting algorithm for large arrays. Selection Sort Algorithm for 2D Arrays The selection sort algorithm for 2D arrays is a straightforward extension of the algorithm for 1D arrays. The following steps describe the algorithm in pseudocode: 1. Iterate through the first row of the array, starting from the second element. 2. Find the smallest element in the row. 3. Swap the smallest element with the first element in the row. 4. Iterate through the remaining rows of the array, repeating steps 1-3 for each row. Once all of the rows have been sorted, the entire array will be sorted. Time Complexity of Selection Sort for 2D Arrays The time complexity of selection sort for 2D arrays is O(n^2), where n is the number of rows in the array. This is because the algorithm must iterate through each row of the array, and then iterate through each element in each row. 4. Merge Sort for 2D Arrays Overview of Merge Sort Merge sort is a sorting algorithm that works by recursively splitting an array into smaller and smaller sub-arrays until each sub-array contains a single element. The sub-arrays are then merged together in sorted order to form a sorted array. Merge sort is a divide and conquer algorithm, meaning that it divides the problem into smaller sub-problems that are then solved recursively. This makes merge sort a very efficient sorting algorithm for large arrays. Merge Sort Algorithm for 2D Arrays The merge sort algorithm for 2D arrays is a straightforward extension of the algorithm for 1D arrays. The following steps describe the algorithm in pseudocode: 1. Recursively split the array into smaller and smaller sub-arrays until each sub-array contains a single row. 2. Merge the sub-arrays together in sorted order to form a sorted array. Once all of the sub-arrays have been merged, the entire array will be sorted. Time Complexity of Merge Sort for 2D Arrays The time complexity of merge sort for 2D arrays is O(n log n), where n is the number of rows in the array. This is because the algorithm must recursively split the array into sub-arrays of size log n, and then merge the sub-arrays together in sorted order. Selection sort and merge sort are two of the most commonly used sorting algorithms for 2D arrays. Selection sort is a simple algorithm that is efficient for small arrays, while merge sort is a more efficient algorithm for large arrays. The following table summarizes the key differences between selection sort and merge sort for 2D arrays: \| Algorithm \| Time Complexity \| Space Complexity \| \| Selection Sort \| O(n^2) \| O(1) \| \| Merge Sort \| O(n log n) \| O(n) \| When choosing between selection sort and merge sort for 2D arrays, it is important to consider the size of the array and the performance requirements. If the array is small, selection sort is a good choice. If the array is large, merge sort is a better choice. Q: How do I sort a 2D array in Java? A: There are a few different ways to sort a 2D array in Java. One common way is to use the Arrays.sort method. This method takes a multidimensional array as its argument and sorts it by the elements in the first column. To sort the array by the elements in the second column, you can use the Comparator.comparing method. Here is an example of how to sort a 2D array by the elements in the first column: int[][] array = {{1, 2}, {3, 4}, {5, 6}}; Arrays.sort(array, (a, b) -> Integer.compare(a[0], b[0])); for (int[] row : array) { for (int value : row) { System.out.print(value + ” “); You can also use the Stream API to sort a 2D array. To do this, you can first convert the array to a Stream of Arrays, then use the sorted method to sort the stream. Here is an example of how to sort a 2D array by the elements in the second column using the Stream API: int[][] array = {{1, 2}, {3, 4}, {5, 6}}; Stream stream = Arrays.stream(array); stream.sorted((a, b) -> Integer.compare(a[1], b[1])) .forEach(row -> { for (int value : row) { System.out.print(value + ” “); Q: What is the best way to sort a 2D array? A: The best way to sort a 2D array depends on the size of the array and the sorting criteria. For small arrays, the Arrays.sort method is a good option. For larger arrays, the Stream API can be more If you need to sort the array by the elements in the first column, you can use the Arrays.sort method with the Comparator.comparing method. For example, the following code sorts a 2D array of integers by the elements in the first column: int[][] array = {{1, 2}, {3, 4}, {5, 6}}; Arrays.sort(array, (a, b) -> Integer.compare(a[0], b[0])); If you need to sort the array by the elements in the second column, you can use the Stream API with the sorted method. For example, the following code sorts a 2D array of integers by the elements in the second column: int[][] array = {{1, 2}, {3, 4}, {5, 6}}; Stream stream = Arrays.stream(array); stream.sorted((a, b) -> Integer.compare(a[1], b[1])) .forEach(row -> { for (int value : row) { System.out.print(value + ” “); Q: What are some common problems when sorting a 2D array? A: There are a few common problems that can occur when sorting a 2D array. • The array may not be sorted correctly. This can happen if the sorting algorithm is not implemented correctly or In this blog post, we have discussed how to sort a 2D array in Java. We have covered three different methods: • The Bubble Sort • The Selection Sort • The Merge Sort We have also provided code examples for each method. Which method you choose to use will depend on the size of your array and the speed at which you need it to be sorted. The Bubble Sort is the simplest method, but it is also the least efficient. The Selection Sort is more efficient than the Bubble Sort, but it is still not as efficient as the Merge Sort. The Merge Sort is the most efficient method, but it is also the most complex. Ultimately, the best way to decide which method to use is to experiment with each method and see which one gives you the best results for your particular application. Here are some key takeaways from this blog post: • Sorting a 2D array in Java can be done using the Bubble Sort, Selection Sort, or Merge Sort algorithms. • The Bubble Sort is the simplest method, but it is also the least efficient. • The Selection Sort is more efficient than the Bubble Sort, but it is still not as efficient as the Merge Sort. • The Merge Sort is the most efficient method, but it is also the most complex. • The best way to decide which method to use is to experiment with each method and see which one gives you the best results for your particular application. Author Profile Hatch, established in 2011 by Marcus Greenwood, has evolved significantly over the years. Marcus, a seasoned developer, brought a rich background in developing both B2B and consumer software for a diverse range of organizations, including hedge funds and web agencies. Originally, Hatch was designed to seamlessly merge content management with social networking. We observed that social functionalities were often an afterthought in CMS-driven websites and set out to change that. Hatch was built to be inherently social, ensuring a fully integrated experience for users. Now, Hatch embarks on a new chapter. While our past was rooted in bridging technical gaps and fostering open-source collaboration, our present and future are focused on unraveling mysteries and answering a myriad of questions. We have expanded our horizons to cover an extensive array of topics and inquiries, delving into the unknown and the unexplored.	{"url":"https://hatchjs.com/sorting-2-dimensional-array-in-java/","timestamp":"2024-11-08T02:02:41Z","content_type":"text/html","content_length":"94346","record_id":"<urn:uuid:63179cbc-3263-4247-9e64-353877b0afe9>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00152.warc.gz"}
My ballmilled Black Powder .. any suggestion? As suggested by a kindly user in APC forum, I created BP with my good ballmill in this way: Mix 1: 75 parts potassium nitrate 5 parts charcoal Mix 2: 10 parts charcoal 10 parts sulphur I used airfloat pine charcoal, potassium nitrate without anticaking and sulphur. Potassium nitrate and charcoal was dried under the sunlight for half day. I mixed twice the two compounds thru a 20 mesh screen. In the video in attachment You can see how burn 1/3 of a tea spoon of this BP into my kitchen sink Can anyone tell me if my BP is fast enough to be considered good? For the momment I will use BP only to coating rice hulls. P.S: the residual was a very small amount of potassium nitrate, but it looks like fine granulated, not pulverized. Edited by MinamotoKobayashi I would say it's fast enough to lift shells but if you want to make a really hard break you might have to tune it some! Testing any pyrotechnics in a home is not a good idea. If you are willing to test them in your home, you are willing to make them there too, IMHO. That has caused a lot of problems for others already. Please don't do it. I would grind the #2 Mix longer, and use a 40 mesh sieve. • 1 David, I live alone in an apartment. I have no open spaces, working at home is my only chance. Don't worry, I'm not a newbye, I work with sugar rockets indoor from many years. The key is to work with small batches and keep the other powders far away, well sealed and placed in other rooms. I'm always protected with goggles, mask, gloves and appropriate cloths. I have a fire estinguisher and wet rags always ready near me. No one except me myself can be injuried in case of bad luck, so don't worry Ok, I will grind the mix2 longer and I will use 40 mesh sieve. The mix 1 after 1 hours tends to create a big lump against the end of the ballmill barrell, also if the compound is well dried. Unluckly the potassium nitrate without anticaking tends always to create big lumps .... Edited by MinamotoKobayashi If you don't have anywhere to work safely (and it sounds like you don't), then you shouldn't be doing this at all. Also, something is not well dried if it's clumping after an hour. Charcoal can hold onto water too. Hi Mumbles. I have well dried both potassium nitrate and carchoal under the sun and inside my ventilated oven at 100 °C. This issue happens only when I'm using potassium nitrate without anticaking. If I use potassium nitrate with anticaking everything goes fine. I have an important question for You: the potassium nitrate with anticaking can cause issues in some uses? Can I replace always the potassium without anticaking with the anticaking version without having troubles? (for example, I heard that the anticaking version it is not suitable to make coated rice hulls ...) Edited by MinamotoKobayashi Please do not put anyone else who lives in your apartment building/complex at such risk! Imagine how upset you would be if a family member of yours was in an apartment complex where someone else caught them on fire. • 1 While I am also concerned about the safety, may I ask, why do you mill in two seperate mixes? I always mixed it all up and milled. While I am also concerned about the safety, may I ask, why do you mill in two seperate mixes? I always mixed it all up and milled. It's quite common to run two "batches" of charcoal, and screen them together, as a mean to minimize the risk of the mill, or any handling in relation to the milling procedure, causing unexpected rapid combustion with undesirable results. Sulfur / charcoal, or KNO3 / charcoal, burns poorly. Combining, and milling, rather then milling the two different compositions, and screening them together, makes a better BP, but has some downsides in the safety department. Most of us decide to deal with those issues when we get a ball mill, some don't. Yes MrB You're right. I alive alone in an apartment and I cannot risk to mill BP indoor. Also If I use brass media balls, gum barrell and screened airfloat charcoal (to elimite also the risk of unwanted small metal pieces), I want to be safe. For eveyone that fear what I have done: it was a 1/2 tea spoon of BP inside a metal kitchen sink. The fuse was locked with a strong tape on the floor. On the left and on the right I have much water, and on the back a fire estinguisher. I was almost naked, and also my hamster was far away from the place. Now anyone explain me how can be dangerous to ignite about 5 grams of BP in such environment !!! Yes MrB You're right. I alive alone in an apartment and I cannot risk to mill BP indoor. Also If I use brass media balls, gum barrell and screened airfloat charcoal (to elimite also the risk of unwanted small metal pieces), I want to be safe. For eveyone that fear what I have done: it was a 1/2 tea spoon of BP inside a metal kitchen sink. The fuse was locked with a strong tape on the floor. On the left and on the right I have much water, and on the back a fire estinguisher. I was almost naked, and also my hamster was far away from the place. Now anyone explain me how can be dangerous to ignite about 5 grams of BP in such environment !!! You were indoors. That is how it is dangerous. Mumbles, I know guys that were outdoors and had severe injuries simply shaking the ball mill barrell with BP inside, while I know people who combine every imprudence possible and imaginable inside the home and never do anything serious. I prepare 1/2 kg sugar rockets and 3" shells in my kitchen every day from 1 year and never had any kind of issues. Doing a firework is a risk, either inside or outside, with or without caution. If the fate want that You must blow up, You cannot do anything. Except to stop making fireworks, of course. Edited by MinamotoKobayashi I build shells and headers using completed stars and powder in my shed but I'd never mill BP, mix comps or God forbid, light any of them in here. I had a neighbor start a grease fire in her kitchen back when I lived in an apartment and if not for my renter's insurance I'd have been homeless and destitute. She would have been my total list of people to kill if I hadn't thought to get insurance. • 1 And when you do have that one incident and hurt not you but the neighbor's kids, you'll drive one more nail into the coffin of amateur pyrotechnics. And then well.....use your imagination. • 1 I'm tired of hauling my gear including generator to my brother's spread to mill powder, so rather than take a chance on blowing a hole in the neighbor's house, I'm going to try DaveF's method of separate milling of the ingredients at home. Like marriage pyro is a hobby designed to ruin stupid people. LOL Oldmarine. In fact I do not have wife nor kids. This is a palace of not-married evergreen singles. And there aren't kids. Instead marriage, I prefer to ruin my life in other ways such as pyros. For the other users: please stop to flame this thread, we are plently OT now ... • 1 Well, most of us don't condone "unsafe" practices. Fiddling with pyro in a rental flat pretty much counts here. Well, what is the punishment inflicted in this forum to a single man who does the pyro in his apartment? Well, what is the punishment inflicted in this forum to a single man who does the pyro in his apartment? Shunning mostly... alternatively, nagging to get such a person to change their ways, heh. To most in this hobby, a person's risk to themselves is theirs to evaluate. The problem comes in with apartments in that a person is risking someone else's life and property, without their consent to the risk. I have even heard of apartments(in addition to all university owned student housing I have looked at) with rules against any open flames for this reason. I understand the matter. I live in this apartment from about 50 years. Regrettable to say, but I'm surrounded of assholes, dickheads and ugly people. The only good soul in this condominium is a lovely cocker dog called Ok, for the love of this dog I will search a cottage in open countryside outside the city as soon as possible. I, many here, and most importantly the awesome dog thank you!	{"url":"https://www.amateurpyro.com/forums/topic/12569-my-ballmilled-black-powder-any-suggestion/","timestamp":"2024-11-09T12:54:22Z","content_type":"text/html","content_length":"273257","record_id":"<urn:uuid:0c01818a-482b-4989-adc6-563bd87edee0>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00355.warc.gz"}
The Ultimate CLEP College Mathematics Course (+FREE Worksheets & Tests) The best thorough course to assist you in getting ready to take the CLEP College Math examination! Seeking an ideal as well as a FREE online course to aid you in succeeding with the CLEP College Math exam? If true, go nowhere else! If you need a comprehensive online CLEP College Math course to assist you in improving your comprehension of math and learning every math subject required before the testing date, you are looking at the right info. This is an online course containing all the CLEP College Math subjects. This wonderful CLEP College Math course is the single source required for succeeding when you take the CLEP College Math test. The CLEP College Math course along with more of the Effortless Math Education sources get employed by many CLEP College exam-takers annually to aid them in reviewing core subject zones, brushing up on math, skills, and discovering their fortes and failings, and attaining their top grades via the CLEP College examination. No schedules, so you can learn it at your speed! Each lecture covers examples, notes, practice exercises, as well as other activities which aid people in learning and understanding all the concepts with ease. There is also a FREE The Absolute Best Book to Ace the CLEP College Mathematics Test Original price was: $24.99.Current price is: $14.99. CLEP College Mathematics Complete Course Fractions and Decimals Real Numbers and Integers Proportions, Ratios, and Percent Algebraic Expressions The Perfect Book to Ace the CLEP College Mathematics Test Original price was: $19.99.Current price is: $14.99. Equations and Inequalities Linear Functions Exponents and Radicals Geometry and Solid Figures Statistics and Probability Complex Numbers Trigonometric Functions Take a FREE Looking for the best resource to help you succeed on the CLEP College Mathematics test? The Best Books to Ace the CLEP College Mathematics Test Original price was: $29.99.Current price is: $19.99. Original price was: $25.99.Current price is: $13.99. Original price was: $24.99.Current price is: $13.99. Related to This Article What people say about "The Ultimate CLEP College Mathematics Course (+FREE Worksheets & Tests) - Effortless Math: We Help Students Learn to LOVE Mathematics"? No one replied yet.	{"url":"https://www.effortlessmath.com/blog/the-ultimate-clep-college-mathematics-course/","timestamp":"2024-11-02T22:22:41Z","content_type":"text/html","content_length":"104210","record_id":"<urn:uuid:141868d2-4768-4baf-a4c1-9c5fb6101548>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00453.warc.gz"}
15 ways to play an Eb chord on guitar - JG Music Lessons15 ways to play an Eb chord on guitar 15 ways to play an Eb chord on guitar The Eb chord is a less commonly known chord when first learning to play guitar. The lowercase ‘b’ represents a flat, meaning the note indicated is lowered by a half step. If you look up how to play an Eb chord (E flat), this might come up as a barre chord on the 6th fret, starting on the 5th string. This can be a difficult chord for a beginner, but there are many different ways you can play this chord on the guitar. This lesson covers 15 ways to play an Eb chord on guitar which you can start to incorporate into your playing. Let’s first get started by going over some basic chord theory. Eb chord theory Major triad chords are built upon the chord tones 1, 3, and 5. These chord tones can also be thought of as the scale degrees related to one Major scale. For example, in an Eb Major scale, the notes Eb (1), G (3), and Bb (5) make up an Eb Major chord. You can also think of the step formula for Major chords below. In contrast, minor triad chords contain the chord tones 1, b3, and 5. For example, an Eb minor chord would contain the chord tones Eb, Gb, and Bb. However, we will only be covering the different Major chord variations in this lesson. Now that you know what notes belong to the chord structure let’s look at how to read the chord charts. How to read the chord charts For the charts below: • The top horizontal line of the chord chart represents the high E string and the bottom horizontal line represents the low E string. • The vertical lines separate each fret. • The numbers in the blue dots tell you which fingers to use on the fretting hand. • The letters on the right of the charts tell you what notes you are playing on each string. • Circles on the left represent open strings. • Red X means to avoid that string. You can check this link for more on how to read guitar notation symbols. Eb chord on the 5th string (without a barre) For this first Eb chord shape, you have to make sure to not let the 1st string ring out. You can mute the 1st string letting the bottom part of your first finger lightly touch the string. Eb barre chord on the 5th string Now, we can add one more note to the previous shape. This is probably the most common chord shape that will show up when looking up an Eb chord. This shape comes from the open A Major chord except you have to rearrange your fingers as you barre the 6th fret with your 1st finger. Eb chord 5th string variation Here is another variation you can use for an Eb Major chord starting on the 5th string, 6th fret. This shape uses a wider grip on the fretting hand which takes practice to get comfortable with. This shape comes from the open C Major chord except you have to rearrange your fingers when you add your pinky (4th finger). It looks like this: Eb chord 5th string variation with a mini barre This is similar to the previous chord except you can use your first finger to barre the 1st string as well. It looks like this: Eb chord triad Here is another way you can play the Eb Major chord using a triad shape. This shape is similar to an open A Major chord except you slide all your fingers one fret lower. Or you can use a barre with your first finger to cover multiple strings like this: Eb chord 6th string variation Based on the previous chord, you can also add notes on the 6th and 5th string to make this a full sounding chord like this: Easily look up guitar chords with the Essential Guitar Chords Chart! This chart covers how to play: • Major chords • Minor chords • Major 7 chords • Minor 7 chords • Dominant chords • Half diminished chords • Diminished chords • Chords starting on all (12) root notes • Over 80+ chords! Eb chord on the 4th string This shape comes from the open D Major chord except you have to rearrange your fingers as you add your 1st finger. This shape can feel uncomfortable when first learning it but you will get better at it as you keep reviewing it. Eb chord simple triad If your guitar is suitable to play past the 12th fret, here is an easy way you can play the Eb Major chord by using a simple triad shape. This is very similar to an open C Major chord shape but you move your ring and middle finger down one string and shift the root note to the 13th fret on the 4th string. The shape looks like this: Eb chord triad 2nd inversion 2nd inversion means that the 5th degree of the chord is in the bass. Here, we add our pinky finger to the previous shape which makes the chord sound fuller. You can play it like this: Eb chord mini barre Another way to play this chord is to use a mini barre on the 1st and 2nd strings. The mini barre can be hard at first but it will get easier as you continue to practice it. The chord looks like this: Eb chord 2nd inversion with mini barre Also, adding your pinky to the previous shape makes the chord sound fuller like this: You can also check out this other lesson for more on how to play chord inversions on the guitar. Eb barre chord on the 6th string At this point, we’ve worked on different steps to take before getting to this chord because it requires more strength in your fretting hand. This shape comes from the open E Major chord except you have to rearrange your fingers as you barre the 11th fret with your 1st finger like this: You may also want to check out 5 tips to get better at playing barre chords on guitar. Eb chord spread shapes The following chords are called spread shapes because of the wider space between some of the notes within the chord shape. Because these chord shapes skip a string, they are more suitable for a finger picking style of playing. You might also hear these chords in a more classical music context. To go more in-depth, check out this lesson on how to play spread triad chords on the guitar. Eb spread chord on the 6th string Eb spread chord on the 5th string Eb spread chord on the 4th string Wrapping up Most of the Eb chords we covered here where in root position, meaning the root note is in the bass. However, you have even more variations if you use different chord inversions. This is when you play a chord with notes other than the root in the bass. It’s good to know many possibilities of playing the same chord because you have more flexibility to move around the fretboard. Also, you can use different chord variations when you need a certain note at the top to help define a melody that you are playing over. I hope this helped you understand how to play an Eb Major guitar chord or learn new ways of playing it. You can also try shifting these shapes to play other Major chords on the same string. 📘 Get the free guitar practice guide here! All the best, JG Music Lessons This page includes Amazon sponsored links to products I’ve used and recommend. This means I earn a commission if you click the link and purchase the item, at no additional cost to you! 📙 Kickstart your guitar playing with our step by step guide: Guitar Essentials. 🎸 Don't have a guitar yet? I recommend this one. 🤝 Support the site to help us to create better content for you! Level up with the free guitar practice guide to effectively improve your playing! Get it sent to your email!	{"url":"https://jgmusiclessons.com/15-ways-to-play-an-eb-chord-on-guitar/","timestamp":"2024-11-03T06:53:52Z","content_type":"text/html","content_length":"248563","record_id":"<urn:uuid:8b05a3a6-ad9a-44f1-afbc-13a9d731be61>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00240.warc.gz"}
So, Your Stakeholders Want An Interpretable Machine Learning Model? You are a Data Scientist working for a commercial company. You spent weeks, or maybe even months, developing this deep learning-based model that accurately predicts an outcome of great interest to your business. You proudly presented the results to your stakeholders. Quite annoyingly, though, they did not pay much attention to that cutting-edge approach you used to build the model. Instead of focusing on how powerful the model was, they started asking lots of questions on why some of its predictions looked the way they did. Your colleagues also felt that some of the critical predictors were missing. They could not fully understand how the predictions were so accurate with those features missing. As the model you built was of a black box type, it was challenging for you to give satisfactory answers to all the questions straightaway. So you had to ask for a follow-up meeting and for some time to get prepared. Sounds familiar? I have certainly been there a few times before. It is natural for us as humans to be uncomfortable with and do not trust things we do not understand. This also applies to the Machine Learning model and how people who are not Data Science experts perceive them. However, having an interpretable Machine Learning model is neither always possible nor necessary. To help me explain that to my stakeholders and clients, I have collected a few key ideas on the topic of model interpretability from various sources, including my own experience. I am sharing this collection here in this article. Hopefully, some of my fellow Data Scientists will also find it useful when preparing for similar conversations with their colleagues. Be crystal clear about the model’s purpose Clearly communicating the purpose of a model is one of the crucial factors that drive its adoption by stakeholders. There are several classifications of model purposes (e.g., Calder et al. 2018; Edmonds et al. 2018; Grimm et al. 2020). I personally prefer the one proposed by Leo Breiman, author of the famous Random Forest algorithm. In 2001, Breiman published a paper entitled “Statistical Modeling: The Two Cultures”. This paper has received lots of interest and citations as it for the first time initiated a widespread discussion on model interpretability vs predictive performance According to Breiman, data can be thought of as being generated by a black box, inside which Nature links a vector of input variables x to the outcomes y The author then formulates two main goals of modelling: • information: extracting insights on how Nature is linking x to y; • prediction: providing accurate estimates of y based on the future values of x. When communicating with the model end-users, it is essential to differentiate between these two goals. The reason is that the models used to achieve these goals typically differ in terms of their complexity, interpretability, and predictive power. Articulate the trade-off between interpretability and predictive accuracy Breiman (2001) distinguishes two approaches, or “cultures”, toward the goals of modelling. The first approach, “data modelling”, assumes that the data-generating process can be described by a stochastic model, e.g. response = f(predictors, parameters, random noise).Such models tend to have a limited set of parameters, whose values are estimated from the observed data. Examples include linear regression, logistic regression, Cox regression, etc.: Due to their relatively simple structure, models from this first category are typically used to shed light on how the system of interest operates. For instance, one can directly look at the coefficients of a linear regression model and quickly work out how changing the input values will affect the response variable. This also helps with formulating hypotheses that can subsequently be tested in controlled experiments. Although these models can certainly be used to make predictions, the quality of such predictions is usually not that high. This is in contrast to models produced using the “algorithmic modelling” approach. This approach accepts the fact that the innards of Nature’s black box are complex and unknown. It then tries to find an arbitrarily complex function that provides accurate mapping of the input variables x to the response variables y. Models that belong to this category are typically more complex and fitted using such algorithms as Random Forest, XGBoost, neural nets, etc.: Quality of the models produced with the data modelling approach is usually evaluated using statistical tests for goodness-of-fit and by examining the residuals. The result of this analysis is often binary: the model is either considered “good” or discarded as a “bad” one. In contrast, models built using the algorithmic modelling approach are assessed based on the accuracy of their predictions on an independent dataset. This is an important distinction, as it implies that we do not really care how complex an algorithmic model is or whether it passes statistical tests for goodness-of-fit. All that matters is that the model does not overfit and its predictive power is sufficiently high for the problem at hand. Nowadays, businesses collect large volumes of increasingly more complex data. Solving real-world business problems that require high-quality predictions based on such data requires equally complex modelling. However, complex models are intrinsically more difficult to interpret. Although this trade-off is not always black-and-white, we can conceptually visualise it as follows: It is our job as Data Scientists to articulate this trade-off to the end-users of our models. It can be challenging to do. However, as Cassie Kozyrkovsays in her brilliant article on this topic, “not everything in life is simple” and “wishing complicated things were simple does not make them so.” How about LIME, SHAP, and other methods that “explain” black box models? Interpretable Machine Learning (a.k.a. Explainable AI, XAI) is definitely a hot topic these days. Many academic researchers, developers of open-source frameworks, and vendors of commercial platforms are churning out novel methods to interpret the inner workings of complex predictive models. Examples of some of the well-known techniques include (see Molnar 2020 for a comprehensive overview): □ LIME (Local Interpretable Model-Agnostic Explanations); □ Shapely values and the associated SHAP method; □ individual conditional expectation; □ accumulated local effects plot. First of all, no Data Science project should be developed in a vacuum. This means that business stakeholders should be involved from Day 1. Before jumping into what we as Data Scientists love most — model building and playing with algorithms — we should strive to collect as much domain knowledge from our business colleagues as possible. On the one hand, embedding this knowledge in the form of input features would increase the chance of developing a highly performant model. On the other hand, this would eventually minimise the need to explain how the model works. But sometimes we do develop models without much engagement from our stakeholders (e.g., as part of an R&D project). In such cases, I have found it useful to simply provide a detailed explanation of what input variables go into the model under discussion. Business folks will naturally have an intuition as to what variables are likely to drive the outcome of interest. And if they see that these variables are already part of the model, their trust toward it goes up. Another powerful thing that often works well is exposing the model via a simple interactive web application to illustrate how predictions change depending on the input values. This can be done using any of the popular frameworks, such as Shiny, Dash, Streamlit. Let your stakeholders move those sliders and run the wildest what-if scenarios! This can dramatically improve their understanding of the model, better than any feature importance plot could do. Remind your colleagues that correlation is not causation Predictive models that capture actual mechanistic links between the input and the response variables are rather rare in business settings. This is especially true for the complex algorithmic models that include a large number of predictors. Most of these models make their predictions merely due to the <em>correlation</em> between predictors and the response variable. But, as the saying goes, “ correlation is not causation”, or at least not always. This has two important implications when it comes to interpreting a predictive model. Firstly, it is possible to build a useful predictive model using input variables that have no actual association with the response variable. One can find lots of examples on the Internet of the so-called “ spurious correlations”. Here is one of them: It is easy to build a simple linear regression model that would accurately predict the number of doctorate degrees awarded based on mozzarella cheese consumption. Can this model be successfully used in practice to estimate the number of doctorate degrees awarded in a given year? Thanks to the high correlation between the two variables, definitely yes. But something tells me that any attempt to interpret it would only trigger a good laugh in the room. Secondly, it is often tempting to use insights gained from a predictive model to devise actions for controlling the response variable. However, if such a model is mainly based on non-mechanistic associations, doing so is likely to be meaningless, and sometimes can be even dangerous. For example, the relationship depicted above implies that increasing the per capita consumption of mozzarella cheese would result in more doctorate degrees awarded. Give it a moment to sink in… Would you recommend this to a decision maker whose goal is to strengthen the workforce with more civil engineers educated to a PhD level? Explain the existence of multiple good model By definition, any model is only an approximation of the process that generated the observed data. As this underlying process is unknown, the same data can often be described similarly well by very different models. In Statistics, this phenomenon is known as the “multiplicity of models” (Breiman 2001). This phenomenon causes no problems as long as all we need from a model is high predictive accuracy. However, it becomes problematic if the goal is to gain insights about the data-generating process and then make practical decisions based on this information. The reason is simple: different models that fit the same data well can lead to remarkably different conclusions. And the worst part is that there is no way to tell which of these conclusions are correct (unless they are proved correct in a follow-up controlled experiment). Here is a simple example. Suppose, we have a dataset that describes how a response variable y changes over time These data can be fitted similarly well (e.g., in terms of RMSE) by several structurally different models. For example: The three models and their estimated parameters are as follows: As we can see, Model 1 is a 2nd-degree polynomial, Model 2 — 3rd-degree polynomial, and Model 3 — exponential decay process. Obviously, these models imply different underlying mechanisms of how y changes over time. In fact, this toy example is based on data simulated from the following model that defines an exponential decay process: Thus, Model 3 corresponds to the actual process that generated the data, and it fits that process quite well (in terms of the parameter estimates). However, we would never know this in real life and might wrongly conclude that some other model provides a better description of the underlying process. In practice, using the wrong model for decision making could lead to unforeseeable negative consequences (Grimm et al. 2020). Business users of Machine Learning models often ask to “explain” how models make their predictions. Unfortunately, providing such an explanation is not always possible. This is especially true for complex models whose main purpose is to make accurate predictions. Arguably, most of the models built by Data Scientists nowadays belong to this very category. Nevertheless, engaging stakeholders early on in the project and demonstrating that the model captures their domain knowledge and is well tested can help in building their trust toward that model. This article was originally published on Medium, and republished with the permission of the author. Leave a Comment	{"url":"https://resources.experfy.com/ai-ml/stakeholders-interpretable-machine-learning-model/","timestamp":"2024-11-08T14:56:31Z","content_type":"text/html","content_length":"333373","record_id":"<urn:uuid:604d9e08-d8d3-4b40-a929-35da9e10da86>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00740.warc.gz"}
Properties of waves Students learn about the different properties of waves and further explore the wavelength, frequency, speed. They are given wave speed equations. Students will be able to describe the different components of waves. Review the types of waves shown in the pictures with the class to help identify if they are longitudinal or transversal and to identify the medium the wave moves in. Then have students work in pairs to answer the questions given on the interactive whiteboard. Introduce students to the properties of waves. Tell students that waves have different properties and use light as an example. Ask students to discuss with a partner what the remember about amplitude. Discuss what they came up with as a class and then explain what wavelength is. Give examples of different kinds of waves with varying wavelength and help students understand the difference between langer and smaller wavelengths. Then introduce frequency. Tell students that frequency measures the number of waves that pass through a given amount of time and is measured in hertz (hz). Combine the concepts of frequency and energy together and discuss how waves with higher frequencies have higher energies and waves with lower frequencies have lower energies. But how are these measured? Show students that the wave speed measures how fast a wave is traveling, and show the equations that can be used to calculate the wave speed. Practice calculating the wave speed as a class with the given information. Then ask students to solve for wave speed in groups or pairs. Show students that you can change the wave speed equation to find either wavelength or frequency. Ask partners to determine which equation to use and calculate the wavelength of the note. Students are asked to answer multiple-choice questions covering the key concepts of the lesson. They are then given a few true/false questions and are asked to calculate wavelength or frequency. Remind students that they are now able to describe the different components of waves and that waves are all around us. Being able to determine wave speed is really important when you're talking about a tsunami! To close have students complete an exit slip answering the two questions on the interactive whiteboard. Gynzy is an online teaching platform for interactive whiteboards and displays in schools. With a focus on elementary education, Gynzy’s Whiteboard, digital tools, and activities make it easy for teachers to save time building lessons, increase student engagement, and make classroom management more efficient.	{"url":"https://www.gynzy.com/en-us/library/items/properties-of-waves","timestamp":"2024-11-04T05:25:46Z","content_type":"text/html","content_length":"552930","record_id":"<urn:uuid:30e7e643-c712-490e-83c0-d5bff27c7e9a>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00130.warc.gz"}
How To Teach Geometric Volume To Kids Hui Sieng Hii/iStock/Getty Images Geometric volume is the the amount of space inside a solid shape. To teach geometric volume, first give your students concrete experience with manipulatives so they can fully understand the concept of volume. Then, guide them so they will discover the relationship between surface area and volume so they can predict the formula for volume. Next, give them real-life problems to solve. Discover Volume Instruct your students to construct a rectangular prism with linking cubes. The length should be six cubes, the width four cubes and the height one cube. Guide them to use what they know about the formula for surface area to predict how many cubes they used, and then have them count the cubes to see if their prediction is correct. The answer should be 24 cubes. Next, instruct them to keep the length and width the same, but construct a prism that has a height of two cubes. They should again predict how many cubes they have and count to see if they are correct. The answer should be 48 cubes. Continue with three cubes for the height. Guide them in discovering the formula for volume of a prism, which is length x width x height or l x w x h. Give the students the dimensions of a few rectangular prisms to allow them to practice finding the volume. Volume of a Cylinder Show the students a cylinder and ask them how many cubes would fit it in. Guide them as they discover that it is difficult to measure the volume of a cylinder with cubes because the cubes don't fit into a round space. Remind them about the relationship of surface area of a cube to volume of a cube and see if they can predict a way to solve the problem. Show them that the volume of a cylinder is the surface area of a circle times the height. The surface area of a circle is pi times the radius squared. So to calculate the volume of a cylinder, you take the surface area of a circle times the height, which is pi times the radius squared times the height or pi x r^2 x h. Give them a few examples that have the measurement of the radius, and guide them as they practice. Volume of a Pyramid Show the students a pyramid. Ask them what will be tricky about predicting the volume of a pyramid. Because the sides of a pyramid slant, you can't simply multiply the surface area of the base by the height. The formula for the volume of a pyramid is one-third times the base times the height or 1/3 b x h. Show the students the difference between the height, the distance straight up from the base to the point, and the slant length. Real-Life Application Students will remember how to solve geometric volume much better if they can see its real-life applications. Bring a bag of potting soil that shows the volume in cubic feet and a cylindrical flower pot. Ask the students how they can figure out how many flower pots the bag of potting soil can fill. First, have them make a plan using the knowledge they have about volume. Explain that estimating is okay if the flower pot slopes slightly. Provide the tools they need, such as measuring tape and After they have made a plan, let them make measurements and discoveries on their own. The key here is the process, not getting the exact right answer. For an extension activity, provide them with measurements for a garden box and see how many bags of potting soil they need to fill the box. Cite This Article Burgtorf, Tabitha. "How To Teach Geometric Volume To Kids" sciencing.com, https://www.sciencing.com/teach-geometric-volume-kids-2090535/. 24 April 2017. Burgtorf, Tabitha. (2017, April 24). How To Teach Geometric Volume To Kids. sciencing.com. Retrieved from https://www.sciencing.com/teach-geometric-volume-kids-2090535/ Burgtorf, Tabitha. How To Teach Geometric Volume To Kids last modified March 24, 2022. https://www.sciencing.com/teach-geometric-volume-kids-2090535/	{"url":"https://www.sciencing.com:443/teach-geometric-volume-kids-2090535/","timestamp":"2024-11-07T08:57:24Z","content_type":"application/xhtml+xml","content_length":"73869","record_id":"<urn:uuid:8054b8c6-1829-40b0-94a4-b26a8a945e9f>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00107.warc.gz"}
Important Lie group representations in various dimensions and quantum field theories I was reading a nice paper by Seiberg on 5d susy gauge theories. Just in the introduction I stumbled upon something I had never thought about: "The spinor representation of SO(4,1) is four dimensional and is pseudoreal. Since the vector of SO(4,1) is in the antisymmetric product of two spinors, the miniml SUSY algebra is generated by two charges." This is is from hep-th/9608111. My question goes as following: How can we determine such stuff? How can I know if the spinor representation of SO(something) is something dimensional? How can I find out about the isomorphisms between various Lie groups important for QFTs? Is there a list which physicists use? Is there a general reference where we can consult on such issues for any space-time dimension and any QFT? If not would it not be useful to have one? Maybe a vague question but being in the beginning of my grad studies this is a very relevant question for people like me. Any help would be of great appreciation. The best general reference (but not specifically for QFT) from a physicists point of view is probably the book R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications, Dover Publications 2006. For a list of exceptional Lie algebra/Lie group isomorphisms see, e.g.: there are also corresponding isomorphisms for the real versions of the groups. This is an interesting text on its own and thanks for the information. Despite that, I have in mind something that is in direct connection with supersymmetry and string theory. E.g. something that would include exceptional Lie groups and their isomorphisms with other Lie groups and their relation to supersymmetry and string theory. For example in GSW there is some discussion on E8. Maybe such a generic reference does not exists though. Some useful reference is the Appendix B of volume 2 of Polchinski's book on string theory. This Appendix is called "Spinors and supersymmetry in various dimensions", which seems to me to be the kind of things you are interested in. This Appendix is maybe not totally complete and does not contain many proofs but it is a good starting point. Very nice explanations related to the subject can be found in the Lubos Motl's post http://motls.blogspot.co.uk/2013/04/complex-real-and-pseudoreal.html  Appendix B of Polchinski is very useful indeed but its main topic is supersymmetry in various dimensions and how to reduce it. Surely it covers some parts of my question. As does the blog post of Lubos you mention as does another blog post of Lubos which gives a short review on the exceptional Lie groups. This is why i said that what I am asking might not exists. It seems that we could be making a useful guide in here though.	{"url":"https://www.physicsoverflow.org/24700/important-representations-various-dimensions-quantum-theories","timestamp":"2024-11-07T22:20:52Z","content_type":"text/html","content_length":"154634","record_id":"<urn:uuid:f8299f2c-d6e1-4b4d-8380-342b7a08d7c3>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00344.warc.gz"}
Undergraduate research Each summer the RTG hosts an undergraduate summer research program, coordinated by RTG postdocs and graduate students. Students perform research under the guidance of a faculty or postdoctoral mentor, they attend and present in group meetings, and write a final research report with the help of the coordinators. Students also present their research to the RTG community and the broader Below are some projects that have been done in the AM-SURE program. AM-SURE 2023 The AM-SURE 2023 program took place May 22-July 28 in the summer of 2023, and was coordinated by Olivia Pomerenk, Ryan Shìjié Dù, and Fortino Garcia. Below is a list of students, their mentors and projects (topics, slide decks, and reports). AM-SURE 2022 The students that participated in the in-person 10-week program in the summer of 2022 (late May-July), and their projects/mentors, are: 1. Emma Modrick, Role of turbulent flows in plankton ecology (Smith) 2. Edward Gilman, Rectified motion induced by non-antiperiodic excitations (Aref Hashemi) 3. Alison Tatsuoka, Internal gravity waves in time-dependent stratifications (Samuel Boury) 4. Pietro Topa, Aerodynamic stability of gliding and soaring flyers (Leif Ristroph) 5. Nigel Shen, Improving the particle in cell method for plasma simulation (Antoine Cerfon) 6. Athena Liu & Emily Bunnapradist , Efficient and interpretable modeling of cortical network dynamics through machine learning (Megan Morrison and Zhuo-Cheng Xiao) 7. Winston Liang, Analyzing how limit cycles turn active matter into robots (Bob Kohn) 8. Julie Zhu, Optimization for designing quantum logic gates (Georg Stadler and Fortino Garcia) 9. Eleven Chen, Simulation of a rotating cylinder in gravitational flow , see also movie below (Charles Peskin) AM-SURE 2021 The AM-SURE program will take place from June 1st - July 30th 2021, most likely in virtual format but with potentially some in-person activities. The following students will take part in the program: AM-SURE 2020 While the AM-SURE program was cancelled in the Summer of 2020 due to the Covid pandemic, there were a number of students that were transfered into the SURE program and co-funded, and did research remotely on the following projects: 1. Modeling and Simulation of Bacteria Population Dynamics using Markov Chain, Amy Dai with Eric Vanden-Eijnden as mentor. 2. Mathematical Model for an Optimally Fenestrated Fontan Circulation, Zan Ahmad with mentor Charles Puelz. 3. Inverse Scattering and Riemann-Hilbert Problems, Ron Nissim with mentor Perci Deift. 4. Latent Factor Discovery in Markov Process through Optimal Transport, Nhi Pham with mentor Esteban Tabak. 5. Optimal Transport Based Incomplete Data Clustering and Imputation, Junyi Bob Zou with mentor Esteban Tabak. 6. Active Particles in Active Environments, Tanya Wang with mentors Sophie Marbach and Ruben Zakine (see movie below). AM-SURE 2019 The AM-SURE 2019 program took place May 28-Aug 2 in the summer of 2019, and was coordinated by Rob Webber and Charles Puelz. Below is a list of students, their mentors and projects (topic and 1. Vaisnav Gajaraj Mentor: Esteban Tabak Weighted Adaptive Optimal Transport Using Quasi Newton Methods 2. Paulina Czarnecki Mentors: Calina Copos and Jennifer Crodelle Building a mathematical model of the Merkel cell 3. Zach Danial Mentor: Charles Puelz Modeling Differences between Therapeutic Plasma Exchange Configurations 4. Alexandre Milewski Mentor: Esteban Tabak A Minmax algorithm for Optimal Transportation 5. Yuliang "Scott" Shi Mentor: Charles Peskin Synchrony and Asynchrony of a Neural Population with Spontaneous Leaking and Shunting Inhibitions 6. Guanhua Sun Mentor: Miranda Holmes-Cerfon The Dynamics of a Polygon in a Swirling System (see below) AM-SURE 2018 The AM-SURE 2018 program took place May 29-Aug 3 in the summer of 2018, and was coordinated by Jason Kaye and Pejman Sanaei. Below is a list of students, their mentors and projects (topic and 1. Peilin Zhen Mentor: Dimitris Giannakis ENSO Forecasting Using Reproducing Kernel Hilbert Spaces 2. Alexandra Kuznetsov Mentor: Charlie Peskin Fluid Dynamics of Fetal Circulation 3. Taylor Meredith Mentors: Jennifer Crodelle & Calina Copos A Mathematical Model of the Neuromuscular Junction and Muscle Contraction 4. Nick Lewis Mentor: Leif Ristroph Force Analysis on Swimming Bodies in Stable Configurations 5. Ling Lan Mentor: Miranda Holmes-Cerfon Self-Folding Metasheets: Folded States and Assignments of Fewest Creases 6. Tianrui Xu Mentor: Charlie Peskin Mathematical Models for Red Blood Cells (see animation below)	{"url":"https://math.nyu.edu/dynamic/research/pages/research-and-training-group-mathematical-modeling-and-simulation/research/undergraduate-research/","timestamp":"2024-11-06T09:39:48Z","content_type":"text/html","content_length":"32616","record_id":"<urn:uuid:47de4289-3a3b-415c-90ad-eda709e12d86>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00468.warc.gz"}
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Understanding Absolute Value: What It Means and Why It Matters - techyktimes.com122 Understanding Absolute Value: What It Means and Why It Matters The absolute value of a number is an important math concept that tells us how far a number is from zero. It doesn’t care about whether the number is positive or negative. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5! This means both numbers are the same distance away from zero on the number line. Knowing the absolute value helps us understand distances and differences between numbers. When we find the absolute value of the difference between two numbers, we can see how far apart they are. This is very useful in math and in everyday life. What is Absolute Value The absolute value of a number tells us how far that number is from zero on the number line. It is written as \|x\|, where x is the number. For example, if we take the number 3, its absolute value is 3, written as \|3\| = 3. If we look at -3, its absolute value is also 3, written as \|-3\| = 3. This shows us that both 3 and -3 are the same distance from zero, which is 3 units. Understanding this concept is very important in math. Absolute value helps us ignore the signs of numbers. This means we focus only on how far the number is from zero, not whether it’s positive or negative. This idea is useful in many areas, such as measuring distances or working with temperature changes. When we think about distances in the real world, we often think of absolute value without even realizing it. For example, if you walk 5 steps forward and then 5 steps back, your total distance walked is 10 steps. Even though you moved in both directions, you can see that the absolute distance remains the same. This simple idea helps us see why absolute value is so useful. In conclusion, absolute value is all about distance. It helps us understand numbers better by showing us how far they are from zero, regardless of their signs. This makes it an essential part of math that we use every day. Why Do We Use Absolute Value Absolute value is used in many areas of math and science. One big reason we use it is to compare numbers. For instance, if you want to see which number is bigger, you can look at their absolute values. This way, you know how far they are from zero. This method makes it easier to understand which numbers are larger, even if one is positive and the other is negative. Another important use of absolute value is in solving equations. Sometimes, we face problems where we need to find the distance between two numbers. For example, if you have two points on a number line, the absolute value of their difference tells you how far apart they are. This can be helpful in many situations, like measuring lengths or finding temperatures. In real life, absolute value helps us make decisions based on distances. For example, if you want to know how far away a friend is, you can use absolute value to calculate the distance, whether they are to the left or right of you. This can help you figure out the best way to meet them. Finally, using absolute value in daily life can make problem-solving easier. By focusing on distance rather than signs, we simplify our calculations and understand the situation better. Whether in math class or at home, understanding absolute value can help us solve problems more effectively. How to Find the Absolute Value of a Number Finding the absolute value of a number is very simple! If the number is positive, the absolute value is the number itself. For example, \|4\| = 4. But if the number is negative, the absolute value is the same number without the negative sign. So, \|-4\| = 4. This means both positive and negative numbers can have the same absolute value. To practice finding absolute value, you can use a number line. Start by marking the number on the line. Then, see how far it is from zero. If the number is to the right, it’s positive, and if it’s to the left, it’s negative. No matter which way you go, the distance is what matters. You can also find the absolute value of fractions. For instance, if you have \|−2/3\|, you can simply drop the negative sign, and it becomes 2/3. This shows that absolute value works with all kinds of numbers, not just whole numbers. In summary, finding absolute value is an easy task. Just remember to drop the negative sign if the number is negative and keep it the same if it’s positive. With practice, you will quickly become a pro at finding absolute values! Examples of Absolute Value in Real Life Absolute value is not just a math concept; it appears in many real-life situations. One example is when we talk about temperature. If the temperature is 30 degrees Celsius outside, that’s a positive number. However, if it drops to -30 degrees Celsius, both temperatures have an absolute value of 30. This shows how far the temperature is from freezing, regardless of whether it is hot or cold. Another example is in sports. Imagine a basketball player scores 10 points in one game and loses 10 points in another game. The absolute value of their scores helps us see how well they performed. Whether they gained or lost points, we can compare their performances based on distance from zero. Absolute value can also help when traveling. If you drive 50 miles north and then 50 miles south, the distance you traveled is 100 miles. Even if you change directions, the total distance remains the same. This shows that knowing the absolute value of distances helps us understand our travels better. In conclusion, absolute value plays a significant role in our daily lives. Whether measuring temperature, comparing sports scores, or tracking travel distances, this concept helps us understand the world around us. By focusing on distance rather than signs, we make our lives easier. Absolute Value on a Number Line A number line is a useful tool to visualize absolute value! It is a straight line with numbers placed at equal intervals. The center of the line is zero, with positive numbers on the right and negative numbers on the left. This setup helps us see how far each number is from zero. When we look at absolute value on a number line, we can easily spot distances. For instance, if you want to find the absolute value of -7, you can locate -7 on the left side of zero. Then, measure how many units away it is from zero. In this case, it is 7 units away, so \|-7\| = 7. You can practice using a number line with different numbers. Place any number on the line, then count how far it is from zero. This visual method makes it easier to understand absolute value because you can see the distances clearly. Overall, using a number line to explore absolute value helps us understand how numbers relate to each other. It gives us a clear picture of distances and makes learning math more fun and Comparing Positive and Negative Numbers When we compare positive and negative numbers, absolute value becomes very helpful. Often, we think that positive numbers are bigger than negative ones. However, absolute value helps us see the distance from zero, allowing us to compare them fairly. For example, \|5\| = 5 and \|-5\| = 5. They are the same distance from zero. Sometimes, people might be confused about which number is larger. Let’s look at -2 and 3. Here, -2 is less than 3 because it is further left on the number line. However, if we look at their absolute values, we see that \|-2\| = 2 and \|3\| = 3. This shows us that 3 is further from zero, even though -2 is a smaller number. In real life, comparing numbers helps us make choices. For example, if you are choosing between two games, one might have a score of -10 and the other +5. Absolute value helps you see how far apart those scores are from zero. This way, you can decide which game was more successful! In conclusion, absolute value plays a crucial role when comparing positive and negative numbers. It helps us understand distances from zero, making comparisons easier and clearer. By using absolute values, we can make better decisions in our daily lives. The Importance of Absolute Value in Math Absolute value is very important in math because it helps simplify problems. When we know how far numbers are from zero, we can focus on the essential parts of a problem. This makes it easier to solve equations and understand relationships between numbers. In algebra, for instance, absolute value is often used to solve equations like \|x\| = 3. This means that x can be either 3 or -3. By understanding absolute value, we can find all possible solutions to problems, which is a vital skill in math. Furthermore, absolute value is used in statistics. When we analyze data, we often look for averages or differences. Using absolute values helps us ignore negative signs and focus on the sizes of the numbers. This allows us to see trends and patterns more clearly. In summary, the importance of absolute value in math cannot be overstated. It simplifies problems, helps us solve equations, and is useful in statistics. By mastering this concept, we gain valuable skills that will help us in many areas of mathematics. In conclusion, absolute value is a simple yet important concept in math. It helps us understand how far numbers are from zero, no matter if they are positive or negative. By learning about absolute value, we can solve problems more easily and make better sense of numbers in real life. Whether we are comparing scores, measuring distances, or solving equations, absolute value is a tool we can always use. Getting comfortable with absolute value makes us stronger in math. The more we practice finding absolute values and using them in different situations, the better we will understand math concepts. So, let’s keep exploring and practicing! Remember, math can be fun, and knowing about absolute value is one step towards becoming a math expert.	{"url":"https://techyktimes.com/2024/10/16/absolute-value/","timestamp":"2024-11-10T22:02:00Z","content_type":"text/html","content_length":"66366","record_id":"<urn:uuid:17421b30-7344-4950-a701-5d0f32d632ef>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00069.warc.gz"}
CMLS \| CRAN/E Constrained Multivariate Least Squares CRAN Package Solves multivariate least squares (MLS) problems subject to constraints on the coefficients, e.g., non-negativity, orthogonality, equality, inequality, monotonicity, unimodality, smoothness, etc. Includes flexible functions for solving MLS problems subject to user-specified equality and/or inequality constraints, as well as a wrapper function that implements 24 common constraint options. Also does k-fold or generalized cross-validation to tune constraint options for MLS problems. See ten Berge (1993, ISBN:9789066950832) for an overview of MLS problems, and see Goldfarb and Idnani (1983) for a discussion of the underlying quadratic programming algorithm. • Version1.0-1 • R versionunknown • Needs compilation?No • Last release03/31/2023 This package has been downloaded 662 times in the last 30 days. The following heatmap shows the distribution of downloads per day. Yesterday, it was downloaded 23 times. Data provided by cranlogs • Depends2 packages • Reverse Depends1 package • Reverse Imports1 package • Reverse Suggests1 package	{"url":"https://cran-e.com/package/CMLS","timestamp":"2024-11-02T02:04:22Z","content_type":"text/html","content_length":"47848","record_id":"<urn:uuid:3d26e932-04dc-40be-86da-8dc426571d8d>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00086.warc.gz"}
Papers with Code - Path Length Regularization Explained Path Length Regularization is a type of regularization for generative adversarial networks that encourages good conditioning in the mapping from latent codes to images. The idea is to encourage that a fixed-size step in the latent space $\mathcal{W}$ results in a non-zero, fixed-magnitude change in the image. We can measure the deviation from this ideal empirically by stepping into random directions in the image space and observing the corresponding $\mathbf{w}$ gradients. These gradients should have close to an equal length regardless of $\mathbf{w}$ or the image-space direction, indicating that the mapping from the latent space to image space is well-conditioned. At a single $\mathbf{w} \in \mathcal{W}$ the local metric scaling properties of the generator mapping $g\left(\mathbf{w}\right) : \mathcal{W} \rightarrow \mathcal{Y}$ are captured by the Jacobian matrix $\mathbf{J_{w}} = \delta{g}\left(\mathbf{w}\right)/\delta{\mathbf{w}}$. Motivated by the desire to preserve the expected lengths of vectors regardless of the direction, we formulate the regularizer as: where $y$ are random images with normally distributed pixel intensities, and $w \sim f\left(z\right)$, where $z$ are normally distributed. To avoid explicit computation of the Jacobian matrix, we use the identity $\mathbf{J}^{\mathbf{T}}_{\mathbf{w}}\mathbf{y} = \nabla_{\mathbf{w}}\left(g\left(\mathbf{w}\right)·y\right)$, which is efficiently computable using standard backpropagation. The constant $a$ is set dynamically during optimization as the long-running exponential moving average of the lengths $\|\|\mathbf{J}^{\mathbf{T}} _{\mathbf{w}}\mathbf{y}\|\|_{2}$, allowing the optimization to find a suitable global scale by itself. The authors note that they find that path length regularization leads to more reliable and consistently behaving models, making architecture exploration easier. They also observe that the smoother generator is significantly easier to invert. Task Papers Share Image Generation 52 17.87% Image Manipulation 14 4.81% Face Generation 13 4.47% Disentanglement 13 4.47% Diversity 11 3.78% Face Recognition 10 3.44% Translation 7 2.41% Conditional Image Generation 7 2.41% Face Swapping 6 2.06% Component Type 🤖 No Components Found You can add them if they exist; e.g. Mask R-CNN uses RoIAlign	{"url":"https://paperswithcode.com/method/path-length-regularization","timestamp":"2024-11-09T23:43:42Z","content_type":"text/html","content_length":"80212","record_id":"<urn:uuid:bc6e0222-241a-45a7-af8e-70c605f4b8a4>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00719.warc.gz"}
Global Index Quick Reference Yorick Function Reference Advanced Array Indexing • A scalar index or the start and stop of an index range may be non-positive to reference the elements near the end of a dimension. Hence, 0 refers to the final element, -1 refers to the next to last element, -2 to the element before that, and so on. For example, x(2:-1) refers to all but the first and last elements of the 1-D array x. This convention does NOT work for an index list. • A range function ifunc may be followed by a colon and an index range start:stop or start:stop:step in order to restrict the indices to which the range function applies to a subset of the entire dimension. Hence, x(min:2:-1) returns the minimum of all the elements of the 1-D array x, excluding the first and last elements. • An index specified as a scalar, the start or stop of an index range, or an element of an index list may exceed the length of the indexed dimension ID, provided that the entire indexing operation does not overreach the bounds of the array. Thus, if yis a 5-by-6 array, then y(22) refers to the same datum as y(2,5). • The expression z(..) - using the rubber-index operator .. - refers to the entire array z. This is occasionally useful as the left hand side of an assignment statement in order to force broadcasting and type conversion of the right hand expression to the preallocated type and shape z. • The expression z() - using the rubber-index operator - collapses a multidimensional array z into a one-dimensional array. Even more useful as z(*,) to preserve the final index of an array and force a two-dimensional result.	{"url":"http://doc.gnu-darwin.org/refcard/qrfunc06.html","timestamp":"2024-11-03T09:45:46Z","content_type":"text/html","content_length":"6934","record_id":"<urn:uuid:f1bc96cc-185a-4068-84d8-bbbda9379778>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00646.warc.gz"}
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Implementing String Pattern Matching Using DFAs I took a course called Digital Systems Design in my previous semester and ended up really loving it. It was probably my favourite course that semester. In the course we learnt about basic logic gates, combinational and sequential circuits, finite state machines, programmable logic arrays, etc. I found all of this very interesting and dove deeper into these topics. In this post, we'll focus on of these topics, Finite State Machines (FSMs) and use them to implement string pattern matching. Finite State Machines are computational models used to design both programs and sequential circuits. They have a set of finite states, transitions between states, and actions, making them ideal for modelling behaviour that can be broken down into distinct steps. 1. States: The different modes or conditions the system can be in. 2. Transitions: Moving from one state to another, triggered by specific inputs or events. 3. Inputs: Signals or events that cause the state to change. 4. Outputs: Actions or signals that result from the current state or a state change. Let's consider a basic FSM designed to recognise binary strings that end with "01." 1. S0: The initial state. 2. S1: State after reading '0'. 3. S2: State after reading '01' (accepting state). Current State Input Next State Description S0 0 S1 Transition to S1 on input '0' S0 1 S0 Remain in S0 on input '1' S1 0 S1 Remain in S1 on input '0' S1 1 S2 Transition to S2 on input '1' S2 0 S1 Transition to S1 on input '0' S2 1 S0 Transition to S0 on input '1' In this FSM, starting from the initial state S0, the machine reads each bit of the input string. If it ends in "01", the FSM will be in state S2, indicating a successful recognition of the pattern. There are two main types of FSMs: Deterministic Finite Automata (DFA) and Non-Deterministic Finite Automata (NFA). DFA: In a DFA, each state has exactly one transition for each possible input. This makes them more predicate and easier to design. The above example that we just saw is an example of a DFA. NFA: An NFA, on the other hand, can have multiple transitions for the same input, including transitions to multiple states or none at all. This makes NFAs more flexible but also harder to implement and reason about. Now that we know the basics of FSMs, and understand how DFAs work, we can implement string pattern matching by using DFAs. The program will take two strings as input: a pattern string and an input string. If the pattern string is present in the input string, it will return true. Otherwise, it will return false. For example, if the pattern string is "abc" and the input string is "ahabchf", the program should return true, since the pattern "abc" is present in the input string. On the other hand, if the pattern string is "def" and the input string is "ahabchf", the program should return false, as the pattern "def" is not found in the input string. We'll be using Go in this blog post as it is very simple and easy to understand and you can follow along in other languages easily. First, we need to define the structure of our DFA. A DFA consists of a set of states, transitions between states based on input symbols, a start state, and one or more accept states. package main type DFA struct { numStates int transitions map[int]map[rune]int startState int acceptStates map[int]bool Here, DFA is a struct with the following fields: • numStates: The number of states in the DFA. • transitions: A map representing state transitions. Each state maps to another map where input symbols (runes) map to the next state. • startState: The start state of the DFA. • acceptStates: A set of accept states. We use a map for easy lookup. Let's also create a function to initialise a DFA. func NewDFA(numStates int, transitions map[int]map[rune]int, startState int, acceptStates map[int]bool) DFA { return &DFA{ numStates: numStates, transitions: transitions, startState: startState, acceptStates: acceptStates, This function just creates a DFA with the provided parameters and returns a pointer to it. Now, we need to build the DFA for a specific pattern. This involves setting up the states and transitions based on the pattern. • We need to determine the number of states required. The number of states required is equal to the length of the pattern plus one. This is because each character in the pattern corresponds to a state, and there is an additional state for the start state. • We also need to create a map to hold transitions for each state. This will be empty initially. • For each character in the pattern, we also need to set the transition from current state to the next state. • The last state (equal to the length of the pattern) will be an accept state. func buildDFA(pattern string) DFA { numStates := len(pattern) + 1 transitions := make(map[int]map[rune]int) for i := 0; i < numStates; i++ { transitions[i] = make(map[rune]int) for i, char := range pattern { transitions[i][char] = i + 1 acceptStates := map[int]bool{numStates - 1: true} return NewDFA(numStates, transitions, 0, acceptStates) • We calculate the number of states as len(pattern) + 1. • We initialise the transitions map to hold transitions for each state. • Then we iterate over the pattern and for each character, we set the transition from the current state to the next state. • Lastly we create an acceptStates map where the last state is marked as the accept state. Now we'll make a function to simulate the DFA on an input string. This function will basically run our DFA and check if it accepts it. func (dfa *DFA) Simulate(input string) bool { currentState := dfa.startState for _, symbol := range input { if nextState, exists := dfa.transitions[currentState][symbol]; exists { currentState = nextState } else { currentState = dfa.startState if dfa.acceptStates[currentState] { return true return dfa.acceptStates[currentState] The algorithm begins at the DFA's initial state. For each symbol in the input string, it checks if a valid transition exists from the current state. If so, it moves to the next state. Otherwise, it resets to the start state. If the current state becomes an accept state at any point, it returns true. Finally, after processing all symbols, it returns whether the final state is an accept state. We're pretty much done! Let's test our DFA with various input strings to see if it correctly matches the pattern. func main() { pattern := "abc" dfa := buildDFA(pattern) inputStrings := []string{ "xxabcxx", // Output: True (pattern "abc" is in the string) "abc", // Output: True (pattern "abc" matches the entire string) "ababc", // Output: True (pattern "abc" is in the string) "defabcghi", // Output: True (pattern "abc" is in the string) "abdefgh", // Output: False (pattern "abc" is not in the string) "aabbcc", // Output: False (pattern "abc" is not in the string) for _, input := range inputStrings { result := dfa.Simulate(input) fmt.Printf("Input: %q -> Output: %v\n", input, result) We first build the DFA for the pattern "abc" and then simulate the DFA on various input strings. And this works flawlessly! Input: "xxabcxx" -> Output: True Input: "abc" -> Output: True Input: "ababc" -> Output: True Input: "defabcghi" -> Output: True Input: "abdefgh" -> Output: False Input: "aabbcc" -> Output: False That was an intro to a very basic implementation of a DFA. DFAs are powerful tools that can be applied in various areas beyond pattern matching. They are used in the design of lexers, which are crucial in the process of compiling programming languages. DFAs also play a vital role in network protocols and text parsing algorithms. DFAs are also used in digital circuit design to model the behavior of sequential logic circuits. They help in the development of microprocessors. NFAs, the other type of FSMs, are actually used to build regex engines, making them essential for complex pattern matching tasks in text processing and search algorithms. Let me know if you guys would be interested in learning about NFAs or exploring more advanced applications of DFAs and NFAs in computational theory and practical implementations. Thank you for reading this and I hope you liked it!	{"url":"https://www.nexxel.dev/blog/dfa","timestamp":"2024-11-03T02:46:01Z","content_type":"text/html","content_length":"102555","record_id":"<urn:uuid:027e97f4-1c46-4401-b7c6-c492bdde2f99>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00893.warc.gz"}
Maximum sum in sequence Maximum sum in sequence Given a string of integers separated by a single space. Find a sequence of numbers in which the sum of the elements is maximum. For example, for string "2, -5, 1, 2, -2, 2" solution is the sequence "1 2" with sum = 3. Print max sum only.	{"url":"https://php.land/problems/13","timestamp":"2024-11-06T00:39:15Z","content_type":"text/html","content_length":"27068","record_id":"<urn:uuid:14b712f3-1e31-46b8-ad74-bc7aaf1fa7bd>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00699.warc.gz"}
**day lengths = drive chain **day 10 school days Well good morning moving inverse square professors. There is 24 hours in an earth day. There is also 24 hours in a Mars day. This morning you have a flight path to rotation rates for your fill in impostor professor. And this morning, professors, we are going to call Sir Isaac Newton a stupid elf. One who caused mathematics to explode into a false science called "mathematical fizzdics". Well, what we will really be doing is considering the earth-Mars 24 hour system. We will find it very difficult to do this without stopping at regular intervals and quietly whispering to each other "fee, fo, fi, fum, the world just got trolled for three hundred years by your silly Englishmun". Professors, garden path planetary motion professors will get to have more idea if that moving sun Copernican update ever sees the light of day. Apart from a transit being an alignment of two planets with the sun, the things for you to note are the inner two planets are like the moon. Have rotation periods of the order of their orbital periods. And outer adjacent planets are pairs with similar rotation periods. If you can note that, it's all pretty interesting for a moving inverse square law professor. Now, you can look it up or work it out yourself. Venus turns backwards on its axis once whilst this fixed sun professor planet we are on does 2/3's of its solar cycle. And, every 584 earth days, the same face of Venus is always towards our planet when Venus passes between us and the sun. There are a few other little rotational/cyclical ratios between the inner three planets as well. You'll find them when you do your research and investigations. So professors, when you get to see the tides of a planet as equal and opposite, in time you should see that, minus a moon or moons, the solar low tide axis of a planet becomes a circle around the sun at a planet's distance from the sun. Then, if the earth - moon high tides run through the Venus inverse square law during a transit, the low tide axis of the earth - sun system gets marginally shifted out of this circle toward the 'orbits' of the next planet in and the next planet out as the earth moves forward. At the same time the Venus inverse square law is being turned backwards as Venus and the earth move forward. If you get some spare time after your chores tonight, you could do worse than having a go at it. It's complex. It appears that the earth's lunar tides are really the earth's solar tides but getting moved around the earth by the moon. Naturally an impostor professor will never get much worthwhile worked out. There may not be anything in it. Alternatively, you do sort of need a spatial picture of the structure of an inverse square law field in your head first for all this. Professors, if these diagrams have meaning, their key is the different relative speeds of the 'orbit' hopping tidal axes. As the planets move a quarter of their ways around the sun, the axes move from a high tide axis to mid tide axes for the outer planet. And the tangent approximates being the true low tides axis of an inner planet. And also sorry about the stupid anus joke. It seems to have slipped in from the fart class next door. And it wouldn't hurt to keep an open mind about the Martians. If a flight path to rotation rates can be an impostor professor, it means the unexpected does Professors of the fixed sun variety, it pains an impostor flight path to rotation rates professor to say this. Until you are having a crack at similar and synchronised rotation rates of adjacent planets, you are grade 2 trolls hoping to one day be as good a troll as a stupid English elf. To explain this further, you do in fact have a condition known as ETA. So professors, please treat yourselves and each other kindly. At this stage there is no known cure for Extreme Truth Aversion. Hold each others hand as you cross the road. The unfortunate side of this ETA condition is it can cause Sir Isaac Newton induced delusions about Johannes Kepler's three laws of planetary motion. As you know, the sun is still fixed for you. • The orbit of a planet is an ellipse with the Sun at one of the two foci. • A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. • The preferred flight path to rotation rates layout of Kepler's third law is below. Professors, Kepler's third law says nothing but a planet's speed relative to the sun is a consequence of the sun's inverse square law, not a consequence of some original momentum or whatever your ETA condition is still unfortunately trolling out. How Sir Isaac was originally so stupid to miss this you may never know. Well you might. Just be careful not to mention the war. Sir Isaac was a bizarre trolling elf with stupid English desire to perform an abstract fixed sun intellectual utopia between Italy's inertial circles and Germany's ellipses. So professors, the understanding of these three laws will have the motion of the sun's inverse square law field completely factored into the three laws. The basic explanation of the third law is almost undoubtedly that all descents due to gravity are curving relative motions. The explanation of the ellipse is likely to be found in the rotation rate table. That is Kepler's third law is causing the second law and the first law is just a statement in deference to a perfect circle around a fixed sun. It is interesting stuff for a genuine moving sun professor. Yes. Rotation rates entering Kepler's work maybe a chance to flick your professional fixed sun celestial conscience away from trolling an original bang into societies. Allowing rotation rates/day lengths to check into your celestial outlook would be rather good. The thing to remember is all these diagrams are travelling at 220 km/sec. Or some such speed. They are diagrams of the positions of adjacent planets a quarter cycle after an inner planet's transit of the next planet out. If a moving inverse square law professor can get on top of rotation rates, they will illuminate a planet. These are all scale diagrams minus the ellipses and minus the angle of the path of the sun to the paths of the planets. They all have a curious approximate tangent or true low tide axis. And, interestingly, after a quarter cycle, the earth - Venus tide axes in question are very close to a right angle whilst the Venus 'orbit' of the sun is the one closest to that of a circle. Professors, before your garden path planetary motion professor cranks up again, you could whack the various ellipses on and have some fun with it. The interesting thing is the tangent from an inner planet is directed in the region of the next planet out a quarter cycle beyond the transit of the inner planet. The way the planets are always tending towards a complete alignment suggests the inverse square laws of the planets are a tension within the motion of the sun's inverse square law. On one hand the planets have the relative speed that the motion of the sun's inverse square law supplies at a planet's distance from the sun. (Kepler's third law) On the other, adjacent planetary inverse square laws are tidally pushing on each other with their various relative speeds within the motion of the sun's inverse square law and inspiring mutual relative speeds for each other. These inspirations appear as the rotation rates of the planets and the ellipses (Kepler's second law). Maybe anyway. Moving inverse square law professors will work it out. Pluto's inverse square law seems to be marginally outside the tension. Not sure. Conjecture about his relationship with Brahe aside, that Johannes Kepler was a beauty. Not really the Bode perspective, but the distances of the planets from the sun looks like being to do with each other and it's likely to be the planets that are turning the sun's inverse square law. Time for your paper plane and orange juice break. Welcome back professors. Hopefully rotation rate considerations have refreshed you enough to take on a boring task. We now have to call Sir Isaac Newton the super earth troll. If we could avoid doing this, we could get our togs on and go for a dip in tidal champagne. Really professors, it should be time for you to be organising your moving inverse square laws social functions. Celebrate the motions of inverse square laws and the whole world will celebrate with you. It's post Sir Isaac party time for you. For now Sir Isaac saying one mass was a part cause of its attraction to another mass was the give away about us having a trolling elf on our hands. How could the earth help the moon draw the earth to the moon? There is silly and there is English troll man. Without knowledge of how oppositely directed inverse square laws can mathematically or physically co-exist in space, or unify as one in space acting in two directions at once, well the elf did give us a few clues about his trolling. Opposite vectors impact upon each other. Courtesy of government funded education, the elf's failure to investigate the arithmetic of the opposite directions of inverse square laws meant the celestial outlook of the planet was to fall into hands of the apprentice trolls. Otherwise known as TMMPs or the morons mathematical physicists. Of course the G in Cavendish experiments does seem to be genuine. It is a moving sun professor's job after class to work out just what it means. The small masses are cancelled out and take no part in the derivation. And the large mass doesn't move. It appears that the experiments show M/(g.d.d) = a constant for all values of M where M is a mass, d is a distance from the centre of M and g is a rate of acceleration at d towards the centre of M. The tides say there is much more to it than that. But it does look like there is a basic gravity constant found from a multiplication of mass by its surface area. After that, professors, if you get around to reckoning that the 0.512 km/sec approximate straight line earth daily speed change must mean that there is a system of 14 day pushes between our earth and moon inverse square laws, what we probably have is the evolution of critical knowledge in the wings. Space is matter. If so, there will be a force away from our earth as in the earth's atomic mass displacing spontaneous space particles and creating an inverse square law acceleration field around the earth. A spontaneous space particle being what automatically exists to fill a void. The trick being spherical (four dimensional) particles can never exactly fill a void. The opposite force will be traceable to the extremity of space. Have fun working it out but the reason of a curved acceleration towards the path of this planet will or would be along the lines of increasing spontaneous space particle size as the surface area around the earth increases. The larger the space particles, the longer it takes for atomic mass to fall between the particles. Just have fun with it all, smell your roses. You might come up with it a bit better but an inverse square law in space says the nature of space changes with vertical distance. Finally, super fixed sun professor, in some ways the celestial woes you are currently causing us began with Geometric Euclid. Not with your good friend, Sir Isaac The Elf Who Came To Town In The Total Nude. Geometric Euclid lived before anybody even came up with a heaven and hell B.C. A.D. calendar. Some say Geometric was born in the once highly intelligent circle drawing Middle East over two thousand years ago. Others say he was a Trojan horse and lived on a sunny Greek island with a donkey. Over to you Geometric. That might be enough from you, Geometric. Remember starting that infinite straight line joke. It's now rotation rate school time. We now have gig after gig of memory and heaps of WiFi all over your planet. That infinite straight line joke of yours is interwoven into all this with grade two trolls saying there is a space time continuum. And the grade two trolls wouldn't know what time was if they fell over it on the way back from their next semester. Laugh you may, from all accounts your WiFi truly sucked. Look who's laughing now. If there are ever any moving inverse square professors, you are going to have to work the universe out for this planet. Look at the stars at night and estimate the size of space in all directions at once for a start is the advice. As we said at the beginning of the lesson, Sir Isaac Newton was a years ago mathematical elf who caused a mathematics to explode into untruth. Importantly, elves forever professors trolling out every particle in the universe is helping cause every other particle in the universe to be falling every which-a-way at once. Sir Silly Elf evidently wanted to be smartest troll in the big smart troll room. And things got worse. His calculus came to dominate the big smart troll room. Calculus equates the infinitesimal with zero and the very large with infinity. These are errors. The infinitesimal exists and infinity doesn't. Unfortunately for the goblin sector of the universe, calculus is a rough mathematical tool, not the perfection hyped up goblins credit it with being. Nearly lunchtime for you professors. If you have been mocking your seemingly impertinent elf calling fill in flight path to rotation rates impostor professor, well, fair enough. On the other hand, if you aren't ridiculing and you get yourselves past undressed eighteenth century goblins, you could do your best with the galactic situation the radio telescope has discovered us to be in. Make a plan for the future, etc. We are...... 1/ On a galactic journey. 2/ On a planet 3/ With a similar rotation rate to an immediate outer adjacent planet 4/ With an immediate inner adjacent planet turning in sync with the forward galactic movement of our planet. 5/ With thousands of trolling elf professors still saying every particle in the universe attracts every other particle in the universe. It's been fun getting into a digital age with your elf's mutual law of gravitation, professors. But time for us to move on from the past centuries trolling and onto your fine latter day discovery of the motions of the stars. This afternoon and weather permitting we will be studying the wind and visiting a national park. If its raining please bring your gas marks. We will then be staying indoors and studying the wondrous odour of elves. Professors, if your garden path planetary motion professor returns, remember you can only call a professor stupid when they are. This rotation rate class is now dismissed. Goodbye and good luck with your chores.	{"url":"https://www.whyvenusturnsbackwards.com/day-lengths--drive-chain.html","timestamp":"2024-11-14T17:26:38Z","content_type":"text/html","content_length":"59717","record_id":"<urn:uuid:c55bc8e6-723d-4c97-9419-63e64ef958d0>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00065.warc.gz"}
Geometric Properties of an Equilateral Triangle Aim: To check the accuracy of the geometric properties calculation for a rod cross-section in the form of an equilateral triangle. Name of a file with the initial data: Triangle.cns Formulation: Check the accuracy of the torsional geometric properties calculation for a rod cross-section in the form of an equilateral triangle. References: Young W.C., Budynas R.G., Roark's Formulas for Stress and Strain, New York , McGraw-Hill, New York, 2002. Initial data: ν = 0.3 - Poisson’s ratio; a = 40 cm - side length of an equilateral triangle. Design model: The design model is created by triangulation (the number of triangles ≈ 3000) on the basis of a model of the external contour. The external contour is an equilateral triangle. The number of vertices of the contour in a model is 3. Results Obtained in Consul Design model, coordinate and principal axes, center of mass, ellipse of inertia, core of the section Comparison of results: Parameter Theory CONSUL Deviation, % Torsional moment of inertia, I[t ]cm^4 55425,625 54477,143 1.71 Y-coordinate of the shear center, y[b] cm 20 19,999 0,005 Z-coordinate of the shear center, z[b] cm 11,547 11,589 0,36 Notes: Geometric properties can be determined analytically by the following formulas: \[ I_{t} =\frac{\sqrt 3 }{80}a^{4}; \] \[ y_{b} =a/2; \] \[ z_{b} =\frac{a}{2\sqrt 3 }. \]	{"url":"https://scadsoft.com/tests_consul/en/index/test/3","timestamp":"2024-11-14T21:04:43Z","content_type":"text/html","content_length":"7625","record_id":"<urn:uuid:a5d700ab-af8f-442c-83a4-02023d15cecd>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00219.warc.gz"}
Histograms with equal-width bins in MariaDB Histograms with equal-width bins are easy to construct using samples. For this it's enough to look through the given sample set and for each value from it to figure out what bin this value can be placed in. Each bin requires only one counter. Let f be a column of a table with N rows and n be the number of samples by which the equal-width histogram of k bins for this column is constructed. Let after looking through all sample rows the counters created for the histogram bins contain numbers c[1],..,c[k]. Then m[i]= c[i]/n * 100 is the percentage of the rows whose values of f are expected to be in the interval (max(f)-min(f))/k (i-1), max(f)-min(f))/k i-1). It means that if the sample rows have been chosen randomly the expected number of rows with the values of f from this interval can be approximated by the number m[i]/100 N. To collect such statistics it is suggested to use the following variant of the ANALYZE TABLE command: ANALYZE FAST TABLE tbl [ WITH n ROWS ] [SAMPLING p PERCENTS ] PERSISTENT FOR COLUMNS (col1 [IN RANGE r] [WITH k INTERVALS],...) □ 'WITH n ROWS' provides an estimate for the number of rows in the table in the case when this estimate cannot be obtained from statistical data. □ 'SAMPLING p PERCENTS' provides the percentage of sample rows to collect statistics. If this is omitted the number is taken from the system variable samples_ratio. □ 'IN RANGE r' sets the range of equal-width bins of the histogram built for the column col1. If this is omitted then and min and max values for the column can be read from statistical data then the histogram is built for the range [min(col1), max(col1)]. Otherwise the range [MIN_type(col1), MAX_type(col1) is considered]. The values beyond the given range, if any, are also is taken into account in two additional bins. □ WITH k INTERVALS says how many bins are included in the histogram. If it is omitted this value is taken from the system variable histogram_size.	{"url":"https://jira.mariadb.org/browse/MDEV-12313","timestamp":"2024-11-06T17:17:51Z","content_type":"text/html","content_length":"92720","record_id":"<urn:uuid:24d17835-dc36-4dc0-bd6c-9550ccc4cbf9>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00019.warc.gz"}
Ultimate Guide to the AP Calculus AB Exam 2024 (2024) What’s Covered: • What Does the AP Calculus AB Exam Cover? • Sample AP Calculus AB Exam Questions • AP Calculus AB Exam Score Distribution, Average Score, and Passing Rate • Tips for Preparing for the Exam • How Will Your AP Scores Affect Your College Chances? AP Calculus is a popular course for high schoolers, particularly those planning to pursue a college education. Hundreds of thousands of high schoolers each year study to obtain a passing/high score on the AP Calculus AB Exam so that they can “test out” of math distribution requirements in the early university years and save time and money. In 2022, over 250,000 of the 1.2 million students taking AP exams took the AP Calculus AB exam. This places it among the top 4 most popular AP exams. If you are interested in taking the AP Calculus AB exam, whether you have taken the class or are planning to self-study, read on for a breakdown of the test and advice on how to best prepare for it. What Does the AP Calculus AB Exam Cover? The purpose of the AP Calculus AB exam is to test your knowledge of specific “big concepts” that you have learned either through taking the AP Calculus AB course or through self-study. The “big concepts” of AB Calculus, as defined by College Board, are: • Limits • Derivatives • Integrals and the Fundamental Theorem of Calculus With regard to limits, students should be comfortable with computing limits, including one-sided limits, limits at infinity, the limit of a sequence, and infinite limits. The exam will also test each student’s ability to estimate the limit of a function at a point and apply limits to understand the behavior of a function near a point. With regard to derivatives, students should be comfortable with finding the slope of a tangent line to a graph at a point and using a graph to determine whether a function is increasing or decreasing. Students should also be able to find concavity and find extreme values. Additionally, the exam will require students to solve problems involving rectilinear motion. Finally, with regard to integrals, students should be able to use various techniques and methods to approximate an integral. Students should also be familiar with area, volume, and motion applications of integrals, as well as with the use of the definite integral as an accumulation function. How Long Is the AP Calculus AB Exam? What Is the Format? The AP Calculus AB exam is one of the longest AP exams, clocking in at three hours and 15 minutes. It has two sections. The first section contains 45 multiple choice questions, spans one hour and 45 minutes, and accounts for 50% of your total score. The second section consists of six free response questions, spans one hour and 30 minutes, and accounts for the remaining 50% of your score. Each section is divided into two parts, Part A and Part B. Students are permitted to use calculators during one part and not allowed to use them during the other. Section Skill Assessed Types of Question Number of Scoring Questions Weight Section I, Part A Multiple Choice without Graphing Algebraic, exponential, logarithmic, trigonometric, and general types of functions 30 33.3% Section I, Part B Multiple Choice with Graphing Calculator Analytical, graphical, tabular, and verbal types of representations 15 16.7% Section II, Part Free Response with Graphing Calculator Various types of functions and function representations and a roughly equal mix of procedural and 2 16.7% A conceptual tasks Section II, Part Free Response without Graphing Questions that incorporate a real-world context or scenario into the question 4 33.3% B Calculator Can I Use a Calculator? While taking the AP Calculus AB exam, you may use a scientific calculator on Part B of the multiple choice section and on Part A of the free response section. Your calculator should be able to plot the graph of a function within an arbitrary viewing window, find the zeros of functions, numerically calculate the derivative of a function, and numerically calculate the value of a definite integral. More information and a list of acceptable calculator models can be found in the official Calculator Policy. Sample AP Calculus AB Exam Questions Multiple Choice: Section I, Part A Note: A calculator may not be used on questions on this part of the exam. 1. The graphs of the functions f and g are shown above. The value of is (A) 1 (B) 2 (C) 3 (D) nonexistent (A) 6 (B) 2 (C) 1 (D) 0 Multiple Choice: Section I, Part B Note: A graphing calculator is required for some questions on this part of the exam. 1. The derivative of the function f is given by At what values of x does f have a relative minimum on the interval 0 < x < 3? (A) 1.094 and 2.608 (B) 1.798 (C) 2.372 (D) 2.493 2. The second derivative of a function g is given by For -5 < x < 5, on what open intervals is the graph of g concave up? (A) -5 < x < -1.016 only (B) -1.016 < x < 5 only (C) 0.463 < x < 2.100 only (D) -5 < x < 0.463 and 2.100 < x < 5 Free Response: Section II, Part A Note: A graphing calculator is required for problems on this part of the exam. 1. Let R be the region in the first quadrant bounded by the graph of g, and let S be the region in the first quadrant between the graphs of f and g, as shown in the figure above. The region in the first quadrant bounded by the graph of f and the coordinate axes has area 12.142. The function g is given by and the function f is not explicitly given. The graphs of f and g intersect at the point (A) Find the area of S. (B) A solid is generated when S is revolved about the horizontal line y = 5. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. (C) Region R is the base of an art sculpture. At all points in R at a distance x from the y-axis, the height of the sculpture is given by h(x) = 4 – x. Find the volume of the art sculpture. Free Response: Section II, Part B Rochelle rode a stationary bicycle. The number of rotations per minute of the wheel of the stationary bicycle at time t minutes during Rochelle’s ride is modeled by a differentiable function r for 0 ≤ t ≤ 9 minutes. Values of r(t) for selected values of t are shown in the table above. (A) Estimate r’(4). Show the computations that lead to your answer. Indicate units of measure. (B) Is there a time t, for 3 ≤ t ≤ 5 at which r(t) is 106 rotations per minute? Justify your answer. (C) Use a left Riemann sum with the four subintervals indicated by the data in the table to approximate Using correct units, explain the meaning of in the context of the problem. (D) Sarah also rode a stationary bicycle. The number of rotations per minute of the wheel of the stationary bicycle at time t minutes during Sarah’s ride is modeled by the function s, defined by for 0 ≤ t ≤ 9 minutes. Find the average number of rotations per minute of the wheel of the stationary bicycle for 0 ≤ t ≤ 9 minutes. AP Calculus AB Exam Score Distribution, Average Score, and Passing Rate While many exam distributions fall along a bell curve, with the majority of students receiving a score of 3, the AP Calculus AB exam shows a flatter distribution. Simply put, many students do well and many students do poorly. In 2022: • 20.4% of test-takers received a 5 • 16.1% of test-takers received a 4 • 19.1% of test-takers received a 3 • 22.6% of test-takers received a 2 • 21.7% of test-takers received a 1 This means that 55.6% of students who took the exam received a 3 or higher (typically considered passing). Note: The credit you will receive for AP exam scores varies widely from school to school. For example, prestigious schools (and even prestigious programs at schools) might accept only a 4 or a 5 to receive course credit. Though a score of 3 is typically considered passing, it’s not always enough. You can use this search tool to see what scores will allow you to receive credit at a specific college or university. Tips for Preparing for the Exam Step 1: Assess Your Skills Take a practice test to assess your initial knowledge of the material. It’s important to know where you are, so that you know how far you need to go. Keep in mind that Calculus is an age-old study, so you can use practice tests from before you were even born and you’ll be assessing/learning just the same! There are a couple of options for taking practice tests: • Print a practice exam and self-proctor • Use a diagnostic test offered through a commercial study guide • Talk to your teacher about proctoring a practice exam after school or over the span of a few lunch periods The 2012 exam has been openly published by the College Board and might be a good place to start. The College Board also has free response questions from the last few decades published online, though you should note that these are not complete assessments. Once you have taken your formative assessment, score it to identify the areas you already understand and those in need of improvement. Note: When grading the free response portion of the exam, make sure you grade yourself based on the rubric! Act like you are an AP scorer, scrutinizing and nitpicking every portion of your answer. The little points add up, and your area of improvement could very well be “needing to show my work.” Step 2: Study the Material After taking your assessment, you should be able to identify areas that need improvement. These areas could be related to content—not knowing which technique should be used to approximate which type of integral or not understanding the relationship between concavity and limits on a graph. Alternatively, the areas you struggle with might have more to do with form—like struggling to read graphs or conceptualize tables. Identify your areas for improvement, write them down, and focus on one area during each study session. Look over your mistakes and put in the work to understand them. Watch videos online about specific concepts, read sections in books about them, and talk to your friends and classmates about them. Then do it again and again and again until the areas you struggle with become areas you excel in. Some students choose to use commercial study guides when studying. This can be extremely beneficial, depending on your learning style. That said, if you choose to use a commercial study guide, use it in conjunction with your initial assessment. Study books are divided into sections organized around both big and small concepts. Don’t get stuck reading a guide front to back and don’t waste time on content that you have already mastered! Lastly, you might consider looking into the free resources that are available online! For decades, AP teachers have been publicly posting complete study guides, review sheets, and test questions. Use these for your benefit. Step 3: Practice Multiple Choice Questions Once you feel like you’ve mastered the concepts you initially struggled with, put them into action by answering some multiple choice practice questions. The College Board provides a set of sample questions with scoring explanations. Additionally, the College Board Course Description includes many practice multiple choice questions along with explanations of their answers. As you go through these, try to keep track of which areas are still tripping you up, and go over those concepts again until you have a better grasp on them. Focus on understanding what each question is asking and keep a running list of any vocabulary that is still unfamiliar to you. Step 4: Practice Free Response Questions When you score your own formative assessment, you will notice that every step you take to arrive at a solution to a free response question must be clearly notated for the exam reader. Even if you use your calculator to solve an equation, compute a numerical derivative, or find a definite integral, write the equation, derivative, or integral first. Otherwise, you can lose little points—and little points add up! The free response portion of the AP Calculus AB exam tests your ability to solve problems using an extended chain of reasoning. In most cases, an answer without supporting work will receive no credit. This means that, as you answer practice free response questions, you are not just practicing getting the right answer, but getting the right answer in the right way! You can get a better understanding of the free response section’s scoring by reading scoring commentary from the Development Committee and authentic examples of student responses and their scoring explanations from previous exam administrations. Step 5: Take Another Practice Test Every couple of weeks, when you are feeling confident or when you just want to see your progress, we recommend that you take another complete practice test. This will allow you to see which areas have improved the most and which areas still need improvement. Taking new practice tests at some interval will serve as a progress report of sorts. Step 6: Exam Day Specifics In 2024, the AP Calculus AB Exam will be administered on Monday, May 13 at 8 AM local time. The day before, make sure you have everything you need, and then focus on getting a good night’s sleep. Studies show that being well-rested is far more likely to lead to improved performance than last-minute cramming! How Will Your AP Scores Affect Your College Chances? WhileAP scores themselves don’t play a major role in the college admissions process, having AP classes on your transcript can be a crucial part of your application, especially at highly selective institutions. College admissions officers want to see that you enjoy challenging yourself intellectually, and that you’re capable of handling college-level coursework, and taking AP classes demonstrates both of those qualities. The main benefit of scoring high on AP exams comes once you land at your dream school, as high scores can allow you to “test out” of entry-level requirements, often called GE requirements or distribution requirements. This will save you time and money. If you’re starting to think about what schools you should apply to, we recommend that you use CollegeVine’s free chancing engine. This tool will consider your test scores, GPA, extracurriculars, and more, to calculate your chances of acceptance at various schools and to help you decide where to apply. Itcan also give you suggestions for how to boost your chances of acceptance—for example, by taking more AP classes in your junior or senior year.	{"url":"https://victoriantraditions.net/article/ultimate-guide-to-the-ap-calculus-ab-exam-2024","timestamp":"2024-11-07T17:15:15Z","content_type":"text/html","content_length":"132098","record_id":"<urn:uuid:51656872-2f14-4731-adc0-af3fb569f333>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00055.warc.gz"}
Sections of the StatPages.net ( │ {{ x.Name }} │ │ │ │ {{ x.Name }} │ © StatPages Web Pages that Perform Statistical Calculations! The web pages listed below comprise a powerful, conveniently-accessible, multi-platform statistical software package. There are also links to online statistics books, tutorials, downloadable software, and related resources. These pages are located on servers all over the world, and are the result of much cleverness and hard work on the part of some very talented individuals. So if you find a page useful it would be nice to send the authors a short e-mail expressing your appreciation for their hard work and generosity in making this software freely accessible to the world. Table of Contents for this page... Other Statistical Resources... There are a bewildering number of statistical analyses out there, and choosing the right one for a particular set of data can be a daunting task. Here are some web pages that can help: As you can see from looking at the StatPages.org web site, there are many "stand-alone" web pages that are each designed to perform only a single test or calculation. In addition, some talented individuals and groups have created coherent website that perform an entire suite of calculations, with a logical organization and consistent user interface. Each of these web sites is really a fairly complete online statistical software package in itself. Here are some of these "comprehensive" statistical analysis web sites: • Statigraphics Stratus-- a browser-based version of Stratigraphics statistical software. Provides plotting, probability distributions, summary statistics, one-, two-, and multiple-sample analysis, time-series analysis, regression analysis, curve-fitting, attribute estimates, ANOVAs, Statistical Process Control, smoothing, power/sample-size calculations, and other statistical analyses.Also provides access to over 50 applets in which you can enter data, compute statistics, create tables and graphs, and print out the results. The free "Guest" version supports up to 100 rows and 10 columns of data. For larger data sets, a single-user copy or a corporate deployment license can be purchased. To use the Guest version, click here. • OpenEpi Version 2.2 -- OpenEpi is a free, web-based, open source, operating-system-independent series of programs for use in public health and medicine, providing a number of epidemiologic and statistical tools. Version 2 (4/25/2007) has a new interface that presents results without using pop-up windows, and has better installation methods so that it can be run without an internet connection. Version 2.2 (2007/11/09) lets users run the software in English, French, Spanish, or Italian. • SOCR -- Statistics Online Computational Resource. A very comprehensive collection of online calculators and other interactive resources, including: Distributions (interactive graphs and calculators), Experiments (virtual computer-generated analogs of popular games and processes), Analyses (collection of common web-accessible tools for statistical data analysis), Games (interfaces and simulations to real-life processes), Modeler (tools for distribution, polynomial and spectral model-fitting and simulation), Graphs, Plots and Charts (comprehensive web-based tools for exploratory data analysis), Additional Tools (other statistical tools and resources), SOCR Wiki (collaborative Wiki resource), Educational Materials and Hands-on Activities (varieties of SOCR educational materials), SOCR Statistical Consulting and Statistical Computing Libraries. • SciStatCalc -- a very good web site (thank you Alijah Ahmed!), with online calculators for many of the common statistical probability functions and significance tests, and pages that explain the concepts and formulas behind the tests. Calculating pages provide flexible input options (type the numbers in, or read them from a text fiile), and well--organized output of results, with interpretations and graphical displays. • MedCalc -- Two different web sites: • ProtoGenie -- a free extensible web-based environment for research design and data collection for surveys, experiments, clinical trials, time series, cognitive and vision research, and methods courses. Lets you specify groups and define measurement and treatment events and their sequencing. The goal is to let users move smoothly from research design and data collection to interim and final statistical analysis. • The Calcugator -- a calculator, plotting engine, and programming environment. Also available as a free stand-alone downloadable program. Simple to use; rivals programs like MATLAB, with 200 functions/operators to perform real, integer, rational, complex, boolean, statistical, vector, array and matrix computations. Both the input and output of the program are displayed on standard windows which can be further edited, saved, merged, print-previewed and printed. Allows rapid creation of 2D and 3D plots of functions, polar and parametric displays, bar, pie, pareto and xy charts. All plots can be configured using the mouse (zooming, panning, selecting). Titles and labels are supported, and all figures created by the Calcugator can be exported into popular file formats or pasted into an editable window. As a programming environment it has a simple and compact language with identical syntax to Java/C/C++, and allows user-defined functions. • SISA (Simple Interactive Statistical Analysis) -- SISA allows you to do statistical analysis directly on the Internet. Click on one of the procedure names below, fill in the form, click the button, and the analysis will take place on the spot. Study the user friendly guides to statistical procedures to see what procedure is appropriate for your problem. • The WebMath page performs a large number of numeric calculations and symbolic algebraic manipulations of the type that might arise in high school / college algebra and calculus, including some elementary statistical calculations. In doing so, it provides a detailed step-by-step explanation of how it arrived at the answer. • AppOnFly has a different approach -- the company maintains Windows computers with a wide selection of Windows software, including utilities for accessing PDF, ZIP, graphics and other files, web browsers, various office suites (MS Office, Libre Office, Apache OpenOffice, WordPerfect Office), and statistical packages (SPSS, NCSS, R), to mention a few. They then provide apps for accessing this Windows desktop environment from any device -- computer, smartphone, tablet (Windows, Mac OS, iOS, Android). This is a pay-for service, but they offer one-month free trials. • Expression Evaluators -- type in any numeric expression; the computer will evaluate it and display the results... • Calculators -- pages that look and act like a pocket calculator... • Plotters -- type in any algebraic function; it displays the graph... □ Function plotter -- Lets you zoom in and out to view any portion of the graph. (Needs Java.) □ Function plotter -- Produces a small 3D plot of almost any function or relation found in high school and undergraduate college mathematics. Plots functions of the form y = f(x), such as y = x2 or y = 3x + 1, or relations of the form f(x,y) = g(x,y), such as x2 + y2 = 4. (but Flash Player needed) □ Linear Programming Grapher-- Enter a linear function of two variables to be minimized, and any number of linear inequality expressions, and the page will instantly solve it and display a graph showing the feasible region and the constraints. □ Simplex Tool -- Similar to the Linear Programming Grapher, but works with functions of more than two variables, and doesn't graph the results. • Integrators -- type in any function; the computer displays the indefinite integral function (if one exists) and/or the value of the definite integral (area under the curve) between two • Interactive Programming Environments -- These pages implement various mathematical programming languages. You can enter commands or entire programs (type or copy/paste) into the web page, and they will be executed immediately. □ Rweb -- an interactive web-based interface to the "R" statistical programming language (similar to S or S-plus) □ Mx -- -- a matrix algebra interpreter and numerical optimizer for exploration of matrix algebra. Many built-in fit fuctions for structural equation modeling and other statistical modeling. Has fitting fuctions like those in LISREL, LISCOMP, EQS and CALIS, along with facilities for maximum likelihood estimation of parameters from missing data structures, under normal theory. Users can easily specify complex 'nonstandard' models, define their own fit functions, and perform optimization subject to linear and nonlinear equality or boundary constraints. □ More calculators -- a list free online/downloadable calculators. • Probability Integrals -- these pages take the place of a handbook of statistical functions. They're arranged with the most comprehensive,multi-function pages first... □ These pages contain calculations for a very wide assortment of probability distribution functions, including Normal, Bivariate Normal, Student t, Chi-Square, Fisher F, Bivariate Normal, Noncentral Student t, Non-central Chi-Square, Non-central Fisher F, Poisson, Log-normal, Exponential, Beta, Gamma, Logistic, Binomial, Negative Binomial, Multinomial, Cauchy, Gumbel, Laplace, Pareto, Weibull, Uniform (continuous and discrete), Triangular, Geometric, and Hypergeometric: ☆ Xuru's page to calculate PDFs, CDFs, and their complementary and inverse, along with expected values, mean, variance, skewness & kurtosis, for binomial, geometric, negative binomial, Poisson, hypergeometric, normal, chi-square, Student t and Fisher F distributions. ☆ Very sophisticated interactive page for over 65 continuous and discreet statistical distribution functions -- Select a function from a menu, and it will show you a graph of that function along with its properties. You can click on the graph to select limits, and it will show you the left, middle and right integrals. □ These pages each compute probabilities for the four most common probability distributions: □ These pages each compute probabilities and/or inverses for a specific distributions: □ This page contains links to printable copies (in Adobe Acrobat PDF format) of many statistical tables including some for which no "calculating pages" are available • Random Number Generators... □ Random integers -- generates any number of random integers, uniformly distributed between any two limits □ Generate tables of random integers from any specified range, or random values from a Normal distribution with any specified mean and SD. □ Random fractional numbers -- generates any number of random numbers, each a fraction between 0 and 1 with 8 digits after the decimal point □ Randomly assign subjects to treatment groups -- can randomly choose a group for each subject, or randomly shuffle subjects within groups. □ Research Randomizer -- generates one or more sets of random numbers from a specified range, with or without repeats, sorted or unsorted. □ Block Randomizer -- assigns subjects randomly to different groups, with multiple blocking to ensure that imbalances are kept under control if the study is terminated prematurely □ Random assignment of subjects to one or more groups -- three variations: 1. generates M groups of N numbers each by distributing the numbers from 1 to MN randomly into the M groups 2. generates M blocks of N numbers each by randomly shuffling the numbers from 1 to N in each block 3. generates a subset of N numbers by random selection from a list of the numbers from 1 to M • Combinatorial Objects Server -- generates an incredible assortment of... □ Permutations and their restrictions □ Subsets or Combinations □ Permutations or Combinations of a Multiset □ Set Partitions □ Numerical Partitions and relatives □ Binary, rooted, free and other trees □ Necklaces, Lyndon words, DeBruijn Sequences □ Irreducible and Primitive Polynomials over GF(2) □ Ideals or Linear Extensions of a Poset □ Spanning Trees and other Subgraphs of a Graph □ Unlabelled Graphs □ Pentomino Puzzles, Polyominoes, n-Queens □ and other puzzles and Miscellanea • Confidence Intervals... • Tolerance Intervals... □ Tolerance Intervals for the Normal Distribution. (Don't confuse tolerance intervals with confidence intervals!) A tolerance interval for a measured quantity is the interval in which there is a specified likelihood that a specified fraction of the population's values lie. This page will calculate 1-sided and 2-sided tolerance intervals for any specified population fraction, and for any specified level of confidence, from the mean and standard deviation of a finite sample, under the assumption that the population is normally distributed. These calculations are also available in a downloadable Excel spreadsheet: tolintvl.xls . • Single-Population Tests... □ Sign and Binomial test -- test an observed proportion against a proposed population proportion □ An excellent One-Sample Student t Test page -- enter or paste raw data, or enter mean, SD or SEM, and N □ One-sample Student t test for Mean vs. a Specified Value -- for up to 80 observations, and a postulated population mean. □ Test for Asymmetry around zero -- Enter a set of numbers (usually a mix of positive and negative numbers), and the program will apply a non-parametric test (originally created by R. A. Fisher) of whether the numbers are consistent with a population frequency distribution that is symmetrical around zero (but does not necessarily have to be normal). It is a frequentist test to work Darwin's experiment with matched pairs, and experiments like it. □ Test for the mean being greater than some specified value. This unusual test is Bayesian and frequentist at the same time. The null hypothesis asserts some value for the mean of a population of positive numbers; the alternative hypothesis says the mean is higher than that. This test gives a Bayesian likelihood ratio that is also an upper bound on the p-value of the frequentist □ Test observed vs. expected rates of occurrence of events, based on Poisson distribution; also includes confidence intervals and analysis of rate-ratios (such as Standardized Mortality Ratio, Morbidity Ratio, and Comparative Mortality Figure) □ Similar to above, but used to study the distribution of accidents and events at the individual level □ Exact confidence intervals around a rate-ratio, using Liddell's method (also contains a number of common approximations, for comparison) □ Test observed vs expected proportions, based on the Binomial distribution □ Binomial Test -- whether the number of "successes" differ from what was expected based on the number of trials and the probability of success. □ Similar to above, but deals with the probability of a particular sample size, given an observed 'x' number positive (or white, or car crashes) vs. an expected 'U' proportion positive □ Compatibility of Multi-Counts -- tests whether up to 14 observed event counts (each over the same amount of time) are consistent with a single expected event rate. □ Runs Test for Randomness -- Enter up to 80 numbers, and this page will calculate a runs test to see if the numbers form a random sequence □ Testing the Variance -- of up to 80 observations against a postulated population variance. □ Analyze observed proportions in samples from finite populations, based on the Hypergeometric distribution □ Test for Normality -- Enter up to 80 numbers, and this page will test for normality based on the Jarque-Bera statistic □ Test for Homogeneity of a Population -- enter form 25 to 84 values; page provides information to test whether histogram is unimodal. □ Shapiro-Wilk Test for Normality -- enter numbers into page, or read them from a text file. Performs normality test, also shows a histogram of the data. For a description of the test, along with the formulas and programming, click here. □ Test for Normality -- enter up to 42 sets of [value, frequency]; page will calculate skewness, kurtosis, and Liliefors test for consistency with a normal distribution. □ Test for Uniform Distribution -- enter up to 42 sets of [value, frequency]; page will calculate the Kolmogorov-Smirnov test for consistency with a uniform distribution. □ Testing Poisson Process -- enter up to 14 sets of [value, frequency]; page will calculate a Chi square test for consistency with a Poisson distribution. □ Lilliefors Test for Exponential Distribution -- tests whether a set of observed values are consistent with an exponential distribution. • Chi-Square "Goodness of Fit" test for observed vs expected counts (NOT from Contingency Tables)... • Measurement Errors and Error Propagation... • Student t-test (for comparing two samples)... • ANOVA (Analysis of Variance) -- comparison of two or more samples ... □ One-Way and Factorial ANOVA for uncorrelated samples (extension of unpaired Student t-test to more than 2 groups)... □ Repeated-Measures ANOVA for correlated samples (extension of paired Student t-test to more than 2 matched measurements)... □ Bartlett's Test for Equality of Multi-variances -- for up to 14 sets of [N, variance]. □ Bartlett's test for equality/homogeneity of variances for three or more groups. Also produces a scatter plot of all the groups. For a description of the test, along with the formulas and programming, click here. □ Post-hoc Tests -- After doing a two-way (or other) ANOVA, post -hoc tests (also called post tests) compare individual pairs of groups. This calculator does not perform the ANOVA calculations, but takes the output from an ANOVA (residual means square error, degrees of freedom) performs a post-hoc test between any pairs of cells that you select (using cell means and N's), at whatever alpha you specify. □ Tukey LSD (Least Significant Difference), using the standard table produced by an ANOVA □ Scheffe Least Significant Difference, using data from a standard ANOVA table and the N's for the two groups being compared • Non-parametric tests (use these when the data is not normally distributed)... • Comparison of proportions between two groups... □ Comparison of two proportions between two groups (each given as # successes / # of trials). Shows confidence intervals, and interprets the results of the comparison. □ Paired Preferences Test -- Enter the sample size, and the two percentages (preferring A and preferring B), and this program will calculate the T score and significance level. This page is based on a normal approximation to the binomial distribution, and should not be used if the sample size is less than 30. • Comparison of Event Rates between two groups... □ a very polished calculator for comparing two event rates (number of events in a certain amount of time). Shows confidence intervals around each event rate, and interprets the significance of the difference between the rates of the two groups. • Sequential Analysis -- each subject's data (usually paired comparisons) is tested as it becomes available, and a decision is made to accept or to reject the null hypothesis or to keep testing. □ by Paired Preferences -- Each pair of observations is compared and rated qualitatively as "preferring A" or "preferring B" □ by Paired Differences -- Each pair of numbers is subtracted to obtain a difference • Chi-Square tests... • Three-dimensional Tables (2x2x2)... • Fisher Exact tests for contingency tables... • Test differences between two observed proportions, based on the Binomial distribution • Barnards Test (2x2) -- An exact test for 2x2 tables that is exact (like the Fisher test), but can be more powerful than the Fisher test (more likely to produce significance). For an explanation, click here. • Contingency table for sequenced categories (Ordinal by Ordinal, 5-by-5 table or less) • Contingency table for sequenced categories This is a re-implementation of John Pezullos original page above, accommodating for 2x2 or more (i.e. N-by-M) contingency tables • Contingency table for sequenced categories, 5-by-2 table, with exact probability calculations • McNemar's test to analyze a matched case-control study, with a good explanation • McNemar's test for 2x2 paired tables -- For a background explanation, with formulas and examples, click here. • Cochrane's Q Test -- An extension of the McNemar test to 2xN tables. For an explanation, click here. • Exact Bayes test for independence in r by c contingency tables -- Can also handle comparison of observed-vs-expected, and observed-vs-uniform situations. • Comparison of ratings or rankings by different raters... • Chi-Square "Goodness of Fit" test for observed vs expected counts (NOT from Contingency Tables)... □ Chi Square test -- takes observed values, and expected values that can be specified as expected occurrences, or percentages or fractions of the total. Data can be typed in or copied and • Straight Lines and Correlation Coefficients... • Correlation Tests... □ Spearman's rank correlation (non-parametric)... □ Calculate Pearson, Spearman or Kendall Correlation Coefficient from a N × M 2D data matrix. ☆ Write, copy/paste (Excel or other spreadsheet) or load data from a csv file. ☆ First row may include column names. Specify which columns to test for correlation. ☆ Optional specify: confidence level, continuity correction, exact p-value and alternative hypothesis. □ Pearson Correlation Coefficient -- also produces a scatterplot of the data. For a description of correlation coefficients, click here. □ Spearman Rank Correlation Coefficient -- a non-parametric substitute for the Pearson correlation coefficient. This page also produces a scatterplot of the data. For a description of correlation coefficients, click here. □ Testing the Correlation Coefficient -- enter up to 42 r values, along with a postulated population r value. □ Comparison of two sets of (X,Y) data to see if they are consistent with the same straight line (tests whether the slopes are different, and whether the lines are vertically distinct) □ Comparing Two Linear Regressions -- Enter two sets of [x,y] values; page calculates two straight lines, then compares slopes and intercepts. □ Test for Several Correlation Coefficients -- enter up to 14 sets of [N, r]; page will test whether all r's are consistent with a single population r value. □ Biserial correlation coefficient from summary data (N, mean, SD) of the X and Y variables □ Lin's "concordance correlation coefficient" -- first proposed by Lin (1989) for assessment of concordance in continuous data. A breakthrough in assessing agreement between alternative methods for continuous data. Seems to avoid the shortcomings of correlation coefficient r, paired t-tests, least squares analysis for slope and intercept, coefficient of variation, intraclass correlation coefficient.. It is robust on as few as 10 pairs of data. □ Manipulation of a correlation matrix -- you enter the N-by-N correlation matrix, the page computes all Partial Correlation Coefficients, all Standardized Partial Regression Coefficients, and the Multiple Correlation Coefficient for each variable. • Beyond Simple 2-parameter Curve-fitting... □ Very general nonlinear least-squares curve fitter -- almost any function you can write-- up to 8 nonlinear parameters, up to 10 independent variables. □ Performs nonlinear least-square regression as above but will handle more than 8 parameters and includes plotting option. □ MyCurveFit.com -- an easy-to-use curve-fitting page. Offers 13 pre-defined functions (no initial guesses required), along with the ability to fit a general non-linear function you provide (along with initial guesses). Displays the results graphically, along with the formula of the fitted curve. Several types of unequal data-point weighting are provided. Lets you generate predicted values (interpolated and extrapolated) from the fitted curve. Lets you save results in Excel and PDF formats. □ ZunZun non-linear least-squares curve-fitter -- with an enormous list of pre-defined 2-D and 3-D functions, and extensive graphical and statistical output. □ Another non-linear least-squares curve fitter -- with graphical output! Choose one of 15 pre-defined nonlinear functions of one variable and up to three parameters. □ 3-D Regression and Interactive Graph (by MiaBella LLC) -- a powerful web page that fits a linear function of two predictor variables (Z = a + bX + c*Y), and displays a very elegant 3-D scatterchart of the {X,Y,Z} points and the fitted plane. You can rotate the graph in three dimensions using the mouse, and you can see the X, Y, and Z values of any point (say, an outlier) by clicking on the point. □ Polynomial Regression -- fit polynomials of degree 2 through 10. □ Multiple Linear Regression -- fit functions of more than one predictor variable. □ Multiple Polynomial Regression -- fit functions of one or more predictors, each expressed as polynomials, up to the order you specify. □ Nonlinear Regression -- Automatically fits over 100 of the most commonly-occurring non-linear functions (gaussians, sigmoidals, rationals, sinusoidals, etc.), and then ranks them according to □ Compare the fit of two models to your data. Which model fits better? Enter goodness-of-fit (SSQ, or weighted SSQ) and # of data points and # of parameters for each model. The calculator will compare the models using Akaike's method, , then the F test. □ Fit "rational functions" (also called "Pade functions") to {X,Y} data. A rational function is a fraction whose numerator and denominator are both polynomials in X. They can fit a broader range of functions than polynomials alone can -- they can fit data where the Y value "levels off" to a horizontal line for very large or small X, and can fit functions that have "singularities" (Y shoots to infinity at some value of x). This curve-fitter is part of an extensive set of online calculators to solve problems in structural engineering (bending and buckling of beams and plates, etc.) at the Software for Structures web site. □ Univariate and multiple regression, with very extensive graphical output (histograms, scatterplots, scatterplot matrices) and residual analysis (QQ, histogram, residuals vs dependent or predictors). Very intuitive point-and-click interface, dynamically customized for your data. (When you get to the Rweb page, scroll down to the Analysis Menu and select Regression.) □ Multiple Linear Regression -- up to 16 data points and up to 4 independent variables; calculates fitted model, and a large number of residual analysis statistics. □ Quadratic Regression -- Fits a least squares parabola to up to 84 data points, and provides extensive residual analysis. □ Multiple regression, if you already have the correlation coefficient matrix between all independent and dependent variables... □ Fit any of five families of curves (linear, polynomial, exponential, descending exponential, Gaussian) and draw a graph □ Logistic Regression, if the dependent variable is restricted to two values (such as whether an event did or did not occur) □ Logistic Regression -- extends John C Pezzullos page (above) to handle power models and let you calculate Predicted Probability for specific covariable patterns. □ Regression by Prevalence -- when you have data on the number of occurrences and non-occurrences of something over a set of time intervals. Tests whether the probability of the occurrence shows a trend over time. □ Test Bias Assessment Program, computes statistics to help you decide if test scores predict a criterion differently across subgroups • Time Series Analysis... • Kaplan-Meier Survival Plot and LogRank Test -- Type or copy/paste data, or read it in from a file. Prepares tables, graphs (with 95% confidence intervals), and statistical comparison output. Can accommodate two or more groups, and can perform stratified log-rank test. Uses the R statistical engine on the ShinyApps server to provide very high-quality output. Written by Soren Merser. • Kaplan-Meier Survival Plot -- for one or more groups. Draws K-M curves with optional confidence bands (ordinary, log, or log-log type, at the 50, 80, 90, or 95% conf. level). This is part of Peter Rosenmai's EurekaStatistics web site (a blog about statistics and R). • Kaplan-Meier Survival Plot and LogRank -- calculates survival curves (with confidence bands), and performs a LogRank test test to comparing survival curves between two groups. • Life Table (Kaplan-Meier) -- Enter the number died and censored at each time period, and the page calculates the cumulative survival probability and 95% confidence intervals. Also graphs the survival curve, and exports the data, so you can create a better graph using another program. • Cox Proportional Hazards Survival Regression Analysis -- specify each subject's observation time and status (last seen alive or dead), and any number of independent variables (predictors, confounders, and other covariates). This web page will perform a proportional-hazards regression analysis and return the regression coefficients, their standard errors, hazard (risk) ratio, and their confidence intervals, and the baseline survivor curve, along with goodness-of-fit information. You can also use a faster version by Ronald Brand (Leiden University), or an enhanced version by Kevin Sullivan (Emory University) that has illustrative examples and explanatory material. • CoxReg -- performs Cox Proportional Hazards Regression. You can copy/paste data from Excel, or upload a CSV file. Produces a regression table report, survival plot, survival table, log-rank test, and a predicted survival plot for specified covariable patterns. Uses the R statistical engine on the ShinyApps server to provide very high-quality output. Written by Soren Merser. • Compare Average Survival Time between two distributions -- Enter the number of events and the average time to event for each of two groups. The calculator will display the confidence interval around each mean time, and will compare the two mean times. (Assumes an exponential-shaped survival curve.) • Bayesian Credibililty Analysis -- allows the credibility of a clinical trial finding to be assessed in the light of current knowledge. This page takes the odds ratio and its confidence interval from a clinical trial, and uses a newly-developed Bayesian method to calculate a quantity called the critical odds ratio (COR). If odds ratios at least as impressive as that indicated by the COR can be justified by existing knowledge, then the results of the clinical trial can be deemed credible. • Etiologic Predictive Value (EPV) -- a new statistical method developed for determining the probability of symptoms being caused by a bacteriological finding, while taking carriers into consideration. To calculate EPV, one must know the number of positive and negative tests among patients and healthy controls as well as the sensitivity of the test. This enables calculating the positive and negative EPV with a 95% confidence interval. • Exact Bayes test for independence in r by c contingency tables -- Can also handle comparison of observed-vs-expected, and observed-vs-uniform situations. • Analysis of "1-degree of freedom" data -- performs interactive frequentist and Bayesian conditional tests for counts data having one degree of freedom. That is, it does hypergeometric, binomial, Poisson, Bessel, and related distributions (for double dichotomies, sign tests, a special kind of structural zero design, etc.). • Bayes' theorem calculations -- takes prior probabilities and conditional probabilities, and calculates revised probabilities. (great for solving certain kinds of brain teaser puzzles) • Interpret P values -- Compute post test probability to take into account the context of the experiment, as expressed by the prior probability that your hypothesis is true. • Bayesian calculations for diagnostic tests -- computes interrelationships among true pos, true neg, false pos, false neg, prevalence, sensitivity, specificity, predictive values, and likelihood ratios (requires JavaScript). • 2-by-2 table analysis (Chi-Square, sensitivity, odds ratio, relative risk, etc. with confidence intervals • Wald's Sequential Probability Ratio's -- for designing a sequential experiment in which a decision is made after each observation either to accept the null hypothesis, accept the alternate hypothesis, or acquire more observations. • Diagnostic Test Calculator -- This calculator can determine diagnostic test characteristics (sensitivity, specificity, likelihood ratios) and/or determine the post-test probability of disease given given the pre-test probability and test characteristics. Given sample sizes, confidence intervals are also computed. • ReliCheck -- an online reliability analysis tool that allows users to check the reliability of the scores on their survey. The free option provides reliability score, statistical strength of survey, general item analysis, and a statistical summary of the survey. Pay-for plans also provide an auto-optimizer, optimization comparison, manual optimizer, and control of survey analysis. • Queueing Theory Calculator -- Performs classic calculations for single-server or multi-server queues (queue length, waiting time, etc.). • Interactive Cross-Validation -- Performs the "leave-one-out" cross-validation inference for: central tendency, least-squares lines, one-dimensional multinomial tables, two-dimensional contingency tables with structural zeroes, k-sample problems, and block-and-treatment designs. The web page is well-documented, with about a dozen examples worked out and explained. • Fittestmodel --an online forum, on which statistical evidence can be presented that is always replicable, testable and extendible at the 'click of a button'. The name Fittestmodel encompasses both the goal and the means of science, namely to find the fittestmodel by fitting, testing and modelling. Users may discuss statistical evidence online or query for results based on search criteria such as dataseries, methods or criteria that measure the 'quality' of results. Publicly available datasets from various sources may be combined into new statistical evidence and statistical techniques will be added on a continuous basis, by user request or otherwise. • Bonferroni adjustment of critical p-values when performing multiple comparisons (has an excellent discussion of this topic) • Multiple comparisons correction (Bonferroni adjustment) • Number Needed to Treat, based on a 2-by-2 table • Detect Outliers -- this calculator performs Grubbs' test, also called the ESD method (extreme studentized deviate), to determine whether one of the values in the list you enter is a signficant outlier from the rest. • Calculate and plot an ROC Curve (for grouped predictor data) • Clustering Calculator generates tree structures of data clustering, and much more • Predictive Value from Sensitivity, Specificity and Prevalence, (when analyzing a clinical test), with a nice explanation • NetMul: a browser interface to a program that performs: □ Principal Coordinate Analysis (PCO) □ co-inertia analysis □ discriminant analysis and within- or between-class analyses □ analyses on distance matrices or neighboring graphs. • Simultaneous Equations and Matrix Inversion -- up to 10 equations (or 10x10 matrix). • Linear Optimization with Tools for Sensitivity Regions -- This page finds the optimal solution, and does a post-optimality analysis of small-size linear programming problems (constrained • Martindale's Reference Desk - Calculators On-Line - Statistics (the grand-daddy of all compendia of calculating web pages) • Biostatistical Calculators: □ Evidence-Based Medicine (EBM) calculator -- From Warren Goff's interestingly-named web site. Analyzes one or more fourfold (2x2) tables; calculates Chi Square, CER, EER, and RR, and parameters related to treatment (RRR, ARR, NNT, NNH, with 95% confidence intervals), diagnosis (Sensitivity, Specificity, PPV, NPV, Prevalence, LR+, LR-, OR, Pre-Odds, Post-Prob), and Harm (RR, OR NNH). Can also compare two different tables. □ Diagnostic Test Evaluation -- from a 2x2 cross-tab of diagnostic test results (positive or negative) vs. true disease state (present or absent), calculates sensitivity, specificity, positive and negative likelihood ratios and predictive values, and disease prevalence, along with their 95% confidence intervals. □ Risk Reduction Calculator -- Given information about the probability of an outcome under control and experimental treatments, this calculator produces measures of risk increase/decrease and number needed to treat or harm, including confidence intervals. If some patients were lost to follow-up, the calculator provides estimates for several different scenarios. □ Compute EC[anything] from EC[50][ ](assuming a standard "Hill-type" dose-response relationship). Very useful in dose-response studies. □ Thorough analysis of 2-by-2 table relevant to Predictions and Diagnostic Tests -- sensitivity, specificity, prevalence, diagnostic accuracy, PPV, post-test probabilities, likelihood ratio □ Calculator to predict the probability of a successful outcome to lumbar disc surgery (based on a logistic model) □ Scoring systems for ICU and surgical patients -- Online calculation of scores used in general or specialized Intensive Care or Anesthesia, including: • Item Analysis -- for multiple choice questionnaires • Statistical Quality Control (SQC) Online -- Online calculators and tutorials to perform SQC annd Statistical Process Control (SPC). Contains: • Online versions of Military & Civilian Standard Tables: MS-105E / ANSI/ASQC Z1.4, ISO 2859 (sampling plans for attribute data), MS-414 / ANSI/ASQC Z1.9 (sampling plans for measurement data, and MS-1235C (sampling inspection plans for continuous production, Procedure CSP-1). • Online Calculators for Process Capability Index (Cp), MTBF Calculator for a system given the part (component) failure rate, and Control Charts and Runs Rules (Switching Rules for MS-105E, Continuous Sampling CSP-1, Western Electric Rules, and System Reliability for consecutive-type systems) • Queuing Theory Calculator -- a remarkably powerful web calculator that can solve a wide variety of queueing problems: single-server, multiple-server, infinite-server, infinite or finite waiting room, Erlang loss model, and machine interference model (with or without spare machines). Provides detailed output in the form of averages, standard deviations, and frequency distributions in the form of tables and graphs. • Structural Engineering Calculators, from BuildingsGuide.com -- currently includes ASCE 7-05 Code calculators for Snow Loading Analysis, Ice Loading Analysis for WT, MT & ST shapes, for W, M, S & HP shapes, and for C & MC shapes; Seismic Base Shear for single-level buildings, and Wind Loading Analysis for low-rise buildings. • Decision Making in Economics and Finance: • ABC Inventory Classification -- an analysis of a range of items, such as finished products or customers into three "importance" categories: A, B, and C as a basis for a control scheme. This pageconstructs an empirical cumulative distribution function (ECDF) as a measuring tool and decision procedure for the ABC inventory classification. • Inventory Control Models -- Given the costs of holding stock, placing an order, and running short of stock, this page optimizes decision parameters (order point, order quantity, etc.) using four models: Classical, Shortages Permitted , Production & Consumption, Production & Consumption with Shortages. • Optimal Age for Replacement -- Given yearly figures for resale value and running costs, this page calculates the replacement optimal age and average cost. • Single-period Inventory Analysis -- computes the optimal inventory level over a single cycle, from up-to-28 pairs of (number of possible item to sell, and their associated non-zero probabilities), together with the "not sold unit batch cost", and the "net profit of a batch sold". • Investment Derivative Calculations -- A very elaborate online calculator and real-time data retrieval system. Includes economic regression analysis. • Black-Scholes Calculator -- to place a value on stock options. • Bardahl Calculator -- to compute the reasonable working capital needs of a corporation. • Probabilistic Modeling: □ Bayes' Revised Probability -- computes the posterior probabilities to "sharpen" your uncertainties by incorporating an expert judgement's reliability matrix with your prior probability vector. Can accommodate up to nine states of nature. □ Decision Making Under Uncertainty -- Enter up-to-6x6 payoff matrix of decision alternatives (choices) by states of nature, along with a coefficient of optimism; the page will calculate Action & Payoff for Pessimism, Optimism, Middle-of-the-Road, Minimize Regret, and Insufficient Reason. □ Determination of Utility Function -- Takes two monetary values and their known utility, and calculates the utility of another amount, under two different strategies: certain & uncertain. □ Making Risky Decisions -- Enter up-to-6x6 payoff matrix of decision alternatives (choices) by states of nature, along with subjective estimates of occurrence probability for each states of nature; the page will calculate action & payoff (expected, and for most likely event), min expected regret , return of perfect information, value of perfect information, and efficiency. □ Multinomial Distributions -- for up to 36 probabilities and associated outcomes, calculates expected value, variance, SD, and CV. □ Revising the Mean and the Variance -- to combine subjectivity and evidence-based estimates. Takes up to 14 pairs of means and variances; calculates combined estimates of mean, variance, and □ Subjective Assessment of Estimates -- (relative precision as a measuring tool for inaccuracy assessment among estimates), tests the claim that at least one estimate is away from the parameter by more than r times (i.e., a relative precision), where r is a subjective positive number less than one. Takes up-to-10 sample estimates, and a subjective relative precision (r<1); the page indicates whether at least one measurement is unacceptable. □ Subjectivity in Hypothesis Testing -- Takes the profit/loss measure of various correct or incorrect conclusions regarding the hypothesis, along with probabilities of Type I and II errors (alpha & beta), total sampling cost, and subjective estimate of probability that null hypothesis is true; returns the expected net profit. Check out the PowerAndSampleSize.com web site, which contains (at last count) 19 interactive calculators for power or required sample size for many different types of statistical tests: testing 1 mean, comparing 2 or more means, testing 1 proportion, comparing 2 or more proportions, testing odds ratios, and two 1-sample tests (normal and binomial-based). This site also provides calculators for non-inferiority and equivalence studies. The web pages display graphs that dynamically show how power varies with various design parameters as you change other parameters. Also, look at the very general and elegant power/sample-size calculator by Russel Lenth (U of Iowa). It handles tests of means (one or two samples), tests of proportions (one or two samples), linear regression, generic chi-square and Poisson tests, and an amazing variety of ANOVAs -- 1-, 2-, and 3-way; randomized complete-block; Latin and Greco-Latin squares; 1-stage, 2-stage, and factorial nested designs; crossover; split-plot; strip-plot; and more! This calculator is implemented in Java, and can be run as a web page, or can be downloaded to your computer to run offline as a stand-alone application. Here's a collection of online power calculator web pages for specific kinds of tests: • For one-group tests (comparing the sample to a specified value) or for paired two-group tests... • For designing surveys (sample size and confidence intervals for proportions, based on sample size, with or without corrections for finite populations: • For two-group tests... □ Comparing means for two independent samples... □ Difference between two proportions (as, for example, by a Chi Square test on a 2-by-2 cross-tab)... • For ANOVAs and other multi-group comparisons... • For regressions and correlation tests... • Other power calculations... • Links to printable copies (in Adobe Acrobat PDF format) of many power tables including: Z Test, t-Test for One Sample or Two Related Samples, t-Test for Two Independent Samples, Analysis of Variance, Correlation Coefficient, and Required Sample Size for various tests • Wald's Sequential Probability Ratio's -- for designing a sequential experiment in which a decision is made after each observation either to accept the null hypothesis, accept the alternate hypothesis, or acquire more observations. • Experimental Design... □ WebDOE^(tm) -- for "design of experiments". Searches for I-, D- and A-optimal designs over continuous spaces. Factors may be continuous, fixed-level, or qualitative. The site can handle inequality and equality (e.g., mixture) constraints; provides color plots; performs one-click, run-order-randomization; allows design import/export interoperable with most 3rd-party analysis software; provides OLS and BLUP fits; and includes an extensive Classical Design Library(tm), including factorial, fractional-factorial, Box-Behnken, central-composite, Plackett-Burman, orthogonal array, and uniform designs. All designs may be evaluated under the I-, D-, and A-, and S-optimality criteria, as well as for the maximum distance between nearest-neighbor pairs of design points (maximin criterion). The My WebDOE(tm) feature allows users to store their designs, evaluations, and fits on-line. There is no need for user-provided candidatepoints. □ Design and Analysis of Comparative Experiments website by Horticulture Research International -- provides facilities for the design and analysis of of comparative experiments for biological and agicultural research based on a range of experimental block and treatment structures. Constructs simple experimental designs interactively and also constructs appropriate statistical software for the analysis of the designs. Handles Randomised block, Split-plot, Latin and incomplete Latin square, Trojan and incomplete Trojan square designs. □ Tables of Latin Squares for constructing "Williams design" experiments, in which every subject receives every treatment. These designs are balanced for first-order carry-over (residual effects). Tables are provided for experiments ranging from 2 to 26 treatments. Tables can also be downloaded as a text file and as an Excel spreadsheet. □ More Latin Squares □ Sample-size calculations for parallel-group equivalence and superiority trials with continuous or binary outcome variables. □ EDGAR -- generates experimental designs and randomizes the position of experimental treatments in the design, so that the subsequent analysis of the data is comparatively straightforward □ Type I & II error criteria. [see Simon, Controlled Clin Trials, 10:1-10,1989] Please send all suggestions for new pages, notifications for dead links, and other requests in an e-mail to statpages.org@gmail.com	{"url":"https://statpages.info/","timestamp":"2024-11-02T20:01:56Z","content_type":"text/html","content_length":"140893","record_id":"<urn:uuid:24301930-5029-476e-9eb3-ec85ac9c7c87>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00603.warc.gz"}
OpenStax College Physics, Chapter 28, Problem 41 (Problems & Exercises) (a) Calculate the speed of a $1.00 \textrm{ }\mu\textrm{g}$ particle of dust that has the same momentum as a proton moving at $0.999c$. (b) What does the small speed tell us about the mass of a proton compared to even a tiny amount of macroscopic matter? Question by is licensed under CC BY 4.0 Final Answer a. $1.12 \times 10^{-8} \textrm{ m/s}$ b. This small velocity of the dust particle says the proton has a very significantly smaller mass than the dust. Solution video OpenStax College Physics, Chapter 28, Problem 41 (Problems & Exercises) vote with a rating of votes with an average rating of. Video Transcript This is College Physics Answers with Shaun Dychko. We are given the velocity of a proton which is 0.999c and we are given the mass of a speck of dust which is 1 microgram which we convert into kilograms by multiplying 1 times 10 to the minus 6 grams by 1 kilogram for every 1000 grams giving us 1 nanokilogram, well which is kind of a funny way of saying things, two prefixes together but anyway, it's 1 times 10 to the minus 9 kilograms. And we write it this way because we always want meters, kilograms and seconds in our units in our formulas, mks units. OK. So we are told that the momentum of the dust particle is the same as the momentum of the proton and with that being the case, what must the velocity of the dust particle be? So we have the relativistic momentum of the dust particle is the Lorentz factor times the mass of the dust particle times its velocity and that equals the Lorentz factor of the proton times the proton's mass times the velocity of the proton. And then we substitute for the Lorentz factor, in both cases here and then I'm gonna plug in numbers to figure out what is the momentum of the proton. So we have the mass of the proton— 1.673 times 10 to the minus 27 kilograms— times its velocity which is 0.999 times the speed of light and divide that by square root of 1 minus 0.999 squared because this 0.999 is the factor times c which then gets squared and then divided by c squared and the c squared's canceled. And this works out to 1.12069 times 10 to the minus 17 kilograms meters per second; that's the momentum of a proton. And that is going to be equal to the momentum of the dust particle. And now we have to solve this for the velocity of the dust particle. We'll begin by squaring both sides and that gives us m d squared u d squared over 1 minus u d squared over c squared equals the momentum of the proton squared. And then we'll multiply both sides by this denominator here so both sides get multiplied by 1 minus velocity of the dust particle squared over c squared. And on the left side that just cancels away and we are left with the numerator here. And on the right side, we'll distribute the momentum of the proton into this bracket and so we have momentum of the proton squared minus velocity of the dust particle squared times the momentum of the proton squared over c squared. Then we'll collect the terms containing the factor u d on the same side and so this term gets moved to the left and then factor out the u d squared from both terms and we are left with u d squared times mass of the dust particle squared plus momentum of the proton squared over c squared equals this momentum of the proton squared which is left over on the right hand side. Then divide both sides by this bracket here and then take the square root of both sides and we are left with the velocity of the dust particle equals the momentum of the proton divided by the square root of the mass of the dust particle squared plus momentum of the proton squared over c squared and now we can plug in numbers. So this is our momentum of the proton that we calculated before divided by the square root of the mass of the dust particle which is 1 times 10 to the minus 9 kilograms squared plus momentum of the proton squared divided by speed of light squared and that gives 1.12 times 10 to the minus 8 meters per second. That is a very very very small speed and so that shows that despite the proton's very high speed, the proton's small mass compensates for that high speed such that the momentum of the proton is really small. And so the dust particle needs a mere 1.12 times 10 to the minus 8 meters per second of velocity in order to have the same momentum as that very fast proton which says that the mass of the proton is very significantly smaller than the mass of the dust.	{"url":"https://collegephysicsanswers.com/openstax-solutions/calculate-speed-100-mutextrmg-particle-dust-has-same-momentum-proton-moving","timestamp":"2024-11-08T17:53:05Z","content_type":"text/html","content_length":"172395","record_id":"<urn:uuid:022d6e1e-a009-4c8c-a6d8-7432b5921d4d>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00836.warc.gz"}
Frequently Asked Interview Questions and Answers Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it's supposed to talk about but is always spreading around. A mathematician is a machine for turning coffee into theorems Thanks m4 maths for helping to get placed in several companies. I must recommend this website for placement preparations.	{"url":"https://m4maths.com/frequently-asked-placement-questions.php?UID=730919","timestamp":"2024-11-03T22:51:18Z","content_type":"text/html","content_length":"91749","record_id":"<urn:uuid:791b7bd9-c35a-4dab-bc81-1c072e31b82d>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00465.warc.gz"}
Explaining the Difference Between Odd and Even Numbers Sometimes we think everyone knows the difference between an odd and even number. When I was teaching my remedial math college class, we were learning the divisibility rules, the first of which is that every even number is divided by two. I wrote the number "546" on the board and asked the class if this was an odd or even number. I had one student who disagreed with the group answer of even. I asked him why he thought the number was odd, and he replied, "Because it has a "5" in it. " It was obvious this student got all the way through high school without a clear understanding of odd and even numbers. So the moral to this story is to be sure to discuss the difference between an even and an odd number with your students. A good definition for an even number is that it can be put into groups of two without any left over, like giving each person a partner. But when you have an odd number of things and put them into groups of two, one will always be left out. Try this approach. Make your hands into fists and place them side by side as seen in the illustration. Say a number. Now count, and as you count, put up one finger for each number said, alternating between hands, with fingers touching. For instance, if you said “3”, you would count one, (left pointer fingerup) two, (right pointer finger up and touching the other pointer finger) three, (left middle finger up). Three is an odd number because one finger does not have a partner to touch. Here is the sequence to use if the number given were "2". Two is an even number because each finger has a partner. Repeat this several times, giving the students odd as well as even numbers. By always having a concrete visual (their fingers) will help the kinesthetic and visual learner to "see" the odds and Activities such as this can be found in a math booklet entitled Number Tiles for The Primary Grades. It contains 17 different math problem solving activities that extend from simple counting, to even and odd numbers, to greater than or less than to solving addition and subtraction problems.	{"url":"https://gofigurewithscipi.blogspot.com/2013/04/odd-man-out.html","timestamp":"2024-11-07T23:06:09Z","content_type":"application/xhtml+xml","content_length":"144301","record_id":"<urn:uuid:e473ef55-341e-43a5-a6d7-1eaf50801c21>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00762.warc.gz"}
Two Players Game Based on Schrödinger Equation Solution 1. Introduction A physical or a socioeconomical system (described through quantum mechanics or game theory) is composed by n members (particles, subsystems, players, states, etc.). Each member is described by a state or a strategy which has assigned a determined probability ${\rho }_{ij}$. In evolutionary game theory, the system is defined through a relative frequencies vector x whose elements can represent the frequency of players playing a determined strategy. The evolution of the density operator is described by the von Neumann equation which is a generalization of the Schrödinger equation. It is a basic equation and a basic assumption of quantum mechanics proposed by Schrödinger, an Austrian physicist. So people started to use quantum language (entropy function) to study game theory (Orrell, Firstly, Shubik (1999) finds there are three basic sources of uncertainty in an economy: exogenous, strategic, and quantum. The first involves the acts of nature, weather, earthquakes, and other natural disasters or favorable events over which we have no control. Strategic uncertainty is endogenous and involves our inability to predict the actions of competitors. Later in their paper (Haven et al., 2018), they say in quantum mechanics, a state is formalized with a wave function, which is complex valued. That state will now form part of a Hilbert space. Position and momentum in quantum physics are real-valued, and one needs to find so called operators in the Hilbert space which can represent those real quantities. In Drabik (2011), the author introduces the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties, but he just lists all the physics information, not exactly gives a connection with game theory. These work (Hubbard, 2017; Hidalgo, 2007a, 2007b) focus on entropy (mostly is minmax question) to analysis the iteration of the game. But we want to analyze the game strategy based on Schrödinger equation solution (which also represents the state). We use the distance of two states to represent “good” or “bad” for two players and the “jump” between two different states is exactly the player’s strategy for the next game around (Samuelson, 1997). Our paper concludes four sections, in the second section, we will give the model of Schrödinger equation and game theory separately. In third section, we give some basic theorems, examples and proof. In the last section, we have our conclusions and discussions. 2. Model 2.1. Schrödinger Equation At the beginning of the twentieth century, experimental evidence suggested that atomic particles were also wave-like in nature. For example, electrons were found to give diffraction patterns when passed through a double slit in a similar way to light waves. Therefore, it was reasonable to assume that a wave equation could explain the behaviour of atomic particles. Schrödinger was the first person to write down such a wave equation. The eigenvalues of the wave equation were shown to be equal to the energy levels of the quantum mechanical system, and the best test of the equation was when it was used to solve for the energy levels of the Hydrogen atom, and the energy levels were found to be in accord with Rydberg’s Law. In this part, we will give the exact Schrödinger equation, for simplifity, the system is closed which means two players can not be affteced by outside factors. So the potential can only change with people’s different thoughts. Also, each one can do optimal choices instead of information loss during their decision. The details will be discussed in the next sections. Assumption 1. For a fixed time $t={t}_{0}$, for each player, they each only have two states, i.e., for player A, he has states ${i}_{A}$ and ${j}_{A}$, similarliy, for player B, he has states ${i}_ {B}$ and ${j}_{B}$. And the states represents different solutions of the equation. Assumption 2. For each player, they have their own same equation with different initial values. There is no entanglement between these two quantum phenomenon. Schrödinger developed a differential equation for the time development of a wave function. Since the Energy operator has a time derivative, the kinetic energy operator has space derivatives, and we expect the solutions to be traveling waves, it is natural to try an energy equation. The Schrödinger equation is the operator statement that the kinetic energy plus the potential energy is equal to the total energy. Traditionally, the Schrödinger equation is used to express the evolution of a quantum particle on the surface by its wave function $\varphi \left(x,t\right)$ : $\begin{array}{l}i\hslash \frac{\partial \varphi \left(x,t\right)}{\partial t}=-\frac{{\hslash }^{2}}{2m}{abla }^{2}\varphi \left(x,t\right)+v\left(x,t\right)\varphi \left(x,t\right),\text{\hspace {0.17em}}\left(t,x\right)\in \left(0,\infty \right)×R,\\ \varphi \left(x,0\right)={\varphi }^{0}\left(x\right)\end{array}$(1) where $abla$ is the gradient operator at x, ${abla }^{2}$ is the Laplacian, m is the mass, $\hslash$ is the reduced Planck constant, $v\left(x,t\right)$ is the real time-dependent potential, and ${\ varphi }^{0}\left(x\right)$ is the initial wavefuntion. But here we use this equation to express player’s choice moving and simplify the model as $m=\hslash =1$, the potential v is time-independent. Then the modified equation for player A changes to: $i\frac{\partial {\varphi }_{A}\left(x,t\right)}{\partial t}=-\frac{1}{2}\Delta {\varphi }_{A}\left(x,t\right)+{v}_{1}\left(x\right){\varphi }_{A}\left(x,t\right){\varphi }_{A}\left(x,0\right)={\ varphi }^{0}\left(x\right)$(2) Similarly, for player B, his equation is: $i\frac{\partial {\varphi }_{B}\left(x,t\right)}{\partial t}=-\frac{1}{2}\Delta {\varphi }_{B}\left(x,t\right)+{v}_{2}\left(x\right){\varphi }_{B}\left(x,t\right){\varphi }_{B}\left(x,0\right)={\ varphi }^{1}\left(x\right)$(3) Since the Schrodinger equation is like the “heat equation” (only difference is time t changes to it, so from the fundamental solution of heat equation, we know that there is also “fundamental solutions” for Schrödinger. After the comparsion, for the Schrödinger equation, we need the calculation of $\sqrt{i}$, which in one dimension situation. Actually the sqaure root of i has two roots which is suitable for our player’s two states in a time. 2.2. Game Theory Game theory is a set of techniques to study the interaction of “rational” agents in “strategic” settings. Here “rational” measn the standard thing in economic: maximizeing the obejectives functions subject to conditions; “strategic” means the player care not only their own actions, but also about the actions taken by other player. Modern game theory becomes a field of research from the work of John von Neumann. In 1928, he wrote an important paper about two-person zero-sum games. In 1944, he and Oscar Morgenstern published their classic book (Von Neumann & Morgenstern, 1947), Theory of Games and Strategic Behavior, theta extended the work on zero-sum games, and alsp started cooperative game theory. In the early 1950’s, John Nash made his contributions to non-zero-sum games (Nash Jr., 1950) and started bargaining theory. After that, there was an explosion of theoerical and applied work in game theory and the methodology was well along its way to its current status as a tool (Shubik, 1999; Samuelson, 1997; Selten, 1975; Samuelson, 2016). And in our paper we will focus on noncooperative game theory, which means the former takes each player’s individual actions as primitives, whereas the latter takes joint actions as primitives. And we have the following assumptions about the players: Assumption 3. The number of players is 2, player A and player B. Assumption 4. There is no outside factors affecting their strategies. Assumption 5. Each one is smart enough to have the optimal choice and no information loss when they have the decision. From the Schrödinger equation, The conservation law is true. Definition 1. Players has no information loss during any time they make the decision is the ${L}^{2}$ norm integration of their “equation” solution from $-\infty$ to $\infty$ is always constant 1. ${\int }_{-\infty }^{\infty }{\|{\varphi }_{j}\left(x,t\right)\|}^{2}\text{d}x=1,j=A,B$ Since this integral must be finite (unity), we must have the solution $\varphi \left(x,t\right)\to 0$ as $x\to \infty$ in order for the integral to have any hope of converging to a finite value. The importance of this with regard to solving the time dependent Schrödinger equation is that we must check whether or not a solution $\varphi \left(x\right)$ satisfies the normalization condition. Definition 2. (Distance Between Different States). Distance between two state i and j is defined as: Definition 3. (Information of Strategy Sets). A collection of information set, I is a set of linear combination of two solutions for a fixed time $t={t}_{0}$, e.g. player A at time $t={t}_{0}$, his information set is: $I=\left\{a×{\varphi }_{Ai}\left(x,{t}_{0}\right)+b×{\varphi }_{Aj}\left(x,{t}_{0}\right)\right\}$ Here ${\varphi }_{Ai}\left(x,{t}_{0}\right),{\varphi }_{Aj}\left(x,{t}_{0}\right)$ are the basic solutions of the equation. It is a mixed strategy for player A since he has two pure strategy distributions. $a,b$ satisfying ${\|a\|}^{2}+{\|b\|}^{2}=1$. Just like the famous Schrödinger’s cat paradox which stated by Schrödinger in 1935. He presented a case of cat in a box which has fifty percent of survive and fifty percent it may die. So if we open the box, we can find the cat is alive or dead, but when we close the bos, there are infinity states it can be. According to this, we can explain the startegy: when we do the choice, we only have A and B these two choices. But when we are thinking, no one knows what we are thinking and actually we have infinity thoughts in our own Definition 4. (States Evolution as Strategy Change). When player A starts to change his strategy according to his guess of player B’s behavior, state change means the evolution for the Schrödinger solution. If his initial state is i, and the state changes to j after time t, the relation between i and j is Of course the time is a continuous parameter we obvious have $\underset{t\to 0}{\mathrm{lim}}j=i$ Definition 5. (Strictly Dominant Strategy) Similiarly as the definition in traditional game theory, a startegy state ${A}_{i}$ is a strictly dominant strategy for player A is for all ${\stackrel{¯} {A}}_{i}e {A}_{i}$, and all states ${B}_{j}$ for player B, $Dis\left({A}_{i},{B}_{j}\right)<Dis\left({\stackrel{¯}{A}}_{i},{B}_{j}\right)$. Definition 6. A state i and j for A and B is a Nash Equilibrium if and only if their distance is the least, i.e., for any other states ${i}^{\prime }$ and ${j}^{\prime }$, $Dis\left(i,j\right)\le Dis \left({i}^{\prime },{j}^{\prime }\right)$. It also has another name: Stable Equilibrium. Remark 1. This idea is from the model of the electron. The internal power between two electron is related to their distance, more closeness more power. If they are far away, exact little power between them, we do not care about these two electron. The two players are the “opponents” and “partner”, player A is affteced by B and player B is affected by A. So there should be more “power” between them. Definition 7. (Uncertainty principle for player) Any player of two can not exactly guess what his opponent’s strategy in the next step for what probability. Remark 2. The uncertainty principle is one of the most famous ideas in physics. It tells us there is a fuzziness about the behavior of quantum particles and we can not determine particle’s position x and momentum p at the same time. There is a famous inequality derived by Werner Heisenberg: ${\sigma }_{x}{\sigma }_{p}\ge \frac{\hslash }{2}.$ where $\hslash$ is the reduced Planck constant: $\hslash /\left(2\pi \right)$. In two-players game, x represent their opponent’s behavior set (which is also the information set), p represets the related probability to take such decision. This phenomenon can not happen: player B continues his strategy always whatever A’s strategy is, then $\Delta x=\Delta p=0$, a contradiction with the uncertainly principle. In next section, we will give the example and proof about this. 3. Basic Theorem Theorem 3.1. A player can have at most one strictly dominant strategy. Proof. If we assume player A has two strictly domiant strategy and each one is state ${i}_{1}$ and ${i}_{2}$, then for any state ${i}_{A}e {i}_{1}$ and states j for player B, we have the inequality: Same idea for state ${i}_{2}$, we still have the inequality: We pick ${i}_{A}={i}_{2}$ in the first inequality and pick ${i}_{A}={i}_{1}$ for the second one, which is a contradiction. $■$ Remark 3. There can be no strategy state i for player A such that for all $\stackrel{¯}{i}$ of A and j of B, $Dis\left(i,j\right)<Dis\left(\stackrel{¯}{i},j\right)$. B is the same. Theorem 3.2. The game system is closed under the time-evolution, which means ${L}^{2}$ norm of the state (solution) is always 1. Proof. It is obvious from the property that ${\|{\text{e}}^{iHt}\|}^{2}=1$. $■$ Theorem 3.3. The time evolution operator is only related to its end time: intial time ${t}_{0}$ and ending time ${t}_{1}$, it has no relation with the middle states from ${t}_{0}$ to ${t}_{1}$. From the strategy idea, two players will have the decision in a fixed time and the opponent does not care about your thinking process. Proof. Assume we have the inital state $i\left({t}_{0}\right)$ and start to evolve to time ${t}_{1}$, there are two possibilities: 1) First one is directly “jump” from ${t}_{0}$ to ${t}_{1}$ ; 2) Second part we have many “stopping thinking time” ${t}_{2},{t}_{3},\cdots ,{t}_{n}$, until ${t}_{1}$. Compare these two states: ${\text{e}}^{iH\left({t}_{1}-{t}_{n}\right)}{\text{e}}^{iH\left({t}_{n}-{t}_{n-1}\right)}\cdots {\text{e}}^{iH\left({t}_{2}-{t}_{0}\right)}{i}_{{t}_{0}}={\text{e}}^{iH\left({t}_{1}-{t}_{0}\right)}{i} We find they have the same result and finish the proof. $■$ Theorem 3.4. Two players will get Ne (Nash Equilibrium) in a period time. Proof. If we consider two players evolve separately, which means player A is from state j to state ${\text{e}}^{iH{t}_{0}}j$, and player B is from state i to state ${\text{e}}^{iH{t}_{1}}i$, then calculate their distance: So we can only consider the state i evolution! Assume we evolve after time t, then the distance between these two is: $\begin{array}{c}Dis\left(j,{\text{e}}^{iHt}i\right)={‖j-{\text{e}}^{iHt}i‖}^{2}\\ ={‖j‖}^{2}+{‖i‖}^{2}-2Re\left(j{\text{e}}^{iHt}i\right)\\ =2-2Re\left(j{\text{e}}^{iHt}i\right)\end{array}$(5) which is function of t and we want to minimize the $Dis$, so need to make sure $Re\left(j{\text{e}}^{iHt}i\right)$ as big as enough. Now we write the state in the linear combination of energy eigenstate ${E}_{p}$ : $j=\underset{p=1}{\sum }\text{ }\text{ }{\alpha }_{p}{E}_{p}$ $i=\underset{p=1}{\sum }\text{ }\text{ }{\beta }_{p}{E}_{p}$ And each constane ${\alpha }_{p}$, ${\beta }_{p}$ can be expressed as the norm times the exponential function of phase: ${\alpha }_{p}=\|{\alpha }_{p}\|{\text{e}}^{i{\omega }_{p}^{1}}$ ${\beta }_{p}=\|{\beta }_{p}\|{\text{e}}^{i{\omega }_{p}^{2}}$ $\begin{array}{c}j{\text{e}}^{iHt}i=\underset{p=1}{\sum }\text{ }\text{ }{\alpha }_{p}{E}_{p}{\text{e}}^{iHt}\underset{p=1}{\sum }\text{ }\text{ }{\beta }_{p}{E}_{p}\\ =\underset{p=1}{\sum }\|{\alpha }_{p}\|{\text{e}}^{i{\omega }_{p}^{1}}{E}_{p}{\text{e}}^{iHt}\underset{p=1}{\sum }\|{\beta }_{p}\|{\text{e}}^{i{\omega }_{p}^{2}}{E}_{p}\end{array}$(6) For fixed p, $p=1$ situation: $\begin{array}{c}\|{\alpha }_{1}\|{\text{e}}^{i{\omega }_{1}^{1}}{E}_{1}{\text{e}}^{iHt}\|{\beta }_{1}\|{\text{e}}^{i{\omega }_{1}^{2}}{E}_{1}=\|{\alpha }_{1}\|\|{\beta }_{1}\|{\text{e}}^{i{\omega }_{1}^{1}} {E}_{1}{\text{e}}^{iHt}{\text{e}}^{i{\omega }_{1}^{2}}{E}_{1}\\ =\|{\alpha }_{1}\|\|{\beta }_{1}\|{\text{e}}^{i{\omega }_{1}^{1}}{\text{e}}^{-i{\omega }_{1}^{2}}{\text{e}}^{i{E}_{j}t}\\ =\|{\alpha }_{1}\|\| {\beta }_{1}\|{\text{e}}^{i\left({E}_{j}t+{\omega }_{1}^{1}-{\omega }_{1}^{2}\right)}\\ =\|{\alpha }_{1}\|\|{\beta }_{1}\|\left(\mathrm{cos}\left({E}_{j}t+{\omega }_{1}^{1}-{\omega }_{1}^{2}\right)+i\ mathrm{sin}\left({E}_{j}t+{\omega }_{1}^{1}-{\omega }_{1}^{2}\right)\right)\end{array}$(7) Return back to Equation (6), we have the final formula: $j{\text{e}}^{iHt}i=\underset{p=1}{\sum }\|{\alpha }_{p}\|\|{\beta }_{p}\|\mathrm{cos}\left({E}_{j}t+{\omega }_{1}^{1}-{\omega }_{1}^{2}\right)+i\underset{p=1}{\sum }\|{\alpha }_{p}\|\|{\beta }_{p}\|\mathrm {sin}\left({E}_{j}t+{\omega }_{1}^{1}-{\omega }_{1}^{2}\right).$ To maximize the Equation (5) is equal to: $\mathrm{max}Rej{\text{e}}^{iHt}i=\mathrm{max}\underset{p=1}{\sum }\|{\alpha }_{p}\|\|{\beta }_{p}\|\mathrm{cos}\left({E}_{j}t+{\omega }_{1}^{1}-{\omega }_{1}^{2}\right)=\underset{1}{\sum }\|{\alpha }_{p} \|\|{\beta }_{p}\|$ Since $\|\mathrm{cos}\theta \|\le 1$ for any $\theta$. Here we will use the following lemma to make sure we can take the equality for special t. Lemma 3.5. There exists infinite $t\in \left[0,\infty \right)$ such that $\mathrm{cos}\left({E}_{p}t+{\omega }_{p}^{1}-{\omega }_{p}^{2}\right)=1$for each p and the period time is related to ${E}_{1} $ and ${E}_{2}$. Proof. We focus on $p=2$, $\left(p>2\right)$ is the same extension. Assume there exists two numbers ${k}_{1}$ and ${k}_{2}$ such that the following equalities satisfy: If we rewrite these equations with t, we have the following equality: $\left(2{k}_{1}\pi +{\omega }_{1}^{2}-{\omega }_{1}^{1}\right){E}_{2}=\left(2{k}_{2}\pi +{\omega }_{2}^{2}-{\omega }_{2}^{1}\right){E}_{1}$ $2{k}_{1}{E}_{2}\pi +\left({\omega }_{1}^{2}-{\omega }_{1}^{1}\right){E}_{2}=2{k}_{2}{E}_{1}\pi +\left({\omega }_{2}^{2}-{\omega }_{2}^{1}\right){E}_{1}$ ${k}_{1}{E}_{2}-{k}_{2}{E}_{1}=\frac{\left({\omega }_{2}^{2}-{\omega }_{2}^{1}\right){E}_{1}-\left({\omega }_{1}^{2}-{\omega }_{1}^{1}\right){E}_{2}}{2\pi }$ ${k}_{1}=\left({k}_{2}+\frac{{\omega }_{2}^{2}-{\omega }_{2}^{1}}{2\pi }\right)\frac{{E}_{1}}{{E}_{2}}-\frac{{\omega }_{1}^{2}-{\omega }_{1}^{1}}{2\pi }$ Obviously we can choose suitable ${\omega }_{1}^{1},{\omega }_{1}^{2},{\omega }_{2}^{1},{\omega }_{2}^{2}$ such that their difference is some integer q times $2\pi$, according from the famous Bohr formula: ${E}_{n}=\frac{{E}_{1}}{{n}^{2}}$, so $\frac{{E}_{1}}{{E}_{2}}$ is the rational expression $\frac{{n}_{1}^{2}}{{n}_{2}^{2}}$, pick suitable ${k}_{2}$ such that ${k}_{1}$ is also an integer. Then go back to the t equation to get t. Simliarly, for $p>2$, we can still find their least common multiple. $■$ Example 1. (For Definition 7) The prison’s dilemma is a standard example of a game analyzed in game theory and we will use it first as an example for the uncertainty. 1) If A and B each betray the other,each of them serves two years in prison; 2)If A betrays B but B remains silent,A will be set free and B will serve three years in prison (vice versa). 3)If A and B both remain silent,both of them will serve only one year in prison. So actually each player is in the dilemmas and no one knows his/her opponent’s strategy for the next step. It is a classical application of the “Uncertainty Principle”. Example 2. (This example is from the lecture notes (Ferguson, 2005) (Odd and Even) Player A and B simultaneously call out one of the numbers one or two. Player A’s name is Odd; he wins if the sum of the numbers is odd. Player B’s name is Even; she wins if the sum of the numbers is even. The amount paid to the winner by the loser is always the sum of the numbers in dollars. We choose $X=\left\ {1,2\right\},Y=\left\{1,2\right\}$ and the table is following: Let us analysis the game from Player A’s point of view.Suppose he calls “one”3/5ths of the time and “two”2/5ths of the time at random.In this case, 1)If B calls “one”,A loses 2dollars 3/5ths of the time and wins 3dollars 2/5ths of the time;on average,he wins 0.It is a even game in the long run. 2)If B calls “two”,A wins 3dollars 3/5ths of the time and loses 4dollars 2/5ths of the time and average he wins 1/5. Clearly if A mixed his choices in this given way,the game has two ending:even or A wins 0.2dollar on the average every time. 1)If we think about after a long time “even”,A and B have no change,without loss of generality,the schedule for A is 1,1,1,2,2.Then B starts to think if he can do some change and earn money.So when A is “asleep”,she chooses 2when A is 1and she chooses 1when A is 2.Then each time she can earn 3dollars,A is losing! So based on such situation happen,A should be clear each step and do some changes which is hard for B to guess A’s strategy. 2)Similarly,for second situation.B calls “two”and A wins 0.2dollar average time.A is happy since he can earn money without doing any change,but B want to “save”money unless each game she will lose 0.2average.So she will call “one”without any dilemma,at that situation,A get nothing (since the average payoff is 0),so he will try to make some changes.In that case,each one will behave randomly without fixed strategy. It satisfies the uncertainty principle. However, player A can not player know B’s strategy, can he guess her probability for the next step? Of course he can, this is the following theorem from the quantum mechanics. Theorem 3.6. For player A, he can guess the probability of player B’s from state ${j}_{1}$ to ${j}_{2}$ at time t: ${P}_{{j}_{1}\to {j}_{2}}\left(t\right)={\|{C}_{2}\left(t\right)\|}^{2}$ Here ${C}_{2}\left(t\right)$ is definded as: ${C}_{2}\left(t\right)=-i{\int }_{0}^{t}\text{ }\text{ }{{H}^{\prime }}_{21}\left({t}^{\prime }\right)\mathrm{exp}\left(i{\omega }_{0}{t}^{\prime }\right)\text{d}{t}^{\prime }$ ${H}^{0}$ is the initial Hamiltoian operator: $-\frac{1}{2}\Delta +{v}_{1}$. The player A has a time dependent perturbation ${H}^{\prime }\left(t\right)$, and ${{H}^{\prime }}_{12}={j}_{1}{H}^{\prime }{j}_{2}$, ${{H}^{\prime }}_{21}={\left({{H}^{\prime }}_{12}\right)}^{*}$, ${\omega }_{0}=\frac{{E}_{2}-{E}_{1}}{\hslash }={E}_{2}-{E}_{1}$. We write $H={H}^{0}+{H}^{\prime }\left(t\right)$. The proof is similar from the reference book (Griffiths, 2007). Proof. To begin with, let us suppose that thare are just two states ${j}_{1},{j}_{2}$, then the solution function $\varphi \left(t\right)$ can be expressed by the combinations of these two: $\varphi \left(t\right)={C}_{1}\left(t\right){\varphi }_{1}{\text{e}}^{-i{E}_{1}t}+{C}_{2}\left(t\right){\varphi }_{2}{\text{e}}^{-i{E}_{2}t}.$ And now since we have the perturbation, the new Schrödinger equation is: $H\varphi =i\frac{\partial \varphi }{\partial t}$ Then combine these two together and cancel the term, hence ${C}_{1}\left[{H}^{\prime }{\varphi }_{1}\right]{\text{e}}^{-i{E}_{1}t}+{C}_{2}\left[{H}^{\prime }{\varphi }_{2}\right]{\text{e}}^{-i{E}_{2}t}=iK$ $K={\stackrel{˙}{C}}_{1}{\varphi }_{1}{\text{e}}^{-i{E}_{1}t}+{\stackrel{˙}{C}}_{2}{\varphi }_{2}{\text{e}}^{-i{E}_{2}t}$ To isolate ${\stackrel{˙}{C}}_{1}$, we use the trick: Take the inner product with ${\varphi }_{1}$, and exploit the orthogonality of ${\varphi }_{1}$ and ${\varphi }_{2}$, conclude that: ${\stackrel{˙}{C}}_{1}=-i\left[{C}_{1}{{H}^{\prime }}_{11}+{C}_{2}{{H}^{\prime }}_{12}{\text{e}}^{-i\left({E}_{2}-{E}_{1}\right)t}\right]$ ${\stackrel{˙}{C}}_{2}=-i\left[{C}_{2}{{H}^{\prime }}_{22}+{C}_{1}{{H}^{\prime }}_{21}{\text{e}}^{-i\left({E}_{2}-{E}_{1}\right)t}\right]$ Then after simplifying the equation: ${\stackrel{˙}{C}}_{1}=-i{{H}^{\prime }}_{12}{\text{e}}^{-i{\omega }_{0}t}{C}_{2}$ ${\stackrel{˙}{C}}_{2}=-i{{H}^{\prime }}_{21}{\text{e}}^{i{\omega }_{0}t}{C}_{1}$ Since our ${H}^{\prime }$ is “small”, we can solve the equation in a process of successive approximations. Suppose the particle starts out in the lower state: After the comparsion of zero order and first order, we can have our final conclusion (skip the detail here): ${C}_{2}\left(t\right)=-i{\int }_{0}^{t}\text{ }\text{ }{{H}^{\prime }}_{21}\left({t}^{\prime }\right)\mathrm{exp}\left(i{\omega }_{0}{t}^{\prime }\right)\text{d}{t}^{\prime }$ which means the player B can guess player A’s moving probability in a sense. Vice versa, player A can guess player B’s. $■$ 4. Conclusion and Discussions In our article, we firstly combine the two-players strategy game and Schrödinger equation together, have a connection, successfully explain the game evolution using solution state. It transfers the economics problem to the physical question. Also, we determine the “good” or “bad” based on the distance of two states which is clear and easy to compare and apply the famous quantum mechanics results into the game theory, however we still cannot exactly transfer the game “language” into the initial potentials ${v}_{1},{v}_{2}$ or the equation directly, which is an limitation. And we hope to get the game strategy based on the equation solution (states) totally. However, the distance we defined in the previous section is in the eigenstate basis, but when we perform an measurement of the whole system, we need a transformation for the computational basis, also we will get a probability of getting to the exact state, which helps us approximate the opponent’s strategy. It is an ongoing project.	{"url":"https://www.scirp.org/journal/paperinformation?paperid=116768","timestamp":"2024-11-01T22:06:26Z","content_type":"application/xhtml+xml","content_length":"208607","record_id":"<urn:uuid:70f62687-c953-4c1e-a103-bcae2d33ee70>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00575.warc.gz"}
Implements the midpoint of max spread splitting rule. A rectangle is cut through $ (\mathrm{Mind}+\mathrm{Maxd})/2$ orthogonal to the dimension with the maximum point spread $ [\mathrm{Mind},\mathrm{Maxd}]$. Expects for the first template argument a model of the concept SearchTraits, for example the type CGAL::Search_traits_3< Cartesian<double> >. Expects for the second template argument a model of the concept SpatialSeparator. It has as default value the type, CGAL::Plane_separator<Traits::FT> See also	{"url":"https://doc.cgal.org/5.5.2/Spatial_searching/classCGAL_1_1Midpoint__of__max__spread.html","timestamp":"2024-11-06T08:40:37Z","content_type":"application/xhtml+xml","content_length":"12080","record_id":"<urn:uuid:a0e4f4ce-2dc2-4e1a-b5b1-c8eadad85285>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00681.warc.gz"}
55 square meter to square feet 6. Conversion Examples: Providing step-by-step examples of converting specific measurements from square meters to square feet will assist readers in grasping the conversion process more effectively. These examples should cover a range of values. One essential aspect of understanding conversions from square meters to square feet is through step-by-step examples. By providing readers with these examples, the conversion process becomes more accessible and comprehensible. These examples should cover a range of values to cater to varying needs and scenarios. For instance, let’s take a look at converting a measurement from 20 square meters to square feet. To convert, you’ll need to multiply the measurement in square meters by the conversion factor of 10.764. So, 20 square meters multiplied by 10.764 equals 215.28 square feet. By following this simple calculation, readers can easily convert any given measurement from square meters to square feet. In another example, let’s consider a larger measurement of 100 square meters. Applying the same conversion factor, multiplying 100 square meters by 10.764 results in 1,076.4 square feet. By showcasing examples like these, readers can grasp the conversion process and apply it to different values effectively. Additionally, it is crucial to include examples that cover a range of values, such as small, medium, and large measurements. This variation ensures that readers can understand the conversion process in different contexts and scenarios. It’s through these step-by-step examples that the conversion from square meters to square feet becomes more tangible and easier to grasp for readers. Converting measurements from square meters to square feet is a common task that individuals often encounter in various industries and everyday life. To help readers grasp the conversion process more effectively, it is essential to provide step-by-step examples that cover a wide range of values. By presenting these examples, readers can gain a better understanding of the calculations involved and apply them confidently in their own situations. One example of converting square meters to square feet could involve a small room with dimensions of 10 square meters. To convert this measurement to square feet, multiply the value by the conversion factor of 10.764. By performing this calculation, the result would be approximately 107.64 square feet. This example demonstrates how a simple multiplication can transform one unit of area to another, providing readers with a clear illustration of the conversion process. Another example could involve a larger area, such as a backyard measuring 500 square meters. Using the same conversion factor of 10.764, multiplying 500 by this value gives us approximately 5,381.2 square feet. By showcasing this conversion, readers can observe how the process remains consistent regardless of the size of the area being converted. By presenting these step-by-step examples of converting specific measurements from square meters to square feet, readers can gain a solid understanding of the conversion process. This knowledge will enable them to solve conversion problems with confidence, whether they are working on construction projects, managing real estate, or simply converting areas in their everyday lives.	{"url":"https://convertertoolz.com/sq-m-to-sq-ft/55-square-meter-to-square-feet/","timestamp":"2024-11-09T13:48:54Z","content_type":"text/html","content_length":"42759","record_id":"<urn:uuid:2c1c46c5-ddea-4e36-9721-72e28f6dbe51>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00057.warc.gz"}
Issues with importing bundler.out alignment I'm trying to import scene and mesh from RealityCapture, to take advantage of the great texturing capabilities of Photoscan. The scene is exported from RC in bundler format but when importing in Photoscan, the mesh is translated on the z axis with respect to the cameras (see attached screenshot). I imported the same mesh and the same bundler.out with meshlab and the alignment shows correct there, therefore it is not a problem on the export side, but Photoscan is rendering a translated mesh, or translated camera positions. Any suggestion how this could be fixed on my side, or any hope to get a patch for this ? thank you in advance	{"url":"https://www.agisoft.com/forum/index.php?topic=6270.msg30329","timestamp":"2024-11-05T16:11:21Z","content_type":"application/xhtml+xml","content_length":"62053","record_id":"<urn:uuid:c99ecdca-259b-4b30-980a-bdb5b462ac31>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00264.warc.gz"}
“Antimatter” is one of the big stars in the new Ron Howard film “Angels & Demons.” After seeing the movie, people may wonder how much of the science in the film is actually real. SMU Physics Professor Fredrick Olness says the new action thriller exploits cutting-edge science to create an exciting tale of science fiction mystery and imagination. “Angels & Demons” takes key ideas that are based upon scientific fact, Olness comments, and then exaggerates the details for the purpose of storytelling — and that’s the transformation from “science” to “science fiction.” In the movie, which opened May 15, members of a centuries-old secret society steal a small container of antimatter from the CERN particle physics laboratory in Europe and threaten to blow up the Vatican. Tom Hanks, as a Harvard professor, tries to stop the society. “Angels & Demons” is billed as the prequel to the 2006 box-office hit “The Da Vinci Code,” both of which are based on books by best-selling author Dan Brown. When asked to separate fact from fiction, Olness noted: Pictured right: Atlas collision event • While it is also true that CERN has created antimatter, it would take more than a billion years (with current technology) to make the quantity of antimatter described in the movie. If you collected all the antimatter that CERN has ever created, it would only power an electric light bulb for a few minutes. • It is true that when antimatter and matter meet, they annihilate into pure energy; however, antimatter is not a source of energy. The production of antimatter is very inefficient, so it takes much more energy to create the antimatter than you get back. • It is also true that we are able to store antimatter, but scientists don’t actually keep antimatter on the lab shelf. Even small quantities of antimatter are difficult to store. Charged antimatter can be stored in a “magnetic bottle,” but the repulsive force of the antimatter charges greatly limits the quantity. Uncharged (neutral) antimatter cannot be contained by a “magnetic • The CERN laboratory was established in 1954 and has a long history of important scientific discoveries. Two of the discoveries from the CERN lab have been awarded Nobel Prizes, and CERN is the birthplace of the World Wide Web. Olness spent his 2007-08 sabbatical in residence at CERN as part of a team of SMU scientists working with the Large Hadron Collider, which is featured in the opening scenes from “Angels & Demons.” The collider, known as the LHC, is the world’s largest and highest-energy particle accelerator. Located near Geneva on the French-Swiss border, the LHC consists of a 17-mile, circular ring of magnets that lies 100 meters beneath the earth’s surface. “Having spent a year at CERN, I particularly enjoyed the special effects during the LHC scene.” Olness commented. “They paid attention to the details, and even made the background dialogue in the LHC control room credible.” The purpose of the LHC is to collide two counter-rotating beams of protons traveling at nearly the speed of light. The idea is to smash the protons into smaller particles, and to then gather the mountain of data that results from these “events.” The data will help scientists understand what may have occurred when our Universe came into existence just after the Big Bang. As noted in the movie, LHC scientists are searching for the hypothesized “God particle,” or more scientifically the “Higgs boson.” As a theoretical physicist, Olness develops the computer models necessary to decipher the results of the LHC experiments. In addition to expanding our knowledge of fundamental science, research at CERN has contributed to important technological innovations such as the World Wide Web, massively parallel (GRID) computing, and improvements in medical imaging. Tom Hanks toured CERN in February and was visibly impressed with its massive LHC particle accelerator, according to a CERN web site about the science behind the movie. Olness, with wand, gives a nod to “Star Wars” at the 2001 SMU Physics Circus Hanks commented at CERN: “Magic is not happening here, magic is being explained here.” CERN quotes Hanks as saying the movie “Angels & Demons” will inspire kids to take a greater interest in science. Related links: CERN: “Angels & Demons” CERN FAQ: Angels & Demons Fredrick Olness home page Olness’ tour of CERN CERN Scientists: Large Hadron Collider rap Movie trailer: Angels & Demons Dan Brown: Angels & Demons CERN: The basics Labreporter.com: The science behind the Large Hadron Collider CERN: The God particle SMU Physics Department Dedman College of Humanities and Sciences At 10 p.m. on a Saturday night in April, a handful of SMU scientists continue working at the European Organization for Nuclear Research, called by its acronym CERN, in Geneva, Switzerland. A scattering of lights illuminates the windows in several buildings along the Rue Einstein, where researchers from dozens of countries and hundreds of institutions are combining their expertise on the Large Hadron Collider (LHC) — the biggest physics experiment in history. Ryszard Stroynowski, chair and professor of physics at SMU, points out each building in succession to a group of visitors. “By October, every light in every one of these windows will be on all night,” he says. By then, the LHC is expected to be fully tested and ready to work. When the largest particle accelerator ever constructed becomes fully operational, it will hurl protons at one another with precision to a fraction of a micron and with velocities approaching the speed of light. These conditions will allow physicists to recreate and record conditions at the origin of the universe — and possibly discover the mechanisms that cause particles in space to acquire their differences in mass. For Stroynowski, who has worked for almost 20 years to help make the experiment a reality, words seem inadequate to capture the anticipation surrounding its imminent activation. “It is somewhat like that of a 6-year-old kid on Christmas Eve, waiting for Santa Claus,” he says. “The time stretches almost unbearably long.” The LHC will be the site of several experiments in high-energy physics with high-profile collaborators such as Harvard and Duke and national laboratories including Argonne, Brookhaven, Lawrence Berkeley and Fermilab. None of the experiments is more imposing than ATLAS, one of two general-purpose particle detectors in the LHC array. At about 42 meters long and weighing 7,000 tons, ATLAS fills a 12-story cavern beneath the CERN facilities in Meyrin, Switzerland, just outside Geneva. It is a tight fit: ATLAS overwhelms even the vast space it occupies. A catwalk, not quite wide enough for two people to stand side by side, encircles the device and allows an occasional dizzying view into its works. Size Matters The detector’s scale will help to focus and release the maximum amount of energy from each subatomic collision. A series of bar codes on each of its parts ensure that the detector’s components, whether palm-sized or room-sized, are aligned and locked with the perfect precision required for operability. Scientists from 37 countries and regions and 167 institutions participated in its design and construction. As U.S. coordinator for the literal and experimental heart of the ATLAS detector — its Liquid Argon Calorimeter — Stroynowski is helping to finalize the last details of the detector’s operation in anticipation of the extensive testing, scheduled to begin in August. He leads an SMU delegation that includes Fredrick Olness, professor, and Robert Kehoe and Jingbo Ye, assistant professors in the SMU Department of Physics in Dedman College. SMU scientists are completing work on the computer software interfaces that will control the device, which measures energy deposited by the flying debris of smashed atoms. A cadre of University graduate students and postdoctoral fellows also is working on data processing for ATLAS’ 220,000 channels of electronic signals, an information stream larger than the Internet traffic of a small An estimated 53,000 visitors crowded the CERN facilities on the organization’s “Day of Open Doors” April 6, eager for a glimpse of the work that CNN International has named one of the “Seven Wonders of the Modern World.” At the beginning of May, the areas were sealed off in preparation for the first round of testing. Computers will remotely control the ATLAS experiment, which will not be touched by human hands because of the radiation released by the atomic collisions. Safety is the reason for the elaborate lockdown procedure involving more than 80 keys, each coded to a different individual’s biometric data. The system is designed to lock out any use of the device if even one key is unaccounted for. “ATLAS has been built to run for at least 15 years with no direct human intervention,” Stroynowski says. “It will be as if we have shot it into space.” Currently, the initial test run is scheduled to begin Sept. 1. The Waiting Game Once data start streaming in, the game of expectations management begins. The ATLAS detector will produce a staggering amount of raw information from each collision, and the most useful bits will be few and far between. Out of 40 million events per second, the researchers hope to pinpoint 10 events a year. The challenge seems a little like looking for a needle in a haystack the size of Mars. “We may get what we’re looking for on the first try, or it may take us three years to find anything we can use,” Stroynowski says. “A big part of our job is to make sure we’re ready when we do.” Among those entrusted with that task are graduate students and postdoctoral fellows in SMU’s Physics Department, including Rozmin Daya, Kamile Dindar, Ana Firan, Daniel Goldin, Haleh Hadavand, Julia Hoffman, Yuriy Ilchenko, Renat Ishmukhametov, David Joffe, Azeddine Kasmi, Zhihua Liang, Peter Renkel, Ryan Rios and Pavel Zarzhitsky. “I came to SMU for postdoctoral work specifically because of the department’s involvement in the ATLAS project,” says David Joffe, a native of Canada who received his Ph.D. in physics from Northwestern University. “For particle physicists, being part of this is really a once-in-a-lifetime opportunity.” For Julia Hoffman, who received her doctorate from Soltans Institute for Nuclear Studies in her native Poland, that opportunity has meant expanding her own horizons. “I learn new, and I mean really new, things every day,” she says. “Different programming languages, different views on physics analysis. I’m learning how it all works from the inside. I work with students and gain new responsibilities. This kind of experience means better chances to find a permanent position that will be as exciting as this one.” The SMU group works with formulae based in Monte Carlo methods, the “probabilistic models that use repeated random sampling of vast quantities of numbers” to impose a semblance of order on the chaos created when atoms forcibly disintegrate. Results are highly detailed simulations of known physics that will help make visible the tiny deviations researchers hope to detect when ATLAS begins taking These unprecedented computing challenges also have become an impetus for new SMU research initiatives. James Quick, SMU associate vice president for research and dean of graduate studies, hopes to contain ATLAS’ vast data-processing requirements with a large-capability computing center located on campus. Quick visited CERN in April to discuss the details with Stroynowski and other key personnel. The proposed center would provide a first-priority data processing infrastructure for SMU physicists and a powerful new resource for researchers in other schools and departments. During the inevitable LHC downtime, as beams are calibrated and software is debugged, the SMU center’s computing power would be available for campus researchers in every field across engineering, the sciences and business. “The ATLAS experiment presents an opportunity for the University to step up in a big way, and one that will benefit the entire campus,” Quick says. He envisions a data processing farm of 1,000 central processing units, each connected to an Internet backbone to allow the fastest possible return on SMU’s ATLAS input. Speed and access are the keys, Stroynowski says, paraphrasing Winston Churchill: “The winner gets the oyster, and the runner-up gets the shell.” Those who have made their careers in high-energy physics are well aware of the stakes involved in the LHC, he adds, and being the first to process certain data could separate a potential Nobel Prize winner from those who will make the same discovery a day late. As a group, high-energy physicists are accustomed to taking the long view — and for SMU researchers, the long view has been especially helpful. The ghost of the Superconducting Super Collider, which would have made its home in North Texas, still shadows the recent triumphs at CERN. The SSC brought Stroynowski to the University, and its 1993 demise through congressional defunding was the impetus for the LHC project. The questions haven’t gone away because the experiment has changed venues, Stroynowski says. Yet even now, as the first test nears, his anticipation is tempered by caution. “I don’t think we’ll get a beam all the way around [the LHC tunnel] on the first try,” he says. Indeed, the subject of whether scientists will achieve a beam collision during the first tests or after additional calibration has been the subject of a few lively wagers. “I think we’ll have to wait at least a few more weeks for that milestone,” he adds. “But in this case, I’ll be more than happy to be wrong.” — Kathleen Tibbetts SMU has an uplink facility on campus for live TV, radio or online interviews. To speak with Dr. Biehl or Dr. D’Mello or to book them in the SMU studio, call SMU News & Communications at 214-768-7650 or UT Dallas Office of Media Relations at 972-883-4321. SMU is a private university in Dallas where nearly 11,000 students benefit from the national opportunities and international reach of SMU’s seven degree-granting schools. For more information see	{"url":"https://blog.smu.edu/research/tag/cern/page/2/","timestamp":"2024-11-05T22:47:51Z","content_type":"text/html","content_length":"93055","record_id":"<urn:uuid:8571ae43-3d81-48b6-b5c0-53c48524033a>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00877.warc.gz"}
Linear interpolation in SAS SAS programmers sometimes ask about ways to perform one-dimensional linear interpolation in SAS. This article shows three ways to perform linear interpolation in SAS: PROC IML (in SAS/IML software), PROC EXPAND (in SAS/ETS software), and PROC TRANSREG (in SAS/STAT software). Of these, PROC IML Is the simplest to use and has the most flexibility. This article shows how to implement an efficient 1-D linear interpolation algorithm in SAS. You can download the SAS program that creates the analyses and graphs in this article. Linear interpolation assumptions For one-dimensional linear interpolation of points in the plane, you need two sets of numbers: 1. Data: Let (x1, y1), (x2, y2), ..., (xn, yn) be a set of n data points. The data should not contain any missing values. The data must be ordered so that x1 < x2 < ... < xn. These values uniquely define the linear interpolation function on [x1, xn]. I call this the "sample data" or "fitting data" because it is used to create the linear interpolation model. 2. Values to score: Let {t1, t2, ..., tk} be a set of k new values for the X variable. For interpolation, all values must be within the range of the data: x1 ≤ t[i] ≤ xn for all i. The goal of interpolation is to produce a new Y value for each value of t[i]. The scoring data is also called the "query data." Interpolation requires a model. For linear interpolation, the model is the unique piecewise linear function that passes through each sample point and is linear on each interval [x[i], x[i+1]]. The model is usually undefined outside of the range of the data, although there are various (nonunique) ways to extrapolate the model beyond the range of the data. You fit the model by using the data. You then score the model on the set of new values. The following SAS data sets define example data for linear interpolation. The POINTS data set contains fitting data that define the linear model. The SCORE data set contains the new query points at which we want to interpolate. The linear interpolation is shown to the right. The sample data are shown as blue markers. The model is shown as blue lines. The query values to score are shown as a fringe plot along the X axis. The interpolated values are shown as red markers. The data used for this example are: /* Example data for 1-D interpolation / data Points; / these points define the model / input x y; data Score; / these points are to be interpolated / input t @@; 2 -1 4.8 0 0.5 1 9 5.3 7.1 10.5 9 For convenience, the fitting data are already sorted by the X variable, which is in the range [0, 10]. The scoring data set does not need to be sorted. The scoring data for this example contains five special values: • Two scoring values (-1 and 10.5) are outside of the range of the data. An interpolation algorithm should return a missing value for these values. (Otherwise, it is extrapolation.) • Two scoring values (0 and 1) are duplicates of X values in the data. Ideally, this should not present a problem for the interpolation algorithm. • The value 9 appears twice in the scoring data. Linear interpolation in SAS by using PROC IML As is often the case, PROC IML enables you to implement a custom algorithm in only a few lines of code. For simplicity, suppose you have a single value, t, that you want to interpolate, based on the data (x1, y1), (x2, y2), ..., (xn, yn). The main steps for linear interpolation are: 1. Check that the X values are nonmissing and in increasing order: x1 < x2 < ... < xn. Check that t is in the range [x1, xn]. If not, return a missing value. 2. Find the first interval that contains t. You can use the BIN function in SAS/IML to find the first value i for which x_i <= t <= x_{i+1}. 3. Define the left and right endpoint of the interval: xL = x_i and xR = x_{i+1}. Define the corresponding response values: yL = y_i and yR = y_{i+1}. 4. Let f = (t - xL) / (xR - xL) be the proportion of the interval to the left of t. Then p = (1 - f)yL + fyR is the linear interpolation at t. The steps are implemented in the following SAS/IML function. The function accepts a vector of scoring values, t. Notice that the program does not contain any loops over the elements of t. All statements and operations are vectorized, which is very efficient. / Linear interpolation based on the values (x1,y1), (x2,y2),.... The X values must be nonmissing and in increasing order: x1 < x2 < ... < xn The values of the t vector are linearly interpolated. proc iml; start LinInterp(x, y, _t); d = dif(x, 1, 1); /* check that x[i+1] > x[i] / if any(d<=0) then stop "ERROR: x values must be nonmissing and strictly increasing."; idx = loc(_t>=min(x) && _t<=max(x)); / check for valid scoring values / if ncol(idx)=0 then stop "ERROR: No values of t are inside the range of x."; p = j(nrow(_t)ncol(_t), 1, .); /* allocate output (prediction) vector / t = _t[idx]; / subset t values inside range(x) / k = bin(t, x); / find interval [x_i, x_{i+1}] that contains s / xL = x[k]; yL = y[k]; / find (xL, yL) and (xR, yR) / xR = x[k+1]; yR = y[k+1]; f = (t - xL) / (xR - xL); / f = fraction of interval [xL, xR] / p[idx] = (1 - f)#yL + f#yR; / interpolate between yL and yR / return( p ); / example of linear interpolation in SAS / use Points; read all var {'x' 'y'}; close; use Score; read all var 't'; close; pred = LinInterp(x, y, t); create PRED var {'t' 'pred'}; append; close; Visualize a linear interpolation in SAS The previous program writes the interpolated values to the PRED data set. You can concatenate the original data and the interpolated values to visualize the linear interpolation: / Visualize: concatenate data and predicted (interpolated) values */ data All; set Points Pred; title "Linear Interpolation"; title2 "No Extrapolation"; proc sgplot data=All noautolegend; series x=x y=y; scatter x=x y=y / markerattrs=(symbol=CircleFilled size=12) name="data" legendlabel="Data"; scatter x=t y=Pred / markerattrs=(symbol=asterisk size=12 color=red) name="interp" legendlabel="Interpolated Values"; fringe t / lineattrs=(color=red thickness=2) name="score" legendlabel="Values to Score"; xaxis grid values=(0 to 10) valueshint label="X"; yaxis grid label="Y" offsetmin=0.05; keylegend "data" "score" "interp"; The graph is shown at the top of this article. A few noteworthy items: • The values -1 and 10.5 are not scored because they are outside the range of the data. • The values 0 and 1 correspond to a data point. The interpolated value is the corresponding data value. • The other values are interpolated onto the straight line segments that connect the data. Performance of the IML algorithm The IML algorithm is very fast. On my Windows PC (Pentium i7), the interpolation takes only 0.2 seconds for 1,000 data points and one million scoring values. For 10,000 data points and one million scoring values, the interpolation takes about 0.25 seconds. The SAS program that accompanies this article includes timing code. Other SAS procedures that can perform linear interpolation According to a SAS Usage Note, you can perform linear interpolation in SAS by using PROC EXPAND in SAS/ETS software or PROC TRANSREG in SAS/STAT software. Each has some limitations that I don't like: • Both procedures use the missing value trick to perform the fitting and scoring in a single call. That means you must concatenate the sample data (which is often small) and the query data (which can be large). • PROC EXPAND requires that the combined data be sorted by X. That can be easily accomplished by calling PROC SORT after you concatenate the sample and query data. However, PROC EXPAND does not support duplicate X values! For me, this makes PROC EXPAND unusable. It means that you cannot score the model at points that are in the original data, nor can you have repeated values in the scoring data. • If you use PROC TRANSREG for linear interpolation, you must know the number of sample data points, n. You must specify n – 2 on the NKNOTS= option on a SPLINE transformation. Usually, this means that you must perform an extra step (DATA step or PROC MEANS) and store n – 2 in a macro variable. • For scoring values outside the range of the data, PROC EXPAND returns a missing value. However, PROC TRANSREG extrapolates. If t < x1, then the extrapolated value at t is y1. Similarly, if t > xn , then the extrapolated value at t is yn. I've included examples of using PROC EXPAND and PROC TRANSREG in the SAS program that accompanies this article. You can use these procedures for linear interpolation, but neither is as convenient as PROC IML. With effort, you can use Base SAS routines such as the DATA step to implement a linear interpolation algorithm. An example is provided by KSharp in a SAS Support Community thread. If you want to perform linear interpolation in SAS, the easiest and most efficient method is PROC IML. I have provided a SAS/IML function that implements linear interpolation by using two input vectors (x and y) to define the model and one input vector (t) to specify the points at which to interpolate. The function returns the interpolated values for t. 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Editorial for SRM 577 div1 hard: BoardPainting It is up: http://apps.topcoder.com/wiki/display/tc/SRM+577#BoardPainting I thought I understood the solution to this problem. During the match, I was pretty sure it was min cut but I had no idea how. Then rng_58 sent me an explanation on how to make the min cut algorithm. So during the week I focused on distractions such as trying to find a proof for the easy solution in div2 hard (Hardest solution to prove in a while, I am not even sure if it is possible to prove it :/). And then with trying to think of a good way to explain div1 medium. Then yesterday as I was getting ready to explain this problem, I suddenly noticed that, although I understood the solution, I had no idea of why it works or how to think of it. So I spent some hours figuring things out. I think the explanation is still not very good though. It is very impressive to find that this problem has a polynomial time algorithm. Back in 2007, the SRM 383 version of this problem taught me dynamic programming using bitmasks (Hence why I remember so much about this problem). Who would think it was possible to also learn max flow from it? No comments :	{"url":"https://www.vexorian.com/2013/05/editorial-for-srm-577-div1-hard.html","timestamp":"2024-11-09T14:18:53Z","content_type":"text/html","content_length":"100306","record_id":"<urn:uuid:d58f54e5-cc60-48f1-b78d-f22f9d02c38a>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00408.warc.gz"}
Methodology for measuring uncertainty in ONS local authority mid-year population estimates: 2012 to 2016 The Uncertainty Project was established as part of the Migration Statistics Improvement Programme (MSIP 2008 to 2012). Working in collaboration with Southampton Statistical Sciences Research Institute (S3RI), this project aimed to provide users of Office for National Statistics (ONS) local authority mid-year population estimates with more information regarding their quality. This report summarises the methodology for deriving the statistical measure of uncertainty associated with the local authority mid-year population estimates. We use the cohort component approach to create the local authority mid-year population estimates. The cohort component method uses the 2011 Census for the population base and then incorporates natural change (births and deaths), net international migration and net internal migration, and other adjustments (for example, asylum seekers). The methodology for deriving the statistical measure of uncertainty applies the same processes to derive simulated distributions for each component. These are then combined using the cohort component formula to derive the uncertainty associated with the local authority mid-year estimates. Early research identified the census, international migration and internal migration as the 3 components with the greatest impact on uncertainty. The methodology to quantify uncertainty is therefore based on these 3 components. Because the mid-year estimates combine various data sources and processes to derive each component, we have used different methods to produce the simulated distributions for each component. This working paper describes these methods and the subsequent measures of uncertainty for each local authority for the years 2012 to 2016. Summary statistics of the final output are also included. Nôl i'r tabl cynnwys This project reflects the combined efforts of the Demographic Methods Centre within ONS Methodology and the Southampton Statistical Sciences Research Institute (S3RI). ONS would particularly like to acknowledge the contribution of Professor Peter W.F. Smith from the University of Southampton. Nôl i'r tabl cynnwys The local authority mid-year estimates refer to the usually resident population on 30 June of the reference year^1. Published annually, the estimates are based on the previous census and are updated each year using the cohort component method. Currently, users have to wait 10 years until the next census before they have an indication of the uncertainty associated with the mid-year estimates. The Uncertainty Project aims to provide more timely quality information for the mid-year estimates. This follows original recommendations from the Migration Task Force (2006), the UK Statistics Authority report (Migration Statistics: The Way Ahead (UK Statistics Authority 2009a) and Principle 4 of the Code of Practice for Official Statistics (UK Statistics Authority 2009b). The Uncertainty Project originally included 2 streams of work. The first involved the development of Quality Indicators, which was completed in 2012 (ONS 2012a). These report the percentage of local authority population or households with characteristics associated with uncertainty in the mid-year estimates and are published annually with the mid-year estimates. The second stream, which is the focus of this report, was the development of measures of statistical uncertainty. Measures for 2002 to 2010 were published by the Office for National Statistics (ONS) as research outputs in 2012 (ONS 2012b). The methods have been adapted following the 2011 Census to reflect changes in the methodology to produce the mid-year estimates. Development of the methodology for the uncertainty measures has been a collaborative project between the Southampton Statistical Sciences Research Institute (S3RI) and the Demographic Methods Centre, within Population Methodology and Statistical Infrastructure, in ONS Methodology. This working paper updates the 2012 report that was published with the 2002 to 2010 series. We welcome your feedback, both on the methods used and the results of this research. Notes for: Introduction 1. For the mid-year estimates, ONS uses rules to assign usual residence where this could be ambiguous: students are considered to be usually resident at their term-time address; armed forces personnel are usually resident at the place where they spend most of their time; prisoners are usually resident at the prison estate if they have a conviction of 6 months or more and international migrants are usually resident if they intend to stay in the UK for 12 months or more. Nôl i'r tabl cynnwys 5. Developing a statistical measure of uncertainty “Uncertainty” is defined here as the quantification of doubt about a measurement. The 3 main sources of uncertainty associated with the mid-year population estimates are: the census base; international migration; and internal migration (moves between local authorities). For more detail on the early feasibility work for the uncertainty measures, see ONS (2010). Uncertainty in the other components of change (births, deaths, asylum seekers, armed forces, prisoners) is not reflected in the methodology and is assumed for now to be zero. This assumption will be reviewed as part of future methodological development. For each of the 3 components associated with uncertainty, the estimation process that is used to produce the mid-year population estimates is replicated and the replicates are used to simulate a range of possible values that might occur. The simulated distributions for each component are combined, iteration by iteration, mirroring the standard cohort components approach that is used for the published mid-year estimates. Thus, in year t: From the resulting distribution of plausible estimates for each local authority, the principal measure of uncertainty is calculated as the relative root mean squared error^1 (see Equation 5.12). This takes into account bias in the estimated values and allows uncertainty to be compared between local authorities. This methodology uses statistical bootstrapping to create simulated distributions for each of the 3 components of the mid-year estimate that contribute the most to statistical uncertainty: the census, internal migration and international migration. Statistical bootstrapping is a method for assigning measures of accuracy to sample estimates (Efron and Tibshirani 1993). It falls under the broader class of re-sampling methods. Bootstrap techniques allow estimation of the sampling distribution of almost any statistics, from which uncertainty measures such as variance, standard deviation and bias can be derived. Bootstrap techniques can be either parametric or non-parametric. Parametric bootstrapping assumes an underlying distribution and simulates from this distribution. Non-parametric bootstrapping makes no distributional assumptions and re-samples (with replacement) directly from the observed data. Bootstrapping from the observed data, for example, from the International Passenger Survey, creates simulated datasets, which theoretically reflect the sampling error in the original samples. The bootstrapping techniques used in the estimation of uncertainty for the mid-year estimates are summarised in Table 1. Further details on bootstrapping techniques are detailed in the subsequent sections of this report. Table 1: Re-sampling methods used in the construction of uncertainty for ONS mid-year estimates Component Re-sampling method Type of bootstrap Census base Uses published variances and assumes that errors are normally distributed. Parametric Correction of census base Assumes that the coefficient of variation for this 3-month component is the same as the coefficient of variation around the 2012 mid-year estimate estimates to mid-year and that errors are normally distributed. Parametric Uncertainty from International Passenger Survey (IPS) sampling and imputation: Re-sampling with replacement from the IPS, with 1,000 new samples then Non-Parametric re-run through IPS imputation. International in-migration Uncertainty from the use of administrative data to allocate in-migrants to local authorities: Uses a benchmark approach, comparing administrative Parametric using a distributions to 2011 census-based ones, to derive variances for each administrative data source used. Errors are assumed to be log-normally benchmark International out-migration Re-sampling with replacement from the IPS, then repeating Poisson regression modelling on 1,000 simulated datasets. Non-parametric Adopts a benchmark approach. Re-samples residuals from the non-linear regression model of the log of the ratio of 2011 Census to Patient Register Re-sampling Internal migration internal local authority transitions. Sampled residuals are then added to predicted values from the model, which is updated with contemporaneous residuals using a covariates for the inter-censal period. benchmark Source: Office for National Statistics Download this table Table 1: Re-sampling methods used in the construction of uncertainty for ONS mid-year estimates .xls (28.2 kB) 5.1 The 2011 Census base Taken once every 10 years, the census is the “gold standard” for estimating the population. The mid-year estimate in the year of the census is based on the census estimate of the usually resident population. The mid-year estimate then allows for population ageing, births, deaths, internal and international migration and minor population changes that take place between census day (27 March) and 30 June. Measuring uncertainty around the 2011 Census is relatively straightforward, since we publish comprehensive information about the quality of the census estimates. The 2011 Census estimates and the published variances (ONS 2013) for local authorities are used to specify the distribution (assumed to be normal) of uncertainty around the census component. Parametric bootstrapping from this normal distribution was used to create 1,000 simulations for the census component for each local authority. Correcting for the mid-year reference point We allow for uncertainty around the correction that we apply to update the census estimates to the mid-year population. One option would be to measure uncertainty around the international and internal migration components within this adjustment. However, for the purpose of these research statistics, we take a simpler approach. We create 1,000 plausible values for the correction through bootstrapping: 1. This involves first calculating the 2012 uncertainty, including all 3 components and the composite calculations described in this section, without making any allowance for the 3-month March to June 2011 adjustment. This provides a coefficient of variation (CV) around the 2012 local authority-level estimates. 2. Simulated values for the 3 month census to mid-year period are created using parametric bootstrapping. The coefficient of variation is assumed to be the same as for the 2012 mid-year estimate (calculated without the additional census day to mid-year uncertainty), distributed normally, and the mean is taken as the difference between the published 2011 mid-year estimate and the 2011 Census estimate. 3. These values are then added to the census simulations, to then feed into the composite process. Note that the base year component cannot be finalised until all other components, and the (initial) composite, have been completed. The 2012 composite is run a second time to include the uncertainty around the 3-month adjustment. 5.2 International migration Methods for producing local authority estimates of international migration for the mid-year estimates Our local authority mid-year estimates include an estimate of the people going to or coming from a local authority who intend to be long-term international migrants. Long-term migrants are defined as those who intend to stay for more than one year (immigrants) or who are departing to take up residence abroad for a minimum of a year, having already lived in the country of departure for more than a year (emigrants). International migration to and from England and Wales is estimated from the International Passenger Survey (IPS) (see ONS 2015). The IPS operates at UK ports of arrival and departure. It is the only source on UK migration that identifies people who meet the definition of a long-term international migrant, as someone who changes their country of residence for more than 12 months. Migration estimates from the IPS are based on a small sample and cannot reliably be disaggregated down to local authority level. To achieve migrant estimates at lower geographic levels, we use different methods for immigrants and emigrants. The approach for immigrants identifies migrant “streams” based on responses to the IPS question on the main reason for migrating. This distinguishes between first-time migrants and returning migrants who were born outside of the UK, on the one hand, and UK-born returning migrants on the other. These are differentiated because returning UK-born migrants are believed to have different local authority distributions to foreign-born migrants and interact with the administrative sources differently. Administrative and census data are then used to distribute different types of migrants across local authorities. See Section 5.2.1 for further detail on international immigrants. For emigrants, IPS totals are firstly distributed across New Migration Outflow (NMGo) geographic levels. The IPS-based NMGo totals are then estimated for local authorities using Poisson regression modelling. (Until 2010, this “constrained and then modelled” approach was applied to both the immigrant and the emigrant IPS totals to achieve local authority distributions.) 5.2.1. International in-migration First-time migrants and returning migrants born outside of the UK are split into streams: students, workers or “other” (see ONS 2011). The “other” category includes children (those aged 15 and under and non-working 16 year-olds), 17 to 59 year-olds who are not migrating to work or study and people aged 60 and over who are not working. Each stream of immigrants is distributed to local authorities using the distributions observed in administrative data that are relevant to that group. Where census data are used, the 2011 distributions are used for each year following the census but for other administrative sources, the distributions vary annually. For students, the approach uses data from the Higher Education Statistics Agency (HESA) for students in higher education and from the Department for Business, Innovation and Skills (BIS) and Welsh government (WG) for further education students. People immigrating for work are distributed to local authorities using the Department for Work and Pensions’ Migrant Worker Scan (MWS), which provides a count of foreign nationals who applied for a National Insurance number. “Other” migrants are distributed to local authorities using the NHS Patient Register “Flag 4” information. “Flag 4” status is given to people entering the NHS from abroad for the first time. UK-born returning migrants are also split into migrant streams, as earlier in this section, and then the 2011 Census is used to create their local authority distributions. Asylum seekers are distributed to local authorities using information from the National Asylum Support Service (NASS). Figure 1 illustrates the streaming and the administrative sources that are used. Figure 1: International in-migrants in the mid-year estimates Download this image Figure 1: International in-migrants in the mid-year estimates .png (56.0 kB) 5.2.1.1 Measuring uncertainty in the local authority in-migration estimates To capture uncertainty in the estimates of international in-migration, 2 potential sources of error are identified: • sampling and imputation error within the International Passenger Survey (IPS) • the distribution of immigrants to local authorities using administrative data could be incorrect We assume that there is no uncertainty associated with the asylum seeker stream. 5.2.1.2 Bootstrapping to capture sampling and imputation error in the IPS To capture the error from the IPS, 1,000 simple random samples are re-drawn from the IPS, with replacement after each record is selected. Earlier research investigated how best to take account of the complex sample design and weighting methods used to create national-level migrant estimates from the IPS. The complex sample design of the IPS and non-sampled international travel routes and time periods mean that weights are used to create national estimates of international travellers. Two possible approaches to re-sampling weighted data are to draw a simple random sample, with replacement, or to resample with a probability that is proportional to the inverse of the IPS sample weight. Research concluded that the former, “simple bootstrap” was preferred (Ou and Smith, 2012). The IPS data imputation process is applied to each of these bootstrapped samples. For more details see ONS (2014). 5.2.1.3 Bootstrapping to capture error from using administrative data to distribute in-migrants to local authorities Bootstrapping from the IPS generates 1,000 alternative IPS national-level counts of immigrants for each stream. To capture uncertainty from the administrative-based distribution of the IPS total to local authorities, we create 1,000 alternative local authority distributions for each stream. These are applied, iteration by iteration, to the IPS national stream totals to create 1,000 alternative local authority counts for each stream, which are then combined by LA across each stream to give 1,000 alternative immigrant totals for each local authority. The administrative sources used to derive local authority distributions of immigrant numbers cannot be bootstrapped in the same way as from the IPS. Instead, a parametric bootstrapping approach is adopted where for each stream we simulate the local authority counts from a statistical (parametric) distribution where the mean is given by the observed local authority count, with a variance that reflects the uncertainty associated with the particular administrative data source for that stream. 5.2.1.4 The parametric bootstrap approach for foreign-born and UK-born returning migrants As described in Section 5.2.1, the national-level estimates of foreign-born immigrants from the IPS are distributed to local authorities using the administrative data source relevant to each stream and the national-level estimates of UK-born returning migrants from the IPS are distributed to local authorities using the 2011 Census data. Bootstrapping for both types of migrant assumes that the errors in local authority level counts have a log-normal distribution. Using the log-normal distribution avoids producing negative values in the bootstrap samples. The log normal distribution has the form: where Z is a random normal covariate with mean 0 and variance 1, and μ and σ are the mean and standard deviation of the logarithm of the log normal distribution respectively. The administrative and census data counts are simulated from the log-normal as: The administrative and census data counts used to produce the mid-year estimates are used to calculate the μ for each stream, while the method for estimating the variance σ differs between the foreign-born migrants and UK-born returning migrants. 5.2.1.5 Bootstrap simulations for the UK-born returning migrants Unlike the census population estimates for local authorities that were used in section 53.1, the variances for the 2011 Census estimates used to distribute the IPS estimates for the streams of UK-born returning migrants were not directly estimated. However, our ONS research into the variability of 2011 Census estimates at sub-local authority level (ONS 2014) was adapted to give local authority level estimates of the variation. The research was based on a small sample of local authorities. These were chosen to be representative of different types of area and areas with low response rates were over-represented. Therefore, checks on the representativeness of variance were made and further examination showed little sensitivity to any over- estimation that might have As the variability was determined from a sample of local authorities for the bootstrap sample the coefficient of variation v was taken from the study and the observed Y_i are the Census counts used to produce the mid-year estimates. So that here: 5.2.1.6 Bootstrap simulations for foreign-born migrants Variances for the administrative sources that are used to distribute foreign-born migrants to local authorities were estimated using census data as a benchmark. For each stream, the 2011 Census figures for the same or similar subgroup were created for individual local authorities and the 2 sets of estimates were compared. The bootstrapping assumes that the census estimates X[i] in the ith local authority are close to the true value, and that the estimate from the administrative source Y[i] is related to the census estimate in the following manner: Here α is a constant factor representing the over- or under-count in the administrative source. As it is assumed to be constant across all local authorities and only proportions are taken from the administrative data, it has no impact on the estimation of immigration and can be ignored. Then σ^2 is the variance of log (Y[i] / X[i]) across local authorities in the UK. A separate value is calculated for each stream. The administrative data counts are simulated from the log-normal as: The Y[i] are the administrative data counts used to produce the mid-year estimates and so here μ = log Y[i]. 5.2.1.7 Combining the IPS and administrative data simulations to create 1,000 simulated in-migration estimates The simulated local authority counts for each stream are used to generate 1,000 local authority distributions for each stream. These distributions were then applied, iteration by iteration, to the 1,000 IPS simulations to create 1,000 IPS-based local authority distributions for each stream. The different streams are summed within each local authority to create 1,000 simulated in-migrant counts for each local authority. These simulated counts were used to produce the composite measure of uncertainty described in the following section. The processes are summarised in Figure 2. Figure 2: Overview of the simulation process for international immigrants Download this image Figure 2: Overview of the simulation process for international immigrants .png (8.4 kB) 5.2.2 International out-migration 5.2.2.1 Overview of the estimation process for international out-migration in the mid-year population estimates Similarly to international immigration, the process to estimate international emigration uses the International Passenger Survey (IPS). However, we use different methods to produce international immigration and emigration estimates. IPS estimates cannot be used directly at the local authority level. To produce international emigration estimates at lower levels of geographies, a multi-stage approach is applied to constrain and calibrate the flows, with a statistical model used to distribute the final flows to local authority level. Figure 3 shows an overview of the process used to distribute national level emigration to local authority level. Figure 3: Overview of method for distributing national level emigration to local authority level Download this image Figure 3: Overview of method for distributing national level emigration to local authority level .png (7.2 kB) For international emigration estimates, IPS local authority estimates are first averaged across 3 years (the reference year and the 2 preceding years). These averages are then constrained to New Migration Geography Outflow (NMGo) levels and estimated for local authorities using Poisson regression modelling. The Poisson regression model draws on available and reliable local authority data as predictors (covariates) to model the international emigration estimates at local authority level. The covariates include a range of census, administrative and survey data. The Poisson regression model is based on a strong association between the model covariates and emigration at the local authority level. In order to improve consistency in the time series, we developed a fixed Poisson regression model with a number of significant covariates (6 were used for 2012 to 2016). The output from the multi-stage estimation process is a set of emigration estimates for each local authority for a single year (for example, 2012). A final correction is made to account for the age-sex constraining step, which was introduced as an improvement to international migration methods in 2009 (ONS 2009a, b). 5.2.2.2 Deriving uncertainty around the international emigration estimates To measure uncertainty around the emigration component of the mid-year estimates, we create 1,000 plausible local authority emigration estimates using non-parametric bootstrapping from the IPS. The IPS is re-sampled, with replacement, 1,000 times to create 1,000 datasets. Where the mid-year estimates process averages IPS local authority estimates across 3 years (the reference and preceding 2 years’ of data), the uncertainty measures average equivalent local authority estimates, drawn from 3 sets of simulated IPS datasets (the reference and preceding 2 years’). These average values are passed through the multi-stage estimation process for emigration, mirroring the process used for the mid-year estimates. This produces 1,000 new local authority international emigration estimates. The uncertainty process is summarised in Figure 4. Figure 4: Overview of method for deriving simulated distribution for emigration Download this image Figure 4: Overview of method for deriving simulated distribution for emigration .png (6.7 kB) 5.3 Internal migration 5.3.1 Overview of the estimation process for internal migration in the mid-year population estimates The mid-year population estimation process uses the Patient Register Data Service (PRDS), NHS Central Register (NHSCR) and Higher Education Statistics Agency (HESA) data to derive estimates of internal migration by local authority. Changes in GP registrations are used as a proxy for internal migration. The PRDS records change of address data captured when individuals re-register with a GP. Address changes between 2 time points are captured by comparing successive annual downloads of the Patient Register. We assume a time lag of one month between moving and re-registering with a GP. This approach does not capture multiple moves during the year or moves by people missing from one of the data downloads, including under-1s, international migrants or people who die between downloads. To capture these, Patient Register data are calibrated upwards to the more comprehensive data provided by the NHSCR. NHSCR data are available at regional, not local authority, level. A further refinement is the use of HESA data, which more accurately captures the migration patterns of students in higher education. This adjusts for the known problem of under-recording of students moving to and from university in GP re-registration data. Figure 5: Overview of the simulation process for internal migration for year x Download this image Figure 5: Overview of the simulation process for internal migration for year x .png (9.6 kB) 5.3.2 Measuring uncertainty in the internal migration estimates - an overview To capture uncertainty in the estimates of internal migration we create a simulated distribution of estimates, using a benchmark approach. We achieve this through modelling internal migration flows using the 2011 internal migration Census transitions data as a benchmark of the “true” measure of internal migration^2. To ensure comparability with Patient Register (PR) transitions, the 2011 Census data excluded Home Armed Forces (HAF) personnel, Foreign Armed Forces (FAF) personnel and their dependants, prisoners and movers with an origin outside of the UK. We calculate the ratio of census to PR transitions in 2011 by sex, single year of age, and local authority for inflows and outflows separately. This ratio provides a measure of error in the PR (including the HESA adjustment). We use the log of these ratios as the basis for a model. This methodology report refers to these as log scaling factors: We assume the relationship between the PR transitions and census transitions remains constant over the decade, given the covariates. The observed relationship in 2011 is used to “scale up or down” the PR transitions in subsequent years. 5.3.3 Cluster analysis Log scaling factor profiles (for inflows and outflows) were inconsistent across local authorities and showed some age-related peaks and troughs. Clustering local authorities based on their scaling factor profiles identified distinct clusters of local authorities with similar age-sex log scaling factor profiles, using K-means clustering. We ran the K-means cluster analysis for 3 clusters, to maintain consistency with the 2002 to 2010 uncertainty measures. K-means cluster analysis requires a set of starting values. We use 25 sets of “scrambled midpoints” as starting values and exclude scaling factors for those aged over 57 due to the high incidence of missing or zero scaling factors in older ages and their dominating impact on cluster definition. Males and females are clustered separately. Optimal clustering solutions are selected for both inflows and outflows by comparing mean distance from cluster centre, cluster sizes, cluster distinctions (distances between clusters) and cross-tabulation of cluster memberships between variant results. Multivariate analysis of variance (MANOVA) tests also checked and confirmed cluster significance for the selected variants and runs. All final variants were highly significant (p<0.0001). We assigned all those local authorities excluded from the final solution to a cluster according to the least Euclidean distance (across all relevant scaling factor variables) from the cluster centre. Local authority membership of each cluster varied between inflows and outflows for some local authorities, and by sex. 5.3.4 Model fitting We fit a non-linear regression model to the 2011 log scaling factors, based on a 7-parameter Rogers-Castro (1981) age-migration schedule to estimate the mean of the scaling factor distributions. This was carried out separately by direction of flow, sex and cluster (12 models in total). Age-migration curves are generally associated with migration flows; however, they also provided a reasonable initial fit for the log scaling factors. To achieve the optimal fit by cluster, direction of flow and sex, for each model we focus predominantly on the childhood and labour force curves and exclude log scaling factors for those aged over 57, where data are either missing or very unstable (due to small flows). We also exclude log scaling factors for those aged 20 and 21 in some clusters where the log scaling factor profile did not fit the curve (anomalous patterns in some local authorities are the result of students leaving Higher Education). To further improve the fit, we add a step change in the overall level parameter so that the level of the curve is lower for younger ages than for older ages. For each sex (y) by cluster model: Census = Adjusted 2011 Census transitions for age x, sex y in local authority k PR = 2011 PR transitions for age x, sex y in local authority k d[i] = Local authority-specific covariates, i = 1,2,3 a[0] ,a[1] … a[7] = Rogers Curve parameters b[1] ,b[2] ,b[3] = Covariate parameters I[j] (x) = Indicator variable: 1 if j=x and 0 otherwise e = are independent, normally distributed error terms with mean 0 and non- constant variance L = sets the age at which the step-change ends and lies between 16 and 22 years, depending on sex, direction of flow and cluster. 5.3.5 Further covariates Other covariates allow further variation by local authority within clusters and over time. After investigating covariates used for the 2002 to 2010 uncertainty measures and alternative additional covariates, for 2012 to 2016 we chose: • regional gross disposable household income (GDHI) for NUTS 3 region^3 • proportion of international immigrants (expressed as a percentage of total population) • Index of Multiple Deprivation 5.3.6 Simulation of distributions We fit the non-linear regression model with local authority-specific covariates to the 2011 log scaling factors. The model estimates predicted values as well as residuals (calculated as the difference between observed and predicted log scaling factors) for each local authority by age and sex and flow direction. As census data are not available for years 2012 to 2016, for these years we do the following (see Figure 5): 1. Use the non-linear regression model, using the 2011 model parameters, along with updated local authority-specific covariate data for each year, to predict the scaling factors for the given year. 2. Re-sample 1,000 times the raw residuals from the 2011 model (by direction of flow, cluster and sex). 3. Add the re-sampled (bootstrapped) raw residuals to the predicted scaling factors to give 1,000 simulated log scaling factors for the given year by age, sex and direction of flow, for each local The variance of the residuals was non-constant over the age distribution. Prior to re-sampling, we divided each set of residuals into “pots” with similar variance. This ensures that for a specific observation we draw values from a pot of residuals with a realistic variance for this local authority, age and sex. 5.3.7 Back transforming the data For each 1,000 simulated log scaling factors, we back transform by taking the exponential and multiplying by the Patient Register data for the relevant age, sex and local authority for our specified year. This is illustrated by the formula for 2012: This creates 1,000 estimated transitions for each age, sex, direction of flow, and local authority combination. Internal migration estimates used in the mid-year population estimates relate to moves and not transitions. In the mid-year estimation process, Patient Register Data Service transitions are adjusted upwards to data on moves based on NHS Central Register totals at the former health authority level. For the current measures, we assume no error in this adjustment process and apply an additive adjustment to convert our 1,000 simulated transitions into moves. This adjustment up-scales the estimates but does not impact on the measure of uncertainty for the individual internal inflow and outflow components. We aggregate the resulting moves to the local authority level. 5.4 Composite measure The final stage of the methodology for deriving a statistical measure of uncertainty is to combine the simulated distributions, reflecting the uncertainty for each of the 3 components (2011 Census base, international migration and internal migration) into a single composite measure for each local authority for each year. The cohort component approach for deriving the mid-year estimates (MYEs) is used as a template. The simulated estimates for the base, international and internal migration are combined with the non-varying components, iteration by iteration, to create 1,000 simulated MYEs for each local authority. The procedures differ for the census year (2011) and the following intercensal years (2012 to 2016). The procedure for 2011 is given in equation (5.10) and for years 2012 to 2016 in equation (5.11). For each iteration in 2011: P[k] ^(2011)(i) = simulated population at mid-year 2011 for local authority k for iteration i cen[k] ^(i) = simulated 2011 Census estimate in local authority k for iteration i m[k] ^(i) = simulated value for the census day to 30 June 30th correction in local authority k for iteration i For each of the iterations i in the years 2012 to 2016 we use the cohort component method: P[k] ^(t) = simulated population in mid-year t for local authority k b[k] ^(t-1)(t) = births between mid-year t-1 and mid-year t for local authority k d[k] ^(t-1)(t) = deaths between mid-year t-1 and mid-year t for local authority k in[k] ^(t-1)(t) = simulated internal in-migration between mid-year t-1 and mid-year t for local authority k o[k] ^(t-1)(t) = simulated internal out-migration between mid-year t-1 and mid-year t for local authority k im[k] ^(t-1)(t) = simulated international in-migration between mid-year t-1 and mid-year t for local authority k em[k] ^(t-1)(t) = simulated international out-migration between mid-year t-1 and mid-year t for local authority k Uncertainty is measured directly from the final composite distribution for each local authority. The primary “uncertainty measure” reported in this research is the “root mean squared error” (RMSE). When measured as a percentage of the mean of the simulated composite measures, this becomes the “relative root mean squared error’” (RRMSE), calculated as: where P^(t)(i) is the simulated value for the year t and iteration i and p̄^(t) represents the mean of the simulated values n is the number of simulations and MYE is the mid-year estimate. This measure acknowledges the bias in the simulations and allows meaningful comparison across all 348 local authorities. We have also standardised our figures to the 2011 census estimate for each local authority, to support comparisons over time and place. We also provide the proportional contribution that each component (2011 Census, internal migration and international migration) makes to the primary uncertainty measure. We have identified three methods for deriving 95% confidence intervals for the published MYEs. Our preferred method is the bias-adjusted confidence intervals, but we supply all 3 to support your understanding of our methodological approach and of the options available: 1. Empirical confidence intervals for each local authority are created by ranking the 1,000 simulated values of the population estimate P~k ^(t) and taking the 26th and 975th values as the lower and upper bounds respectively. As the observed MYE generally differs from the median of the simulations, this confidence interval is not centred about the MYE and in some extreme cases the MYE is outside the bounds of the empirical 95% confidence interval. 2. Centred empirical confidence intervals are created by moving the empirical 95% confidence intervals so that they are centred about the observed MYEs. The difference between the median of the simulated values and the observed MYE is subtracted from each of the lower and upper bounds. While the width of the confidence interval remains the same it does not account for the bias component due to the difference between the MYE and the median of the simulation. 3. Bias-adjusted confidence intervals are calculated as the MYE plus or minus ±1.96 multiplied by RMSE. The RMSE is the variability of the simulated values around the MYE. This confidence interval will be symmetric about the MYE and will include a measure of uncertainty due to bias between the MYE and the simulations. We favour the bias-adjusted confidence interval because it is wider, reflecting the difference between the published mid-year estimate and the mean of the simulated composite measures. The discrepancy between the published mid-year estimate and the mean of the simulated composite measures may arise for a number of reasons, including: • the uncertainty methodology only accounts for uncertainty in the census, international and internal migration components • the assumptions underlying the uncertainty or MYEs methodology • the uncertainty figures are estimates, and so are subject to some uncertainty themselves We have also specifically identified the undercounting of young males in the internal migration component of the MYEs, to help explain this discrepancy. We interpret the bias-adjusted confidence intervals in the following way. If the assumptions we have made in estimating uncertainty are correct, we would expect these intervals on average to capture the mid-year population 95% of the time. However, if the bias is relatively large then these confidence intervals will be conservative, i.e., have coverage greater than 95%. Use and interpretation of the confidence intervals will be reviewed as we approach the 2021 census when uncertainty around the MYEs is at its highest level. Notes for: Developing a statistical measure of uncertainty 1. This is calculated as the root mean squared error between the simulations and the mid-year estimate, as a percentage of the mean of the simulations. 2. The uncertainty measures process has not estimated uncertainty in census migration flows. If some quantification of uncertainty in census migration flows was available it could be incorporated into the uncertainty measures process after the internal migration modelling. The impact of this would be to widen the empirically derived confidence intervals. 3. Nomenclature of Territorial Units for Statistics (NUTS), NUTS 3 is the classification for unitary authorities or districts in England, or groups of unitary authorities in Wales. Nôl i'r tabl cynnwys Research-based uncertainty measures for 2012 to 2016 are published alongside this working paper. The measures include: The spreadsheets are interactive. They allow you to select a local authority and then view either 1) the proportions of uncertainty that are attributable to each of the 3 main components, or 2) their confidence intervals, over time. Tabulated measures include, for each local authority: • the published mid-year estimate (MYE) • uncertainty measure (percentage of population) (the relative root mean squared error (RRMSE)) • the percentage contribution of each component (2011 Census, internal migration, international migration) to the uncertainty measure • the upper and lower bounds of the bias-adjusted confidence intervals (the empirical and centred confidence intervals are supplied in the interactive spreadsheet) 6.1 Measure of uncertainty (relative root mean squared error) Table 2 shows the root mean squared error, as a percentage of the mean of the simulated composite measure, or relative root mean squared error (RRMSE). Reflecting the rolled-forward nature of the methodology for deriving our mid-year population estimates, uncertainty increases over time as we move further away from the 2011 Census. For just under half of local authorities (173) this increase was relatively small, and the uncertainty measure remained within 0 to 2% of the simulated local authority population by 2016. Of the remaining 175 local authorities, 17 have a measure of uncertainty that is greater than 5% of the local authority population by 2016. Although column 2 shows local authorities with a RRMSE greater than 10% in 2016, this applies only to the City of London (RRMSE equals 13.26%) which, because of its small size, can be regarded as an outlier. Table 2 shows that, in 2016, for most (331) local authorities the RRMSE lies between 0 and 5%, of which the majority are less than 2%. In addition to the City of London, local authorities with RRMSEs over 5% in 2016 are Stratford on Avon (RRMSE equals 5.10%), Oxford (5.34%), Southwark (5.42%), Westminster (5.71%), Camden (5.72%), Brent (6.17%), Tower Hamlets (6.19%), Kensington and Chelsea (6.23%), Bournemouth (7.30%), Kingston upon Thames (7.76%), Exeter (7.88%), Merton (7.92%), Reading (8.14%), Wandsworth (8.92%), Cambridge (8.97%) and Hammersmith and Fulham (9.98%). Table 2: 2012 to 2016 range for the root mean squared error of the simulations, as a percentage of the mean of the simulated composite measures (relative root mean squared error, RRMSE) Year Range (%) ˂2% 2 to less than 5% ≥5% 2012 0.36 to 7.01 340 7 1 2013 0.41 to 10.76 319 28 1 2014 0.49 to 11.76 281 64 3 2015 0.53 to 12.41 218 120 10 2016 0.58 to 13.26 173 158 17 Source: Office for National Statistics Download this table Table 2: 2012 to 2016 range for the root mean squared error of the simulations, as a percentage of the mean of the simulated composite measures (relative root mean squared error, .xls (27.1 kB) To allow comparison with the 2002 to 2010 uncertainty measures, Table 3 provides the relative standard deviations (for 2012 to 2016), presented as a percentage of the mean of the simulated composite measure. This measures deviation from the mean of the simulations rather than from the MYE, as for the RRMSE. Table 4 provides the equivalent measures from 2002 to 2006. Table 3: 2012 to 2016 range for the relative standard deviation, as a percentage of the mean of the simulated composite measures Year Range (%) ˂2% 2 to less than 5% ≥5% 2012 0.35 to 5.39 343 4 1 2013 0.40 to 10.66 333 14 1 2014 0.46 to 11.39 329 18 1 2015 0.48 to 11.81 322 25 1 2016 0.50 to 12.61 305 41 2 Source: Office for National Statistics Download this table Table 3: 2012 to 2016 range for the relative standard deviation, as a percentage of the mean of the simulated composite measures .xls (27.1 kB) Table 4: 2002 to 2006 range for the relative standard deviation, as a percentage of the mean of the simulated composite measures Year Range (%) ˂2% 2 to less than 5% ≥5% 2002 0.34 to 10.87 365 10 1 2003 0.36 to 16.08 359 16 1 2004 0.38 to 19.65 356 19 1 2005 0.40 to 18.76 350 25 1 2006 0.41 to 18.02 341 33 2 Source: Office for National Statistics Download this table Table 4: 2002 to 2006 range for the relative standard deviation, as a percentage of the mean of the simulated composite measures .xls (27.1 kB) Table 4 shows that this measure is broadly consistent between the 2 decades. The 2002 to 2006 outlier, which was also the City of London, had a more extreme relative standard deviation of 18.02% in 2006, compared with 12.61% in 2016. There were 376 local authorities in the 2002 to 2006 series and 348 in 2012 to 2016, following reclassification in 2009. 6.2 Proportional contributions from the 3 components Tables 5, 6 and 7 summarise the relative contributions to uncertainty that come from the 2011 Census, internal migration and international migration components of the mid-year population estimates. Table 5 shows that in 2012 for the majority of local authorities (330), the greatest proportion of uncertainty came from the census component. In 2012, uncertainty as measured by the relative root mean squared error (RRMSE) was less than 2% for the majority of local authorities (340) (see Table 2). The influence of the census on uncertainty declines over time and by 2016 the census accounted for 50% of uncertainty in 155 local authorities. The influence of other components becomes more visible over time. In 2016, international migration accounted for more than 50% of uncertainty in 93 local authorities, while internal migration accounted for over 50% of the uncertainty in just 17 local authorities. Table 5: Number of local authorities by percentage of overall uncertainty from the 2011 Census base Year Range (%) ˂25% 25 to less than 50% 50 to less than 75% ≥75% 2012 8 to 99 2 16 52 278 2013 2 to 98 17 48 112 171 2014 2 to 96 26 79 118 125 2015 1 to 95 51 97 122 78 2016 1 to 94 85 108 94 61 Source: Office for National Statistics Download this table Table 5: Number of local authorities by percentage of overall uncertainty from the 2011 Census base .xls (27.1 kB) Table 6: Number of local authorities by percentage of overall uncertainty from international migration Year Range (%) ˂25% 25 to less than 50% 50 to less than 75% ≥75% 2012 0 to 90 321 16 10 1 2013 0 to 98 259 55 22 12 2014 0 to 98 249 57 29 13 2015 0 to 98 215 66 46 21 2016 1 to 99 175 80 52 41 Source: Office for National Statistics Download this table Table 6: Number of local authorities by percentage of overall uncertainty from international migration .xls (27.1 kB) Table 7: Number of local authorities by percentage of overall uncertainty from internal migration Year Range (%) ˂25% 25 to less than 50% 50 to less than 75% ≥75% 2012 0 to 45 336 12 0 0 2013 0 to 53 298 49 1 0 2014 1 to 61 258 83 7 0 2015 1 to 65 242 94 12 0 2016 1 to 66 229 102 17 0 Source: Office for National Statistics Download this table Table 7: Number of local authorities by percentage of overall uncertainty from internal migration .xls (27.1 kB) 6.3 Bias-adjusted 95% confidence intervals Table 8 shows that for the majority of local authorities, the width of the bias-adjusted 95% confidence interval relative to the mean of the simulated composite measures is less than 10% (227 in 2016). As expected, the width of the confidence interval relative to the population increases over time as we move further away from the census. Use and interpretation of the confidence intervals will be reviewed as we approach the 2021 census when uncertainty around the MYEs is at its highest level. Table 8: Bias-adjusted 95% confidence interval range, as a percentage of the mean of the simulated composite measures Year Confidence interval range (%) ˂5% 5 to less than 10% 10 to less than 20% 20 to less than 50% ≥50% 2012 1.40 to 27.47 306 40 1 1 0 2013 1.62 to 42.16 236 96 15 1 0 2014 1.86 to 45.70 161 159 25 3 0 2015 1.99 to 47.71 123 159 57 9 0 2016 2.27 to 51.98 89 138 105 15 1 Source: Office for National Statistics Download this table Table 8: Bias-adjusted 95% confidence interval range, as a percentage of the mean of the simulated composite measures .xls (27.6 kB) Nôl i'r tabl cynnwys Our mid-year population estimates are the best estimates of the usually resident population that are currently available between the decennial census years. The processes used to derive the mid-year estimates are complex, with many different components. Some uncertainty around them is, therefore, expected. However, the complexity of the methodology makes it impossible to estimate this uncertainty directly. The methodology described in this working paper aims to quantify uncertainty and to give an indication of the relative contribution to this uncertainty by each of the 3 components identified as having the greatest impact on uncertainty: the 2011 Census base, international and internal migration. We have used the relative root mean squared error (RRMSE) as the primary measure of uncertainty. This measure resembles the relative standard deviation, but incorporates an adjustment for bias in the estimates. Our estimates show that out of the 348 local authorities in 2012, for 340 (98%) this was less than 2%. By 2016, there were 173 local authorities (just under 50% of the total) that had RRMSEs of less than 2%, but only 17 local authorities (5% of the total) had RRMSEs exceeding 5%. The uncertainty methodology is based on 3 components with the greatest impact on uncertainty, so does not incorporate all of the uncertainty associated with all of the data sources and processes involved in the production of mid-year estimates. These should therefore be considered to be conservative estimates of uncertainty. Bias in the mid-year estimates, which is represented by the difference between the median of the simulated populations for each year and the corresponding published mid-year estimate, is primarily attributable to the discrepancy between our modelled post-census internal migration flows and the corresponding flows in the published mid-year estimates. Our methods for measuring uncertainty assume that the relationship between the census and the Patient Register (supplemented by Higher Education Statistics Agency) measure remains constant over time, given the covariates. Increasingly we suspect that this does not hold, given recent initiatives within the NHS to clean their Patient Registers. List-cleaning activity is geographically uneven and will generate anomalous simulated internal migration flows. This aspect of the methodology will be reviewed in future. Nevertheless, our chosen confidence intervals are bias-adjusted and thereby allow for the increased uncertainty in the estimates for the affected areas. The proportional contributions to uncertainty from the 2011 Census, internal and international migration follow expected patterns. The relative influence of the 2011 Census on uncertainty declines over time, as the estimates for areas with high population churn are more heavily influenced by the internal and international migration components. Every care has been taken to implement and quality assure the methodology and outputs. However, this approach depends on the assumptions made when constructing them and the input data used to generate the outputs. Sometimes, the method generates extreme values that would be unlikely to arise in reality. This does not undermine our confidence in the methodology or the data, but emphasises the need for caution in interpreting these results. We welcome comments and observations on these research methods and results. This project has involved applying statistical bootstrapping in a range of contexts and on a range of data sources. As we increasingly move towards statistics that integrate survey, administrative and other sources, the relevance of these approaches is becoming more apparent. Nôl i'r tabl cynnwys Efron, B. and Tibshirani, R.J. (1993). An Introduction to Bootstrap, London, Chapman and Hall Office for National Statistics (2006). Report of the inter-departmental Task Force on Migration Statistics. Office for National Statistics ONS (2008 to 2012). Migration Statistics Improvement Programme (MSIP). Office for National Statistics (2009a). Estimating international long-term immigration by local authority (LA). Office for National Statistics (2009b). Estimating international long-term emigration by local authority (LA). Office for National Statistics (2010). Improving Migration and Population Statistics - Quality measures for population estimates. Office for National Statistics (2011). Improved Immigration Estimates to Local Authorities in England and Wales: Overview of Methodology. Office for National Statistics (2012a). Uncertainty in local authority mid-year population estimates quality indicators. Office for National Statistics (2012b). Uncertainty in local authority mid-year population estimates. Office for National Statistics (2013). 2011 Census Confidence Intervals. Office for National Statistics (2014). International Passenger Survey (IPS) Methodology. Office for National Statistics (2015). International Passenger Survey Quality and Methodology Information. Office for National Statistics (2016). Methodology Guide for Mid-2015 UK Population Estimates (England and Wales). Ou, X. Smith, P.W. (2012). The Developed Methodology to Estimate Statistical Error of Mid-year Local Authority Emigration Estimates. Southampton Statistical Sciences Research Institute, unpublished report for the Office for National Statistics. Rogers, A. and Castro, L. J. (1981). Model Migration Schedules. Laxenburg: International Institute for Applied Systems Analysis, Research Report, RR-81-30. Sexton, C.J., Brown, J., Taylor, A., Abbott, O. (2014). The Quality of Existing Small Area Census Attribute Data. Office for National Statistics, unpublished report. UK Statistics Authority (2009a). Migration Statistics: The Way Ahead. UK Statistics Authority (2009b). Code of practice for Official Statistics. 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Study of Torsion Effects on Building Structures Having Mass and Stiffness Irregularities Volume 04, Issue 06 (June 2015) Study of Torsion Effects on Building Structures Having Mass and Stiffness Irregularities DOI : 10.17577/IJERTV4IS061059 Download Full-Text PDF Cite this Publication Rajalakshmi K R , Harinarayanan S, Jiji Anna Varughese , Girija K, 2015, Study of Torsion Effects on Building Structures Having Mass and Stiffness Irregularities, INTERNATIONAL JOURNAL OF ENGINEERING RESEARCH & TECHNOLOGY (IJERT) Volume 04, Issue 06 (June 2015), http://dx.doi.org/10.17577/IJERTV4IS061059 • Open Access • Total Downloads : 1857 • Authors : Rajalakshmi K R , Harinarayanan S, Jiji Anna Varughese , Girija K • Paper ID : IJERTV4IS061059 • Volume & Issue : Volume 04, Issue 06 (June 2015) • DOI : http://dx.doi.org/10.17577/IJERTV4IS061059 • Published (First Online): 02-07-2015 • ISSN (Online) : 2278-0181 • Publisher Name : IJERT • License: This work is licensed under a Creative Commons Attribution 4.0 International License Text Only Version Study of Torsion Effects on Building Structures Having Mass and Stiffness Irregularities Rajalakshmi K R & Harinarayanan S Sree Narayana Gurukulam College of Engineering, Ernakulam, Kerala, INDIA Jiji Anna Varughese & Girija K Government Engineering College, Barton Hill, Trivandrum, Kerala, INDIA Abstract: Irregular buildings constitute a large portion of the modern urban infrastructure. The group of people involved in constructing the building facilities, including owner, architect, structural engineer, contractor and local authorities, contribute to the overall planning, selection of structural system, and to its configuration. This may lead to building structures with irregular distributions in their mass, stiffness and strength along the height of building. When such buildings are located in a high seismic zone, the structural engineers role becomes more challenging. Therefore, the structural engineer needs to have a thorough understanding of the seismic response of irregular structures. In recent past, several studies have been carried out to evaluate the response of irregular buildings. This paper presents the details of the non-linear dynamic analysisperformed on mass and stiffness irregular buildings.It is established that irregular buildings are subjected to largedisplacements compared to regular buildings and localized damages nearthe regions of irregularity. Special care needs to be taken while designing such buildings. Keywords:Torsional response; Seismic behaviour; Irregular structures; Dynamic analysis; Design lateral foces; Linear static analysis; Non linear time history analysis; Mass irregularity; Stiffness irregularity; Setbacks; Ultimate yielding; Torsional effects It would be ideal if all buildings have their lateral-load resisting elements symmetrically arranged and earthquake ground motions would strike in known directions.Due to scarcity of land in big cities, architects often propose irregular buildings in order to utilize maximum available land area and to provide adequate ventilation and light in various building components. However, it is quite often that structural irregularity is the result of a combination of both types. Most buildings have some degree of irregularity in the geometric configuration or the distribution of mass, stiffness, and/or strength. Due to one or more of these asymmetries, the structures lateral resistance to the ground motion is usually torsionally unbalanced creating large displacement amplifications and high force concentrations within the resisting elements which can cause severe damages and at times collapse of the structure. Eccentric arrangement of non-structural components, asymmetric yielding, presence of rotational component in ground motions and the variations in the input energy imparted by the ground motions also contribute significantly to the torsional response of buildings.In India, failure of two most famous apartments during the 2001 Bhuj earthquake was reported due to torsional response. 1. 1 Design considerations in seismic codes: An asymmetric building structure (torsionally-unbalanced) can be defined as one in which for a purely translational motion, the resultant of the resisting forces does not pass through the centre of mass (Humar and Kumar, 1999) [12]. When strained into the inelastic range, torsional motions in such structures will lead to displacements and ductility demands much larger than those in symmetric buildings (torsionally-balanced) which have similar characteristics. In general, the torsion arising from eccentric distribution of mass and stiffness can be taken into account by describing an incremental torsion moment (T) in each storey equal to the shear (V)in that storey multiplied by the eccentricity (e), measured perpendicular to the direction of applied ground motion. A precise evaluation of the torsion response is quite complicated because the coupled lateral torsion vibration modes of the entire structure are to be considered by performing a two or three dimensional response calculations. Torsional effects may significantly modify the seismic response of buildings. These effects occur due to different reasons, such as no uniform distribution of the mass, stiffness and strength, torsional components of the ground movement, etc. As a result, the lateral ductility capacity of the system may be smaller than the lateral ductility capacity of the elements. Design codes incorporate special requirements to take into account the torsional effects, which usually imply the amplification of eccentricity and the consideration of an accidental eccentricity. These are static responses should be amplified for dynamic response using the response spectrum amplification factor for the fundamental torsion frequency of the structure.Most current codes use accidental eccentricity value of 5% of the plan dimension of the storey perpendicular to the direction of applied ground motion. The accidental torsion may be considered as an increase and also as a decrease in the eccentricity.The eccentricity of the centre of stiffness from the centre of mass is found from kyi xi and eRy kxj y j uncoupled elastic torsional frequency to the uncoupled elastic translational frequency or equivalently, the ratio of torsional to translational stiffness in the elastic range. The uncoupled elastic translational frequency and the uncoupled elastic torsional frequency are defined as K / m wherekyi andkxj are the stiffness of frames in the y- and x- y y directions respectively, and xiandyj , the respective distances measured from the centre of mass. K R / mr2 The eccentricity of the centre of strength from centre of mass is given by whereKy is the sum of the elastic stiffness of planes in the y-direction and KRis the torsional stiffness about the centre of stiffness. The uncoupled frequency ratio is defined as n m V y ' K R Vyi xi e i 1 and e j 1 xi i R 2 r K (2) y y i 1 j 1 If R is greater than 1, the response is mainly translational and the structure is considered as torsionally stiff; on the other hand, if R is less than 1, the response is affected by whereVyiand Vxj are the design base shear strengths of frames in the y- and x- directions, respectively. Torsional response of asymmetric structures responding to seismic excitation is complex involving both strength and stiffness eccentricities as well as torsional mass inertia (Priestley et al., 2007)[11]. The displacements 1 and 2 of the stiff and flexible sides can be obtained by knowing the translational displacement of CMand the twist angle which is given by VBy eRx (3) J 1 n k (x e )2 m k ( yj e )2 torsion and the structure is treated as torsionally flexible. Various researchers conducted analytical and experimental studies on stepped and set-back buildings (where a narrow tower projects from a wide base) and came up with contradictory results which are specific to the building models they had selected. As per Priestley (2007) [11], in buildings which are stepped along one direction only, the stepped frames are not much influenced by the irregularty and only the frames in the perpendicular direction will have some effect due to the stepping. The regularity of building can be quantified using regularity/ irregularity indices, based on the geometry of the building. Karavasilis et al. (2008) [10] had proposed two irregularity indices ( s , storey-wise and b , bay- wise) as follows: R,eff el , yi i Rx el ,xj Ry sys i1 j 1 1 ns 1 L 2. LATEST RESEARCH WORKS ON ASYMMETRIC s ' 1 Li 1 1 nb 1 H b n 1 H N. P Modakwan, S. S Meshram and D. W. Guwatre (2014) [1] studied the different irregularity and torsional response due to plan and vertical irregularity in buildings and analyzed cross shape and L shape buildings while earthquake forces acts and calculated the additional shear due to torsion in the columns.It is concluded that the re- entrant corner columns are needed to be stiffened for shear force in the horizontal direction perpendicular to it as significant variation is seen in these forces. Significant b 1 i 1 Where ns is the number of storeys of the frame and nb is the number of bays at the first storey of the frame. Hi and Li are the height and width of the ithstorey. However, this does not give a measure of the overall irregularity in the building. Sarkar et al. (2008)[8] proposed a single regularity index () which is based on the dynamic behaviour of the structure and is given below: variation in moments, especially for the higher floors about axis parallel to earthquake direction, care is needed in design of members near re-entrant corners. A number of parameters govern the response of asymmetric buildings, but the one that has the most significant effect is the torsional stiffness (M/) (Humar and Kumar, 1999) [11]. It is to be noted that all in-plane structural elements (both parallel and perpendicular to the earthquake motion) contribute to the torsional stiffness. On the basis of analytical studies on elastic and inelastic behaviour, they concluded that the most important parameter governing the torsional response is the ratio of where 1 is the first mode participation factor for the stepped frame and 1,ref is the first mode participation for the regular frame without steps. Even though this approach seems to be more logical, one has to do a modal analysis to obtain the regularity index. Sarkar et al. had also proposed a correction factor ( ) for the code proposed empirical formula for fundamental period of regular building to get that of stepped frame. It is given by, the building. It is concluded that the analytical natural period depends on the mass and stiffness of each model 1 2(1 )(2 1) for 0.6 1.0(8) and is therefore different for models with different amounts of eccentricity and where stiffness of infill walls is considered or ignored. It can be observed that models where stiffness of infill walls is considered to have 1. G. Maske and P S Pajgade (2013)[2] studied the influence of the torsion effects on the behavior of the structure. Two cases are considered for the study. Case one is without considering torsion and case two is considering torsion. The Indian standard code of practice IS-1893 (Part I: 2002) guidelines and methodology are used for analysis and design. Results are compared in terms of % Ast in columns. They conducted the structural analysis and design of four storey reinforced concrete asymmetric frame building with the help of Etab software. 1. A. A. Rahman and G. Deshmukh (2013)[3] studied the proportional distribution of lateral forces evolved through seismic action in each storey level due to changes in stiffness of frame on vertically irregular frame. As per the Bureau of Indian Standard (BIS) 1893:2002(part1) provisions, a G+10 vertically irregular building is modeled as an simplified lump mass model for the analysis with stiffness irregularity at fourth floor. They studied the response parameters like story drift, story deflection and story shear of structure under seismic force under the linear static & dynamic analysis. The analysis focused on the base shear carrying capacity of a structure and performance of structure. They concluded that a building structure with stiffness irregularity provides instability and attracts huge storey shear. A proportionate amount of stiffness is advantageous to control over the storey and base shear.E Tab was used for modeling and Q. Z. Khan, A. Tahir and S. S. Mehboob (2013)[4] studied theperformance evaluation of reinforced concrete buildings with vertical irregularities (i.e., setbacks). A five story vertically regular building is designed by equivalent static load method of seismic analysis by using UBC (Uniform Building Codes) 1997. Nine vertically irregular models are derived from the regular building by omitting different stories at different heights creating setbacks. For numerical solution ETABs nonlinear version software is used. The study as a whole is a slight attempt to evaluate the effect of vertical irregularities on RC buildings, in terms of dynamic characteristics such as story displacement, overturning moment, base shear, story drift and participating mass ratio. They concluded that the irregularity established due to setbacks, that even very large variation of irregularity distribution in elevation causes reasonable modifications of the seismic response with respect to the reference regular case. Maximum story drift and story displacement will increase as the vertical irregularities increase in models. B.G.N. Kumar and A. Gornale (2012)[5] studied the performance of the torsionally balanced and unbalanced buildings also called as symmetric and asymmetric buildings subjected to pushover analysis. The buildings have unsymmetric distribution of stiffness in storeys. Also studies are conducted on the effect of eccentricity between centre of mass (CM) and centre of story stiffness (CR) and the effect of stiffness of infill walls on the performance of significantly lower fundamental natural period as compared to models where stiffness of infill walls ignored. 1. DETAILS OF BUILDING MODELS A 30-storeyed regular reinforced concrete moment resisting frame building model(R1) is prepared in SAP 2000 and preliminary dimensioning of structural members is done (Table 1).Shear walls are provided as a lateral load resisting system as shown in Figure 1. The structure is designed as per the various load combinations as givenin IS 456:2000. Both linear and non-linear analyses are performed. Moment-rotation relation (hinge properties) are generated using Modified Mander model for stress-strain curves of concrete (Panagiotakos and Fardis, 2001) and Indian Standard IS 456:2000 stress-strain curve for reinforcing steel. Figure 1: Column layout of the building model R1 TABLE 1: STRUCTURAL ELEMENT SIZES Structural elements Sizes(mm) Beams 350 x 600 Columns 800 x 800, 700 x 700, 600x 600 Slab 120 mm thick Shear walls 400, 350, 300 thick at various levels Three types of irregular buildings are considered in the present study, viz., mass irregular, stiffness irregular and setback buildings. Table 2 shows the details of irregular buildings generated from the regular building (R1). Mass irregularity is generated by increasing the live load on half the portion of the building plan from 2 kN/m2 to 5 kN/m2 at 5,10,15,20,25thstorey (Figure 2). TABLE 2: TYPE OF BUILDING MODELS Type of building model Model designaton Mass irregular building model M1 Stiffness irregular building Setbacks S1 Figure 2: Mass irregular building model plan Lateral stiffness irregularity is generated in the elevation of the structure by increasing the height of the columns to 4.5m at 4,9,14 and 19th floors.p=3m,p=4.5m. (Figure 3) Figure 3: Elevation of the stiffness irregular building model L1 Setbacks are generated in the regular building model at 15,20, and 25th floors (Figure 4). Figure 4: Elevation of the setback generated building model S1 2. ANALYSIS OF BUILDING MODEL Non-linear time history analysis will give the response of the structure at various time instants during the application of ground motion accelerogram.The minimum number of records required for time history analysis is three and the maximum response shall be used for design purpose. However, when a set of at least seven ground motions is used, the structural engineer canuse the mean structural response (FEMA P695,2009). Three accelerograms are taken from the strong motion database(http://www.strongmotioncenter.org/)of Centre for Engineering Strong Motion Data, USA.The records are made consistent with IS 1893:2002 spectrum using the program SEISMOMATCH and were scaled to have a PGA of 0.3g. The maximum of the responses obtained from the three analyses is reported as the response of each building 3. RESULTS AND DISCUSSIONS Figure 5 shows the displacement of building model (R1) for the three time histories. It is clear from the figure that ALTADENA gives the maximum response. A maximum displacement of 180mm is observed for the 30th floor level. The combination of inelastic hinges at the ends of beams and columns which when formed in a building eventually makes it unstable and causes it to collapse and is called collapse mechanism. Good ductility is achieved in a building when the collapse mechanism is of the desirable type. In such a case, the hysteretic loops of its load deformation curve are stable and full. This type of hysteretic loops imply good energy dissipation in the building through each of the inelastic hinges at the beam ends. Such a behaviour is observed in buildings that fail in sway mechanism,which ensures that beam yields before failure, and ductile flexural damages occur at beam ends. This happens when the building has strong column weak beam design (in which the beams are made to be weaker in bending moment capacity and ductile links, and columns stronger in bending moment capacity). Hinge formation in building model R1 at the end of time history is shown in Figure 6. It is found that hinges corresponding to yield level are formed in beams and at ground floor column base. This is a desirable mechanism. Figure 6: Elevation of building model R1 having hinge formation For mass irregular building model (M1), (Figure 7), ALTADENA gives the maximum response.More number of hinges are formed on and near the irregularity applied floors (Figure 8), compared to regular building model (R1). Storey-drift ratio ratio 0 0.20.40.60.8 1 1.21.41.6 alt array altadena reference Figure 5: Comparison of storey displacement from Alt,Altedena and Array for building model R1 Inter- storey drift (%) Figure 7: Comparison of storey-drift ratio ratio from Alt,Altedena,Array for building model M1 Figure 8:Hinge formation in model M1 For stiffness irregular building model (L1), (Figure 9), ALTADENA gives the maximum response.The displacement for stiffness irregular building model L1 is more as compared to the building model R1. More number of hinges are formed on and near the irregularity applied floors (Figure 10), compared to regular building model (R1).Confinementreinforcement have to be provided near and on the stiffness irregular floors. Same is the case with setback building model (S1). Figures 11 and 12.Hinges are developed in columns particularly near the setback portion. More damages can occur near the setback portion. Special care should be given in the design of components of the structure particularly near the setback regions. Storey displacement graph array altedena Figure 9:Comparison of storey displacement from Alt,Altedena,Array for building model L1 Figure 10: Hinge formation on building model L1 Storey displacement graph alt array Figure 11:Comparison of storey displacement from Alt,Altedena,Array for building model S1 Figure 12: Hinge formation on setback building model S1 4. SUMMARY Review of literature on asymmetric buildings reveals that irregularities due to asymmetric distribution of mass, stiffness and strength are sources of severe damage because they result in floor rotations in addition to floor translations. A common form of vertical irregularity arises from reduction of the lateral dimension of the building along its height and such buildings are known as stepped buildings. This building form is becoming increasingly popular in modern multistorey building construction mainly because of its functional and aesthetic architecture. In particular, such a stepped form provides for adequate daylight and ventilation in the lower storeys in an urban locality with closely spaced tall buildings. Vertically irregular buildings (like open ground storey and stepped buildings) are common in India, but are more vulnerable to earthquake shaking. The collapses of irregular buildings during recent earthquakes have raised many questions regarding the adequacy of current seismic provisions to prevent collapse of such buildings. The present study confirms that the design of irregular buildings need special care and enhancement of member sizes are required at regions of irregularity. New design methods are needed which can improve the performance of such buildings under expected seismic shaking. 1. Nehe P. Modakwar,Sangita S. Meshram, Dinesh W. Gawatre, Seismic Analysis Of Structures with Irregularities,IOSR Journal of Mechanical and Civil Engineering,Volume 3, Issue 2,March- April 2014 2. Sachin G. Maske, Dr. P. S. Pajgade,Torsional Behaviour of Asymmetrical Buildings,International Journal of Modern Engineering Research, Vol.3, Issue.2, March-April. 2013 pp- 1146-1149. 3. Shaikh Abdul Aijaj Abdul Rahman, Girish Deshmukh, Seismic Response of Vertically Irregular RC Frame with Stiffness Irregularity at Fourth Floor, International Journal of Emerging Technology and Advanced Engineering, Volume 3, Issue 8, August 2013 4. Qaiser uz Zaman Khan, Asif Tahir , Syed Saqib Mehboob Professor,Investigation of Seismic Performance of Vertically Irregular Reinforced Concrete Buildings, Life Science Journal 2013 5. Dr. B.G. NareshKumar and Avinash Gornale,Seismic Performance Evaluation of Torsionally Asymmetric Buildings, International Journal of Science and Engineering Research, Volume 3, Issue 6, June 6. C V R Moorthy, Indian institute of technology, Kanpur, India, 7. Sarkar, P., A.M. Prasad and D. Menon (2010) Vertical geometric irregularity in stepped building frames. Engineering Structures, 32, 2175-2182 8. Karavasilis, T.L., N. Bazeos and D.E. Bekos (2008) Seismic response of plane steel MRF with setback: estimation of inelastic deformation demands. Journal of Construction Steel Research, 64, 9. Priestley, M.J.N, G.M. Calvy and M.J. Kowalsky Displacement-based seismic design of structures IUSS press, Pavia, Italy, 2007. 10. Humar, J.L. and P. Kumar (1999) Effect of orthogonal in- plane structural elements on inelastic torsional response. Earthquake Engineering and Structural Dynamics, 28, 1071- 1097. 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Power BI Statistical Analysis Using The “Magic” Dataset Call This blog will show you how to do advanced inferential Power BI statistical analysis quickly and easily using what I like to call “Magic” Data Set Call. You can watch the full video of this tutorial at the bottom of this blog. The Magic data set call lets you step out of Power Query into R or Python, run a lot of advanced analyses, and then seamlessly jump back into Power Query and continue processing your data. It also allows you to create a new function to solve problems related to prime numbers. Power BI Statistical Analysis Data Set The data set we’ll use for our example today comes from the Enterprise DNA Data Challenge 23, which focuses on Healthcare data for a substance abuse treatment program. As you can see in the image below, it involves pre-tests and post-tests for patients to measure the effect of the treatment programs they underwent. In the Overall View – Patients and Treatments below, we’ll find box plots of the general data for pre-treatment and post-treatment scores. You’ll notice that both plots look similar to each other and only have a slight difference their medians. However, it’s important to remember that looks can be deceiving, particularly for non-normal data. Therefore, we can’t necessarily say that those two data are equal. There are many cases where you can look at data from Visualization and not be able to tell whether the differences they are showing are significant or not from a statistical standpoint. So, how sure are we that the differences we’re seeing are real instead of just artifacts of the sample we’re analyzing? Answering this question is impossible by using Power BI alone. Paired T-Test Power BI can’t do this sort of statistical analysis for more complex tests on data that doesn’t fit the simple inferential statistics we might want to use. I examined the data we’re analyzing and found that they are non-normal. We typically need to do a paired t-test to examine our hypothesis of the difference between the pre-treatment and post-treatment scores. This test requires normality in the differences between the two scores, which appears we don’t have in this case. Nevertheless, we’re still going to test that. If we find out it’s true that the difference in the data is normal, then there’s another test we will want to run, and I’ll show you how to do it. Power BI Statistical Analysis Main Data The image above is our main data launched in Power Query, which has a date, patient ID, and numerous other demographic data we analyzed and tested. But there are only three data that we need to be looking at here. First is the DLA1 or the daily living activities no. 1, the pre-test before their treatment. Second is the DLA2, the after-treatment and the last is the DLADelta, which is the difference between the Normally, we start with the source and do all sorts of data transformations here. We then call the R script if we need to do an unpivot, data cleaning, or other processing. But since this data is very clean, all we need to do at this point is go to the R script from the Transform tab. Power BI Statistical Analysis in R Script The image above shows the script we need for our Power BI statistical analysis, and we’ll go over every step. Inside the highlighted section we find the libraries we want to enter in our scipt to call four packages, broom, nortest, PairedData, and dplyr. Each package is like an add-in in R for running specific types of analyzes. After entering our libraries and their packages, we call in our data set, where the magic happens. The data set takes everything that happens in the R script, which is just the data itself and feeds it into the OrigData table with no transformations needed. Shapiro-Wilk Test We’ll also call a couple of technical tests in our script. The first one is called Shapiro-Wilk, which tests the normality of the data. All we need to do is call the column that we want to test ( OrigData$DLADelta) and send the results to this tidy function which puts the results in a nice table form. Anderson-Darlin Test The second one is the Anderson-Darling Test, which is another normality test. It will call in the same column to ensure that were running a complete test. We’ll also send this test to the tidy Wilcoxon Signed Rank Test We are also running a non-parametric test, which compares what happens in the data before and after. This test is called the Wilcoxon signed-rank test. Compared to the t-test, it doesn’t assume anything about the underlying distribution making it more flexible. However, it is less powerful in distinguishing differences than a parametric test or one that assumes normality. But since that assumption doesn’t hold in this case, we will run the none-parameter version and call it in our DLA1 and DLA2 columns. We then ensure that the paired data shows a before and after for the same individual with paired = true. Additionally, we have an alternative hypothesis (alternative = “greater”) that assumes the treatment will improve the patient, make insignificant improvements, or make him worse. Finally, we send that out to our tidy function. Bringing All The Tests Together In the last line of our code, we are stacking and appending all three test results from Shapiro, Anderson, and Wilcoxon, into one table called ALL. You can see that we are running plenty of statistical analysis in just four lines of code. Now that we have imported our packages and called in our tests, let’s run our script and see the results by clicking on the OK button. Statistical Table The image above is what we get after running our R script. You can see that it has all these different tables, but the only one we need is the All table because that’s the one that stacks up all the results that we want. So we click on the Name column header, select the All table, and click OK, as shown below. We then expand our table by clicking on the Value column header and selecting Expand. Check every box to select all columns except the one that says, “Use original column name as prefix,” and click Now we have the table we need, as shown in the image below. You can see the statistic, p-value, and the three tests we ran in its columns. Power BI Statistical Analysis Applications There are numerous things we can do with this data. We can go to DAX to run logical tests and calculations, put them in visuals, place them on smart narratives, and many more. If you select Statistics from Queries and Run R Script from Source as shown above, you will find 150 lines of statistical codes. We used these codes at Enterprise DNA for our entire analysis, and this was all run in one step from one data set call. It produces a series of tables that feed our results in the entire analysis. You can see in the Applied Steps below that we took the results of that data set and expanded them by merging. We also removed some columns that we don’t need to clean that table. What we got is 33 different tables of results that came out of that one data set! *** Related Links *** New On Power BI Showcase – Health & Substance Abuse Analysis Scatter Plot In R Script: How To Create & Import Three Ways To Use R Script In Power BI You just learned how powerful the Data Set Call is and the flexibility of what you can do with it. Aside from running statistical analysis, you can also use it for sentiment analysis, web scraping, and machine learning. You can do anything that Python or R can and then feed the results into Power Query. You can then take that out of Power Query and put it into Power BI, visualize and analyze it further, creating an analytical powerhouse! This project aims to implement a full data analysis pipeline using Power BI with a focus on DAX formulas to derive actionable insights from the order data. A comprehensive guide to mastering the CALCULATETABLE function in DAX, focusing on practical implementation within Power BI for advanced data analysis. An interactive web-based application to explore and understand various data model examples across multiple industries and business functions. A comprehensive project aimed at enhancing oil well performance through advanced data analysis using Power BI’s DAX formulas. Learn how to leverage key DAX table functions to manipulate and analyze data efficiently in Power BI. Deep dive into the CALCULATETABLE function in DAX to elevate your data analysis skills. One of the main reasons why businesses all over the world have fallen in love with Power BI is because... A hands-on project focused on using the TREATAS function to manipulate and analyze data in DAX. A hands-on guide to implementing data analysis projects using DAX, focused on the MAXX function and its combinations with other essential DAX functions. Learn how to leverage the COUNTX function in DAX for in-depth data analysis. This guide provides step-by-step instructions and practical examples. A comprehensive guide to understanding and implementing the FILTER function in DAX, complete with examples and combinations with other functions. Learn how to implement and utilize DAX functions effectively, with a focus on the DATESINPERIOD function. Comprehensive Data Analysis using Power BI and DAX Exploring CALCULATETABLE Function in DAX for Data Analysis in Power BI Data Model Discovery Library Optimizing Oil Well Performance Using Power BI and DAX Mastering DAX Table Functions for Data Analysis Mastering DAX CALCULATETABLE for Advanced Data Analysis Debugging DAX: Tips and Tools for Troubleshooting Your Formulas Practical Application of TREATAS Function in DAX MAXX in Power BI – A Detailed Guide Leveraging the COUNTX Function In Power BI Using the FILTER Function in DAX – A Detailed Guide With Examples DATESINPERIOD Function in DAX – A Detailed Guide	{"url":"https://blog.enterprisedna.co/power-bi-statistical-analysis-using-the-magic-dataset-call/","timestamp":"2024-11-12T19:28:41Z","content_type":"text/html","content_length":"492388","record_id":"<urn:uuid:09d31d0f-4ea4-498a-9698-fecfe552d173>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00463.warc.gz"}
Machine Learning: Experimental Evaluation of Inductive Hypotheses \| Exams Health sciences \| Docsity Download Machine Learning: Experimental Evaluation of Inductive Hypotheses and more Exams Health sciences in PDF only on Docsity! 1 1 CS 391L: Machine Learning: Experimental Evaluation Raymond J. Mooney University of Texas at Austin 2 Evaluating Inductive Hypotheses • Accuracy of hypotheses on training data is obviously biased since the hypothesis was constructed to fit this data. • Accuracy must be evaluated on an independent (usually disjoint) test set. • The larger the test set is, the more accurate the measured accuracy and the lower the variance observed across different test sets. 3 Variance in Test Accuracy • Let errorS(h) denote the percentage of examples in an independently sampled test set S of size n that are incorrectly classified by hypothesis h. • Let errorD(h) denote the true error rate for the overall data distribution D. • When n is at least 30, the central limit theorem ensures that the distribution of errorS(h) for different random samples will be closely approximated by a normal (Guassian) distribution. P (e rr or S( h) ) errorS(h)errorD(h) 4 Comparing Two Learned Hypotheses • When evaluating two hypotheses, their observed ordering with respect to accuracy may or may not reflect the ordering of their true accuracies. – Assume h1 is tested on test set S1 of size n1 – Assume h2 is tested on test set S2 of size n2 P (e rr or S( h) ) errorS(h) errorS1(h1) errorS2(h2) Observe h1 more accurate than h2 5 Comparing Two Learned Hypotheses • When evaluating two hypotheses, their observed ordering with respect to accuracy may or may not reflect the ordering of their true accuracies. – Assume h1 is tested on test set S1 of size n1 – Assume h2 is tested on test set S2 of size n2 P (e rr or S( h) ) errorS(h) errorS1(h1) errorS2(h2) Observe h1 less accurate than h2 6 Statistical Hypothesis Testing • Determine the probability that an empirically observed difference in a statistic could be due purely to random chance assuming there is no true underlying difference. • Specific tests for determining the significance of the difference between two means computed from two samples gathered under different conditions. • Determines the probability of the null hypothesis, that the two samples were actually drawn from the same underlying distribution. • By scientific convention, we reject the null hypothesis and say the difference is statistically significant if the probability of the null hypothesis is less than 5% (p < 0.05) or alternatively we accept that the difference is due to an underlying cause with a confidence of (1 – p). 2 7 One-sided vs Two-sided Tests • One-sided test assumes you expected a difference in one direction (A is better than B) and the observed difference is consistent with that assumption. • Two-sided test does not assume an expected difference in either direction. • Two-sided test is more conservative, since it requires a larger difference to conclude that the difference is significant. 8 Z-Score Test for Comparing Learned Hypotheses • Assumes h1 is tested on test set S1 of size n1 and h2 is tested on test set S2 of size n2. • Compute the difference between the accuracy of h1 and h2 • Compute the standard deviation of the sample estimate of the difference. • Compute the z-score for the difference )()( 21 21 herrorherrord SS −= 2 22 1 11 ))(1()())(1()( 2211 n herrorherror n herrorherror SSSS d −⋅ + −⋅ =σ d d z σ = 9 Z-Score Test for Comparing Learned Hypotheses (continued) • Determine the confidence in the difference by looking up the highest confidence, C, for the given z-score in a table. • This gives the confidence for a two-tailed test, for a one tailed test, increase the confidence half way towards 100% 2.582.331.961.641.281.000.67z-score 99%98%95%90%80%68%50%confidence level ) 2 )100( 100( C C −−=′ 10 Sample Z-Score Test 1 Assume we test two hypotheses on different test sets of size 100 and observe: 30.0)( 20.0)( 21 21 == herrorherror SS 1.03.02.0)()( 21 21 =−=−= herrorherrord SS 0608.0 100 )3.01(3.0 100 )2.01(2.0 ))(1()())(1()( 2 22 1 11 2211 =−⋅+−⋅= −⋅ + −⋅ = n herrorherror n herrorherror SSSS dσ 644.1 0608.0 1.0 == = d d z σ Confidence for two-tailed test: 90% Confidence for one-tailed test: (100 – (100 – 90)/2) = 95% 11 Sample Z-Score Test 2 Assume we test two hypotheses on different test sets of size 100 and observe: 25.0)( 20.0)( 21 21 == herrorherror SS 05.025.02.0)()( 21 21 =−=−= herrorherrord SS 0589.0 100 )25.01(25.0 100 )2.01(2.0 ))(1()())(1()( 2 22 1 11 2211 =−⋅+−⋅= −⋅ + −⋅ = n herrorherror n herrorherror SSSS dσ 848.0 0589.0 05.0 === d d z σ Confidence for two-tailed test: 50% Confidence for one-tailed test: (100 – (100 – 50)/2) = 75% 12 Z-Score Test Assumptions • Hypotheses can be tested on different test sets; if same test set used, stronger conclusions might be warranted. • Test sets have at least 30 independently drawn examples. • Hypotheses were constructed from independent training sets. • Only compares two specific hypotheses regardless of the methods used to construct them. Does not compare the underlying learning methods in general.	{"url":"https://www.docsity.com/en/docs/experimental-evaluation-evaluating-inductive-hypotheses-exam-1-n-1/6558893/","timestamp":"2024-11-09T00:35:05Z","content_type":"text/html","content_length":"236765","record_id":"<urn:uuid:2de46a5b-8dea-4f26-a0e3-b00ed96665d4>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00706.warc.gz"}
Quiz-3: Mathematics and Pedagogy MCQ Question with Answer : Exam Portal Quiz-3: Mathematics and Pedagogy MCQ Question with Answer Directions (Q. 1–30): Answer the following questions by selecting the most appropriate option. Q1. The length, breadth and height of a cuboid are 4 cm, 3 cm and 2 cm, respectively. What will be the lateral surface area of the cuboid? (a) 28 cm^2 (b) 14 cm^2 (c) 24 cm^3 (d) 12 cm^2 Q2. If F = number of faces, V = number of vertices and E = number of edges, which of the following is correct? (a) 6F – 3V = E (b) F + V = E (c) F + V = E + 2 (d) F + V = E – 2 Q3. Which of the following is an example of a two dimensional shape? (a) Sphere (b) Cone (c) Line (d) Square Q4. Which of the following points is on ∠ABC? (a) P (b) Q (c) R (d) Both Q and R Q5. What is the difference in the place value and the face value of 1 in 9199? (a) 101 (b) 100 (c) 99 (d) 91 Q6. Which of the following statements is correct? (a) An even number is always a composite number. (b) An odd number is always a prime number. (c) A natural number is a positive integer. (d) A prime and a composite number are always co primes. Q7. Two numbers are in the ratio of 5:6. If their HCF is 3, the two numbers are (a) 75 and 108 (b) 18 and 15 (c) 15 and 18 (d) 5 and 6 Q8. The value of 7654 – 3456 – 2345 is (a) 1111 (b) 6543 (c) 1853 (d) 13455 Q9. The cost of a Parker pen is Rs. 50. What is the cost of 25 such pens? (a) Rs. 125 (b) Rs. 1250 (c) Rs. 1025 (d) Rs. 1205 Q10. The sum of all the positive factors of 32 is… (a) 64 (b) 120 (c) 60 (d) 63 Q11. If a car covers 250 metres in 1 minute, how much distance will it cover in 35 minutes? (a) 8.750 km (b) 8.75 km (c) 87500 cm (d) 8750 km Q12. 350g sugar can be kept in one bag. To keep 17.5kg sugar, how many bags will be required? (a) 20 (b) 50 (c) 40 (d) 60 Q13. How many litres are there in 7.2 kilolitres? (a) 720 (b) 72 (c) 7200 (d) 72000 Q14. How many minutes are there in a week? (a) 10080 (b) 1080 (c) 10800 (d) 168 Q15. Find the next term in 2, 3, 5, 7, 11, 13…. (a) 15 (b) 17 (c) 18 (d) 19 Q16. Van Hiele’s ‘Levels of Geometric Thinking’, a student who can sort out rectangles from an assorted collection of shapes is at (a) Level 2: Informal Deduction (b) Level 3: Formal Deduction (c) Level 0: Visualization (d) Level 1: Analysis Q17. The main goal of mathematics education is to (a) help the students to understand mathematics (b) develop useful capabilities (c) develop children’s abilities for mathematization (d) Formulate theorems of geometry and their proofs independently Q18. A student identifies rectangles among four-sided figures on the basis of their properties (“It’s a rectangle because it has one set of opposite sides longer than the other set of opposite sides and opposite sides are parallel, and…”). According to Van Hiele’s ‘Levels of Geometric Thinking’, this student is at (a) Level 2 – Informal deduction (b) Level 3 – Formal deduction (c) Level 0 – Visualisation (d) Level 1 – Analysis Q19. NCF 2005 talks about teaching ambitious, coherent and important mathematics. Here, what does ‘coherent’ mean? (a) To achieve the higher aim rather than only the narrow aim. (b) Linking mathematics with other subjects (c) Providing activity oriented education (d) Using ICT in the classroom Q20. “Students’ ability to come up with a formula is more important than being able to correctly use well-known formulae”. Which learning approach do you think is best suited for this? (a) Contextual learning (b) Constructivism (c) Cooperative learning (d) Mastery learning Q21. A student was asked to express 5 m in cm. His answer was 50 cm. What type of error is it? (a) Regrouping error (b) Basic fact error (c) Wrong algorithm (d) Incorrect operation Q22. What is the meaning of the term ‘tyranny of the right answer’? (a) Putting the students under pressure to compare different methods of solving a problem (b) Applying one algorithm that has been taught and getting that ‘one right answer (c) Presenting too many ways to solve a problem and confusing the students (d) Giving the students too much freedom to apply their mind Q23. Which suggestion should be avoided in the textbook of mathematics for primary classes? (a) Textbooks should use language that a child would normally speak and understand. (b) Too many pictures should be avoided and maximum space should be given to practice sums. (c) The texts and visuals should be sensitive to concerns of gender and equality. (d) Mathematical concepts should be used in tandem with concepts of other subjects to build a deeper understanding of mathematics. Q24. The curriculum (NCF 2005) at the primary stage is not in favour of (a) Giving due place to non-number areas of mathematics such as space, visual patterns and data handling (b) Development of number sense including number patterns (c) Teaching children very big numbers to enhance the child’s cognitive capacity (d) Building a stronger conceptual base for fractions and decimals Q25. At the primary level, the use of tangram, dot games, patterns, etc. helps students (a) Enhance spatial understanding ability (b) Develop the sense of comparing numbers (c) Strengthen calculation skills (d) Understand basic operations Q26. Tangrams are not useful in developing (a) Visual-spatial skills (b) Concept of place value (c) An understanding of geometry vocabulary (d) An understanding of relationships between different shapes Q27. Which manipulative would you select to teach the concepts of area and perimeter to class IV students? (a) Abacus (b) Geoboard (c) Fraction discs (d) Base ten blocks Q28. Ravi is able to tell the correct number of objects in a small collection. He is at the (a) Operational phase (b) Emergent phase (c) Quantifying phase (d) Partition phase Q29. Sheenu can perform simple additions/subtractions (e.g. 2 + 3 or 4 – 2) that are given as word problems in a story through role play. He is at (a) Matching phase (b) Emergent phase (c) Quantifying phase (d) Partition phase Q30. Which one of the following is not a mathematical process? (a) Measurement (b) Visualisation (c) Estimation (d) Memorisation Read Important Article Leave a Comment	{"url":"https://examportal.xyz/mathematics-and-pedagogy-mcq-question/","timestamp":"2024-11-08T14:13:01Z","content_type":"text/html","content_length":"187835","record_id":"<urn:uuid:871cc423-bafd-40f4-93d1-0a8434c2a9d4>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00208.warc.gz"}
Introduction to Bootstrap Methods with Applications to R It was bootstrapping that made me start off on my statistics journey years ago. I have very fond memories of the days when I could understand simple things in statistics without resorting to complicating looking formulae. A few lines of code were all that was needed. Slowly I became more curious about many things in statistics and that’s how my love affair with stats began. There are two bibles that any newbie to bootstrap should go over; one by Efron & Tibshirani and the other by Davison & Hinkley. Any other specific topics, you can always understand by reading papers. It is always a nice feeling for me to read stuff about bootstrapping. However reading this book was an extremely unpleasant experience. In the recent years with the rise of R, many authors have started writing books such as “Introduction to ____( fill in any statistical technique that you want to) using R”. With many more people adopting R, these books hope to fill the need of a data analyst who might not be willing immerse himself/herself in to the deep theories behind a technique. The target audience might want some package that can be used to crunch out numbers. Fair enough. Not everyone has the time and inclination to know the details. There are some amazing books that fill this need and do it really well. Sadly, this book is not in that category. Neither does it explains the key functions for using bootstrapping nor does it explain the code that has been sprinkled in the book. So, the R in the title is definitely a misleading one. Instead of talking about the nuances of the various functions based on author’s experience, all one gets to see is some spaghetti code in the book. I can’t imagine an author using 15 pages of the book (that too within a chapter and not the appendix) in listing various packages that have some kind of bootstrap function. That’s exactly the authors of this book have done. Insane! This book gives a historical perspective of various developments around bootstrapping techniques. You can’t learn anything specific from the book. It just gives a 10000 ft. overview of various aspects of bootstrapping. I seriously do not understand why the authors has even written this book. My only purpose in writing this review is to dissuade others from reading this book and wasting their time and money. The bootstrap is one of the number of techniques that are a part of a broad umbrella of nonparametric statistics that are commonly called resampling methods. It was the article by Brad Efron in 1979 that started it all. The impact of this important publication can be gauged by the following statement in Davison and Hinkley’s book : The idea of replacing complicated and often inaccurate approximations to biases, variances and other measures of uncertainty by computer simulation caught the imagination of both theoretical researchers and users of statistical methods Efron’s motivation was to construct a simple approximation to Jackknife procedure that was initially developed by John Tukey. Permutation methods were known since 1930s but they were ineffective beyond small samples. Efron connected bootstrapping techniques to the then available jackknife, delta method, cross validation and permutation tests. He was the first to show that bootstrapping was a real competitor to jackknife and delta method for estimating the standard error of an estimator. Throughout 1980s to 1990s, there was an explosion of papers on this subject. Bootstrap was being used for confidence intervals, hypothesis testing and more complex problems. In 1983, Efron wrote a remarkable paper that showed that bootstrap worked better than crossvalidation in classification problems of a certain kind. While these positive developments were happening, by 1990s, there were also papers that showed bootstrap estimates were not consistent in specific settings. The first published example of an inconsistent bootstrap estimate appeared in 1981. By the year 2000, there were quite a few articles that showed that bootstrapping could be a great tool to estimate various functions but it can also be inconsistent. After this brief history on bootstrapping, the chapter goes in to defining some basic terms and explaining four popular method; jackknife, delta method, cross validation and subsampling. Out of all the packages mentioned in the chapter (that take up 15 pages), I think all one needs to tinker around to understand basic principles are boot and This chapter talks about improving the point estimation via bootstrapping. Historically speaking, the bootstrap method was looked at, to estimate the standard error of an estimate and later for a bias adjustment. The chapter begins with a simple example where bootstrap can be used to compute the bias of an estimator. Subsequently a detailed set of examples of using bootstrapping to improve cross validation estimate are given. These examples show that there are many instances where Bootstrapped crossvalidation technique gives a better performance than using other estimators like CV, 632 and e0 estimators. About estimating a location parameter for a random variable from a particular distribution, MLE does a great job and hence one need not really use bootstrapping. However there are cases where MLE estimates have no closed form solutions.In all such cases, one can just bootstrap away to glory. In the case of linear regression, there are two ways in which bootstrapping can be used. The first method involves residuals. Bootstrap the residuals and create a set of new dependent variables. These dependent variables can be used to form a bootstrapped sample of regression coefficients. The second method is bootstrapping pairs. It involves sampling pairs of dependent and independent variable and computing the regression coefficients. Between these two methods, the second method is found to be more robust to model misspecification. Some of the other uses of bootstrapping mentioned in the chapter are: • Dealing with heteroskedastic errors by using wild bootstrap • Nonlinear regression • Non parametric regression • Application to CART family (bagging, boosting and random forests) My crib about this chapter is this : You are introducing data mining techniques like LDA, QDA, bagging etc. in a chapter where the reader is supposed to get an intuition about how bootstrapping can be used to get a point estimate. Who is the target audience for this book ? A guy who is already familiar with these data mining techniques would gloss over the stuff as there is nothing new for him. A newbie would be overwhelmed by the material. For a guy who is not a newbie and who is not a data mining person, the content will be appear totally random . Extremely poor choice of content for an introductory book. Confidence Intervals One of the advantages of generating bootstrapped samples is that they can be used to construct confidence intervals. There are many ways to create confidence intervals. The chapter discusses bootstrap-t, iterated bootstrap, BC, BCa and tiled bootstrap. Again I don’t expect any newbie to understand clearly these methods after reading this chapter. All the author has managed to do is to give a laundry list of methods and give some description about the methods.And Yes, an extensive set of references that makes you feel that you are reading a paper and not a book. If you want to really understand these methods, the bibles mentioned at the beginning are the right sources. Hypothesis testing For simple examples, hypothesis testing can be done based on the confidence intervals obtained via bootstrap samples. There are subtle aspects that one needs to take care of, such as sampling from the pooled data etc. Amazing that the author doesn’t even provide some sample code to illustrate this point. The code that’s provided does sampling from individual samples. Instead code should have been provided to illustrate sampling from pooled data. Again poor choice on the way to present the content. Time Series The chapter gives a laundry list of bootstrap procedures in the context of time series; model based bootstrap, non overlapping block bootstrap, circular bootstrap, stationary bock bootstrap, tapered block bootstrap, dependent wild bootstrap,sieve bootstrap. Again a very cursory treatment and references to a whole lot of papers and books. The authors get it completely wrong. In an introductory book, there must be R code, there must be some simple examples to illustrate the point. Instead if you see a lot of references to papers and journal articles, the reader is going to junk this book and move on Bootstrap variants The same painful saga continues. The chapter gives a list of techniques – Bayesian bootstrap, Smoothed bootstrap, Parametric bootstrap, Double bootstrap, m-out-of-n bootstrap, and wild bootstrap. There is no code whatsoever to guide the reader. The explanation given to introduce these topics is totally inadequate. When the bootstrap is inconsistent and How to remedy it ? This chapter gives a set of scenarios when the bootstrap procedure can fail • For small sample sizes less than 10, bootstrapped sample is not reliable • Distributions that have infinite second moments • Estimating extreme values • Unstable AR processes • Long memory processes This is the worst book that I have read in the recent times. The authors are trying to cash in on the popularity of R. The title of the book is completely misleading. Neither is it an introduction to bootstrap methods nor is it an introduction to R methods for bootstrapping. All it does is give a cursory and inadequate treatment to the bootstrap technique. Do not buy or read this book. Total waste of time and money.	{"url":"https://www.rksmusings.com/2014/09/13/introduction-to-bootstrap-methods-with-applications-to-r/","timestamp":"2024-11-08T17:11:28Z","content_type":"text/html","content_length":"19650","record_id":"<urn:uuid:33cd57c7-85e0-40cd-a238-bb18cdde690d>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00497.warc.gz"}
It can't work, can it? - Climate Discussion Nexus Michael Moore’s explosive new documentary also raises a perennial debate about the environment, resource depletion and so on going back to the dreary Thomas Malthus, namely whether ingenuity can win the race with scarcity. To put it bluntly, are humans primarily mouths or hands? Moore like Malthus thinks we’re mouths, and elbows. So did doomster Paul Ehrlich, who lost a very famous bet with hyperoptimist Julian Simon about commodity prices in 1990. But can new forms of energy and other technologies really keep us ahead permanently? According to Gale Pooley and Marian Tupy at HumanProgress, things are still looking good. There is a certain spurious precision to their claim that the Earth was “570.9 percent more abundant in 2019 than it was in 1980”. We don’t tolerate decimal places in measurements of global temperature and we’re not going to put up with them in measurements of “global abundance.” There was a famous exchange between Milton and Rose Friedman in 2001 where he, a great enthusiast for econometrics, said “There’s a phrase written on the entrance to one of the social sciences buildings at the University of Chicago, which is the statement” and Rose chimed in “If you can’t measure it, measure it anyway.” As she knew, the actual phrase he was about to cite was “When you cannot measure something, your knowledge is meager and unsatisfying.” But sometimes you can’t get mathematical precision except at the cost of accuracy, and we have to do our best. And the basic approach of HumanProgress is sound: Figure out how many hours a person has to work to get a fixed amount of various basic things from coffee to tin to shrimp. (Yes, for some reason shrimp is on their top-50 list along with stuff you’d expect like chicken, crude oil and soybeans, and a few other oddities like sunflower oil, logs and If you like that sort of thing you can quibble with some of their mathematical gymnastics. But it remains true that the human population is far higher than people like Ehrlich ever thought it could get yet, instead of starvation reaching prosperous countries, famine has been largely driven even from poorer ones. One resource-shortage idea that just won’t die is “peak oil”. It was once said to doom our civilization that we would have to stop using fossil fuels, as it is now said to doom our civilization that we won’t stop, as Jennifer Marohasy recalled in juxtaposing Moore’s new documentary with the fact that the price of oil, incredibly, fell below zero late this April because it was so abundant compared to our needs. Of course there is only so much of it in total, as there is only so much matter and energy in the universe. But if we ever really do find that we cannot locate more coal, oil and natural gas, or that we cannot afford to burn what we do find, the price will inevitably rise and people will find alternatives, including known ones like nuclear and ones we haven’t yet devised because we haven’t had to. Innovation is, by definition, unpredictable; virtually nobody saw the Age of Oil coming even in the early 19^th century, as the iron age came as a shock to the Bronzies some 3000 years ago, so we aren’t going to predict what will happen. We will predict what won’t. The human race will not exhaust its ingenuity. Indeed, most of our problems come not from what we have not managed to invent but what we have and that pattern is very likely to continue. Including this business about quantifying everything to a spurious degree of decimal places. In making this point we do not dismiss the notion that so many billions of people are stressing the natural environment. We are, from encroachments on ecosystems to plastic in the oceans. (In fact one striking scene early in Moore’s documentary shows how thoroughly lit the developed world is at night, underlining to what an unprecedented extent one species does now dominate the globe.) But where you find significant harm to the planet, you almost certainly find people too poor, too hard-pressed to survive, to concern themselves with caring for nature or to be able to afford it. One day the world will end, swallowed by the sun, whacked by a giant comet or otherwise overcome by the slings and arrows of cosmic fortune. But there is no reason to think that we cannot extend our days a great deal through hard work of the mental as well as physical sort including finding new and better ways to use resources that bring more benefits at lower costs including to the planet. Certainly we’ve done surprisingly well thus far.	{"url":"https://climatediscussionnexus.com/2020/04/29/it-cant-work-can-it/","timestamp":"2024-11-05T06:13:30Z","content_type":"text/html","content_length":"89729","record_id":"<urn:uuid:04e41cd6-73be-433a-ab85-9dac4190642e>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00316.warc.gz"}
Free Printable Number Flash Cards Free Printable Number Flash Cards - Plus there’s a black and white version for economical printing colorful number flashcards to print… these number flashcards are full of brilliant color and texture. Have your child practice looking at each number, saying it aloud and then maybe relating it to the number. Web these free printable number flashcards include numbers from one to one hundred as well as function signs. You will find multiple versions of colorful number cards starting from zero to number. Web just like sight words are important in reading, recognizing numbers and counting is important in math. This set of number flashcards also includes numbers, math symbols, and counting cards… The printable number flashcards below are in a large format (4 to a page) and cover numbers from 1 to 100 in an easily printable pdf. Web this set of free printable number flashcards with pictures includes numbers as pictorial representations, numerals and words. 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Enum Excel2007Function Represents functions added in Excel 2007. Assembly: Syncfusion.XlsIO.Base.dll public enum Excel2007Function Name Description AVERAGEIF Returns the average (arithmetic mean) of all the cells in a range that meet a given criteria AVERAGEIFS Returns the average (arithmetic mean) of all cells that meet multiple criteria. BESSELI Returns the modified Bessel function In(x). BESSELJ Returns the Bessel function Jn(x). BESSELK Returns the modified Bessel function Kn(x). BESSELY Returns the Bessel function Yn(x). BIN2DEC Converts a binary number to decimal. BIN2HEX Converts a binary number to hexadecimal. BIN2OCT Converts a binary number to octal. COMPLEX Converts real and imaginary coefficients into a complex number. CONVERT Converts a number from one measurement system to another. Returns a key performance indicator (KPI) name, property, and measure, and displays the name and property in the cell. A KPI is a quantifiable measurement, such as monthly gross CUBEKPIMEMBER profit or quarterly employee turnover, used to monitor an organization's performance. CUBEMEMBER Returns a member or tuple in a cube hierarchy. Use to validate that the member or tuple exists in the cube. CUBEMEMBERPROPERTY Returns the value of a member property in the cube. Use to validate that a member name exists within the cube and to return the specified property for this member. CUBERANKEDMEMBER Returns the nth, or ranked, member in a set. Use to return one or more elements in a set, such as the top sales performer or top 10 students. CUBESET Defines a calculated set of members or tuples by sending a set expression to the cube on the server, which creates the set, and then returns that set to Microsoft Office Excel. CUBESETCOUNT Returns the number of items in a set. CUBEVALUE Returns an aggregated value from a cube. DEC2BIN Converts a decimal number to binary. DEC2HEX Converts a decimal number to hexadecimal. DEC2OCT Converts a decimal number to octal. DELTA Tests whether two values are equal. ERF Returns the error function. ERFC Returns the complementary error function. GESTEP Tests whether a number is greater than a threshold value. HEX2BIN Converts a hexadecimal number to binary. HEX2DEC Converts a hexadecimal number to decimal. HEX2OCT Converts a hexadecimal number to octal. IMABS Returns the absolute value (modulus) of a complex number. IMAGINARY Returns the imaginary coefficient of a complex number. IMARGUMENT Returns the argument theta, an angle expressed in radians. IMCONJUGATE Returns the complex conjugate of a complex number. IMCOS Returns the cosine of a complex number IMDIV Returns the quotient of two complex numbers. IMEXP Returns the exponential of a complex number. IMLN Returns the natural logarithm of a complex number. IMLOG10 Returns the base-10 logarithm of a complex number. IMLOG2 Returns the base-2 logarithm of a complex number. IMPOWER Returns a complex number raised to an integer power. IMPRODUCT Returns the product of from 2 to 29 complex numbers IMREAL Returns the real coefficient of a complex number IMSIN Returns the sine of a complex number IMSQRT Returns the square root of a complex number IMSUB Returns the difference between two complex numbers IMSUM Returns the sum of complex numbers. OCT2BIN Converts an octal number to binary. OCT2DEC Converts an octal number to decimal. OCT2HEX Converts an octal number to hexadecimal. SUMIFS Adds the cells in a range that meet multiple criteria	{"url":"https://help.syncfusion.com/CR/aspnet/Syncfusion.XlsIO.Excel2007Function.html","timestamp":"2024-11-14T05:14:13Z","content_type":"text/html","content_length":"26167","record_id":"<urn:uuid:e511a39c-6e67-4f11-a8c2-b776a6933152>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00521.warc.gz"}
Day 20 Advent of Code 2022 - Day 20 Day 20: Grove Positioning System Useful Links Concepts and Packages Demonstrated Page Navigation Problem Intro This one was quite tricky, but not nearly as hard as yesterday. And it ultimately ends up being very little code. We need to find the grove, and we have the coordinates. But they’re in some sort of encrypted format: The encrypted coordinates are a list of numbers. We need to decrypt them using a process called mixing: • Process each number in its original order in the list. • Move that number forwards or backwards a number of places; the number of places to move is given by the number’s value. • The list is circular, so a number that is moved can wrap around either end. Part 1 What is the sum of the three numbers that form the grove coordinates? We’re told that the grove coordinates can be found by looking at the 1000th, 2000th, and 3000th numbers after the value 0, wrapping around the list as necessary. The real challenge here is that we need to move the numbers in the order in which they were originally listed, but any given number’s position will continue to change as we go. My strategy is: • Read our input list into a deque, since a deque provides a circular list implementation with the ability to rotate a value any arbitrary number of places. • As we read the numbers, enumerate them, so that we always know the original number position. Thus, our deque is composed of tuples of (original index, value). • Now, perform n iterations, where n is the length of the input list: □ Rotate our numbers so that the next pair is at the left end. □ Pop this pair and retrieve the value, i.e. the number of places we need to move this pair by. □ Now rotate the deque by this amount. The result is that the number after the insertion point will now be at the front. □ Finally, add our popped pair back at the right hand end. Thus, it is logically inserted before the pair now at position 0. □ When each iteration has completed, the number at the end will always be the number that moved. Here’s my mix() function: def mix(enumerated: deque): """ Perform the mix algorithm on our enumerated deque of numbers """ # Move each number once, using original indexes # We can't iterate over actual values from enumerated, since we'll be modifying it as we go for original_index in range(len(enumerated)): while enumerated[0][0] != original_index: # bring our required element to the left end current_pair = enumerated.popleft() shift = current_pair[1] % len(enumerated) # retrieve the value to move by; allow for wrapping over enumerated.rotate(-shift) # rotate everything by n positions enumerated.append(current_pair) # and now reinsert our pair at the end # print(enumerated) # for debugging return enumerated Although we could rotate each number by the actual value of that number, this is very inefficient. That’s because if the value of the number is larger than the length of our deque, most of those rotations will be redundant. We only want to rotate by our number, modulo the length of the deque. And here’s how we read in the data and mix it: def main(): with open(INPUT_FILE, mode="rt") as f: data = list(map(int, f.read().splitlines())) # Part 1 enumerated = deque(list(enumerate(data.copy()))) # deque of tuples of (original index, value) enumerated = mix(enumerated) If we enable the print() statement with the sample data, we get output that looks like this: deque([(2, -3), (3, 3), (4, -2), (5, 0), (6, 4), (1, 2), (0, 1)]) deque([(3, 3), (4, -2), (5, 0), (6, 4), (0, 1), (2, -3), (1, 2)]) deque([(5, 0), (6, 4), (0, 1), (1, 2), (3, 3), (4, -2), (2, -3)]) deque([(6, 4), (0, 1), (1, 2), (4, -2), (2, -3), (5, 0), (3, 3)]) deque([(0, 1), (1, 2), (2, -3), (5, 0), (3, 3), (6, 4), (4, -2)]) deque([(3, 3), (6, 4), (4, -2), (0, 1), (1, 2), (2, -3), (5, 0)]) deque([(5, 0), (3, 3), (4, -2), (0, 1), (1, 2), (2, -3), (6, 4)]) See how the pair that last moved is always at the end? Now we’re ready to find the grove coordinates. We know we need to find the 1000th, 2000th and 3000th numbers that are after 0. So I’ve implemented this function which retrieves the value of any number in the deque which is n items after the position of the number 0: def value_at_n(values: list, n: int): """ Determine the value at position n in our list. If index is beyond the end, then wrap the values as many times as required. """ digit_posn = (values.index(0)+n) % len(values) return values[digit_posn] Then all we need to do is call this function with 1000, 2000 and 3000: coord_sum = 0 for n in (1000, 2000, 3000): coord_sum += value_at_n([val[1] for val in enumerated], n) print(f"Part 2: {coord_sum}") Part 2 Oh, decryption just got a bit more complicated: 1. Multiply each number in the original list by the decryption key value. 2. Then mix the list 10 times. Then, as before: What is the sum of the three numbers that form the grove coordinates? Part 2 results in much larger starting numbers, and many more mix iterations. If we had been rotating by the value of the number, this would be a problem for us. We would find Part 2 takes too long. Fortunately, we’re already only rotating by the modulo, so the larger number values makes little difference to us. For Part 2, I only need to add this: # Part 2 new_data = [valDECRYPTION_KEY for val in data] enumerated = deque(list(enumerate(new_data))) # new deque for _ in range(10): # run the mix 10 times, but always with same enumeration (starting order) enumerated = mix(enumerated) coord_sum = 0 for n in (1000, 2000, 3000): coord_sum += value_at_n([val[1] for val in enumerated], n) print(f"Part 2: {coord_sum}") It uses a list comprehension to multiply each initial input value by the decryption key. We then build a new deque from this new list of numbers. And then we simply mix the deque 10 times, as The final code looks like this: from collections import deque from pathlib import Path import time SCRIPT_DIR = Path(__file__).parent INPUT_FILE = Path(SCRIPT_DIR, "input/sample_input.txt") # INPUT_FILE = Path(SCRIPT_DIR, "input/input.txt") DECRYPTION_KEY = 811589153 def main(): with open(INPUT_FILE, mode="rt") as f: data = list(map(int, f.read().splitlines())) # Part 1 enumerated = deque(list(enumerate(data.copy()))) # deque of tuples of (original index, value) enumerated = mix(enumerated) coord_sum = 0 for n in (1000, 2000, 3000): # Turn our enumerated list into a list coord_sum += value_at_n([val[1] for val in enumerated], n) print(f"Part 1: {coord_sum}") # Part 2 new_data = [valDECRYPTION_KEY for val in data] enumerated = deque(list(enumerate(new_data))) # new deque for _ in range(10): # run the mix 10 times, but always with same enumeration (starting order) enumerated = mix(enumerated) coord_sum = 0 for n in (1000, 2000, 3000): coord_sum += value_at_n([val[1] for val in enumerated], n) print(f"Part 2: {coord_sum}") def mix(enumerated: deque): """ Perform the mix algorithm on our enumerated deque of numbers """ # Move each number once, using original indexes # We can't iterate over actual values from enumerated, since we'll be modifying it as we go for original_index in range(len(enumerated)): while enumerated[0][0] != original_index: # bring our required element to the left end current_pair = enumerated.popleft() shift = current_pair[1] % len(enumerated) # retrieve the value to move by; allow for wrapping over enumerated.rotate(-shift) # rotate everything by n positions enumerated.append(current_pair) # and now reinsert our pair at the end # print(enumerated) return enumerated def value_at_n(values: list, n: int): """ Determine the value at position n in our list. If index is beyond the end, then wrap the values as many times as required. """ digit_posn = (values.index(0)+n) % len(values) return values[digit_posn] if __name__ == "__main__": t1 = time.perf_counter() t2 = time.perf_counter() print(f"Execution time: {t2 - t1:0.4f} seconds") And the output looks like this: Part 1: 5904 Part 2: 8332585833851 Execution time: 7.8667 seconds Not too bad.	{"url":"https://aoc.just2good.co.uk/2022/20","timestamp":"2024-11-14T10:37:29Z","content_type":"text/html","content_length":"30202","record_id":"<urn:uuid:0b654a0d-9d56-4d87-b2ca-a77d1005d33f>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00576.warc.gz"}
Math, Grade 6, Getting Started, Properties of Operations Justify Equivalent Expression for 58 • 31 Work Time Justify Equivalent Expression for 58 • 31 • Are these expressions equivalent? 58 ⋅ 31 • Use the properties of operations to show each of the steps taken to determine if the expressions are equivalent or not. • What questions did you ask yourself before you worked on this problem? • Why can you change the order of the numbers for addition and multiplication but not for subtraction and division? • How did you know when to use parentheses and when you can remove the parentheses?	{"url":"https://openspace.infohio.org/courseware/lesson/2059/student/?section=5","timestamp":"2024-11-02T21:43:15Z","content_type":"text/html","content_length":"32008","record_id":"<urn:uuid:b6e1138d-2646-4b18-8c0d-9721b807ce01>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00668.warc.gz"}
A Truck Scheduling Problem for Multi-Crossdocking System with Metaheuristics Computers, Materials & Continua A Truck Scheduling Problem for Multi-Crossdocking System with Metaheuristics 1International University-Vietnam National University, Vietnam National University, HoChiMinh City, 70000, Vietnam 2Faculty of Commerce, Van Lang University, Ho Chi Minh City, 70000, Vietnam *Corresponding Author: Nguyen Van Thanh. Email: thanh.nguyenvan@vlu.edu.vn Received: 29 January 2022; Accepted: 23 March 2022 Abstract: The cross-docking is a very important subject in logistics and supply chain managements. According to the definition, cross-docking is a process dealing with transhipping inventory, in which goods and products are unloaded from an inbound truck and process through a flow-center to be directly loaded onto an outbound truck. Cross-docking is favored due to its advantages in reducing the material handing cost, the needs to store the product in warehouse, as well decreasing the labor cost by eliminating packaging, storing, pick-location and order picking. In cross-docking, products can be consolidated and transported as a full load, reducing overall distribution costs. In this paper, we focus on a truck scheduling at the multi-door, multi-crossdocking network with inventory constraints and process capability constraints. In this model, a truck can visit severals docks for loading or unloading many types products. This situation is very common in reality. This study also developed an exact mathematical model using mixed-integer linear programming (MILP) with the objective of minimizing the makespan to obtaint the benchmark in small scale problems. Large scale problems are solved through Simulated Annealing (SA) algorithm and Tabu Search (TS) algorithm. Performance of these algorithms will be compared to benchmarks obtained from solver as well as to each other. Keywords: Truck scheduling; multi-door; multi-crossdocking network; simulated annealing; tabu search As the global markets on supply chain has seen an influx of competitors during the past few years, it is pertinent that manufactures, retailers and distributors strive to optimize costs to increase their competitiveness. Driven by such demand, the idea of cross docking was hailed. It was defined by [1] that cross-docking is a process dealing with transshipping inventory, in which goods and products are unloaded from an inbound truck and process through a flow-center to be directly loaded onto an outbound truck. The impact of cross-docking was proved to be highly beneficial in reducing warehousing cost, which takes up around 30% of the product sales cost, when Walmart first pioneering its implementation. In 1992, by putting the cross-docking model into effects across 82% of its inventory, Walmart became the most profitable retailer globally, successfully reduced its cost 2%–3% [2]. One of the earliest works addressing short-term scheduling in cross-dock belongs to [3] whose work is renowned for considering 32 models. The general aim was to generate a sequence of receiving inbound and outbound truck at each door to minimize the makespan. Later on, [4] applied and concluded that the TS metaheuristics could effectively solve a cross-docking problem. The literatures regarding truck scheduling are quite well documented over the year. Williams in [5] was the first who contributed his work to this topic’s literature. The problem, with the objective of minimizing the makespan, was solved using genetic algorithm in combination with simulation model. Another study was of [6], which focused on generating sequences of trucks entering the door, and solutions are developed based on different assumptions to the problem. It was concluded that heuristic algorithm performed better or as well as dynamic programming with or without prior assumption of known truck sequencing. Reference [7] tackled a simplified cross-dock model to gain the underlying complexity of truck sequencing problem, which was split into sub problems of inbound and outbound sequencing separately. Reference [8] investigated the truck scheduling problem with constraint of time window and deadline for truck departure. Though the paper successfully touched on real-world constraint, the model was simplified to only cross dock with single inbound/outbound door, which may not be applicable to a real situation [8]. The methodology was developed using a hybrid metaheuristic between SA and Keshtel algorithm. Reference [9] also tackled the truck scheduling problem with time window constraints but expanded the problem to multi-door cross docking system. The objective was minimizing tardiness of outbound truck and proposed TS and SA for generating the solution. For multi-door cross-dock, a few studies have taken the approach similar to that of flow shop with parallel machines. Reference [10] is one of the first research which followed such route. Similarly, [11] also applied the idea to their cases with the addition of time-indexed variables. The problem was approached by using constructive polynomial-time algorithm and more traditional scheduling algorithm like Johnson’s rule-based algorithm [12]. The topic also consists of works from works from [11–14]. The work of [14] was constructed predicated on the work of [10] on the two-stage hybrid cross-docking scheduling. The new work appends that of [10] as the authors used time-indexed model as opposed to the original completion time and precedence model. The study went on to develop the solution using compressed differential heuristic and compared the result coined from both models [14]. The problem continued to be expanded to multi cross-docking system, or cross-dock network. Reference [15] first contributed to this topic with a multi cross-dock model to minimize the operational cost. Aside from the trucking scheduling constraint, inventory balance was calculated to deduce the holding cost and inventory level against the capacity. The solution was generated by TS and SA metaheuristics, which were compared against the simple greedy algorithm [16]. Reference [16] presented their work on multi-cross dock which intimately adhered to the previously proposed notations by [3], therefore shared similarity to that of [13]. The work approached the problem of truck scheduling by using sequencing variable. The limitation, however, is the failure to regard the capacity and the increased complexity from the approach. The problem was solved using firefly and SA metaheuristics. The most recent work was that of [17], in which the problem of truck scheduling to find the minimum makespan was done for a multi-serviced/purposed crossdocking network. The problem was solely approached by devising a MILP model [17]. Other extension of cross-docking and its application can be shown in the works [18], where the authors applied particle swarm optimization (ωc-PSO) to minimize the makespan. A cosine decreasing strategy of inertia weight was applied in this study to balance between exploit and explore. Furthermore, crossover strategy is presented to prevent the algorithm from falling into local optimum. The integrated model of routing inbound vehicles between suppliers and cross-docks and outbound vehicles between cross-docks and retailers was considered in [19]. Different to our work, this study aimed to minimize the total cost by optimizing assignment of products to suppliers and retailers instead of scheduling trucks consideration. The problem was solved through endosymbiotic evolutionary algorithm. Multi-objectives for cross-docking problem was studied by [20 ]. In this study, the authors investigated truck scheduling in a rail–road physical internet cross-docking hub considering energy consumption. The two main objectives were to minimize the energy consumption and cost of outbound truck. The problem was different to this study since main variables were only whether a truck should be assigned to a dock. The multiple-dock visit was not allowed and dock capacity was also not considered in this study. Other extension and related works of cross-dock problems were presented in [21,22]. Though cross-docking problem has been rigorously explored since the 90s, scheduling problems do not take much proportion in the literary vault. For problem regarding multi-cross dock alone, there have only been two papers publicly released, to the best of our knowledge. The aim of this paper is to devise a mathematical model and well as suitable approaches for solution development of large-sized problems to obtain the aim and satisfy all requirement from the company. The model should reflect on the real condition to a certain extent to acquire a level of applicability, which can serve as a foundation for future development. The scope of the problem will fall within the spectrum of crossdocking operational planning through scheduling. However, it will only concern with the exterior operations involving coordinating the trucks, the unloading and loading. This study has some resemblance to the work of [17], however; it differentiates itself with other researches by expanding the problem to multi-door, multi-crossdocking network. Furthermore, the model also allows multi visiting of shipping and receiving trucks to other docks. At each dock, trucks will load or unload some kinds of products which are specified by the dock. Load or unload splitting are also permitted in this model. Dock capacity is also considered here so that the model is very similar to real-practice case. The rest of the paper is organized as follows. Section 2 elaborates on the problem description and crossdocking system, with the corresponding mathematical model, followed by the presenting of algorithms to solve large-sized problems in Section 3. Result analysis is presented in Section 4 and lastly, section 5 recapitulates the paper in discussion and conclusion. In this paper, the study will focus on the cross-docking process which involve separate, multiple docks that have the capability to handle different types of products. All cross docks allow temporary storages, but at the end of the day, the inventory in all cross docks has to be zero. In addition, the layout is symmetrical, meaning there are an equal number of inbound and outbound doors for each dock. We also assume that the inbound doors and outbound doors are separate, meaning each set has single purpose. At all times, each door can only process one truck and preemption is not allowed. Furthermore, the number of loaded products has to be equal or larger than the demand. In our model, the super scripts R and S represent for variables relating to process of receiving and shipping, respectively. r index of receiving trucks, r∈R s index of shipping trucks, s∈S d index of docks, d∈D p index of product types, p∈P t index of time periods, t∈T ωrpR In-transit inventory of unit product p on the receiving truck r ωspS Number of unit product p demanded by the shipping truck s τrR Soonest time receiving truck r enter any dock d τsS Soonest time shipping truck s enter any dock d ρd Capacity of dock ηd Number of inbound/outbound doors at dock d α Time for handling an unit item βdp If dock d can handle product p, βdp=1, otherwise; βdp=0 γ Transition time of the truck between the docks BigM A very large number Cmax The makespan ErdR Entering time of receiving truck r at dock d LrdR Leaving time of receiving truck r at dock d QrdpR Quantity of product p receiving truck r unloaded at dock d XrdhR Binary variable, XrdhR=1 if receiving truck r enters dock d before dock h; otherwise XrdhR=0 YrdpR Binary variable, YrdpR=1 if item p is unloaded by receiving truck r at dock d ZrdR Binary variable, ZrdR=1 if receiving truck r enter dock d; otherwise, ZrdR=0 UrdtR Binary variable, UrdtR=1 if t≥ErdR; otherwise UrdtR=0 VrdtR Binary variable, VrdtR=1 if t≤LrdR; otherwise VrdtR=0 RrdtR Binary variable, RrdtR=1 if ErdR≤RrdtR≤LrdR; otherwise RrdtR=0 NtrdpR Number of product p being unloaded by receiving truck r at dock d up to time t EsdS Entering time of shipping truck s at dock d LsdS Leaving time of shipping truck s at dock d QsdpS Quantity of product p shipping truck s loaded at dock d XsdhS Binary variable, XsdhS=1 if shipping truck s enters dock d before dock h; otherwise XsdhS=0 YsdpS Binary variable, YsdpS=1 if item p is loaded by shipping truck s at dock d ZsdS Binary variable, ZsdS=1 if shipping truck s enter dock d; otherwise, ZsdS=0 USdtS Binary variable, UsdtS=1 if t≥EsdS; otherwise UsdtS=0 VsdtS Binary variable, VsdtS=1 if t≤LsdS; otherwise VsdtS=0 RsdtS Binary variable, RsdtS=1 if EsdS≤RsdtS≤LsdS; otherwise RsdtS=0 NtsdpS Number of product p being loaded by shipping truck s at dock d up to time t Idpt Inventory of product p at dock d at time t Subject to The Eq. (2) claims that the makespan must be greater or equal to the leaving dock time of all shipping trucks The Eqs. (3)–(6) ensure that a receiving truck can only visit a dock if it is allowed and its unloaded quantity to this dock is zero in case of no visitation This imposed the time window constraints on receiving trucks. The receiving truck cannot enter the dock before its allowed soonest enter time in Eq. (7). The Eqs. (10)–(12) state that if a receiving truck visits dock d then dock h, the associating variable ZrdR will be one. Furthermore, the enter time at dock h must be greater or equal to the leaving time of dock d plus traveling time between two docks. The Eq. (13) says that the total unloaded quantity at all docks must be equal to the quantity the receiving truck carrying The Eqs. (14) and (15) ensure that if t is greater than the entering time dock d of receiving truck r, UrdtR=1, otherwise; UrdtR=0 The Eqs. (16) and (17) guarantee that if t is smaller than the leaving time dock d of receiving truck r, VrdtR=1, otherwise; VrdtR=0 The Eqs. (18)–(21) forces the constraint that if t is in the range of entering time and leaving time dock d and the receiving truck r also visits the dock RrdtR=1, otherwise; RrdtR=0 The Eqs. (22) and (23) show that and at any time a receiving truck can only be served by one dock and total number of receiving trucks is served by a dock d cannot be greater than the number of its We also apply the same physical constraints for the shipping trucks, which creates Eqs. (24)–(44). The total unload at a dock is assumed to be affected right after the receiving truck r enter the dock. If VrdtR=0, NtrdpR=Qrdpr otherwise NtrdpR=0. So it can be interpreted as if t is higher than leaving time, i.e., VrdtR=0, the total unload quantity of receiving truck r up to t is equal to its total unload quantity. If t is smaller than leaving time, the total unload quantity at dock is zero. These constraints are shown in Eqs. (45)–(47) The same idea is applied for constructing the constraints of shipping trucks. However; the total load to a shipping truck up to time t is calculated immediately after the shipping trucks enter the docks, UsdtS=1, i.e., t is higher than entering time of shipping truck as shown in Eqs. (48)–(50) By forcing the inventory level is always greater or equal to zero and smaller than capacity through Eqs. (51) and (52), we ensure that the receiving trucks only visits the dock when the dock has enough product for satisfying their load demands. To solve the small-scale problems, CPLEX Optimizer engine which is developed by IBM company was used to create the benchmark. However, due to the NP-hard property of the original problems, when the size increases metaheuristic algorithms must be adopted. In this study, TS and SA are also implemented and results obtained from CPLEX are used as benchmarks. During TA and SA, this study applies two common following algorithms for creating initial solutions and assignment process. The Fig. 1 shows how the initial solutions are created while Fig. 2 explains about the assignment process. TS and SA are chosen is due to its simplicity in the process of creating new solution in the process of exploring and exploiting, and the foundation of such process is the neighborhood search method. In this paper, the neighborhood search is implemented through two swapping methods in Fig. 3. The object of swapping is the sequence of receiving trucks, the sequence of shipping trucks and the sequence of docks for the first truck. These are also the input into the evaluation function to calculate the corresponding makespan. The pseudo code of TS is described in Fig. 4. For simulated annealing algorithm, we verify its performance with two versions. The first one employs the sigmoid function which is presented in Fig. 5. The second one applies the metropolis function which is described in Fig. 6. To conduct result analysis, ten data sets with different scales are considered. The data set information and the results obtained from CPLEX are given in Tab. 1. For small-scaled problems, CPLEX works quite well in terms of run time, which only takes less than 2 minutes to solve. When there is increase in the number of trucks and product quantity, the run time grows exponentially as can be seen from the data set 6 to 10. The comparison between results for both TA and SA and CPLEX are shown in the Tab. 2. In the Tab. 2 the percentage is calculated as Eq. (53) P=makespan of algorithm−makespan of benchmarkmakespan of the benchmark(53) On an overall viewpoint, SA Metropolis algorithm yields most promising results when comparing with 2 other methods in gap. In conclusion, to solve the problem of truck scheduling in crossdocking network, 3 approaches are taken. The first is using MILP in conjunction with CPLEX to solve for the exact solution. However, because of its restriction to small-sized problems, TS and SA are implemented to search for the makespan of large-sized problems. The two metaheuristics exhibit the tradeoff between producing a consistent and good result and having short run time. In general, the results from the approaches proved to be not only optimal and feasible to the constraints of the system, but also managed to adhere and comply to several practical conditions. The result also proves the credibility and feasibility of the model as well as the algorithm. Regarding the all-encompassing and real-life adherent nature of the proposed model, not only does it make a solid contribution to the topic’s literature but also serve as a foundation for further development of the program into software. Further study on this topic can be expanded to include the interior operations of the crossdocking network. Another direction is to expand the problem downstream by combining the truck scheduling problem with the vehicle routing problem to the customers. Although the algorithm obtained reliable results, this study still encountered some challenges in handling the most difficult constraint in the crossdocking problem, the concurrency of load and unload. This concurrency creates challenges in ensuring the feasibility of system state as well as the solutions deriving from the neighborhood. The feasibility is only assured through very carefully checked and revised mechanism. This process sometime takes long time for specific cases. Funding Statement: The authors wish to express their gratitude to International University-Vietnam National University, Van Lang University, Vietnam for financial support for this research. Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study. 1. A. L. Ladier and G. Alpan, “Cross-docking operations: Current research versus industry practice,” Omega, vol. 62, no. 1, pp. 145–162, 2016. [Google Scholar] 2. G. Stalk, P. Evans and L. Shulman, “Competing on capabilities: The new rules of corporate strategy,” Harvard Business Review, vol. 70, no. 2, pp. 57–69, 1992. [Google Scholar] 3. W. Yu, “Operational strategies for cross docking systems,” Ph.D. dissertation, Iowa State University, 2002. [Google Scholar] 4. W. Yu and P. J. Egbelu, “Scheduling of inbound and outbound trucks in cross docking systems with temporary storage,” European Journal of Operational Research, vol. 184, no. 1, pp. 377–396, 2008. [ Google Scholar] 5. D. L. McWilliams, P. M. Stanfield and C. D. Geiger, “The parcel hub scheduling problem: A simulation-based solution approach,” Computers & Industrial Engineering, vol. 49, no. 3, pp. 393–412, 2005. [Google Scholar] 6. M. Y. Maknoon and P. Baptiste, “Cross-docking: Scheduling of incoming and outgoing semi trailers,” International Journal of Logistics Research and Applications, vol. 12, no. 1, pp. 249–261, 2009. [Google Scholar] 7. N. Boysen, M. Fliedner and A. Scholl, “Assembly line balancing: Which model to use when,” International Journal of Production Economics, vol. 111, no. 2, pp. 509–528, 2008. [Google Scholar] 8. A. Golshahi-Roudbaneh, M. Hajiaghaei-Keshteli and M. M. Paydar, “Cross-dock scheduling considering time windows and deadline for truck departures,” Scientia Iranica, vol. 28, no. 1, pp. 532–546, 2021. [Google Scholar] 9. G. Ozden and I. Saricicek, “Scheduling trucks in a multi-door cross-docking system with time windows,” Bulletin of the Polish Academy of Sciences-Technical Sciences, vol. 67, no. 1, pp. 349–362, 2019. [Google Scholar] 10. F. Chen and K. Song, “Minimizing makespan in two-stage hybrid cross docking scheduling problem,” Computers & Operations Research, vol. 36, no. 6, pp. 2066–2073, 2009. [Google Scholar] 11. G. B. Fonseca, T. H. Nogueira and M. G. Ravetti, “A hybrid Lagrangian metaheuristic for the cross-docking flow shop scheduling problem,” European Journal of Operational Research, vol. 275, no. 1, pp. 139–154, 2019. [Google Scholar] 12. T. H. Nogueira, F. B. Coutinho, R. P. Ribeiro and M. G. Ravetti, “Parallel-machine scheduling methodology for a multi-dock truck sequencing problem in a cross-docking center,” Computers & Industrial Engineering, vol. 143, no. 1, pp. 1–20, 2020. [Google Scholar] 13. W. Wisittipanich and P. Hengmeechai, “Truck scheduling in multi-door cross docking terminal by modified particle swarm optimization,” Computers & Industrial Engineering, vol. 113, no. 1, pp. 793–802, 2017. [Google Scholar] 14. P. M. Cota, B. M. R. Gimenez, D. P. M. Araujo, T. H. Nogueira, M. C. Souza et al., “Time-indexed formulation and polynomial time heuristic for a multi-dock truck scheduling problem in a cross-docking centre,” Computers & Industrial Engineering, vol. 95, no. 1, pp. 135–143, 2016. [Google Scholar] 15. P. Chen, Y. Guo, A. Lim and B. Rodrigues, “Multiple crossdocks with inventory and time windows,” Computer & Operations Research, vol. 33, no. 1, pp. 43–63, 2006. [Google Scholar] 16. M. M. Isfahani, R. T. Moghaddam and B. Naderi, “Multiple cross-docks scheduling using two meta-heuristic algorithms,” Computers & Industrial Engineering, vol. 74, no. 1, pp. 129–138, 2014. [ Google Scholar] 17. G. C. Issi, R. Linfati and J. W. Escobar, “Mathematical optimization model for truck scheduling in a distribution center with a mixed service mode dock area,” Journal of Advanced Transportation, vol. 2020, no. 1, pp. 1–13, 2020. [Google Scholar] 18. Y. Ye, J. Li, K. Li and H. Fu, “Cross-Docking truck scheduling with product unloading/loading constraints based on an improved particle swarm optimisation algorithm,” International Journal of Production Research, vol. 56, no. 16, pp. 5365–5385, 2018. [Google Scholar] 19. K. Y. Lee, J. S. Lim and S. S. Ko, “Endosymbiotic evolutionary algorithm for an integrated model of the vehicle routing and truck scheduling problem with a cross-docking system,” Informatica, vol. 30, no. 3, pp. 481–502, 2019. [Google Scholar] 20. T. Chargui, A. Bekrar, M. Reghioui and D. Trentesaux, “Multi-Objective sustainable truck scheduling in a rail-road physical internet cross-docking hub considering energy consumption,” Sustainability, vol. 11, no. 11, pp. 1–23, 2019. [Google Scholar] 21. O. Theophilus, M. A. Dulebenets, J. Pasha, O. F. Abioye and M. Kavoosi, “Truck scheduling at cross-docking terminals: A follow-up state-of-the-art review,” Sustainability, vol. 11, no. 19, pp. 1–23, 2019. [Google Scholar] 22. R. K. Mavi, M. Goh, N. K. Mavi, F. Jie, K. Brown et al., “Cross-docking: A systematic literature review,” Sustainability, vol. 11, no. 11, pp. 1–19, 2020. [Google Scholar] This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	{"url":"https://www.techscience.com/cmc/v72n3/47548/html","timestamp":"2024-11-12T09:55:57Z","content_type":"application/xhtml+xml","content_length":"131838","record_id":"<urn:uuid:1e1b7001-f7e4-4138-80cb-bf7084587f9f>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00640.warc.gz"}
Let a and b be real numbers where a=b=0. Which of the following functions could represent the graph below?f(x)=x(x-a)^3(x-b)^3f(x)=(x-a)^2(x-b)^4f(x)=x(x-a)^6(x-b)^2f(x)=(x-a)^5(x-b) Answer:Option: b is the answer. ( f(x)=(x-a)^2(x-b)^4 )Step-by-step explanation:Clearly from the graph of the function we could see that zero is not a root of the polynomial function hence option (a) ( f(x)=x(x-a)^3(x-b)^3 ) and option (c) ( f(x)=x(x-a)^6(x-b)^2 )are discarded.Now we will check for option (b) and option (d)As the graph touches the x-axis at two point i.e. a and b that means that both the roots of the polynomial equation are of even degree.Hence, the correct option is:option: b ( f(x)=(x-a)^2(x-b)^4 ).	{"url":"https://thibaultlanxade.com/general/let-a-and-b-be-real-numbers-where-a-b-0-which-of-the-following-functions-could-represent-the-graph-below-f-x-x-x-a-3-x-b-3f-x-x-a-2-x-b-4f-x-x-x-a-6-x-b-2f-x-x-a-5-x-b","timestamp":"2024-11-08T11:44:33Z","content_type":"text/html","content_length":"30103","record_id":"<urn:uuid:5058f971-cd3e-4605-a358-d82b20a29ff8>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00182.warc.gz"}
How do you simplify (y/3 + 1)/(y^2/9 - 1)? \| HIX Tutor How do you simplify #(y/3 + 1)/(y^2/9 - 1)#? Answer 1 Factoring the denominator as the difference of squares #color(white)("XXX")=((y/3)+1)/(((y/3)+1)((y/3)-1))# Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer 2 To simplify the expression (y/3 + 1)/(y^2/9 - 1), we can start by factoring the denominator. The denominator can be factored as the difference of squares: (y^2/9 - 1) = ((y/3)^2 - 1^2) = ((y/3 + 1)(y /3 - 1)). Next, we can rewrite the expression as (y/3 + 1)/((y/3 + 1)(y/3 - 1)). Now, we can cancel out the common factor of (y/3 + 1) in the numerator and denominator. The simplified expression is 1/(y/3 - 1). Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer from HIX Tutor When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some Not the question you need? HIX Tutor Solve ANY homework problem with a smart AI • 98% accuracy study help • Covers math, physics, chemistry, biology, and more • Step-by-step, in-depth guides • Readily available 24/7	{"url":"https://tutor.hix.ai/question/how-do-you-simplify-y-3-1-y-2-9-1-8f9af9c0e9","timestamp":"2024-11-08T06:03:25Z","content_type":"text/html","content_length":"574828","record_id":"<urn:uuid:4505c30c-4088-4016-b3fc-a6bf09f601b4>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00605.warc.gz"}
Find 'A' & Solve A-4+3×0+1=? – Math Puzzle Only for Genius Home Puzzles Math Puzzles Find “A” & Solve A-4+3×0+1=? – Math Puzzle Only for Genius Find “A” & Solve A-4+3×0+1=? – Math Puzzle Only for Genius [Series Puzzle #24] This post may contain affiliate links. This means if you click on the link and purchase the item, We will receive an affiliate commission at no extra cost to you. See Our Affiliate Policy for more Take the challenge and solve this Genius Level Math Puzzles – 95% of people answer this puzzle wrong! Math Puzzles Only for Genius with Answer These puzzles, reserved for the sharpest minds, present a unique challenge – finding two solutions that are interconnected. Make a mistake in the first step, and unraveling the puzzle becomes a tricky feat. Your answers must align with the given options to emerge victorious. In this particular math puzzle, your task is to determine the value of “A” from the provided number series. Once you’ve cracked that code, plug in the value of A for the second step of the puzzle and solve the equation. Navigate through the options and choose the correct answer to conquer this brain-teasing challenge. Check out the puzzle question below and let the mental gymnastics begin! 🤓🔢✨ Genius Math Puzzles Question: Find “A” from series: 4, 27, A, 33, 16, 36 and Then solve A – 4 + 3 × 0 + 1 = __? Options: (A) 1, (B) 7, (C) 9, (D) 12 Found the answer? Drop your solution in the comment box below. Didn’t spot your answer among the options? Perhaps the first step needs a closer look. For a helpful nudge: Explore the relationship between the first and second numbers, then the 3rd and 4th, 4th and 5th, and so forth. Identify the pattern and see what the difference is. I’m confident you’ll crack it this time. Take your time! Need confirmation? The answer awaits you at the end of the post. Before you go, why not share this genius math puzzle on your timeline or WhatsApp group? Challenge your friends and see if they can conquer this puzzle too. Stay connected with us on Facebook for a continuous supply of fascinating puzzles and updates. Enjoy the journey of problem-solving! 🧠🔍✨ Search items: Find number in series, Find letter in Series, Math Game, Math Puzzles, Brain Teasers, Logic Puzzles, Find Missing Number, Fun Brain Puzzles, Fun Riddles Brain Teasers, Number Series Riddles, Puzzles and Mind Games, Riddle Brain Teasers, Riddle Websites, Riddles and Mind Games, Solve this if you are a genius, Only for genius, Only for Genius Puzzles, Math Puzzles with Answer, Genius at Work Puzzles, Interesting Puzzle Games, Puzzles, Puzzles Images, Share Puzzles Images,	{"url":"https://picshood.com/find-a-series-puzzle-24/","timestamp":"2024-11-11T14:42:25Z","content_type":"text/html","content_length":"134076","record_id":"<urn:uuid:7548b00e-731d-4125-b278-4eede477187e>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00791.warc.gz"}
New Oberwolfach report: Projectivity of good moduli spaces of semistable quiver representations and vector bundles Don't be fooled into thinking I'm on some paper-finishing spree (I'm not!), but there is another piece of writing you can read: Projectivity of good moduli spaces of semistable quiver representations and vector bundles. 2 weeks ago there was an Oberwolfach workshop on algebraic geometry and noncommutative algebra, at which I spoke about upcoming work with Chiara Damiolini, Hans Franzen, Vicky Hoskins, Sveta Makarova and Tuomas Tajakka on redoing the construction of moduli spaces of semistable quiver representations in the language of algebraic stacks, rather than the original construction using geometric invariant theory. This question was in fact directly inspired by an expository paper written together with Jarod Alper, Daniel Bragg, Jason Liang and Tuomas Tajakka for the analogous question for moduli of vector bundles, where such a construction was known (albeit not in the language of algebraic stacks and their good moduli spaces, which are more recent) due to Faltings. The full paper will be finished soon (but this is a very flexible notion), so for now you'll have to do with an extended abstract that contains more a discussion of how various constructions for curves and quivers are very similar if you look at them in the right way, rather than the details for the proofs. Maybe we should arXiv the expository paper for moduli of vector bundles too. The print version will be available by the end of the year by the way.	{"url":"https://pbelmans.ncag.info/blog/2022/05/18/new-owr/","timestamp":"2024-11-11T16:33:49Z","content_type":"text/html","content_length":"21745","record_id":"<urn:uuid:5753ba25-5523-4fdb-a82c-15247fd9d0ae>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00850.warc.gz"}
Electric Transformer Rating (Explained for Beginners) Electric transformer rating makes or breaks your electrical project. This is because under-rating the transformer can cause it to fail, break down, or be completely damaged. It happened in my work, one of the most critical transformers had serious damage, and we had to replace it ASAP to reconnect loads. In this article, I will discuss, how to rate a transformer, with examples for beginners. Let’s dive into the details. what is an electric transformer rating? Electric transformer ratings refer to the specifications and characteristics that define the performance and capabilities of an electrical transformer. Transformers are essential components in electrical power systems, used to transfer electrical energy between different voltage levels. Key transformer ratings include: 1. Voltage Rating: □ Primary Voltage (Vp): The voltage on the high-voltage side (input side) of the transformer. □ Secondary Voltage (Vs): The voltage on the low-voltage side (output side) of the transformer. 2. Power Rating: □ Apparent Power (S): The product of the voltage and current in a circuit, measured in volt-amperes (VA). It represents the total power in an AC circuit, both real (active) and reactive power. □ Real Power (P): The actual power consumed or delivered by a device, measured in watts (W). □ Reactive Power (Q): The non-working power component due to the phase difference between voltage and current, measured in volt-amperes reactive (VAR). 3. Frequency: □ The frequency of the alternating current (AC) for which the transformer is designed, is typically 50 or 60 Hertz. 4. Temperature Rise: □ The maximum allowable temperature rise of the transformer’s winding and oil insulation above the ambient temperature. 5. Impedance: □ The percentage impedance (%Z) indicates the internal resistance to the flow of current within the transformer. It is expressed as a percentage of the rated voltage. 6. Insulation Class: □ Transformers are assigned insulation classes based on the temperature rise of the winding. Common insulation classes include A, B, F, and H. 7. Cooling Method: □ Transformers are designed for different cooling methods, such as oil-immersed (liquid-filled) or dry-type (air-cooled). 8. Vector Group: □ Describes the phase relationship between the primary and secondary winding voltages. Common vector groups include Yyn0, Dyn11, etc. 9. Efficiency: □ The efficiency of a transformer indicates the ratio of output power to input power, usually expressed as a percentage. 10. Tap Changer: □ Some transformers have tap changers that allow for adjusting the turns ratio and, consequently, the output voltage. Transformer ratings are crucial for ensuring proper operation, efficiency, and safety within an electrical power system. They are specified by standards and regulations to facilitate compatibility and reliability in the grid. Standard KVA Rating of Transformers We use KVA for transformer rating, (KVA means Kilo volt Ampere). To determine the size of the transformer, it is important to determine the load by KVA. However, Transformers are mostly used for the purpose of power distribution, that’s why common standard KVA transformers are commonly used. Two types of transformer KVA ratings are mentioned below. For the Phase Delta Wye transformer 408 to 120/208 common standard KVA ratings are 15 KVA, 30 KVA, 45 KVA, 75 KVA, 112.5 KVA, 225 KVA, 300 KVA, and 500 KVA. For a Single-phase transformer with the size of 277- or 480-volt transformer common standards are 5 KVA, 7.5 KVA, 10 KVA, 15 KVA, 25 KVA, 37.5 KVA, 50 KVA, 75 KVA, and 100 KVA. Please note, Besides the mentioned standard ratings there are other sizes of transformer available. However, the most common size is mentioned above. Transformer KVA Rating Formula The transformer KVA rating formula is derived from the power rating of the transformer. In this article, we will include a formula for both single-phase and three-phase transformers. So, let’s start with the formula of a single-phase Transformer. Single Phase Transformer: Single-phase Transformer Power Rating P = V x I While : P is transformer power in VA, V is transformer voltage, I is Transformer current. Note that transformer power is fixed for low and high-voltage sides. As you know, the transformer affects voltage and current only. In the formula, we use voltage and current of the same side (low or high voltage). Now, KVA Rating for Single Phase Transformer: P = (V x I)/1000 Hence putting the value of Current and voltage we will get the required rating of a single-phase transformer. KVA Rating Formula for Three-phase Transformer: The power rating of the three-phase transformer: P = √3. V x I Hence the rating of the phase transformer in KVA is given below P = (√3. V x I)/1000 How to Increase Transformer Rating? Increasing the transformer rating is possible by increasing the cooling method. Adding new fans or oil pumps increases the transformer rating up to 66%, Some transformers have more than one rated power on the nameplate depending on the cooling stage. Most people think that rating depends upon the power rating formula. I.e. From the formula of power, they can change the rating. But this will need some extra work. By increasing the value of current or voltage different types of losses such as eddy current losses and hysteresis losses occur. Similarly, the same situation occurs for increasing the frequency. And the transformer becomes hot. Hence to increase the rating of the transformer we must try to cool down the transformer. And for this purpose, we will need additional cooling fans to install on the transformer. Also, an automatic system will be required which automatically starts cooling the fan when the core temperature exceeds the specified temperature limit. The more the transformer is cooled, the more power will be transferred from the supply to the load side. Transformer Rating Example We already discussed the KVA rating formula for both single-phase and three-phase transformers. Now let’s take an example to get a better understanding of it. Here we will calculate the KVA rating of both single and three-phase transformers. Single Phase Transformer Rating calculation For a single-phase transformer, the rating formula is given by: P = (V x I)/1000 Assume the voltage and current values as Voltage (V)= 120 V Current (I)= 50A Now put the values in the rating formula of the single-phase transformer to find the KVA rating of the transformer. P = (V x I)/1000 (120 V x 50 A) / 1,000 =6 KVA Hence the rating of a single-phase transformer with 12o Volt and 50 A current is 6 KVA. • 3 Phase Transformer Rating calculation formula To calculate the rating of the transformer we will need to know about the primary and secondary voltages as well as current. Besides this, we will also need to assume a power factor value. Consider the following values on the nameplate of the 100KVA transformer. Primary Voltages or High Voltages (H.V) is 11000 V = 11kV. The primary Current on the High Voltage side is 5.25 Amperes. Secondary voltages or Low Voltages (L.V) is 415 Volts The secondary Current (Current on the Low voltage side) is 139.1 Amperes. Now using the 3 Phase transformer KVA rating formula= P = (√3. V x I) /100 Putting the values of either primary or secondary size we get the rating of the transformer. P = (√3. 11000 x 5.25)/1000 =100 KVA	{"url":"https://www.electrical4uonline.com/transformer-rating-explained-for-beginners/","timestamp":"2024-11-05T12:00:05Z","content_type":"text/html","content_length":"109366","record_id":"<urn:uuid:a36dff66-1406-4723-868d-384759637e6a>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00044.warc.gz"}
AE Brief Applied Calculus This book uses intriguing real-world applications to engage readers' interest and show them the practical side of calculus. Its many applications are related to finance, business, and such general-interest topics as learning curves in airplane production, the age of the Dead Sea Scrolls, Apple and Oracle stock prices, the distance traveled by sports cars, lives saved by seat belts, and the cost of a congressional victory. The Seventh Edition maintains the hallmark features that have made BRIEF APPLIED CALCULUS so popular: contemporary and interesting applications including many that are new or updated); careful and effective use of technology, including graphing calculator and spreadsheet coverage; constant pedagogical reinforcement through section summaries, chapter summaries, annotated examples, and extra practice problems; Just-in-Time algebra review material; and a variety of exercises that allow readers to practice and hone their problem-solving skills. Purchase Enquiry INSTRUCTOR’S eREVIEW COPY Integrating Excel. Diagnostic Test. 1. FUNCTIONS. Real Numbers, Inequalities, and Lines. Exponents. Functions: Linear and Quadratic. Functions: Polynomial, Rational, and Exponential. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. 2. DERIVATIVES AND THEIR USES. Limits and Continuity. Rates of Change, Slopes, and Derivatives. Some Differentiation Formulas. The Product and Quotient Rules. Higher-Order Derivatives. The Chain Rule and the Generalized Power Rule. Nondifferentiable Functions. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Graphing Using the First Derivative. Graphing Using the First and Second Derivatives. Optimization. Further Applications of Optimization. Optimizing Lot Size and Harvest Size. Implicit Differentiation and Related Rates. Differentials, Approximations, and Marginal Analysis. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Cumulative Review for Chapters Exponential Functions. Logarithmic Functions. Differentiation of Logarithmic and Exponential Functions. Two Applications to Economics: Relative Rates and Elasticity of Demand. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Antiderivatives and Indefinite Integrals. Integration Using Logarithmic and Exponential Functions. Definite Integrals and Areas. Further Applications of Definite Integrals: Average Value and Area Between Curves. Two Applications to Economics: Consumers' Surplus and Income Distribution. Integration by Substitution. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Integration by Parts. Integration Using Tables. Improper Integrals. Numerical Integration. Differential Equations. Further Applications of Differential Equations: Three Models of Growth. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. 7. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Optimizing Functions of Several Variables. Least Squares. Lagrange Multipliers and Constrained Optimization. Total Differentials, Approximate Changes, and Marginal Analysis. Multiple Integrals. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Cumulative Review for Chapters 1–7. A. Graphing Calculator Basics. B. Algebra Review. Answers to Selected Exercises. • Geoffrey C. Berresford Dr. Berresford received his Ph.D. from the Courant Institute of Mathematical Sciences at New York University and taught at the State University of New York at Purchase before joining the faculty at the C.W. Post campus of Long Island University. Besides co-authoring four textbooks with Dr. Rockett, he has published papers in differential equations, linear programming, logic, and probability, and has received several teaching awards and the Distinguished Service Award from The Metropolitan New York Section of the Mathematical Association of America. • Andrew M. Rockett After completing his Ph.D. at Stony Brook University, Dr. Rockett joined the mathematics faculty at C.W. Post and began his collaborations with Dr. Berresford. His book with Peter Szusz on CONTINUED FRACTIONS (1992) was hailed by Ivan Niven as "an outstanding addition to the literature of mathematics," and he served the Kappa Mu Epsilon mathematics honor society as editor of the mathematics journal The Pentagon from 1989 to 1995. Dr. Rockett serves as a reviewer for several journals, including Mathematical Reviews for the American Mathematical Society. • A Diagnostic Test has been added to help students identify skills that may need review. This test appears before Chapter 1. • An Algebra Review appears in an appendix, keyed to parts of the text, for additional reference. • New material on parallel and perpendicular lines has been added to Section 1.1, "Real Numbers, Inequalities, and Lines." • Section 3.7, "Differentials, Approximations, and Marginal Analysis," is new to the seventh edition. This section is optional and can be omitted without loss of continuity. • New exercises have been added and over 100 updated (including all of the Wall Street financial exercises) with current real-world data and accompanying sources. New "Explorations and Excursions" exercises give further details or theoretical underpinnings of the topics in the main narrative. • A Diagnostic Test has been added to help you identify skills that may need review. This test appears before Chapter 1. • Many of the book's contemporary and interesting applications use real, sourced data from a wide range of fields including athletics, biomedical sciences, environmental sciences, management science and business, personal finance and management, social and behavioral sciences, and topics of general interest. A globe icon identifies real-world examples. • Sourced exercises establish factual basis and enable further research. • Regression (modeling) exercises in Chapter 1 ask students to use calculators to fit equations to actual data, and illustrate the methods used to develop the models in applied exercises throughout the book. Students can also benefit from optional examples on linear regression, power regression, quadratic regression, and exponential regression. • The book presents substantial treatment of limits involving infinity, graphing rational functions, and elasticity of demand. In addition to these expanded applications, more challenging exercises are included as well as a complete proof of the Chain Rule based on Carathédory's definition of the derivative. • Brief Examples, located immediately to the right of the boxes that summarize results, illustrate and provide immediate reinforcement of the concepts. • Optional Graphing Calculator Explorations and exercises explore new topics, allow students to easily carry out otherwise messy calculations, or show the limitations and pitfalls of technology. To allow for optional use of the graphing calculator, the Calculator Explorations are boxed, and an icon identifies exercises that require a graphing calculator. • Spreadsheet Explorations are included for select chapters of the text for those who prefer Microsoft® Excel or other spreadsheet technology. • Chapter Summaries, organized by section, review key concepts and reference specific review exercises that allow students to check their understanding. Chapter-ending Hints and Suggestions offer special reminders of essential facts or "tricks" that students might otherwise overlook. • The book presents substantial treatment of limits involving infinity, graphing rational functions, and elasticity of demand. In addition to these expanded applications, more challenging exercises are included as well as a complete proof of the Chain Rule based on Carathédory's definition of the derivative. Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.	{"url":"https://prod.cengageasia.com/title/default/detail?isbn=9789815077353","timestamp":"2024-11-05T19:14:02Z","content_type":"text/html","content_length":"58464","record_id":"<urn:uuid:6b1f383a-b269-470f-a0d5-6feb2c9dc773>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00095.warc.gz"}
In the 19th century, people began to study mechanical systems in which motion in a configuration space was constrained by 'no slip' conditions, such as, for example, a wheel or a ball rolling on a plane without slipping. It was immediately noticed that there were many cases in which these 'rolling' constraints did not prevent one from being able to join any two points in a configuration space by an admissible path, and these situations were called 'non-holonomic'. The notion of 'holonomy' arose as a way to quantify and study these 'non-holonomic' systems, and it has turned out to be very fruitful, with many applications in differential geometry and mathematical physics as well as in practical mechanics problems (such as figuring out how to use robot hands to manipulate 3-dimensional objects). In this talk, I'll introduce the ideas that led to the development of the concept of holonomy, show how some simple examples are computed, and describe how even very simple systems, such as a convex surface rolling over another surface without slipping or twisting, can lead to some surprising and exceptional geometry. No expertise in differential geometry will be assumed; if you are comfortable with vector calculus, you can enjoy the talk.	{"url":"https://www4.math.duke.edu/media/videos.php?cat=553&sort=top_rated&time=all_time&page=1&seo_cat_name=","timestamp":"2024-11-04T15:46:35Z","content_type":"text/html","content_length":"217301","record_id":"<urn:uuid:c1f9a0c6-2b0e-401d-b55a-fc0879eb4329>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00761.warc.gz"}
Wave Optics \| Index of Refraction, Thin Film Interference When light shines on a very thin film, interference can occur. Sometimes the interference pattern can be quite striking, as in the case of an oil slick. Here is a cool video displaying thin film interference in action. Pre-lecture Study Resources Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class. BoxSand Videos Required Videos Suggested Supplemental Videos Learning Objectives Atomistic Goals Students will be able to... BoxSand Introduction Wave Optics \| Thin Film Interference Light in a vacuum always travels at a speed c = 2.99 x 10^8 m/s. When any wave is incident on a boundary, like when light travels from the air onto water, some of the wave is reflected and some of it is transmitted. Experiment will show that light appears to slow down while traveling through the water as opposed to the air. This is called the effective speed ($v_{eff}$) of the light in the medium. The Index of Refraction (n) is a measure of the effective speed of light in a medium. Notice, that since nothing can travel faster than the speed of light, that the index of refraction is always greater than or equal to 1. This slowing down of light also causes the wavelength to This is because the constant for a wave across a boundary is the frequency. with $v=f \lambda$, if the frequency is constant and the speed decreases, the wavelength must also decrease. You'll also notice the direction the light travels also changes. The index of refraction can be used to determine how much light bends when traveling from one medium to the next. See Snell's Law of Refraction for more about the bending of light. When light is incident on a boundary where the index of refraction is changing, some of the light is reflected and some of that light is transmitted. This can have interesting effects when light is incident on a very thin film of certain materials. Consider the situation below, which could represent oil on top of water. Air would be the top surface, oil would be the thin film, and water would be the bottom surface. Here light ray (1) is the original light beam incident on the top interface. It splits into two rays - (2) is the reflected ray and (3) is the transmitted ray. The refracted (transimitted) ray (3) then interacts with the bottom interface and the reflected ray is (4) and the transmitted ray is (6). Lastly (4) interacts again with the top surface and some of it is transmitted (5). There are more reflections and transmissions, an infinite number in theory, but the first two are the most dominant due to the intensity decreasing at every interface. Now light rays (2) and (5) can interference with each other. They are coherent since they originated from the same source and there is a Path Length Difference (PLD) between the two. At near normal incidence the PLD is equal to twice the thickness $t$ of the film, $PLD = 2t$. Now before using the standard integer multiple of the wavelength approach to constructive interference, you must first consider phase changes in the reflected When light reflects off a material with a higher index of refraction the reflected wave has a phase shift. The animation on the left shows a wave pulse on a string that displays the same feature. You can see the pulse coming in from the left is upward but reflects downward, shifting the wave a half of a cycle ($\pi$). * Images: Dr. Russel In contrast if light reflects off a material with a lower index of refraction, there is no $\pi$ phase shift. Also notice that the transmitted waves never have any phase shift. All of this means you have find the relative number of phase shifts between the first reflected wave (2) and the second reflected wave (5). An example would be the air => oil => water system described above. Oil has a higher index of refraction than oil, so ray (2) has a $\pi$ phase shift. When ray (3) reflects off the bottom surface, it is in oil and bouncing off water. Since $n_{water} <n_{oil}$ there is no phase shift in reflected ray (4) or in (5) since it is transmitted. Ray (2) and (5) are interfering but there is a relative phase shift between them. So you must switch the conditionals for constructive and destructive interference. │m = 0, 1, 2, ... │ No relative phase shift ($\phi=0$) │ relative phase shift ($\phi=\pi$) │ │ Constructive Interference│ $2t = m \lambda_{film}$ │ $2t = (m+\frac{1}{2}) \lambda_{film}$│ │ Destructive Interference │ $2t = (m+\frac{1}{2}) \lambda_{film}$│ $2t = m \lambda_{film}$ │ Here $\lambda_{film}$ is the wavelength of the light in the film. You can use the index of refraction to determine $\lambda_{film}$ The most common place this effect is observed is on bubbles or oil slicks. The colors you see are because those are the wavelegths that match the conditions for more constructive interference. The colors change because there are different thicknesses in the film. Key Equations and Infographics Now, take a look at the pre-lecture reading and videos below. OpenStax Reading Additional Study Resources Use the supplemental resources below to support your post-lecture study. YouTube Videos Here is a good video on index of refraction, This is an excellent video on the refractive index, Doc Schuster dives in and explains thin film interference with an example This Khan Academy video will help you understand the behavior of light as it passes through and interacts with varying index of the medium. Check out the BU thin film simulation. This is a great way to better understand the physical phenomena. For additional simulations on this subject, visit the simulations repository. For additional simulations on this subject, visit the simulations repository. For additional demos involving this subject, visit the demo repository For additional demos involving this subject, visit the demo repository Oh no, we haven't been able to write up a history overview for this topic. If you'd like to contribute, contact the director of BoxSand, KC Walsh (walshke@oregonstate.edu). Physics Fun Other Resources Problem Solving Guide Use the Tips and Tricks below to support your post-lecture study. 1. The index of refraction is quite often used to determine how much light rays bend upon moving from one material to another. The changing directions effect is a direct consequence of the light changing effective speeds. So the first question is if the problem is about light bending at an interface or is about it changing speeds. If its about changing directions, see Snell's Law of 2. Determine if the index of refraction is increasing or decreasing so that you know if the speed is increasing or decreasing. 3. If the problem involves wavelengths and frequencies, you may have to use the equation $v=f \lambda$. You may also have to use the fact that the frequency is constant accross a border, the wavelength and speed are not. 4. Solve for the desired quantity. (1) Sketch out the standard representation for thin-film interference: two horizontal lines, representing 3 separate media. Label on this sketch the indices of refraction of the three media. The middle medium is the "thin film." (2) Determine the wavelength $\lambda_2$ of your wave inside of the thin film. Remember that maximum constructive interference has to do with whether or not some integer-number of wavelengths fit into some distance, so it is important to know what the wavelength is inside of the medium in which the path-length-difference occurs - which, if you use the standard sketch, is always the middle (or second) medium. (3a) Determine which equation is appropriate for describing constructive interference. To do this, determine whether or not there is a relative phase-shift between the two waves that are interfering. Remember that, at every boundary, some light is transmitted while some is reflected. The reflected light will have a $\pi$ phase-shift if the index of refraction of the medium the wave is traveling into is greater than that which it is leaving. Using the standard sketch, this means the wave reflected off the top surface will have a phase-shift iff $n_2 > n_1$ and the wave reflected off the second surface will have a phase-shift iff $n_3 >n_2$. Transmitted light does not undergo a phase-shift. (3b) If there is a $\pi$ relative phase shift, then: • constructive interference is described by $2t = \left(m + \frac{1}{2}\right) \lambda $, where $t$ is the thickness of the thin film and $\lambda$ is the wavelength of the light within the thin film (so here it takes the value of $\lambda_2$ calculated above, but I have left it as $\lambda$ to be consistent with other resources). • destructive interference is described by $2t = m \lambda$ If there is no relative phase shift between the two waves, then the equations are swapped and $2t = m \lambda$ corresponds to constructive and $2t = \left( m + \frac{1}{2} \right) \lambda$ corresponds to destructive interference. You now have all of the variables you need to finish the problem. Depending on the problem, you may be asked for a couple of different things. One might be a "minimum thickness" - in this case, you want to find the minimum possible value you can find for $t$, which corresponds to the smallest possible $m$ value (usually either $0$ or $1$). Or, you may be asked what wavelengths would produce destructive or constructive interference given some thickness - which is as simple as solving $2t = m \lambda$ for $t$ (or the other equation, depending on the situation). Once you have gone through step 3 above, you have all of the info that can be gleaned algorithmically: the rest is down to correctly interpreting the individual problem and what it is asking for. Misconceptions & Mistakes • ... treat the wavelength as the constant across a boundary. Frequency is what is constant across a boundary. • ... try and use Snell's Law for problems that only involve speed or wavelength changes. If the problem does not involve the bending of light, you do not need to use Snell's Law. • ... believe that a light photon actually travels slower than c. In reality if a photon (bundle of light) exists, it travels at c. In a medium there is vacuum between the atoms and that is where the photons exist. The interaction with the atoms in the medium, via mechanisms like scattering, is what makes the light take longer to travel the same overall distance. • ... read too much into the statement above. You can just treat the light like it's moving slower than c. • There is not one simple equation for thin-film interference - the conditions for maximum and minimum interference change based on the parameters of the problem. You must first determine if there are relative phase shifts! Pro Tips • Sketch a simple physical representation where the wavelength of the light changes and the speeds are labeled on each side of the boundary. • Memorize $v=f \lambda$ and $n=\frac{c}{v_{eff}}$ • Frequency is a property of the source, not the medium. Frequency does not change across a boundary. • Index of Refraction related to speed changes is taught briefly before Thin Film Interference so that you can find the wavelength in the film. If it wasn't for TFI, it would be taught in junction with Snell's Law of Refraction where it is often used as well. • It's not too hard to use the concept of the speed changing across a boundary, coupled with the frequency not changing, to find the change in the wavelength. That feature, along with speed is distance over time and some geometry, makes deriving Snell's Law as a consequence of the speed changing very doable. Go through that derivation and you will have effectively mastered the concept of the index of refraction (at an introductory physics level). • Always draw the same picture for thin-film interference problem: two horizontal lines, labeling the indices of refraction of the different media. This will help you get your bearings on the problem and get most of the relevant information on the page • Being good at thin-film interference problems is all about identifying phase-shifts, since understanding the relative phase-shift between two waves is what dictates which equations to use. Always find phase-shifts first, if you are able, before continuing on the problem. Multiple Representations Multiple Representations is the concept that a physical phenomena can be expressed in different ways. Physical Representations describes the physical phenomena of the situation in a visual way. Physical Representations describes the physical phenomena of the situation in a visual way. Mathematical Representation uses equation(s) to describe and analyze the situation. Graphical Representation describes the situation through use of plots and graphs. Descriptive Representation describes the physical phenomena with words and annotations. Experimental Representation examines a physical phenomena through observations and data measurement. Fundamental examples (1) Light with a wavelength $\lambda = 88.7 MHz $ is broadcast through a medium with an index of refraction $ n = 3$. What is the wave speed of the broadcast? (2) An electromagnetic wave traveling through a medium with index of refract $n= 8$ has a wavelength $\lambda = 1.8 nm$. What is its wavelength in vacuum? (3) You are floating in a pool. Your friend thinks he is such a fast swimmer that he can beat light in a race to the other end of the pool. (your friend is not smart). The pool is 100 m long and you are at one end of it. You have a red laser pointer ($\lambda_{vac} = 700 nm$). (a) If you shine the laser pointer, underwater, long will it take for light to travel down the length of the pool? Your friend swims at a rate of 5 m/s. (b) Who will win the race? Water has an index of refraction $n_w = 1.33$. Solutions found HERE Short foundation building questions, often used as clicker questions, can be found in the clicker questions repository for this subject. (1) Green light with a wavelength $\lambda_{green} = 500 nm$ shines on a soap film (n = 1.33) that has air on either side of it. The light strikes the film perpendicularly. What is the minimum thickness of the film for which an observer would see maximum constructive interference? (2) Orange light with a wavelength $\lambda_{OJ} = 600 nm $ shines on a soap film ($n_{soap}= 1.33$) that is resting on oil ($n_{oil} = 14 $). The top of the soap film is open to the air. What is the minimum thickness of the film for which an observer standing directly overhead would see maximum constructive interference? (3) A glass coverslip is floating on oil in a beaker that is open to the air. The index of refraction for the glass is $n_{glass} = 2.5$ and the refractive index of the oil is $n_{oil} = 18$. Janet wants to measure the minimum thickness of the glass so she sets up a laser that will shoot light normally incident to the surface of the coverslip. The laser is capable of scanning through different wavelengths, and through clever experimentation Janet measures that the minimum thickness of the glass is 114 nm. What are two wavelengths at which Janet measured maximum constructive interference? Solutions found HERE. Short foundation building questions, often used as clicker questions, can be found in the clicker questions repository for this subject. Practice Problems Conceptual problems BoxSand's multiple select problems BoxSand's quantitative problems Recommended example practice problems • Openstax has practice problems toward the end of each section, Website Link For additional practice problems and worked examples, visit the link below. If you've found example problems that you've used please help us out and submit them to the student contributed content	{"url":"https://boxsand.physics.oregonstate.edu/wave-optics-index-refraction-thin-film-interference","timestamp":"2024-11-05T02:37:51Z","content_type":"text/html","content_length":"85415","record_id":"<urn:uuid:5608a36a-8f3a-40c3-834c-2d843c710655>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00365.warc.gz"}
Gas oil ratio calculation formula Figure 3 is a semi-log plot of the gas-oil ratio history to enable proper visibility of the various critical points of production mechanism of shale volatile oil reservoirs. KPIM of Gas/Condensate Productivity: Prediction of Condensate/Gas Ratio Using of gas condensate wells and calculating Condensate Gas Ratio (CGR), using in gas condensate reservoirs and gas liberation in volatile oil reservoirs are 17 Feb 2016 The basic equation used to calculate recoverable oil reserves is inital solution gas-oil ratio (SCFstandard cubic feet/STBstock tank barrels) 11 Jan 2020 Reserve-replacement ratio is the amount of oil added to a company's reserves year, relative to the amount of oil and gas that the company has produced. Any figure greater than 100% likely indicates that the company has 15 Dec 2019 (a) Any oil well producing with a gas-oil ratio in excess of 2,000 cubic feet of its maximum daily oil allowable, as determined by the allocation formula (A) the gas well allowable as calculated by paragraph (1) or (2) of this 4. Laboratory measurement of the. Gas-Oil-Ratio (GOR) from a. Pressurized Liquid Sample. Flash only. This is direct laboratory analysis of the flash gas emitted PVT reports often lists separator corrected Gas/Oil Ratios (GORs), Gas and Oil Formation Volume Figure 1 sketches a DL PVT experiments in a PT diagram. Calculate gas oil ratio GOR and density from oil volume flow rate and gas mole flow rate for two phase oil and gas fluids. GOR is the ratio of gas moles over oil volume. Gas moles are commonly measured as gas volume at standard conditions (eg SCF or SCM). Divide the ounces of gas by the gas-to-oil ratio number in your owner's manual and round the answer to the nearest whole or half number. For example, a 40:1 ratio is 128 ounces divided by 40, which is 3.2, rounded to 3 ounces, needed of 2-cycle oil for 1 gallon of gas. Up until 2009, the oil price to natural gas averaged 10:1, meaning when oil was at $50 a barrel, natural gas would be at $5 per MMBtu. The higher the oil price to natural gas ratio, the greater the demand for oil. If the ratio declines, then the difference in the prices of the two commodities is narrowing. Estimation of Gas Oil Ratio. (PDF Available) in Petroleum and Coal 58(4):539-550 · January 2016 with 1,488 Reads. How we measure 'reads'. A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Select Type of Conversion (Basic, Gas, Fluid, etc.) 2. Select Type of Unit from the drop down 3. Select From Unit and To Unit 4. Enter value for known Unit 5. Click on Convert Divide the ounces of gas by the gas-to-oil ratio number in your owner's manual and round the answer to the nearest whole or half number. For example, a 40:1 17 Feb 2016 The basic equation used to calculate recoverable oil reserves is inital solution gas-oil ratio (SCFstandard cubic feet/STBstock tank barrels) 11 Jan 2020 Reserve-replacement ratio is the amount of oil added to a company's reserves year, relative to the amount of oil and gas that the company has produced. Any figure greater than 100% likely indicates that the company has 15 Dec 2019 (a) Any oil well producing with a gas-oil ratio in excess of 2,000 cubic feet of its maximum daily oil allowable, as determined by the allocation formula (A) the gas well allowable as calculated by paragraph (1) or (2) of this Norwegian Oil and Gas: Guidance on calculating blowout rates and duration for use Similarly, a higher gas-oil ratio (GOR) can lead to more oil on the sea than (1) The average daily oil rate, gas-oil and water-oil ratios for each month table showing the data elements used for calculation of the monthly and cumulative VRR (see. Appendix A). 4. using a volume weighted average formula . 5. gaseous compounds and a Gas-Oil-Ratio or Gas-Water-Ratio. The laboratory results are applied to the annual liquid production rates to calculate Greenhouse. contact the webmaster. Gas Oil Mixture Ratio Calculator. Enter the volume of Gas (petrol): U.S. Gallons \| U.K. Gallons \| Metric Liters. Enter the desired Ratio: :1 Regulation: The Oil and Gas Conservation Regulations, 2012. Order: 499/15 Wells (cont.) 12. Appendix 3: Calculating Net Productive Area . Figure 3 is a semi-log plot of the gas-oil ratio history to enable proper visibility of the various critical points of production mechanism of shale volatile oil reservoirs. Estimation of Gas Oil Ratio. (PDF Available) in Petroleum and Coal 58(4):539-550 · January 2016 with 1,488 Reads. How we measure 'reads'. A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. A ratio (gas to oil ratio) is calculated which lets the analysts know how much gas is produced along with the oil. More specifically, gas to oil ratio is the amount of gas produced from hydrocarbon solution to the volume of oil at standard conditions. Calculate gas oil ratio GOR and density from oil volume flow rate and gas mole flow rate for two phase oil and gas fluids. GOR is the ratio of gas moles over oil volume. Gas moles are commonly measured as gas volume at standard conditions (eg SCF or SCM). Divide the ounces of gas by the gas-to-oil ratio number in your owner's manual and round the answer to the nearest whole or half number. For example, a 40:1 ratio is 128 ounces divided by 40, which is 3.2, rounded to 3 ounces, needed of 2-cycle oil for 1 gallon of gas. Up until 2009, the oil price to natural gas averaged 10:1, meaning when oil was at $50 a barrel, natural gas would be at $5 per MMBtu. The higher the oil price to natural gas ratio, the greater the demand for oil. If the ratio declines, then the difference in the prices of the two commodities is narrowing. Estimation of Gas Oil Ratio. (PDF Available) in Petroleum and Coal 58(4):539-550 · January 2016 with 1,488 Reads. How we measure 'reads'. A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Select Type of Conversion (Basic, Gas, Fluid, etc.) 2. Select Type of Unit from the drop down 3. Select From Unit and To Unit 4. Enter value for known Unit 5. Click on Convert (1) The average daily oil rate, gas-oil and water-oil ratios for each month table showing the data elements used for calculation of the monthly and cumulative VRR (see. Appendix A). 4. using a volume weighted average formula . 5. gaseous compounds and a Gas-Oil-Ratio or Gas-Water-Ratio. The laboratory results are applied to the annual liquid production rates to calculate Greenhouse. contact the webmaster. Gas Oil Mixture Ratio Calculator. Enter the volume of Gas (petrol): U.S. Gallons \| U.K. Gallons \| Metric Liters. Enter the desired Ratio: :1 Regulation: The Oil and Gas Conservation Regulations, 2012. Order: 499/15 Wells (cont.) 12. Appendix 3: Calculating Net Productive Area . Figure 3 is a semi-log plot of the gas-oil ratio history to enable proper visibility of the various critical points of production mechanism of shale volatile oil reservoirs. KPIM of Gas/Condensate Productivity: Prediction of Condensate/Gas Ratio Using of gas condensate wells and calculating Condensate Gas Ratio (CGR), using in gas condensate reservoirs and gas liberation in volatile oil reservoirs are	{"url":"https://bestoptionsyupc.netlify.app/rendina7321hure/gas-oil-ratio-calculation-formula-204","timestamp":"2024-11-08T07:59:20Z","content_type":"text/html","content_length":"36143","record_id":"<urn:uuid:d8256b38-db2a-4625-9dca-6a98d09e4c84>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00517.warc.gz"}
Heterogeneity in meta-analysis - Science without sense... Apples and pears Study of heterogeneity in meta-analysis. Numerical (Q, I, H) and graphical methods (Galbraith and L’Abbé) for the study of heterogeneity of the primary meta-analysis studies. You all sure know the Chinese tale of the poor solitary rice grain that falls to the ground and nobody can hear it. Of course, if instead of falling a grain it falls a sack full of rice that will be something else. There are many examples of union making strength. A red ant is harmless, unless it bites you in some soft and noble area, which are usually the most sensitive. But what about a marabout of millions of red ants? That is what scares you up, because if they all come together and come for you, you could do little to stop their push. Yes, the union is strength. And this also happens with statistics. With a relatively small sample of well-chosen voters we can estimate who will win an election in which millions vote. So, what could we not do with a lot of those samples? Surely the estimate would be more reliable and more generalizable. Turning to substance Well, this is precisely one of the purposes of meta-analysis, which uses various statistical techniques to make a quantitative synthesis of the results of a set of studies that, although try to answer the same question, do not reach exactly to the same result. But beware; we cannot combine studies to draw conclusions about the sum of them without first taking a series of precautions. This would be like mixing apples and pears which, I’m not sure why, should be something terribly dangerous because everyone knows it’s something to avoid. Think that we have a set of clinical trials on the same topic and we want to do a meta-analysis to obtain a global result. It is more than convenient that there is as little variability as possible among the studies if we want to combine them. Because, ladies and gentlemen, here also rules the saying: alongside but separate. Before thinking about combining the results of the studies of a systematic review to perform a meta-analysis, we must always make a previous study of the heterogeneity of the primary studies, which is nothing more than the variability that exists among the estimators that have been obtained in each of those studies. Study of heterogeneity in meta-analysis First, we will investigate possible causes of heterogeneity, such as differences in treatments, variability of the populations of the different studies and differences in the designs of the trials. If there is a great deal of heterogeneity from the clinical point of view, perhaps the best thing to do is not to do meta-analysis and limit the analysis to a qualitative synthesis of the results of the review. Once we come to the conclusion that the studies are similar enough to try to combine them we should try to measure this heterogeneity to have an objective data. For this, several privileged brains have created a series of statistics that contribute to our daily jungle of acronyms and letters. We start with the letters Until recently, the most famous of those initials was the Cochran’s Q, which has nothing to do either with James Bond or our friend Archie Cochrane. Its calculation takes into account the sum of the deviations between each of the results of primary studies and the global outcome (squared differences to avoid positives cancelling negatives), weighing each study according to their contribution to overall result. It looks awesome but in reality, it is no big deal. Ultimately, it’s no more than an aristocratic relative of ji-square test. Indeed, Q follows a ji-square distribution with k-1 degrees of freedom (being k the number of primary studies). We calculate its value, look at the frequency distribution and estimate the probability that differences are not due to chance, in order to reject our null hypothesis (which assumes that observed differences among studies are due to chance). But, despite the appearances, Q has a number of weaknesses. First, it’s a very conservative parameter and we must always keep in mind that no statistical significance is not always synonymous of absence of heterogeneity: as a matter of fact, we cannot reject the null hypothesis, so we have to know that when we approved it we are running the risk of committing a type II error and blunder. For this reason, some people propose to use a significance level of p < 0.1 instead of the standard p < 0.5. Another Q’s pitfall is that it doesn’t quantify the degree of heterogeneity and, of course, doesn’t explain the reasons that produce it. And, to top it off, Q loses power when the number of studies is small and doesn’t allow comparisons among different meta-analysis if they have different number of studies. This is why another statistic has been devised that is much more celebrated today: I^2. This parameter provides an estimate of total variation among studies with respect to total variability or, put it another way, the proportion of variability actually due to heterogeneity for actual differences among the estimates compared with variability due to chance. It also looks impressive, but it’s actually an advantageous relative of the intraclass correlation coefficient. Its value ranges from 0 to 100%, and we usually consider the limits of 25%, 50% and 75% as signs of low, moderate and high heterogeneity, respectively. I^2 is not affected either by the effects units of measurement or the number of studies, so it allows comparisons between meta-analysis with different units of effect measurement or different number of studies. If you read a study that provides Q and you want to calculate I^2, or vice versa, you can use the following formula, being k the number of primary studies: There’s a third parameter that is less known, but not less worthy of mention: H^2. It measures the excess of Q value in respect of the value that we would expect to obtain if there were no heterogeneity. Thus, a value of 1 means no heterogeneity and its value increases as heterogeneity among studies does. But its real interest is that it allows calculating I^2 confidence intervals. Other times, the authors perform a hypothesis contrast with a null hypothesis of non-heterogeneity and use a ji-square or some similar statistic. In these cases, what they provide is a value of statistical significance. If the p is <0.05 the null hypothesis can be rejected and say that there is heterogeneity. Otherwise we will say that we cannot reject the null hypothesis of In summary, whenever we see an indicator of homogeneity that represents a percentage, it will indicate the proportion of variability that is not due to chance. For their part, when they give us a “p” there will be significant heterogeneity when the “p” is less than 0.05. Do not worry about the calculations of Q, I^2 and H^2. For that there are specific programs as RevMan or modules within the usual statistical programs that do the same function. Graphical methods for studying heterogeneity in meta-analysis A point of attention: always remember that not being able to demonstrate heterogeneity does not always mean that the studies are homogeneous. The problem is that the null hypothesis assumes that they are homogeneous and the differences are due to chance. If we can reject it we can assure that there is heterogeneity (always with a small degree of uncertainty). But this does not work the other way around: if we cannot reject it, it simply means that we cannot reject that there is no heterogeneity, but there will always be a probability of committing a type II error if we directly assume that the studies are homogeneous. For this reason, a series of graphical methods have been devised to inspect the studies and verify that there is no data of heterogeneity even if the numerical parameters say otherwise. The most employed of them is, perhaps, the , with can be used for both meta-analysis from trials or observational studies. This graph represents the accuracy of each study versus the standardize effects. It also shows the adjusted regression line and sets two confidence bands. The position of each study regarding the accuracy axis indicates its weighted contribution to overall results, while its location outside the confidence bands indicates its contribution to heterogeneity. Galbraith’s graph can also be useful for detecting sources of heterogeneity, since studies can be labeled according to different variables and see how they contribute to the overall heterogeneity. Another available tool you can use for meta-analysis of clinical trials is L’Abbé’s plot. It represents response rates to treatment versus response rates in control group, plotting the studies to both sides of the diagonal. Above that line are studies with positive treatment outcome, while below are studies with an outcome favorable to control intervention. The studies usually are plotted with an area proportional to its accuracy, and its dispersion indicates heterogeneity. Sometimes, L’Abbé’s graph provides additional information. For example, in the accompanying graph you can see that studies in low-risk areas are located mainly below the diagonal. On the other hand, high-risk studies are mainly located in areas of positive treatment outcome. This distribution, as well as being suggestive of heterogeneity, may suggest that efficacy of treatments depends on the level of risk or, put another way, we have an effect modifying variable in our study. A small drawback of this tool is that it is only applicable to meta-analysis of clinical trials and when the dependent variable is dichotomous. We must weight each study Well, suppose we study heterogeneity and we decide that we are going to combine the studies to do a meta-analysis. The next step is to analyze the estimators of the effect size of the studies, weighing them according to the contribution that each study will have on the overall result. This is logical; it cannot contribute the same to the final result a trial with few participants and an imprecise result than another with thousands of participants and a more precise result measure. The most usual way to take these differences into account is to weight the estimate of the size of the effect by the inverse of the variance of the results, subsequently performing the analysis to obtain the average effect. For these there are several possibilities, some of them very complex from the statistical point of view, although the two most commonly used methods are the fixed effect model and the random effects model. Both models differ in their conception of the starting population from which the primary studies of meta-analysis come. Two models The fixed effect model considers that there is no heterogeneity and that all studies estimate the same effect size of the population (they all measure the same effect, that is why it is called a fixed effect), so it is assumed that the variability observed among the individual studies is due only to the error that occurs when performing the random sampling in each study. This error is quantified by estimating intra-study variance, assuming that the differences in the estimated effect sizes are due only to the use of samples from different subjects. On the other hand, the random effects model assumes that the effect size varies in each study and follows a normal frequency distribution within the population, so each study estimates a different effect size. Therefore, in addition to the intra-study variance due to the error of random sampling, the model also includes the variability among studies, which would represent the deviation of each study from the mean effect size. These two error terms are independent of each other, both contributing to the variance of the study estimator. In summary, the fixed effect model incorporates only one error term for the variability of each study, while the random effects model adds, in addition, another error term due to the variability among the studies. You see that I have not written a single formula. We do not actually need to know them and they are quite unfriendly, full of Greek letters that no one understands. But do not worry. As always, statistical programs like RevMan from the Cochrane Collaboration allow you to do the calculations in a simple way, including and removing studies from the analysis and changing the model as you wish. The type of model to choose has its importance. If in the previous homogeneity analysis we see that the studies are homogeneous we can use the fixed effect model. But if we detect that heterogeneity exists, within the limits that allow us to combine the studies, it will be preferable to use the random effects model. Another consideration is the applicability or external validity of the results of the meta-analysis. If we have used the fixed effect model, we will be committed to generalize the results out of populations with characteristics similar to those of the included studies. This does not occur with the results obtained using the random effects model, whose external validity is greater because it comes from studies of different populations. In any case, we will obtain a summary effect measure along with its confidence interval. This confidence interval will be statistically significant when it does not cross the zero effect line, which we already know is zero for mean differences and one for odds ratios and risk ratios. In addition, the amplitude of the interval will inform us about the precision of the estimation of the average effect in the population: how much wider, less precise, and vice versa. If you think a bit, you will immediately understand why the random effects model is more conservative than the fixed effect model in the sense that the confidence intervals obtained are less precise, since it incorporates more variability in its analysis. In some cases it may happen that the estimator is significant if we use the fixed effect model and it is not significant if we use the random effect model, but this should not condition us when choosing the model to use. We must always rely on the previous measure of heterogeneity, although if we have doubts, we can also use the two models and compare the different results. What if there is heterogeneity? Having examined the homogeneity of primary studies we can come to the grim conclusion that heterogeneity dominates the situation. Can we do something to manage it? Sure, we can. We can always not to combine the studies, or combine them despite heterogeneity and obtain a summary result but, in that case, we should also calculate any measure of variability among studies and yet we could not be sure of our results. Another possibility is to do a stratified analysis according to the variable that causes heterogeneity, provided that we are able to identify it. For this we can do a sensitivity analysis, repeating calculations once removing one by one each of the subgroups and checking how it influences the overall result. The problem is that this approach ignores the final purpose of any meta-analysis, which is none than obtaining an overall value of homogeneous studies. Finally, the brainiest on these issues can use meta-regression. This technique is similar to multivariate regression models in which the characteristics of the studies are used as explanatory variables, and effect’s variable or some measure of deviation of each study with respect to global result are used as dependent variable. Also, it should be done a weighting according to the contribution of each study to the overall result and try not to score too much coefficients to the regression model if the number of primary studies is not large. I wouldn’t advise you to do a meta-regression at home if it is not accompanied by seniors. We´re leaving… And we only need to check that we have not omitted studies and that we have presented the results correctly. The meta-analysis data are usually represented in a specific graph that is known as forest plot. But that is another story… Your email address will not be published. Required fields are marked * Información básica sobre protección de datos Ver más • Responsable: Manuel Molina Arias. • Finalidad: Moderar los comentarios. • Legitimación: Por consentimiento del interesado. • Destinatarios y encargados de tratamiento: No se ceden o comunican datos a terceros para prestar este servicio. El Titular ha contratado los servicios de alojamiento web a Aleph que actúa como encargado de tratamiento. • Derechos: Acceder, rectificar y suprimir los datos. • Información Adicional: Puede consultar la información detallada en la Política de Privacidad. This site uses Akismet to reduce spam. Learn how your comment data is processed.	{"url":"https://www.cienciasinseso.com/en/heterogeneity-in-meta-analysis-2/","timestamp":"2024-11-11T13:38:50Z","content_type":"text/html","content_length":"88642","record_id":"<urn:uuid:98f540ff-e6a4-401f-ac5e-2fffd3cd2c88>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00476.warc.gz"}
Pull an Inverted Mug from the Water NAEST 2019 Screening Test: Pull an Inverted Mug from the Water Jitender Singh Immerse a mug in the bucket of water and invert it i.e., make the mug upside down. Now, hold the mug from its bottom side and starts pulling it up. The force applied by the hand is very small when the mug is completely immersed in the water. This force increases as the mug start coming out of the water. Let us explain this observation. Question: The mass of the empty plastic mug is a few grams. The boy is struggling hard to pull the inverted mug from the bucket of water. Assume that the boy pulls up the mug very slowly. Choose the correct option(s) A. The adhesive forces between mug and water are responsible for the high pulling force by the boy. B. The pulling force by the boy increases linearly with height of the mug above the water surface. C. The atmospheric air pushes the mug downwards and the air (trapped) in the mug pushes the mug upwards. The difference between these forces is approximately equal to the pulling force by the boy. D. The boy is lying, it is very easy to pull the mug. Solution: Let $\rho$ be the density of the water and $h_0$ be the total height of the mug of the cross-sectional area $A$. The mug is completely filled with water because it is inverted after immersing it in the water. However, there is a small amount of air trapped inside the mug near its base. The volume of this air is very small. Let height $h$ of the mug is outside the water. Let $p_0$ be atmospheric pressure and $p$ be the pressure of the trapped air (when the height $h$ of the mug is outside the water). The forces acting on the mug are 1. The force applied by the hand ($F$) in the upward direction 2. The gravitational pull ($mg$) in the downward direction 3. The force due to atmospheric air ($p_0A$) in the downward direction 4. The force due to trapped air ($pA$) in the upward direction The force in the horizontal direction (due to water and air) cancels out due to symmetry. The acceleration of the mug is zero because it is pulled out slowly at a constant speed (assumed). Thus, the net force on the mug is zero i.e., F=(p_0-p)A+mg The pressure of trapped air $p$ is equal to the difference of atmospheric pressure and hydrostatic pressure due to water column above the water surface i.e., p=p_0-\rho g h Eliminate $p$ from the above equations to get F=\rho g h + mg Thus, applied force increases linearly with the height of the mug above the water surface. This force attains a maximum value $\rho g h_0+mg$ i.e., the weight of the mug completely filled with water. After that, the air enters into the mug and the water spills out. Related Topics	{"url":"https://www.concepts-of-physics.com/anveshika/naest-2019-inverted-mug-in-water.php","timestamp":"2024-11-14T17:54:23Z","content_type":"text/html","content_length":"15508","record_id":"<urn:uuid:c4505a45-e3b2-45af-9c6b-d5fc7e87153f>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00835.warc.gz"}
CampusGate: Averages 1/3Averages 1/3 The average weight of the students of a class is 40 kgs. 5 new students with the average weight of 46 kgs having joined the class, the average weight of the class is increased by 2 kg. Find the number of students in the class originally? a. 10 b. 12 c. 14 d. 16 Average temperature from ${9^{th}}$ to ${16^{th}}$ of a month is ${\rm{30}}^{\rm{o}} {\rm{C}}$ and that from ${10^{th}}$ to ${17^{th}}$ is ${\rm{31}}^{\rm{o}} {\rm{C}}$. What is the temperature on $ {17^{th}}$, if temperature on ${9^{th}}$ is ${\rm{35}}^{\rm{o}} {\rm{C}}$? a. 35 b. 37 c. 39 d. 43 The average of 11 observations is 72. If average of first 6 observations is 70 and that of last 6 observations is 71, then the 6th observation is: a. 51 b. 54 c. 55 d. 56 Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: a. 350 b. 370 c. 390 d. 430 11 friends went to a hotel and decided to pay the bill amount equally. But 10 of them could pay Rs. 60 each as a result 11th has to pay Rs. 50 extra than his share. Find the amount paid by him. a. 110 b. 111 c. 115 d. 123 The average marks obtained by some students in an examination is 54. If 20% of the students got a mean score of 90 marks and the 30% of the students got a mean score of 20. Find the average marks of the remaining students. a. 60 b. 62 c. 64 d. 66	{"url":"https://www.campusgate.in/2019/05/averages-1-3.html","timestamp":"2024-11-13T14:43:27Z","content_type":"application/xhtml+xml","content_length":"91348","record_id":"<urn:uuid:27b56301-8355-4acb-be4a-4abed1c585e0>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00487.warc.gz"}
Implicit and explicit dynamics in finite element analysis There are a large number of transient problems in the fields of engineering simulation and scientific computing, which requires appropriate time solvers to obtain solutions effectively and efficiently. Nowadays, we often classify numerical time solvers into two categories: implicit method and explicit method. Both methods have been supported in the structural simulation module of WELSIM. This article will discuss the basics and respective advantages of these two numerical methods. Implicit dynamics method The implicit method is a commonly used method in transient problem simulation. Thanks to the advantages in computational speed and numerical accuracy, implicit has been widely used in general simulations. The most notable feature of the implicit method is to construct and solve the ax=b linear algebra equations in each time step. If the governing equation contains nonlinear factors, a nonlinear solver such as a Newton iterative solver will also be applied. Therefore the implicit method is relatively complicated, it requires more computer memory and more complex software programming. Especially the parallel implementation is more complicated. The implicit method is the default transient solver in WELSIM. For highly nonlinear models, the Newton solver may experience solving difficulties and fail to converge. The advantage of implicit is that there is no need to consider numerical stability, and the time step can be set to a larger value, since the implicit time solvers are unconditionally stable. Besides, various residual convergence criteria ensure computational precision. The common implicit time solvers include Newmark, Hilber-Hughes-Taylor (HHT), Crank-Nicolson, etc. Explicit dynamics method The explicit method is simpler in terms of algorithm, and there is no need to construct linear algebra matrix equations, so there is no need to solve a large ax=b linear algebra equation system. For nonlinear problems, there is no need to use a nonlinear solver, and everything is calculated by a time solver. The explicit method is relatively simple to calculate, relatively easy to program and implement, and requires less hardware memory space. Moreover, it has natural advantages for parallel computing. It can achieve a good speed-up for parallel frameworks such as OpenMP, MPI, or GPU. It has a great convergence advantage for high-speed and high-rate-varying problems. However, the disadvantage is that a small time step must be used to meet the requirement of numerical stability. Common explicit solvers include: Runge-Kutta, central difference method, etc. Using the explicit method in WELSIM is straightforward, you only need to set the Explicit property to true and configure the OpenRadioss. Implicit and explicit are two completely different computational methods that determine different advantages in terms of applications. In general, for large rate change problems, such as large strain-rate problems in structural analysis, high-speed impact, and explosion problems, the explicit method has better solving capabilities. For strongly nonlinear problems, explicit methods can also be applied when the implicit solver fails to converge. However, due to the small time step, the overall computation of the explicit solver takes a long physical time. It is hoped that with the popularization of GPU clusters, the computational time can be significantly reduced through parallel computing. In addition, the accuracy of the explicit method is relatively low, compared with the implicit method. Currently, the best open-source explicit dynamics solver is OpenRadioss, which is fully functional and supports a large number of material models. WELSIM also uses OpenRadioss as the default explicit dynamics solver. For details, see the article “Run OpenRadioss solver for explicit dynamics analysis using WELSIM”. At the same time, the free software MatEditor also supports the generation of OpenRadioss material texts. For details, see the article “Using MatEditor to generate OpenRadioss material data files”. WelSim and the author are not affiliated with the Altair or OpenRadioss team. OpenRadioss is used only as nominative references to the open-source project and software developed and released by the OpenRadioss team. WelSimulation LLC is an independent engineering simulation technology provider, located in Greater Pittsburgh, PA. Its flagship product WESLIM is a general-purpose engineering simulation software with an all-in-one graphical user interface and self-integrated features.	{"url":"https://welsim.com/2023/02/27/implicit-and-explicit-dynamics-in-finite-element-analysis.html","timestamp":"2024-11-12T13:53:04Z","content_type":"text/html","content_length":"21274","record_id":"<urn:uuid:4dcec775-523e-498f-9ba8-c9144dd4f052>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00538.warc.gz"}
Abstract: We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the the probabilistic quantum class BQP: • BQP is low for PP, i.e., PP^BQP=PP. • There exists a relativized world where P=BQP and the polynomial-time hierarchy is infinite. • There exists a relativized world where P=BQP but P <> UP intersect coUP and one-way functions exist. This gives a relativized answer to an open question of Simon.	{"url":"http://facweb.cs.depaul.edu/research/TechReports/abstract97003.htm","timestamp":"2024-11-14T05:06:50Z","content_type":"text/html","content_length":"1983","record_id":"<urn:uuid:e1f263b4-f88b-49ab-99b0-c2806fed1b3e>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00725.warc.gz"}
Let $X$ be a cell complex obtained by attaching a 2-cell to a finite bouquet of circles (for example, a closed surface). In terms of the combinatorial type of the attaching map, the paper gives conditions for the existence of a fixed point free (topological) homeomorphism of the complex $X$. Also, quotients of finite group actions on such complexes are considered as well as a condition under which the induced actions on cohomology are trivial.	{"url":"https://dml.cz/handle/10338.dmlcz/701545","timestamp":"2024-11-03T19:47:25Z","content_type":"text/html","content_length":"12390","record_id":"<urn:uuid:703e29c0-93fc-4d62-9a7f-94e952757c9c>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00286.warc.gz"}
Sample Page - Codepect Can you Backtrack Your Life? In this chapter, we will look at one of the important topics, “recursion”, which will be used in almost every chapter, and also its relative “backtracking”. Any function which calls itself is called recursive. A recursive method solves a problem by calling a copy of itself to work on a smaller problem. This is called the recursion step. The recursion step can result in many more such recursive calls. . It is important to ensure that the recursion terminates. Each time the function calls itself with a slightly simpler version of the original problem. The sequence of smaller problems must eventually converge on the base case. . 4.3 Why we Need Recursion ? Recursion is a useful technique borrowed from mathematics. Recursive code is generally shorter and easier to write than iterative code. Generally, loops are turned into recursive functions when they are compiled or interpreted. Recursion is most useful for tasks that can be defined in terms of similar subtasks. For example, sort, search, and traversal problems often have simple recursive solutions. 4.4 Format of Recursive Function A recursive function performs a task in part by calling itself to perform the subtasks. At some point, the function encounters a subtask that it can perform without calling itself. This case, where the function does not recur, is called the base case. The former, where the function calls itself to perform a subtask, is referred to as the ecursive case. We can write all recursive functions using the format: if(test for the best case) return some base case values else if(test for another base case) return some other base case values //recursive case return(bother work then recursive call); As an example consider the factorial function: n! is the product of all integers between n and 1. The definition of recursive factorial looks like: n!=0 if n=0 n!=n(n-1) ! if n > 0 This definition can easily be converted to recursive implementation. Here the problem is determining the value of n!, and the subproblem is determining the value of (n – l)!. In the recursive case, when n is greater than 1, the function calls itself to determine the value of (n – l)! and multiplies that with n. In the base case, when n is 0 or 1, the function simply returns 1. This looks like the following: // calculates factorial of a positive integer int Fact(int n) { if(n == 1) // base cases: fact of 0 or 1 is 1 return 1; else if(n return 1; else // recursive case: multiply n by (n-1) factorial return nFact(n-1); 4.5 Recursion and Memory (Visualization) Each recursive call makes a new copy of that method (actually only the variables) in memory. Once a method ends (that is, returns some data), the copy of that returning method is removed from memory. The recursive solutions look simple but visualization and tracing takes time. For better understanding, let us consider the following example. //print numbers 1 to n backward int Print(int n) { if(n ==0) // this is the terminating base case return 0; return Print(n-1); // recursive call to itself again For this example, if we call the print function with n=4, visually our memory assignments may look like: Now, let us consider our factorial function. The visualization of factorial function with n=4 will look like: 4.6 Recursion versus Iteration While discussing recursion, the basic question that comes to mind is: which way is better? – iteration or recursion? The answer to this question depends on what we are trying to do. A recursive approach mirrors the problem that we are trying to solve. A recursive approach makes it simpler to solve a problem that may not have the most obvious of answers. But, recursion adds overhead for each recursive call (needs space on the stack frame). Terminates when a base case is reached. • Each recursive call requires extra space on the stack frame (memory). • If we get infinite recursion, the program may run out of memory and result in stack overflow. • Solutions to some problems are easier to formulate recursively. Terminates when a condition is proven to be false. • Each iteration does not require extra space. • An infinite loop could loop forever since there is no extra memory being created. • Iterative solutions to a problem may not always be as obvious as a recursive solution. Recursive algorithms have two types of cases, recursive cases and base cases. • Every recursive function case must terminate at a base case. • Generally, iterative solutions are more efficient than recursive solutions [due to the overhead of function calls]. • A recursive algorithm can be implemented without recursive function calls using a stack, but it’s usually more trouble than its worth. That means any problem that can be solved recursively can also be solved iteratively. • For some problems, there are no obvious iterative algorithms. • Some problems are best suited for recursive solutions while others are not. 4.8 Example Algorithms of Recursion Fibonacci Series, Factorial Finding • Merge Sort, Quick Sort • Binary Search • Tree Traversals and many Tree Problems: InOrder, PreOrder PostOrder • Graph Traversals: DFS [Depth First Search] and BFS [Breadth First Search] • Dynamic Programming Examples • Divide and Conquer Algorithms • Towers of Hanoi • Backtracking Algorithms [we will discuss in next section] 4.9 Recursion: Problems & Solutions In this chapter we cover a few problems with recursion and we will discuss the rest in other chapters. By the time you complete reading the entire book, you will encounter many recursion problems. Discuss Towers of Hanoi puzzle. The Towers of Hanoi is a mathematical puzzle. It consists of three rods (or pegs or towers), and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks on one rod in ascending order of size, the smallest at the top, thus making a conical shape. The objective of the puzzle is to move the entire stack to another rod, satisfying the following rules: Only one disk may be moved at a time. • Each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod. • No disk may be placed on top of a smaller disk. Move the top n – 1 disks from Source to Auxiliary tower, • Move the n th disk from Source to Destination tower, • Move the n – 1 disks from Auxiliary tower to Destination tower. • Transferring the top n – 1 disks from Source to Auxiliary tower can again be thought of as a fresh problem and can be solved in the same manner. Once we solve Towers of Hanoi with three disks, we can solve it with any number of disks with the above algorithm. void Towers OfHanoi(int n, char frompeg, char topeg, char auxpeg){ / If only 1 disk, make the move and return / printf("Move disk 1 from peg %c to peg %c", frompeg, topeg); return; / Move top n-1 disks from A to B, using C as auxiliary / Towers OfHanoi(n-1, frompeg, auxpeg, topeg); / Move remaining disks from A to C / printf("\nMove disk %d from peg %c to peg %c", n, frompeg, topeg); / Move n-1 disks from B to C using A as auxiliary / Towers OfHanoi(n-1, auxpeg, topeg, frompeg); Given an array, check whether the array is in sorted order with recursion. int isArrayInSortedOrder(int Al],int n) if(n == 1) return 1; return (A[n-1] < A[n-2]?0:isArrayInSortedOrder(A,n-1); Time Complexity: O(n). Space Complexity: O(n) for recursive stack space. 4.10 What is Backtracking? Backtracking is an improvement of the brute force approach. It systematically searches for a solution to a problem among all available options. In backtracking, we start with one possible option out of many available options and try to solve the problem if we are able to solve the problem with the selected move then we will print the solution else we will backtrack and select some other option and try to solve it. If none if the options work out we will claim that there is no solution for the problem. Backtracking is a form of recursion. The usual scenario is that you are faced with a number of options, and you must choose one of these. After you make your choice you will get a new set of options; just what set of options you get depends on what choice you made. This procedure is repeated over and over until you reach a final state. If you made a good sequence of choices, your final state is a goal state; if you didn’t, it isn’t. Backtracking can be thought of as a selective tree/graph traversal method. The tree is a way of representing some initial starting position (the root node) and a final goal state (one of the leaves). Backtracking allows us to deal with situations in which a raw brute-force approach would explode into an impossible number of options to consider. Backtracking is a sort of refined brute force. At each node, we eliminate choices that are obviously not possible and proceed to recursively check only those that have potential. What’s interesting about backtracking is that we back up only as far as needed to reach a previous decision point with an as-yet-unexplored alternative. In general, that will be at the most recent decision point. Eventually, more and more of these decision points will have been fully explored, and we will have to backtrack further and further. If we backtrack all the way to our initial state and have explored all alternatives from there, we can conclude the particular problem is unsolvable. In such a case, we will have done all the work of the exhaustive recursion and known that there is no viable solution possible. Sometimes the best algorithm for a problem is to try all possibilities. • This is always slow, but there are standard tools that can be used to help. • Tools: algorithms for generating basic objects, such as binary strings [2npossibilities for n-bit string], permutations [n!], combinations [n!/r!(n – r)!], general strings [k –ary strings of length n has k n possibilities], etc... • Backtracking speeds the exhaustive search by pruning. 4.11 Example Algorithms of Backtracking Binary Strings: generating all binary strings • Generating k – ary Strings • N-Queens Problem • The Knapsack Problem • Generalized Strings • Hamiltonian Cycles [refer to Graphs chapter] • Graph Coloring Problem 4.12 Backtracking: Problems & Solutions Generate all the strings of n bits. Assume A[0..n – 1] is an array of size n. void Binary(int n) { if(n< 1) printf("%s", A); //Assume array A is a global variable A[n-1] = 0; Binary(n - 1); A[n-1] = 1; Binary(n - 1); Let T(n) be the running time of binary(n). Assume function printf takes time O(1). T(n) Sc, = if n < 0 2T(n − 1) + d, otherwise — Using Subtraction and Conquer Master theorem we get: T(n) = O(2n). This means the algorithm for generating bit-strings is optimal. Generate all the strings of length n drawn from 0... k – 1. Let us assume we keep current k-ary string in an array A[0.. n – 1]. Call function kstring(n, k): //Assume array A is a global variable void k-string(int n, int k) { //process all k-ary strings of length m if(n< 1) printf("%s",A); for (int j=0;j<k j a k-string k> Let T(n) be the running time of k – string(n). Then, Using Subtraction and Conquer Master theorem we get: T(n) = O(kn). Note: For more problems, refer to String Algorithms chapter. Finding the length of connected cells of 1s (regions) in an matrix of Os and 1s: Given a matrix, each of which may be 1 or 0. The filled cells that are connected form a region. Two cells are said to be connected if they are adjacent to each other horizontally, vertically or diagonally. There may be several regions in the matrix. How do you find the largest region (in terms of number of cells) in the matrix? The simplest idea is: for each location traverse in all 8 directions and in each of those directions keep track of maximum region found. int getval(int (A)[5], int i,int j,int L, int H){ if (i< 0 \|\| iL \|\| j< 0 \|\| j>= H) return 0; return A[i]]; void findMaxBlock(int (A)[5], int r, int c,int L,int H,int size, bool cntarr,int &maxsize){ if (r= L \|\| c> H) cntarr[r][c]=true; size++; if (size> maxsize) maxsize = size; //search in eight directions int direction[][2]=-1,0), (-1,-1), (0,-1),(1,-1),(1,0), (1, 1), (0,1},{-1,1}}; for(int i=0; i<8; i++) int newi =r+direction[i][0]; int newj-c+direction[i][1]; int val-getval (A,newi,newj,L,H); if (val>0 && (cntarr[newi][new]]==false)){ findMaxBlock(A,newi,newj,L,H,size,cntarr,maxsize); int getMaxOnes (int (A) [5], int rmax, int colmax){ int maxsize=0; int size=0; bool **cntarr-create2darr(rmax,colmax); for(int i=0; i< rmax; i++){ for(int j=0; j< colmax; j++){ findMaxBlock(A,i,j,rmax, colmax, 0,cntarr,maxsize); return maxsize; int zarr cout << "Number of maximum 1s are " << getMaxOnes(zarr,5,5) << endl; Solve the recurrence T(n) = 2T(n – 1) + 2 n At each level of the recurrence tree, the number of problems is double from the previous level, while the amount of work being done in each problem is half from the previous level. Formally, the i th level has 2 i problems, each requiring 2 n–i work. Thus the i th level requires exactly 2 n work. The depth of this tree is n, because at the i th level, the originating call will be T(n – i). Thus the total complexity for T(n) is T(n2 n ).	{"url":"https://codepect.com/sample-page/","timestamp":"2024-11-07T19:23:10Z","content_type":"text/html","content_length":"321648","record_id":"<urn:uuid:2e5dabb7-690a-4236-89fb-f97d2d9fa976>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00234.warc.gz"}
How do you determine if rolles theorem can be applied to f(x) = x^3 - x^2- 20x + 7 on the interval [0,5] and if so how do you find all the values of c in the interval for which f'(c)=0? \| Socratic How do you determine if rolles theorem can be applied to #f(x) = x^3 - x^2- 20x + 7 # on the interval [0,5] and if so how do you find all the values of c in the interval for which f'(c)=0? 1 Answer When we are asked whether some theorem "can be applied" to some situation, we are really being asked "Are the hypotheses of the theorem true for this situation?" (The hypotheses are also called the antecedent, of 'the if parts'.) So we need to determine whether the hypotheses ot Rolle's Theorem are true for the function $f \left(x\right) = {x}^{3} - {x}^{2} - 20 x + 7$ on the interval $\left[0 , 5\right]$ Rolle's Theorem has three hypotheses: H1 : $f$ is continuous on the closed interval $\left[a , b\right]$ H2 : $f$ is differentiable on the open interval $\left(a , b\right)$. H3 : $f \left(a\right) = f \left(b\right)$ We say that we can apply Rolle's Theorem if all 3 hypotheses are true. Is the function in this question continuous on the interval $\left[0 , 5\right]$? Is it differentiable on the open interval $\left(0 , 5\right)$? Is $f \left(0\right) = f \left(5\right)$. If the answer to all three is "yes", then the hypotheses are true and we say that Rolle's Theroem "can be applied". To find all the values of c in the interval for which f'(c)=0, Find $f ' \left(x\right)$, set it equal to $0$, solve the equation list the solutions that are in the interval $\left(0 , 5\right)$. Impact of this question 2062 views around the world	{"url":"https://socratic.org/questions/how-do-you-determine-if-rolles-theorem-can-be-applied-to-f-x-x-3-x-2-20x-7-on-th","timestamp":"2024-11-03T22:47:25Z","content_type":"text/html","content_length":"36325","record_id":"<urn:uuid:b7daefd2-43ae-4a6c-8a11-1b554bf9b33a>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00884.warc.gz"}
seminars - Universal Approximation in Deep Learning Universal approximation, whether a set of functions can approximate an arbitrary function in a specific function space, has been actively studied in recent years owing to the significant development of neural networks. Neural networks have various constraints according to the structures, and the range of functions that can be approximated varies depending on the structure. In this thesis, we demonstrate the universal approximation theorem for two different deep learning network structures: convolutional neural networks and recurrent neural networks. First, we proved the universality of convolutional neural networks. A convolution with padding outputs the data of the same shape as the input data; therefore, it is necessary to prove whether a convolutional neural network composed of convolutions can approximate such a function. We have shown that convolutional neural networks can approximate continuous functions whose input and output values have the same shape. In addition, the minimum depth of the neural network required for approximation was presented, and we proved that it is the optimal value. We also verified that convolutional neural networks with sufficiently deep layers have universality when the number of channels is limited. Second, we investigated the universality of recurrent neural networks. A recurrent neural network is past dependent, and we studied the universality of recurrent neural networks in the past-dependent function space. Specifically, we demonstrated that a multilayer recurrent neural network with limited channels could approximate arbitrary past-dependent continuous functions and L[p] functions, respectively. We also extended this result to bidirectional recurrent neural networks, GRU, and LSTM.	{"url":"http://www.math.snu.ac.kr/board/index.php?mid=seminars&page=1&document_srl=1007988&sort_index=speaker&order_type=desc","timestamp":"2024-11-09T20:18:53Z","content_type":"text/html","content_length":"46851","record_id":"<urn:uuid:3ac0b81b-6172-4af3-ae7c-a57af8f2d3cb>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00197.warc.gz"}
rewrite exponential expressions khan academy answers So let's take the positive exponents. Either way, it is nice to have options. So I'm on Khan Academy and I'm doing equivalent forms of exponential expressions, and I have 4 in a row, and I come across this problem. And that’s the best feature in my opinion. Rewrite in Exponential Form log base 9 of 81=2 \| Mathway We can rewrite this log equation as. Radical Expressions and Equations. I REALLY NEED TO GET THIS PROBLEM PLEASE HELP!!! When a power is raised to another power, you multiply the powers together, and so the m (otherwise written as m/1) and the 1/n are multiplied together.. Use fractions in the powers to indicate that the expression stands for a root or a radical. By … Make the base on both sides of the equation the SAME so that if bM=bN\large{b^{\color{blue}M}} = {b^{\ color{red}N}}bM=bN then M=N{\color{blue}M} = {\color{red}N}M=N 1. In this case, b = 10 b = 10, x = x x = x, and y = 3 y = 3. b = 10 b = 10. x = x x = x. Math is Fun- Exponent Laws : Take notes and then try the 10 question quiz at the bottom of the page, called “Your Turn” Rules for Exponents Could you sent me a link to the exercise you are referring to? Well, what I'm going to show you is one of the reasons, and then we'll see that this is a good definition, because once you learned exponent rules, all of the other exponent rules stay consistent for negative exponents and when you raise something to the zero power. 3) Solve for the variable. 3 = log(x) 3 = log ( x) For logarithmic equations, logb(x) = y log b ( x) = y is equivalent to by = x b y = x such that x > 0 x > 0, b > 0 b > 0, and b ≠ 1 b ≠ 1. I got one wrong and the answer is shown as: = $3^x - 3^x/9$ = $3^x (1 - 1/9)$ = $8/9 * 3^x$ I don't Algebra. • F-IF.8b: Use the properties of exponents to interpret expressions for exponential functions. If the result gives us a negative exponent, we will rewrite it by using the definition of negative exponents, [latex]{a}^{-n}=\frac{1}{{a}^{n}}[/latex]. o que eu quero fazer nesse vídeo aqui é começar com uma expressão exponencial que é bem direto ao ponto muito simples de ser escrita e transformá la numa outra expressão mais cabeluda mais complicada ea explicar porque a gente também gostaria de fazer uma coisa dessas então vamos começar com uma expressão que é a seguinte 1 32 avos vezes 2 elevado até então é uma … The table below shows how to simplify the same expression in two different ways, rewriting negative exponents as positive first, and applying the product rule for exponents first. You can use any bases for logs. Worksheet focuses on rewriting expressions involving radicals and rational exponents using the properties of exponents and operations of integer exponents to radical expressions. 11 x c. 4 8 2) Rewrite each power using radical notation. You may find that you prefer one method over the other. Includes matching, true false, and solving by leaving answers as both a radical and with a fractiona Sal simplifies the complicated expression 256^(4/7) / 2^(4/7) until he finds that the expression is equal to 16. In other words, if you can express the exponential equations to have the same base on both sides, then it is okay to set their powers or exponents equal to each other. So maybe parentheses don't seem like a big deal? We will show the last example again, using this idea. The user is expected to rewrite the expression as a single exponential expression. Check out this problem and the difference in the answer when you work it without the parentheses. Read Online Rational Exponents Worksheets With Answers Rational Exponents 1) Rewrite each radical using rational exponent notation. You should also remember the properties of exponents in order to be successful in solving exponential equations. There are three types of problems in this exercise: Simplify into a single exponent: This problem has a quotient or product that has a common base. This exercise gives several opportunities to manipulate and better understand fractional exponents. When the exponent in the denominator is larger than the exponent in the numerator, the exponent of the quotient will be negative. Rewrite the expression 27^t in the form A⋅B^1−3t Everything after the last caret after B it an exponent. Khan Academy Notes with embedded practice problems. Write with Rational (Fractional) Exponents. (8x+33)1 2 ( 8 x + 33) 1 2. Nossa missão é oferecer uma educação gratuita e de alta qualidade para todos, em qualquer lugar. An alternative method to factoring is to rewrite the expression with fractional exponents, then use the rules of exponents to simplify. Come to Algebra-equation.com and read and learn about operations, mathematics and … is taken, it’s raised to the 1/n power. When the nth root of . Get step-by-step solutions to your Exponential and logarithmic functions problems, with easy to understand explanations of each step. Use n√ax = ax n a x n = a x n to rewrite √8x+33 8 x + 33 as (8x+33)1 2 ( 8 x + 33) 1 2. You will see that there is a column for each method that describes the exponent rule or other steps taken to simplify the expression. The ^ means that the following numbers are an exponent. I was having a lot of problems tackling questions based on exponential form calculator but ever since I started using software, math has been really easy for me. I'm trying to do problems on Khan Academy in the area of 'rewriting exponential expressions.' THANK YOU! Free Exponents Calculator - Simplify exponential expressions using algebraic rules step-by-step This website uses cookies to ensure you get the best experience. First, use this rule for exponents to rewrite the numerator: n√x=x1n. So y^(3/4) is y raised to the 3/4th power. From there since we are multiply two exponents with the same base, we can simply add the exponents. After reviewing the entry ticket, I pass out a reference sheet that summarizes the rules of working with exponents. Solve Exponential and logarithmic functions problems with our Exponential and logarithmic functions calculator and problem solver. Types of Problems. √8x + 33 8 x + 33. a. 3 7 5 b. Then I found a common denominator, and finally added the two exponents. One such source can be found here: Exponent Rules Reference Another great resource is the Monterey Institute website on Rewriting Radical and Rationals.This website is clear-cut and clearly shows a number of examples of how to write radical expressions as rationals and vice versa. Step-by-Step Examples. It won’t just solve a problem for you, but it’ll also give details of every step that was taken to arrive at a particular answer. Next, use this rule of Rewrite a given exponential expression in a specific desired form. 2 - x = frac{ 1 }{ x } ,, quad quad x > 0 . ln (2-x) = ln frac{ 1 }{ x } Applying the method described for this type of logarithmic equation, we obtain. Rewrite exponential expressions (practice), We can write this expression as: 5√xx. A Khan Academy é uma organização sem fins lucrativos. Aprenda a analisar e manipular funções e expressões exponenciais para estudar suas taxas de variação. From simplify exponential expressions calculator to division, we have got every aspect covered. A Khan Academy é uma organização sem fins lucrativos com a missão de oferecer ensino de qualidade … Aprenda Matemática, Artes, Programação de Computadores, Economia, Física, Química, Biologia, Medicina, Finanças, História e muito mais, gratuitamente. Those are pretty intuitive, I think. 2) Get the logarithms of both sides of the equation. 8 3 /4 c. x5 2 3) Find the exact, simplified value of each expression without a calculator.If you are stuck, 431/5 b. Enter YOUR Problem. How to Rationalize a DenominatorWatch the next lesson: https://www.khanacademy.org/math/algebra/exponent-equations/radical_equations/v/solving-radical … Sal solves several problems about the equivalence of expressions with roots and rational exponents. 5√xx⇒x15x. a. For example, identify percent rate of change in functions such as y = (1.02) ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay. Write in Exponential Form. 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Problems, with easy to understand explanations of each step exponential equations • F-IF.8b: use the of! Step-By-Step this website uses cookies to ensure you get the logarithms of both sides of the.. Method that describes the exponent rule or other steps taken to simplify have... Calculator to division, we have got every aspect covered method to factoring is to rewrite the expression in...	{"url":"https://new.paulbulteel.eu/canadian-ulptn/53c68f-rewrite-exponential-expressions-khan-academy-answers","timestamp":"2024-11-02T18:07:53Z","content_type":"text/html","content_length":"22048","record_id":"<urn:uuid:0cbf6706-2f45-44f6-b90c-48749327024d>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00768.warc.gz"}
ThmDex – An index of mathematical definitions, results, and conjectures. Let $X$, $Y$, and $Z$ each be a D11: Set such that (i) $X \times Y \times Z$ and $(X \times Y) \times Z$ are each a D326: Cartesian product Then \begin{equation} \|X \times Y \times Z\| = \|(X \times Y) \times Z\| \end{equation}	{"url":"https://theoremdex.org/r/4632","timestamp":"2024-11-05T19:51:51Z","content_type":"text/html","content_length":"6127","record_id":"<urn:uuid:44ece27f-e2c3-4606-8463-4474344f9449>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00208.warc.gz"}
Law of Cosines: There are times when the Law of Sines cannot solve the triangle because we encounter a triangle with either one of the following two scenarios – SAS (Side-angle-side), or SSS (Side-Side-Side). What should we do then? We consider using the Law of Cosines , which is another formula that models the relationship between the sides and the angles of any triangle. In this section, we will learn about the concept and the usage of the Law of Cosines, also known as the Cosines Rule. For any $\triangle \;ABC$, Use the Law of Cosine when given SSS (all sides), or SAS (angle-sandwich!)	{"url":"https://www.studypug.com/trigonometry-help/law-of-cosines","timestamp":"2024-11-04T05:44:17Z","content_type":"text/html","content_length":"371364","record_id":"<urn:uuid:60088b69-6a0e-4fcb-bfb9-a8ec832738e3>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00019.warc.gz"}
ThmDex – An index of mathematical definitions, results, and conjectures. Let $G$ be a D22: Group such that (i) $Z(G)$ is the D1563: Group centre of $G$ Suppose first that $G$ is Abelian. By definition, $Z(G) = \{ x \in G \mid \forall \, g \in G : x g x^{-1} = g \}$. Since $G$ is a group, the condition for belonging to $Z(G)$ thus obtains the form \ begin{equation} \begin{split} x \in Z(G) \quad & \iff \quad \forall \, g \in G : x g x^{-1} = g \\ & \iff \quad \forall \, g \in G : x g = g x \\ \end{split} \end{equation} Since $G$ is Abelian, the predicate expression "$\forall \, g \in G : x g = g x$" is satisfied by every $x \in G$, whence $Z(G) = G$. The implication in the other direction is established in R755: Group centre is Abelian group . $\square$	{"url":"https://theoremdex.org/r/756","timestamp":"2024-11-10T11:22:55Z","content_type":"text/html","content_length":"6368","record_id":"<urn:uuid:eae9eea7-4647-45f3-9cd2-fa11101b0d84>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00533.warc.gz"}
When quoting this document, please refer to the following DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.13 URN: urn:nbn:de:0030-drops-171354 URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17135/ Li, Yi ; Lin, Honghao ; Woodruff, David P. ; Zhang, Yuheng Streaming Algorithms with Large Approximation Factors We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor α to be much larger than 1. Such algorithms can use significantly less memory than the usual setting for which α = 1+ε for an ε ∈ (0,1). We study large approximations for a number of problems in sketching and streaming, assuming that the underlying n-dimensional vector has all coordinates bounded by M throughout the data stream: 1) For the ?_p norm/quasi-norm, 0 < p ≤ 2, we show that obtaining a poly(n)-approximation requires the same amount of memory as obtaining an O(1)-approximation for any M = n^Θ(1), which holds even for randomly ordered streams or for streams in the bounded deletion model. 2) For estimating the ?_p norm, p > 2, we show an upper bound of O(n^{1-2/p} (log n log M)/α²) bits for an α-approximation, and give a matching lower bound for linear sketches. 3) For the ?₂-heavy hitters problem, we show that the known lower bound of Ω(k log nlog M) bits for identifying (1/k)-heavy hitters holds even if we are allowed to output items that are 1/(α k) -heavy, provided the algorithm succeeds with probability 1-O(1/n). We also obtain a lower bound for linear sketches that is tight even for constant failure probability algorithms. 4) For estimating the number ?₀ of distinct elements, we give an n^{1/t}-approximation algorithm using O(tlog log M) bits of space, as well as a lower bound of Ω(t) bits, both excluding the storage of random bits, where n is the dimension of the underlying frequency vector and M is an upper bound on the magnitude of its coordinates. 5) For α-approximation to the Schatten-p norm, we give near-optimal Õ(n^{2-4/p}/α⁴) sketching dimension for every even integer p and every α ≥ 1, while for p not an even integer we obtain near-optimal sketching dimension once α = Ω(n^{1/q-1/p}), where q is the largest even integer less than p. The latter is surprising as it is unknown what the complexity of Schatten-p norm estimation is for constant approximation; we show once the approximation factor is at least n^{1/q-1/p}, we can obtain near-optimal sketching bounds. BibTeX - Entry author = {Li, Yi and Lin, Honghao and Woodruff, David P. and Zhang, Yuheng}, title = {{Streaming Algorithms with Large Approximation Factors}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)}, pages = {13:1--13:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-249-5}, ISSN = {1868-8969}, year = {2022}, volume = {245}, editor = {Chakrabarti, Amit and Swamy, Chaitanya}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/opus/volltexte/2022/17135}, URN = {urn:nbn:de:0030-drops-171354}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.13}, annote = {Keywords: streaming algorithms, ?\underlinep norm, heavy hitters, distinct elements} Keywords: streaming algorithms, ?_p norm, heavy hitters, distinct elements Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022) Issue Date: 2022 Date of publication: 15.09.2022 DROPS-Home \| Fulltext Search \| Imprint \| Privacy	{"url":"http://dagstuhl.sunsite.rwth-aachen.de/opus/frontdoor.php?source_opus=17135","timestamp":"2024-11-08T20:07:01Z","content_type":"text/html","content_length":"8217","record_id":"<urn:uuid:d55ee4b1-7859-432d-a65a-3c9d97341f7e>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00461.warc.gz"}
The Function ()=5ln(1 ) Is Represented As A Power Series: ()==0[infinity] The power series representation of f(x) centered at x = 0 is: f(x) = ∑(n=0 to ∞) [tex][(-1)^n * (5 * x^(n+1))/(n+1)][/tex]. To find the power series representation of the function f(x) = 5ln(1+x), we can use the Taylor series expansion of ln(1+x). The Taylor series expansion of ln(1+x) is given by: ln(1+x) = x - [tex](x^2)/2 + (x^3)/3 - (x^4)/4[/tex]+ ... Substituting this into the function f(x), we have: f(x) = 5(x -[tex](x^2)/2 + (x^3)/3 - (x^4)/4[/tex] + ...) Expanding this further, we have: f(x) = 5x - [tex](5x^2)/2 + (5x^3)/3 - (5x^4)/4[/tex]+ ... The power series representation of f(x) centered at x = 0 is: f(x) = ∑(n=0 to ∞) [[tex](-1)^n * (5 * x^(n+1))/(n+1)[/tex]] where ∑ represents the summation notation. To know more about Power series representation visit- By the Divergence Theorem, the surface integral over S is F · dS= 0. The Divergence Theorem is a mathematical theorem that states that the net outward flux of a vector field across a closed surface is equal to the volume integral of the divergence over the region inside the surface. In simpler terms, it relates the surface integral of a vector field to the volume integral of its divergence. The Divergence Theorem is applicable to a variety of physical and mathematical problems, including fluid flow, electromagnetism, and differential geometry. To evaluate the surface integral ∫∫S F · dS, where F(x, y, z) = and S is the top half of the sphere x² + y² + z² = 9, we can use the Divergence Theorem, which relates the surface integral to the volume integral of the divergence of F. Note that S is not a closed surface, so we will need to compute integrals over two disks, S1 and S2, such that S = S1 ∪ S2 and S1 ∩ S2 = ∅. We will use the disks S1 and S2 to cover the circular opening in the top of the sphere S. The disk S1 is the disk of radius 3 in the xy-plane centered at the origin, and is oriented downward. The disk S2 is the disk of radius 3 in the xy-plane centered at the origin, but oriented upward. We will need to compute the surface integral over each of these disks, and then add them together. To compute the surface integral over S1, we can use the downward normal vector, which is -z. Thus, we have F · dS = · (-z) = -(x² + sin 12)z - (x+y)z = -(x² + sin 12 + x+y)z. To compute the surface integral over S2, we can use the upward normal vector, which is z. Thus, we have F · dS = · z = (x² + sin 12)z + (x+y)z = (x² + sin 12 + x+y)z. Now, we can apply the Divergence Theorem to evaluate the surface integral over S. The divergence of F is ∇ · F = ∂/∂x (x² + sin 12) + ∂/∂y (x+y) + ∂/∂z z = 2x + 1, so the volume integral over the region inside S is ∫∫∫V (2x + 1) dV = ∫[-3,3] ∫[-3,3] ∫[0,√(9-x²-y²)] (2x + 1) dz dy dx. To compute this integral, we can use cylindrical coordinates, where x = r cos θ, y = r sin θ, and z = z. Then, the volume element is dV = r dz dr dθ, and the limits of integration are r ∈ [0,3], θ ∈ [0,2π], and z ∈ [0,√(9-r²)]. Thus, the volume integral is ∫∫∫V (2x + 1) dV = ∫[0,2π] ∫[0,3] ∫[0,√(9-r²)] (2r cos θ + 1) r dz dr dθ = ∫[0,2π] ∫[0,3] (2r cos θ + 1) r √(9-r²) dr dθ = 2π ∫[0,3] r² cos θ √(9-r²) dr + 2π ∫[0,3] r √(9-r²) dr + π ∫[0,2π] dθ= 0 + (27/2)π + 2π = (31/2)π. Therefore, by the Divergence Theorem, the surface integral over S is ∫∫S F · dS = ∫∫S1 F · dS + ∫∫S2 F · dS= -(x² + sin 12 + x+y)z\|z =0 + (x² + sin 12 + x+y)z\|z = 0 Know more about the Divergence Theorem	{"url":"https://community.carbonfields.net/question-handbook/the-function-5ln1-is-represented-as-a-power-series-0infinity-tnph","timestamp":"2024-11-13T01:29:47Z","content_type":"text/html","content_length":"121383","record_id":"<urn:uuid:1c44cdc2-6eb6-4eb0-9805-702493cc419e>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00220.warc.gz"}
Margin Calcuation in Futures Method for calculating the VaR (EWMA) based Margin The method used to derive the VaR Margin requirements for Futues contracts is based on the Initial Margin methodology suggested in the “Varma Committee Report for Risk Containment in Derivatives 1. The standard deviation (Volatility estimate) of prices is computed using the Exponentially Weighted Moving Average method ("EWMA"). 2. The Standard Deviation (Volatility estimate) at the end of time period t (σt) is estimated using the Standard Deviation (Volatility estimate) at the end of the previous time period. i.e. as at the end of t-1 time period (σt- 1), and the return (rt) observed during the time period t (price difference in previous two days). Formula for Standard Deviation (Volatility Estimate) : □ σ (sigma) means the standard deviation □ λ (Lambda) determines how rapidly volatility estimates changes. The value is taken as 0.99 currently. □ r (return) is defined as the logarithmic return: rt = ln (St/St-1) where St is the price of the Gold at time t. Based on the Standard Deviation, the VaR Margin for a particular day is calculated using the below formula. VaR% = 100 * (EXP(3.5 σ)-1) Initial Margin = Square Root (MPoR Days) * VaR Margin, where MPoR Days = 3 1. The value of Lambda is taken as 0.99. 2. As per L.C. Gupta committee recommendations, Margins for VaR should be based on 3.5 sigma limits. 3.5 sigma provides more than 99.7% confidence level. 3. The VaR margin is multiplied by √3 to cover 3 days of Margin Period of Risk (MPOR) Real Time Computation The margins shall be computed on real time basis. The computation of portfolio initial margin would have two components. The first is the computation of Initial Margin for each individual contract. At the second stage, these contract Initial Margins would be applied to the actual portfolio positions to compute the portfolio initial margin. IIBX Clearing shall update EWMA volatility estimates for contracts at discrete time points each day (with a gap of not more than 2 hours between any two consecutive updates and at the end of the trading session) and the latest available scaled up EWMA volatility estimates would be applied to member/client portfolios on a real time basis. The first Margin file shall be updated before start of market hours, intraday Margin files shall be updated at every two hours interval, and the last Margin file shall be updated at the End of the Day. The margin file shall be available for download from https://derivative.iibx.co.in/IntradayVarMargin	{"url":"https://derivative.iibx.co.in/Risk","timestamp":"2024-11-06T14:55:51Z","content_type":"text/html","content_length":"18650","record_id":"<urn:uuid:01a61c6f-13ef-4164-9efc-420d966f9618>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00660.warc.gz"}
James Wan James earned a BSc with Honours from the University of Melbourne, and a PhD from the University of Newcastle, both in mathematics. His research interests span special functions, computer algebra, and number theory. He has published a number of papers on random walks, and co-authored a book on lattice sums. He has taught Probability, Statistics, and leads the freshmore mathematics courses at SUTD. • J. M. Borwein, R. C. McPhedran, M. L. Glasser, J. Wan and I. J. Zucker, Lattice sums: then and now, Encyclopedia of Mathematics and its Applications 150, Cambridge University Press, in: Encyclopedia of Mathematics and its Applications 150, Cambridge University Press (2013) Selected Publications • J. M. Borwein, D. Nuyens, A. Straub and J. Wan, Some arithmetic properties of short random walk integrals, Ramanujan Journal 26 (2011), 109-132 • J. M. Borwein, A. Straub and J. Wan, Three-step and four-step random walk integrals, Experimental Mathematics 22 (2013), 1-14 • J. M. Borwein, A. Straub, J. Wan and W. Zudilin, with an appendix by D. Zagier, Densities of short uniform random walks, Canadian Journal of Mathematics 64 (2012), 961-990 • H. H. Chan, J. Wan and W. Zudilin, Legendre polynomials and Ramanujan-type series for 1/pi, Israel Journal of Mathematics 194 (2013), 183-207 • J. Wan and W. Zudilin, Generating functions of Legendre polynomials: a tribute to Fred Brafman, Journal of Approximation Theory 164 (2012), 488-503 • H. H. Chan, J. Wan and W. Zudilin, Complex series for 1/pi, Ramanujan Journal 29 (2012), 135-144 • D. Borwein, J. M. Borwein, M. L. Glasser and J. Wan, Moments of Ramanujan’s generalized elliptic integrals and extensions of Catalan’s constant, Journal of Mathematical Analysis and Applications 384 (2011), 478-496 • D. Borwein, J. M. Borwein, J. Wan and A. Straub, Log-sin evaluations of Mahler measures II, INTEGERS 12A (2012), #A5, 30 pages • J. Wan, Moments of products of elliptic integrals, Advances in Applied Mathematics 48 (2012), 121-141 • J. Wan, Some notes on weighted sum formulae for double zeta values. Proc. of the Int. Number Theory Conf. in Memory of Alf van der Poorten (2013), in Springer Proceedings in Mathematics & Statistics 43 (2013), 361-379 • J. Wan, Hypergeometric generating functions and series for 1/pi. ISSAC 2013, Communications in Computer Algebra 47 (2013), 114-115 • J. Wan, Series for 1/pi using Legendre’s relation, Integral Transforms and Special Functions 25 (2014), 1-14 • M. Rogers, J. Wan, and I. J. Zucker, Moments of elliptic integrals and critical L-values, Ramanujan Journal 37 (2015), 113-130 • J. Wan and I. J. Zucker, Integrals of K and E from lattice sums, Ramanujan Journal 40 (2016), 257-278 • S. Cooper, J. Wan and W. Zudilin, Holonomic alchemy and series for 1/pi, Proceedings for ALLADI60 (2017), 179-205 • D. Stenlund and J. Wan, Some double sums involving ratios of binomial coefficients arising from urn models, Journal of Integer Sequences 22 (2019), Article 19.1.8 • Special functions • Number theory • Computer algebra • Classical analysis • Random walks • Lattice sums	{"url":"https://esd.sutd.edu.sg/people/faculty/james-wan","timestamp":"2024-11-14T08:30:29Z","content_type":"text/html","content_length":"159817","record_id":"<urn:uuid:2345981a-f408-4c70-a391-4d99d2f11504>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00391.warc.gz"}
Dear all, I have just recently begun to use uBLAS to do some numerics, solving a system of ordinary linear differential equations. The ODE solver repeatedly invokes a function that computes the right hand side of the ODE, and that contains almost the whole computational effort. In this function, I have about 8 matrix-matrix multiplications (with prod()) and about the same number of additions/subtractions of matrices or multiplications with a scalar. The involved matrices are dense with std::complex<double> entries and are of dimension 800x800. The program, especially the evaluation of the rhs function, seems to be running fairly slow and profiling with gprof shows that the rhs evaluation takes 95% of the computation time. Deeper inspection shows that two versions of indexing_matrix_assign() account for almost all of the time needed. Now comes my question: Is this the expected behaviour for the described situation? Some additional information: I am using uBLAS 1.41.0 with NDEBUG set to Any help is appreciated. Best regards, Heiko SchrÃ¶der	{"url":"https://lists.boost.org/ublas/2010/04/4153.php","timestamp":"2024-11-13T21:19:11Z","content_type":"text/html","content_length":"11184","record_id":"<urn:uuid:298d7fdf-2e6c-4520-8022-ab47e1a7e277>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00331.warc.gz"}
Irreducible Highest Weight Vectors Let $G$ be an affine, connected, reductive group and $X$ a $G$-module. Choose a maximal torus $T\subseteq G$, a Borel $B\subseteq G$ containing $T$ and let $U$ be the unipotent radical of $B$. Denote by the character group of $T$. Let $\Lambda\subseteq\mathbb{X}$ be the set of dominant weight s of $G$ with respect to these choices. We can decompose the graded coordinate ring $\mathbb{C}[X]=\bigoplus_{\lambda\in\Lambda} V_{(\lambda)}$ into its isotypic components $V_{(\lambda)}$ of weight $\lambda$. Let \[ \Lambda_X=\{ \lambda\in\Lambda \mid V_{(\lambda)}\ne\{0\}\} \] be the set of weights that occur in $\mathbb{C}[X]$. Let $V_{(\lambda)}\cong V_\lambda^{\ oplus n_\lambda}$, where $V_\lambda$ is the irreducible module of highest weight $\lambda$. Each $V_\lambda$ has a highest weight vector which is unique up to scaling - let $f_{\lambda 1}, \ldots, f_ {\lambda n_\lambda}\in V_{(\lambda)}$ be linearly independent highest weight vectors. For each $1\le k\le n_\lambda$, if the function $f:=f_{\lambda k}\in\mathbb{C}[X]$ is reducible, then there exist weights $\lambda_1,\ldots,\lambda_r\in\Lambda_X$ such that $\lambda$ is an $\mathbb N$-linear combination of the $\lambda_i$. Indeed, about a year ago this statement was completely unclear to me. However, it's actually not that hard to see and I felt like sharing my proof. Let $Z=\mathrm{Z}(f)$ be the vanishing set of $f$ (with the reduced subvariety structure). Note that $Z$ is $G$-invariant, so we have an action $\alpha:G\times Z\to Z$ induced by the action of $G$ on $X$. Since $\mathbb{C}[X]$ is factorial, we can write $f=f_1^{e_1}\cdots f_r^{e_r}$ as a product of powers of irreducible elements where any two of the $f_i$ are not associated. This corresponds to the decomposition of $Z=Z_1\cup\cdots\cup Z_r$ into its irreducible components $Z_i=\mathrm{Z}(f_i^{e_i})=\mathrm{Z}(f_i)$. Note that all these components have the same dimension. Let $\alpha_i:G\ times Z_i\to Z$ be the restriction of the action morphism $\alpha$. Then, $Z_i\subseteq \mathrm{im}(\alpha_i)$ and $\mathrm{im}(\alpha_i)$ is irreducible of maximal dimension, hence $\mathrm{im}(\ alpha_i)=Z_i$. This implies that $Z_i$ is $G$-invariant. In particular, $g.f_i=uf_i$ for some $u\in\mathbb{C}[X]$ and since the action of $G$ preserves the degree on $\mathbb{C}[X]$, we also have $\ deg(u)=0$. Hence, $u\in\mathbb{C}[X]_0=\mathbb{C}$. This means that $G.f_i = \mathbb{C} f_i$, so $G$ acts by a character on $f_i$. This means that $f_i$ is a highest weight vector of some weight $\ lambda_i$. Consequently, we must have $\lambda = e_1\lambda_1 + \cdots + e_r\lambda_r$ with $\lambda_i\in\Lambda$ corresponding to an irreducible highest weight vector. For $\lambda\in\Lambda_X$, denote by $q(\lambda)$ the number of irreducible highest weight vectors in $V_{(\lambda)}$. We define $M(\lambda):=\{ \mu\in\Lambda_X \mid \lambda-\mu\in\Lambda_X \}$, then \[ q(\lambda) = n_\lambda - \sum_{\mu\in M(\lambda)} q(\mu). \] This formula was the reason why the question interested me in the first place: Let $I\subseteq\mathbb{C}[X]$ be a homogeneous, $G$-invariant ideal. If we already know the multiplicities $m_\lambda$ of $\mathbb{C}[X]\cong\bigoplus_{\lambda\in\Lambda} V_\lambda^{\oplus m_\lambda}$ and we want to know candidates for generators of $I$, there is a randomized procedure that works as follows: + Take $m=m_\lambda$ highest weight vectors $F_1,\ldots,F_m\in\mathbb{C}[X]$ of weight $\lambda$. + Evaluate these vectors at $m$ random points $x_1,\ldots,x_m\in Z(I)$. + If the corresponding matrix $(F_i(x_j))_{ij}$ has full rank, then it is a certificate for the fact that the weight $\lambda$ does not occur in $I$. Now, the above claim tells us that we can start in low degrees and cache evaluations of low-degree highest weight vectors to use them in certificates in higher degrees, saving a lot of work.	{"url":"https://blag.nullteilerfrei.de/2014/05/23/irreducible-highest-weight-vectors/","timestamp":"2024-11-13T01:42:24Z","content_type":"text/html","content_length":"38540","record_id":"<urn:uuid:b6249bfe-f1e1-40a0-a886-81e9c8aa7797>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00658.warc.gz"}
How Are Tensors Immutable In Tensorflow? In TensorFlow, tensors are immutable because once they are created, their values cannot be changed. This means that any operation performed on a tensor does not modify the original tensor, but instead creates a new tensor with the updated values. This design choice ensures that the data integrity of tensors is maintained throughout the computational graph and simplifies the process of debugging and tracking the flow of data within the system. By treating tensors as immutable objects, TensorFlow promotes a more functional style of programming and helps to ensure that operations are performed in a consistent and predictable manner. How can you manipulate tensors in TensorFlow? You can manipulate tensors in TensorFlow using various operations and methods such as tensor addition, subtraction, multiplication, division, reshape, transpose, concatenate, slicing, indexing, element-wise operations, and more. Here is an example of how you can manipulate tensors in TensorFlow: 1 import tensorflow as tf 3 # Create two tensors 4 tensor1 = tf.constant([[1, 2], [3, 4]]) 5 tensor2 = tf.constant([[5, 6], [7, 8]]) 7 # Addition 8 result_addition = tf.add(tensor1, tensor2) 10 # Multiplication 11 result_multiplication = tf.multiply(tensor1, tensor2) 13 # Reshape 14 result_reshape = tf.reshape(tensor1, [4, 1]) 16 # Transpose 17 result_transpose = tf.transpose(tensor1) 19 # Concatenate 20 result_concatenate = tf.concat([tensor1, tensor2], axis=1) 22 # Print results 23 print("Addition Result:\n", result_addition.numpy()) 24 print("Multiplication Result:\n", result_multiplication.numpy()) 25 print("Reshape Result:\n", result_reshape.numpy()) 26 print("Transpose Result:\n", result_transpose.numpy()) 27 print("Concatenate Result:\n", result_concatenate.numpy()) These are just a few examples of how you can manipulate tensors in TensorFlow. TensorFlow provides a wide range of functions and methods to easily manipulate tensors for building deep learning What is the purpose of tensors in TensorFlow? Tensors in TensorFlow are multi-dimensional arrays that are used to represent data in graph computation. The purpose of tensors in TensorFlow is to enable efficient mathematical operations and transformations on data during the execution of a computational graph. Tensors are at the core of TensorFlow's computational model and are essential for defining, manipulating, and passing data between different operations in a graph. They allow for easy and efficient calculations on large multidimensional data sets, making it an ideal framework for machine learning and deep learning What is the rank of a tensor in TensorFlow? The rank of a tensor in TensorFlow refers to the number of dimensions of the tensor. A scalar (a single number) has rank 0, a vector (an array of numbers) has rank 1, a matrix has rank 2, and so on. In TensorFlow, you can get the rank of a tensor using the tf.rank() function. How can you train a neural network using tensors in TensorFlow? To train a neural network using tensors in TensorFlow, you would typically follow these steps: 1. Define your neural network model: This involves creating layers using TensorFlow's high-level API, such as tf.keras.layers.Dense. You can specify the number of neurons, activation functions, and any other parameters specific to your neural network architecture. 2. Compile your model: Once you have defined your model, you need to compile it using the model.compile function. This involves specifying the loss function, optimizer, and any metrics you want to track during training. 3. Prepare your input data: Convert your input data into TensorFlow tensors using tf.constant or tf.Variable. Make sure to standardize or normalize your input data if necessary. 4. Define your training loop: Create a loop that iterates over your training data in batches. For each batch, use the tf.GradientTape context to record the operations for automatic differentiation. 5. Calculate gradients and update weights: Use the gradients calculated by the tf.GradientTape to update the weights of your model using the optimizer. This can be done using the optimizer.apply_gradients method. 6. Monitor training progress: During training, you can monitor the loss and any other metrics by calling the model.fit method with your training data. 7. Evaluate your model: Once training is complete, evaluate your model's performance on a separate validation or test dataset to assess its generalization ability. By following these steps, you can train a neural network using tensors in TensorFlow and optimize it for your specific task. What is the role of placeholders in TensorFlow? Placeholders in TensorFlow are used to create input nodes for feeding data into the computational graph. They allow the value of the input data to be specified at runtime, rather than during the graph construction. Placeholders are typically used for providing input data such as images, labels, or coefficients for a model. They can be thought of as "empty" nodes that will be filled with actual data when the computational graph is executed. By using placeholders, you can define the structure of the input data without having to specify the actual values until runtime. This can be useful for training machine learning models, where the input data may change for each batch of training or evaluation. How can you initialize the weights of a neural network in TensorFlow? In TensorFlow, weights of a neural network can be initialized using various methods, such as: 1. Using predefined initializers provided by TensorFlow, such as tf.initializers.glorot_uniform() or tf.initializers.RandomNormal(). For example: 1 initializer = tf.initializers.glorot_uniform() 2 weights = tf.Variable(initializer(shape=[input_size, output_size])) 1. Using custom initializers by defining a function to generate the initial weights. For example: 1 def custom_initializer(shape): 2 return tf.random.normal(shape, mean=0, stddev=0.1) 4 weights = tf.Variable(custom_initializer(shape=[input_size, output_size])) 1. Initializing weights using a specific distribution, such as normal or uniform distribution. For example: 1 weights = tf.Variable(tf.random.normal(shape=[input_size, output_size], mean=0, stddev=0.1)) By using these methods, you can initialize the weights of a neural network in TensorFlow according to your requirements.	{"url":"https://article-blog.kdits.ca/blog/how-are-tensors-immutable-in-tensorflow","timestamp":"2024-11-01T19:16:57Z","content_type":"text/html","content_length":"150200","record_id":"<urn:uuid:031c7b79-35c9-4b20-ac06-b0e449a60464>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00619.warc.gz"}
An overview of the GMRT Correlator Next: ADC Up: The GMRT Correlator Previous: Introduction Contents A simplified block diagram of the GMRT correlator is shown in Fig. 25.2. The basic units are the analog to digital converters (ADC), the Integral Delay compensation (Delay-DPC) subsystem, the Fourier transform and fractional delay compensation (FFT) subsystem and the multiplier-accumulator (MAC) unit. The data from the MAC output is acquired using a special purpose PC add on card. All of the subsystems, except the ADC, have DSP (digital signal processor) based control circuits. These control circuits are in turn controlled by the data acquisition computer, (i.e. the same machine which acquires the data via the add on card; see Chapter 26 for more details). Next: ADC Up: The GMRT Correlator Previous: Introduction Contents NCRA-TIFR	{"url":"https://www.gmrt.ncra.tifr.res.in/doc/WEBLF/LFRA/node245.html","timestamp":"2024-11-13T12:44:35Z","content_type":"text/html","content_length":"4742","record_id":"<urn:uuid:4e8e4b52-0c5a-40a0-a9e4-4902e239d613>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00364.warc.gz"}
mapping high-dimensional data points to a lower-dimensional space, such as 2D or 3D, in a way that preserves the pairwise similarities between points t-Distributed Stochastic Neighbor Embedding (t-SNE) is a machine learning algorithm used for dimensionality reduction and visualization of high-dimensional data. Developed by Geoffrey Hinton and Laurens van der Maaten in 2008, t-SNE has become a popular method for visualizing complex datasets, particularly in fields like bioinformatics, image processing, and natural language processing. The primary goal of t-SNE is to map high-dimensional data points to a lower-dimensional space, such as 2D or 3D, in a way that preserves the pairwise similarities between points. In other words, if two points are close to each other in the original high-dimensional space, they should also be close in the reduced space, and vice versa. t-SNE starts by measuring pairwise similarities between points in the high-dimensional space using a Gaussian distribution centered at each point. It then constructs a similar probability distribution in the lower-dimensional space. The algorithm iteratively adjusts the lower-dimensional representation to minimize the divergence between the two distributions, typically using the Kullback-Leibler divergence as the objective function. One of the key features of t-SNE is its use of a t-distribution, rather than a Gaussian distribution, to measure similarities in the lower-dimensional space. This results in a "heavier-tailed" distribution that is more robust to the crowding problem, a common issue in dimensionality reduction where points in the lower-dimensional space tend to crowd together. While t-SNE is effective for visualizing high-dimensional data, it has some limitations. The algorithm is computationally intensive, making it less suitable for very large datasets. It is also sensitive to hyperparameters like the perplexity, which controls the balance between preserving local and global structures. Additionally, t-SNE does not provide a deterministic mapping from the high-dimensional space to the lower-dimensional space, meaning that running the algorithm multiple times on the same data may produce different results. In summary, t-SNE is a machine learning algorithm used for dimensionality reduction and data visualization. It aims to preserve the pairwise similarities between data points when mapping them from a high-dimensional space to a lower-dimensional one. The algorithm has been widely adopted for visualizing complex datasets but comes with computational costs and sensitivity to hyperparameters.	{"url":"https://feedsee.com/aiw/T-SNE/","timestamp":"2024-11-05T16:02:59Z","content_type":"text/html","content_length":"4726","record_id":"<urn:uuid:3a1dc16d-8d53-411f-b53c-f2779939978f>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00685.warc.gz"}
Promoting Writing in Mathematics: Prospective Teachersâ€™ Experiences and Perspectives on the Process of Writing When Doing Mathematics as Problem Solving Promoting Writing in Mathematics: Prospective Teachersâ€™ Experiences and Perspectives on the Process of Writing When Doing Mathematics as Problem Solving Keywords: Attitudes, Beliefs, Metacognition, Problem solving, Prospective mathematics teachers, Writing in mathematics Despite a great deal of research on the benefits of writing in mathematics, writing plays a minimal role, if any, in secondary and tertiary mathematics education. In order for teachers to use writing in their classrooms, they themselves have to experience writing mathematics within the teacher education programme. The present paper reports on a study aimed at addressing this gap. In a problem-solving seminar, preservice teachers had an opportunity to experience writing in mathematics and report how this affected their problem-solving processes and shaped their attitudes towards incorporating writing in their classrooms. In order to provide a more detailed description of the phenomenon, four participants were chosen based on their beliefs about mathematics. All of the participants struggled with writing their explanations. Those who used writing as a method to support metacognitive processes while exploring mathematics tended to respond positively to the writing process. The others used writing merely as a method to produce a formal document to be evaluated by the instructor. Consequently, those who viewed writing and doing mathematics as an intertwined process expressed a positive attitude towards using writing in their mathematics classroom. This was, unfortunately, not the case when writing and doing mathematics were seen as two separate processes. Implications for teacher education programmes are presented at the end of the report. Download data is not yet available. Bereiter, C., & Scardamalia, M. (1987). The psychology of written composition. Hillsdale, NJ: Erlbaum. Brown, A. (1987). Metacognition, executive control, self-regulation and other more mysterious mechanisms. In F. Weinert & R. Klume (Eds.), Metacognition, motivation and understanding (pp. 65â€“116). Mahwah, NJ: Erlbaum. Bruder, R., & Collet, C. (2011). ProblemlÃ¶sen lernen im Mathematikunterricht. Berlin: Cornelsen. Carlson, M. P. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success. Educational Studies in Mathematics, 40(3), 237â€“258. College Entrance Examination Board. (1983). Academic preparation for college: What students need to know and be able to do. New York: Author. Cooney, T. J. (1999). Conceptualizing teachersâ€™ ways of knowing. Educational Studies in Mathematics, 38, 163â€“187. Countryman, J. (1992). Writing to learn mathematics. Portsmouth, NH: Heinemann. Cross, D. I. (2009). Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. International Journal of Science and Mathematics Education, 7(5), deFreitas, E. (2008). Troubling teacher identity: Preparing mathematics teachers to teach for diversity. Teaching Education, 19(1), 43â€“55. Ernest, P. (1989). Philosophy, mathematics and education: The state of the art. International Journal of Mathematics Education in Science and Technology, 20, 555â€“559. Ernest, P. (1991). The philosophy of mathematics education. Abingdon, Oxon, UK: Routledge Farmer. Flores, A., & Brittain, C. (2003). Writing to reflect in a mathematics methods course. Teaching Children Mathematics, 10, 112â€“118. Flower, L., & Hayes, J. R. (2009). The cognition of discovery: Defining a rhetorical problem. In S. Miller (Ed.), The Norton book of composition studies (pp. 467â€“478). New York: W.W. Norton. Geeslin, W. E. (1977). Using writing about mathematics as a teaching technique. Mathematics Teacher, 70, 112â€“115. Halloun, I., & Hestenes, D. (1996). Views About Sciences Survey: VASS. Paper presented at the annual meeting of the National Association of Research in Science Teaching, St. Louis, MO. (ERIC Document Reproduction Service No. ED394840). Komorek, E. (2009). Mit Hausaufgaben ProblemlÃ¶sen und eigenverantwortliches Lernen in der Sekundarstufe I fÃ¶rdern. Entwicklung und Evaluation eines Ausbildungsprogramms fÃ¼r MathematiklehrkrÃ¤fte. Berlin: Logos Verlag. Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 48, 225â€“250. Kuzle, A. (2011). Preservice teachersâ€™ patters of metacognitive behavior during mathematics problem solving in a dynamic geometry environment. Doctoral dissertation. The University of Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20â€“40. Lester, F. K. (1994). Musing about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25(6), 660â€“675. Liljedahl, P., Rolka, K., & RÃ¶sken, B. (2007b). Affecting affect: The reeducation of preservice teachersâ€™ beliefs about mathematics and mathematics teaching and learning. In W. G. Martin, M. E. Strutchens, & P. C. Elliott (Eds.), The learning of mathematics (pp. 319â€“330). Reston, VA: National Council of Teachers of Mathematics. Llinares, S. (2002). Participation and reification in learning to teach: The role of knowledge and beliefs. In G. C. Leder, E. Pehkonen, & G. TÃ¶rner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 195â€“209). Dordrecht, The Netherlands: Kluwer. Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1â€“2), 49â€“63. Miller, L. D., & Hunt, N. P. (1994). Professional development through action research. In D. B. Aichele & A. F. Coxford (Eds.), Professional development for teachers of mathematics (pp. 296â€“303). Reston, Va: The National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations for school mathematics of the 1980s. Reston, VA: Author. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Pajares, F. (1992). Teachersâ€™ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332. Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage. Philipp, R. A. (2007). Mathematics teachersâ€™ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning, Vol. 2 (pp. 257â€“315). Charlotte, NC: Information Age. Porter, M., & Masingila, J. (2001). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics, 42(2), 165â€“177. Pugalee, D. K. (2001). Writing, mathematics, and metacognition: Looking for connections through studentsâ€™ work in mathematical problem solving. School Science and Mathematics, 101(5), 236â€“245. Schoenfeld, A. H. (1987). Whatâ€™s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189â€“215). Hillsdale, NJ: Erlbaum. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334â€“370). New York: Macmillan. Sfard, A. (2001). Learning mathematics as developing a discourse. In R. Speiser, C. Maher, & C. Walter (Eds.), Proceedings of the Twenty-first Conference of PME-NA (pp. 23â€“44). Columbus, OH: ERIC Clearing House for Science, Mathematics, and Environmental Education. Silver, E. A. (1987). Foundations of cognitive theory and research for mathematics problem-solving instruction. In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 33â€“60.) Hillsdale, NJ: Erlbaum. Thompson, A. (1992). Teacherâ€™s beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127â€“146). New York: Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Wilson, M., & Cooney, T. J. (2002). Mathematics teacher change and development. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127â€“147). Dordrecht, The Netherlands: Kluwer. Yoo, S. (2008). Effects of traditional and problem-based instruction on conceptions of proof and pedagogy in undergraduates and prospective mathematics teachers. Doctoral dissertation. The University of Texas, Austin. How to Cite Kuzle, A. (2013). Promoting Writing in Mathematics: Prospective Teachersâ€™ Experiences and Perspectives on the Process of Writing When Doing Mathematics as Problem Solving. Center for Educational Policy Studies Journal, 3(4), 41-59. https://doi.org/10.26529/cepsj.222 Authors who publish with this journal agree to the following terms: 1. Authors are confirming that they are the authors of the submitted article, which will be published online in the Center for Educational Policy Studies Journal (for short: CEPS Journal) by University of Ljubljana Press (University of Ljubljana, Faculty of Education, Kardeljeva ploščad 16, 1000 Ljubljana, Slovenia). The Author’s/Authors’ name(s) will be evident in the article in the journal. 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This lesson adapted from Computer Science Unplugged (c) 1998, by Bell, Witten, and Fellows. See http://unplugged.canterbury.ac.nz/ for copyright restrictions. You've probably heard about some of the issues of privacy on the internet, especially related to financial transactions. Indeed, it is often important for computer users to share information with other people, yet still maintain a significant level of privacy. This activity demonstrates that information can be shared without being revealed. 1. A pen and paper or calculator for simple addition. 2. Business cards with salaries, one per student. Lesson Plan: 1. Explain and discuss: grownups are notoriously sensitive about letting other people know how much money they make. Do you have any information you don't want anyone else to know? 2. If the students suggest an interesting type of sensitive information, use it. Otherwise (or in addition) hand out the business card and explain that the class will be able to find the average salary of everyone in the room, but no one will know anyone elses salary. Each student's data will be secret, yet we can obtain useful information from the class! 3. Ask for suggestions about how this might be done, or even whether it can be done. You may need to show the youngest children how we usually find an average. 4. Choose one person to start the process. That person is to select a random number (say between 0 and 500, larger for salaries) and write it down. Then he/she should add to that number the salary found on the business card (or whatever data you're trying to average). Finally he/she whispers the sum to the next person. 5. Each child in succession adds their salary to the total which is making its way around the room. 6. After every student has contributed his/her number, the sum is passed back to the first person, who subtracts the original number from the sum. Then, to get the average, the first person divides by the total number of students, and reports the result. 7. Re-emphasize what has happened. We know the average, but no one knows anyone else's number!! 8. Discussion: Suppose students A, B, C, and D contribute their numbers in that order. Could A and C get together to determine B's number? Could A and D get together to figure out B's number? If not, what can A and D determine? The census bureau uses this technique for some of its financial reporting. Ask the class if they can think of anywhere else this might be useful (the kids might just find it fun to spend a few minutes talking about what kind of data is secret). Have students figure out what they can do if someone in the group lies when reporting their total. Can they think of a way to recover the correct sum without revealing who lied (as long as the liar is willing to admit in secret that they lied, and by how much)? • Addition of any type of number • Division by whole numbers This lesson adapted from Computer Science Unplugged (c) 1998, by Bell, Witten, and Fellows. See http://unplugged.canterbury.ac.nz/ for copyright restrictions.	{"url":"http://mathmaniacs.org/lessons/B-infohiding/index.html","timestamp":"2024-11-07T19:22:33Z","content_type":"text/html","content_length":"8480","record_id":"<urn:uuid:78c81038-268e-4e63-b52a-cf2a683ce05e>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00066.warc.gz"}
A type is LessThanComparable if it is ordered: it must be possible to compare two objects of that type using operator<, and operator< must be a strict weak ordering relation. Refinement of Associated types X A type that is a model of LessThanComparable x, y, z Object of type X Consider the relation !(x < y) && !(y < x). If this relation is transitive (that is, if !(x < y) && !(y < x) && !(y < z) && !(z < y) implies !(x < z) && !(z < x)), then it satisfies the mathematical definition of an equivalence relation. In this case, operator< is a strict weak ordering. If operator< is a strict weak ordering, and if each equivalence class has only a single element, then operator< is a total ordering. Valid expressions │Name│Expression│Type requirements│ Return type │ │Less│x < y │ │Convertible to bool │ Expression semantics │Name│Expression│ Precondition │Semantics│Postcondition│ │Less│x < y │x and y are in the domain of < │ │ │ Complexity guarantees │Irreflexivity │x < x must be false. │ │Antisymmetry │x < y implies !(y < x) [2] │ │Transitivity │x < y and y < z implies x < z [3] │ [1] Only operator< is fundamental; the other inequality operators are essentially syntactic sugar. [2] Antisymmetry is a theorem, not an axiom: it follows from irreflexivity and transitivity. [3] Because of irreflexivity and transitivity, operator< always satisfies the definition of a partial ordering. The definition of a strict weak ordering is stricter, and the definition of a total ordering is stricter still. See also EqualityComparable, StrictWeakOrdering Revised 05 December, 2006 Copyright © 2000 Jeremy Siek, Univ.of Notre Dame (jsiek@lsc.nd.edu) Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)	{"url":"https://live.boost.org/doc/libs/1_82_0/libs/utility/LessThanComparable.html","timestamp":"2024-11-06T13:49:45Z","content_type":"text/html","content_length":"8452","record_id":"<urn:uuid:6da36048-3657-43b6-a847-ce389f297f7f>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00789.warc.gz"}
• Documentation version: 1.2.0 Akaike information criterion A method of comparing two similar models by penalising models with a larger number of parameters. See Akaike information criterion on Wikipedia basin of convergence A set of initial points that lead to the same local minimum under a given iterative algorithm. bobyqa optimisation BOBYQA= Bounded Optimisation by Quadratic Approximation, a none derivative based optimisation method [Powell2009] used by ND method. C++ is a low level programming language which is automatically used by PoPy for some time critical operations C++ on Wikipedia categorical covariates Covariates that indicates membership in one of a set of unordered categories, such as race. The volume of the fluid presented to the eliminating organ (extractor) that is effectively completely cleared of drug per unit time. (Definition from [RowlandTozer2012]), also see Clearance on Compartment Diagram A graphical visualisation of the compartment model, using nodes for compartments and edges for flows between compartments confidence intervals Ranges in which we can be X% confident that a parameter lies. covariance matrix A measure of spread for multiple random variables that may be correlated. See Covariance on Wikipedia Measured or observed quantities that are read in from the input data file. Signified by a c[X] in the model specification file (which could also be thought of as an abbreviation of “column”). They include information such as ID, time, weight, and also measurements such as drug concentration. Cython is an superset of Python that compiles to C++. PoPy uses Cython extensively to process the user config file. See Cython on Wikipedia An online repository of PK/PD models see DDMoRe Website dos prompt The dos prompt command line in Microsoft Windows. This is the older Windows shell, by default with a black background. The removal of a drug from the body. The removal of waste substances from the body including unchanged drugs and metabolic products. Most drug products are eliminated through the kidneys. first order conditional estimation FOCE is a fitting method in Nonmem that uses a first order approximation of the objective function conditioned on optimised random effects for each individual in the population. For a description of PoPy’s implementation of FOCE see FOCE Fitting Method. first pass effect A reduction in the amount of drug entering circulation due to it being metabolised by the liver or gut on its way to the blood system. First pass effect on Wikipedia fixed effects A population-level parameters (usually means) that describe an average from which individuals deviate in a random way, though where the nature of the randomness is known. Signified by f[X] in the model specifications file. Graphviz is open source software used to create Compartment Diagram in PoPy. See Graphviz on Wikipedia Hyper Text Markup Language used on the web and by PoPy to generate summary output. See HTML on Wikipedia importance sampling A method of sampling from a complex distribution by first sampling from a simpler distribution and re-weighting with the ratio of the complex and simpler Wikipedia: <Probability_density_function> . See Importance Sampling on Wikipedia. initial value problem The ordinary differential equations typically solve a dynamic system which has a defined input state and then the system evolves over time according to the ordinary differential equation system. This type of integration problem, typical in PK/PD, is known as a Initial Value Problem. iterative two stage ITS is a fitting method in Nonmem that optimises the objective function by switching between optimising the fixed effects and random effects. joint optimisation and estimation JOE is PoPy’s original fitting method see JOE Fitting Method, it optimises the same objective function as FOCE and ITS and is most similar to ITS in terms of fitting performance. Laplace approximation A method of approximating integrals. See Laplace method on Wikipedia. This objective function is used by LAPLACE and an approximation is used by JOE, FOCE and ITS fitting methods. laplace fitting method A fitting method that uses the Laplace approximation as an objective function. Note JOE, FOCE and ITS use a related, but less computationally expensive objective function. The conditional probability, p(D\|M), of observing data D given a hypothesized model M. This expresses the plausibility of model M given data D, but is a probability distribution over D rather than M. As a result, it cannot be used to compare different models, only different parameter values for the same model. Likelihood on Wikipedia Numerical ordinary differential equation solver [Radhakrishnan1994] available in PoPy, see Example ODE_SOLVER using CPPLSODA. mass balance The principal that matter cannot be created or destroyed within a compartment model, apart from deliberate inputs (e.g doses) and sink compartments that model excretion from the body. See Mass Balance on Wikipedia. Process by which drug is chemically transformed into another substance. Takes place primarily in the liver. Microsoft Windows A popular operating system for personal computers. mixed effect model A structural model that uses both fixed effects and random effects to model population parameters. In practise, all models contain at least one fixed effect, so the key feature is the use of random effects to allow parameters to vary between subjects in the population. model parameters Person-specific PK/PD parameters, usually defined as a function of the fixed effects, random effects and measured covariates. Signified by m[X] in the model specification file. Matlab based PK/PD modelling software. See http://lixoft.com/products/monolix/ Message Passing Interface. A protocol for parallelising software by passing information between processors. See Message Passing Interface on Wikipedia Random displacements added to a signal. See Signal Processing Noise on Wikipedia none derivative estimation ND is PoPy’s newest fitting method see ND Fitting Method, it optimises the same objective function as FOCE and uses the derivative based FOCE fitting method, but also utilises the none derivative BOBYQA algorithm. Nonmem (NONlinear Mixed Effect Modelling) is a Fortran based system for PK/PD modelling. [Bauer2009] objective function The fixed effects and random effects of a model are estimated by minimising the objective function, which is equivalent to maximising the likelihood of the model given the observations. The observed values to be modelled, also known as the dependent variable. These measurements (either synthetic or real) are signified by c[X] in the PREDICTIONS section of a PoPy script file. ordinal covariates Covariates derived from a discretisation of a continuum such that values have a definite order, such as the East Coast Oncology Group status that ranges from 0 (normal) to 4 (most severe). ordinary differential equations Multiple differential equations, each with one independent variable. See Ordinary differential equation on Wikipedia powershell prompt The powershell prompt command line in Microsoft Windows. This is the newer Windows shell, by default with a blue background. practically identifiable A parameter of a model is practically identifiable or estimable, if the true value can be estimated from a finite amount of data. See Identifiability Analysis on Wikipedia practically unidentifiable A parameter that is not practically identifiable The value the model calculates for a given observations, usually a conversion to concentrations via division by the volumes of the compartments. Signified by p[X] in the model specification file. product key The PoPy product key is the unique key that identifies the the current licence. It has a form like ‘XXXX-XXXX-XXXX-XXXX-XXXX-XXXX-XXXX’. See PoPy Activation. Python is a general purpose programming language used in PoPy scripts and to implement PoPy itself. See Python on Wikipedia R is open source statistical software used extensively in the PK/PD community. See R on Wikipedia random effects Deviation from the population-level fixed parameters, with defined distribution parameters. Signified by r[X] in the model specification file. The tendency to for random effects to shrink towards the mean value when data are sparse. Solutions are defined by a .pyml file containing links to .csv files that determine a set of f[X], r[X], m[X], s[X], p[X] variables that represent a candidate solution to a PK/PD model fitting Documentation system used by PoPy and many other Python projects to generate .html and .pdf files. See Sphinx on Wikipedia state parameters The amount - not concentration - of drug in each compartment of the compartment model. Signified by s[X] in the model specification file. stochastic approximation expectation maximisation SAEM is a probabilistic fitting method originally implemented in Monolix and also available in Nonmem. structurally identifiable A parameter of a model is structurally identifiable, if given an infinite amount of data the true underlying parameter value is recoverable. See Identifiability Analysis on Wikipedia structurally unidentifiable A parameter that is not structurally identifiable symmetric positive definite A symmetric positive definite matrix is a matrix whose eigenvalues are all positive. It is the matrix equivalent of having a real valued square root. In PK/PD models a population covariance matrix is required to be symmetric positive definite. See Matrix Definiteness on Wikipedia A measure of spread for a random variable. See Variance on Wikipedia visual predictive check Given a set of f[X] values and a model, new p[X] values are simulated which can then be compared with original c[X] data on a graph. volume of distribution The volume (or volume of distribution) is the theoretical volume that a compartment would need to have to give the concentration of drug found in the blood plasma. See Volume of Distribution on A simple markup language used by PoPy Script File Formats. See YAML on Wikipedia	{"url":"https://product.popypkpd.com/docs/en/1.2.0/handwritten/appendices/glossary/","timestamp":"2024-11-07T13:35:55Z","content_type":"text/html","content_length":"35363","record_id":"<urn:uuid:5d5c926f-4fe3-4dbc-9fc9-8f727b500c9e>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00123.warc.gz"}