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MathPro-S Test
Mathematical Profile Test:Assessment through adouble control gate
The aim of the double control gate is to quickly assess the basic mathematical skills of large groups of students (for example school populations) and identify students who are struggling in
mathematics (1st control gate) and then further investigate the mathematical profile of only those students who are experiencing difficulties (2nd control gate) in order to tailor appropriate
individualised intervention programmes.
The first control gate is implemented with the administration of the short version of the Mathematical Profile Test (MathPro-S Test). The MathPro-S Test consists of four subscales for Grade 1 and
five subscales for Grades 2 - 6 that assess different mathematical skills from each other and aims to outline the basic elements (or a "miniature") of the mathematical profile of the students as well
as to identify students who are struggling in mathematics or who are at risk of learning difficulties in mathematics - Dyscalculia.
• To educators who are interested in to identify students who are experiencing difficulties in Mathematics and need further investigation by an expert.
• To teachers who interested in having an overview of the strengths and weaknesses of the whole class, to adapt their teaching accordingly.
• Τo teachers/experts who are looking for a quick way to assess the performance of students in different mathematical tasks.
• To formal diagnostic bodies for specific learning difficulties who are seeking a short standardized test to assess the mathematical skills.
• To researchers who are looking for a reliable tool to assess mathematical skills.
The MathPro-S Test can be administered by educators or experts who have been certified after attending the corresponding training course. The certified examiners can then purchase as many open
MathPro-S Test licenses as they wish in order to administer them to an equal number of students of the same or different grades. The administration takes place exclusively through the MathPro-S Test
online platform, which is accessible exclusively by the certified examiners.
1. It is administered online through a computer or tablet.
2. It takes 15 minutes on average to complete.
3. The child does not have to write or say anything. Responses are recorded in a database and processed in a way that ensures confidentiality.
4. The instructions of the sub-scales are clear and can be repeated on demand by the user. After the video of the instructions, three practice trials follow.
5. The MathPro-S Test can be easily administered both individually and in groups (for example, administered simultaneously to students in a classroom within a class period - in this case headphones
are required).
6. In all subscales the accuracy of the answers is recorded.
7. The Results Report is automatically exported, once the test is completed. It includes a description of the sub-scales and how they were scored, the examinee's score per sub-scale via an
easy-to-read percentile-graded bar chart, detailed performance tables, and an analysis of the examinee's errors.
8. The automatized process of extracting results without requiring any kind of data to be recorded and sent by the examiner, bypasses the time-consuming process of calculating the raw scores and
then converting them to percentile values by the examiner while eliminating any human error in the calculation.
• To summarise students' strengths and weaknesses in Mathematics by providing a miniature of their individual mathematical profile.
• The early, valid and reliable identification of students who are struggling in Mathematics or may be experiencing learning difficulties in Mathematics - Dyscalculia and require further
• In differentiating mathematics teaching strategies to meet the needs of all students.
The MathPro-S Test subscales
The MathPro-S Test, as shown in the table below, consists of 4 subscales for 1st grade and 5 subscales for grades 2 - 6 which assess different mathematical skills. Each subscale contains 8 trials
which were selected from the corresponding subscales of the full version of the test using the Item Response Theory. The trials of the subscales of the MathPro-S Test have been selected in such a way
that they are more sensitive to assessing students with low or average ability.
Upon completion of the MathPro-S Test, a detailed results report of the student is automatically exported.
The above packages are available only to CERTIFIED EXAMINERS
The second control gate takes place through the administration of the full version of the Mathematical Profile Test. The MathPro Test is an online assessment tool for assessing the mathematical
skills of Grade 1-6 students.
It is a self-administered online tool, which can be administered individually or in groups. It includes 18 subscales which are categorised into mathematical skills based either on specific numerical
cognitive systems (number sense) or general domain cognitive skills (memory, visuo-spatial, reasoning).The MathPro Test is considered a reliable and valid tool which can be used both for large-scale
studies and for the detailed assessment of the mathematical profile of children with (or without) learning difficulties in mathematics - dyscalculia in order to be used for diagnostic purposes.
The in-depth assessment provided by the MathPro Test can be a key tool for diagnosing specific individual mathematical skills deficits. Such an approach is in line with the prevailing view according
to more recent scientific findings, which argue that Learning Difficulties in Mathematics (MLD) - Dyscalculia present heterogeneity and therefore should be assessed at an individual level. This is
also in line with the way of diagnosing MDM-Dyscalculia recommended by the DSM-V (Diagnostic and statistical manual of mental Disorders) with a parallel assessment of additional cognitive and
non-cognitive factors by a multidisciplinary team of specialists.
• To experts who want to determine - diagnose whether a child has learning difficulties in mathematics - dyscalculia. In this case it is possible to identify precisely the mathematical domain where
the problem occurs.
• To specialists who want to investigate both the strengths and weaknesses of a child in mathematics in order to tailor a teaching programme that is compatible with the individualised mathematical
profile of each child, considering mainly his/her strengths.
• To researchers who want to study a wide range of mathematical skills using the most recent methodological tools through a quick and automated way of data collection.
The MathPro Test is currently administered and interpreted exclusively by the MathPro Education science team or by researchers upon request.
1. It is administered online through a computer, regardless of the user's operating system and geographic location, and is completed in 45-60 minutes on average, depending on the pace of the
2. All answers are given solely via the computer mouse, so the child does not need to write or say anything. The answers are recorded in a database and processed in a way that ensures their
3. No trained examiner is required to give instructions as these are given by the computer through animations as well as verbal and written instructions. The instructions for each subscale are clear
and can be repeated on demand by the examinee. After the video instructions, three practice trials follow.
4. It can be easily administered both individually and in groups. In the case of children with specific learning difficulties, individual administration is recommended.
5. It is automatically adapted to the grade of the student by excluding all and/or part of the trials of particular subscales in early grades.
6. In part of the sub-scales, termination criteria are automatically activated (e.g. after 3 consecutive errors).
7. The data (answers of the examinees) are collected in real time on a central server and can be exported in excel format at any time, making statistical processing very easy.
8. The administration and recording of responses takes place seamlessly even if the internet connection is temporarily interrupted or the connection speed is low.
9. The individualized report of the results is automatically extracted immediately after completion of the test and includes scores (percentiles) for each subscale both for accuracy and response
time. Finally, an individualised analysis of errors is carried out, which allows a qualitative analysis of the performance of each examinee.
10. The automated process of extracting the results bypasses the time-consuming process of calculating the initial scores and then converting them into percentiles by the examiner while eliminating
any human error in the calculation.
• For a detail record of the student's strengths and weaknesses in Mathematics,outlining his/her individual mathematical profile, and highlighting the way in which he/she can learn more effectively
• For a valid and reliable diagnosis of specific mathematical skills deficits at an individual level.
• For the selection of mathematics teaching strategies by experts and teachers, which are compatible with the mathematical profile of each pupil, either to address potential difficulties in
mathematics or to improve mathematics achievement , mainly by exploiting pupils' strengths which will compensate for their difficulties, thus providing them with positive motivation to continue,
regardless of the specific difficulty a pupil may have been diagnosed with (e.g. dyscalculia, dyslexia, ADHD, autistic spectrum, etc.).
• For conducting large-scale research studies at an international level. The MathPro Test is available and used for research purposes in English, Greek, French, Italian, Maltese and Dutch, and is
in the process of being adapted to other languages.
The following subscales are selected/adapted by grade either through predefined criteria or through termination criteria (e.g. stop after three consecutive incorrect responses) in those activities
where the trials are of increasing difficulty.
Computer mouse speed
Children are presented on the computer screen with an icon of a cat on the one side and an icon of a spot on the other and are asked to find as quick as possible the cat: “Where is the cat?” by
clicking on it with the computer mouse. This subtest is intended to measure the motor reaction time of using the mouse to control this in Single and Multi-digit Numbers Comparison subtests that use
the mouse for the child’s response production.
Single-digit Number Comparison
Multi-digit Number Comparison
Dots magnitude comparison
The MathPro Test is the fruit of the collaboration of two researchers, Giannis Karagiannakis (University of Athens) from the field of mathematical cognition and Marie-Pascale Noël (Catholic
University of Louvain, Belgium) from the field of child neuropsychology, who are both experts in the development of mathematical skills and learning difficulties in mathematics or dyscalculia.
How reliable and valid is it?
The MathPro Test has so far been administered to populations of primary education school students (grades 1 to 6) in Belgium (Karagiannakis & Nöel, 2020), Greece (Karagiannakis, Roussos, Polychroni,
2021), Italy (Baccaglini-Frank, Karagiannakis, Pini, Termine & Girelli, 2020), Malta (Farrell, Falzon & Karagiannakis, 2020) and the Netherlands (under publication).
The results of the above studies showed that it is a tool that has a satisfactory degree of internal consistency as well as test - retest reliability. It is observed increased performance of students
in the individual subscales across all classes with the level of difficulty of the trials within the subscales varying from grade to grade. Students with math difficulties performed significantly
lower on the MathPro Test than their peers. Students' performance on the MathPro Test in all grades was significantly correlated with performance on a standardized math assessment test confirming the
convergent validity of the instrument.
In summary, the findings so far strongly support the reliability and validity of the MathPro Test as well as the sensitivity of the instrument to the factors of grade level, subtests difficulty, and
math difficulty. | {"url":"https://www.mathpro.education/en/mathpro-test/mathpro-s-test","timestamp":"2024-11-03T18:23:54Z","content_type":"text/html","content_length":"148876","record_id":"<urn:uuid:806fbd5a-3024-47b5-99aa-a8861f39e1b1>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00522.warc.gz"} |
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2.1: One-Sided Limit Types
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A one sided limit is exactly what you might expect; the limit of a function as it approaches a specific x value from either the right side or the left side. One sided limits help to deal with the
issue of a jump discontinuity and the two sides not matching.
Is the following piecewise function continuous?
-x-2 & x<1 \\
-3 & x=1 \\
x^{2}-4 & 1<x
Evaluating One Sided Limits and Continuity
A one sided limit can be evaluated either from the left or from the right. Since left and right are not absolute directions, a more precise way of thinking about direction is “from the negative side”
or “from the positive side”. The notation for these one sided limits is:
\[\lim _{x \rightarrow a^{-}} f(x)\]
\[\lim _{x \rightarrow a^{+}} f(x)\]
The negative in the superscript of a is not an exponent. Instead it indicates from the negative side. Likewise the positive superscript is not an exponent, it just means from the positive side. When
evaluating one sided limits, it does not matter what the function is doing at the actual point or what the function is doing on the other side of the number. Your job is to determine what the height
of the function should be using only evidence on one side.
Take the graph below. What are the one sided limits at -5, -1, 3 and 5?
CK-12 Foundation - CCSA
Each point should have two limits, one from the left and one from the right.
You have defined continuity in the past as the ability to draw a function completely without lifting your pencil off of the paper. You can now define a more rigorous definition of continuity.
Continuity at a point exists when the left and right sided limits match the function evaluated at that point. In other words, a function is continuous at a if:
\[\lim _{x \rightarrow a^{-}} f(x)=f(a)=\lim _{x \rightarrow a^{+}} f(x)\]
For an entire function to be continuous, the function must be continuous at every single point in an unbroken domain.
Example 1
Earlier, you were asked how to confirm the function
-x-2 & x<1 \\
-3 & x=1 \\
x^{2}-4 & 1<x
is continuous. In order to confirm or deny that the function is continuous, graphical tools are not accurate enough. Sometimes jump discontinuities can be off by such a small amount that the pixels
on the display of your calculator will not display a difference. Your calculator will certainly not display removable discontinuities.
You should note that on the graph, everything to the left of 1 is continuous because it is just a line. Next you should note that everything to the right of 1 is also continuous for the same reason.
The only point to check is at x=1. To check continuity, explicitly use the definition and evaluate all three parts to see if they are equal.
\[\lim _{x \rightarrow 1^{-}} f(x)=f(1)=\lim _{x \rightarrow 1^{+}} f(x)\]
and the function is continuous at x=1 and everywhere else.
Example 2
Evaluate the one sided limit at 4 from the negative direction numerically.
\[f(x)=\frac{x^{2}-7 x+12}{x-4}\]
Remember that evaluating numerically means that you should use a table. When creating the table, only use values that are smaller than 4.
│x │3.9│3.99│3.999 │
│f(x)│0.9│0.99│0.999 │
\[\lim _{x \rightarrow 4^{-}}\left(\frac{x^{2}-7 x+12}{x-4}\right)=1\]
Example 3
Evaluate the following limits.
Most of the time one sided limits are the same as the corresponding two sided limit. The exceptions are when there are jump discontinuities, which normally only happen with piecewise functions, and
infinite discontinuities, which normally only happen with rational functions.
The reason why ∞ is preferable in this case is because the two sides of the limit disagree. One side goes to negative infinity and the other side goes to positive infinity (see the graph below). If
you just indicate DNE then you are losing some perfectly good information about the nature of the function.
CK-12 Foundation - CCSA
Example 4
Evaluate the following limits.
Example 5
Is the following function continuous?
Use the definition of continuity.
so this function is discontinuous at x=−1. It is continuous everywhere else.
Evaluate the following limits.
Consider h(x) shown in the graph below.
CK-12 Foundation - CCSA
Review (Answers)
To see the Review answers, open this PDF file and look for section 14.6.
Term Definition
continuity Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at
every single point in an unbroken domain.
Continuous Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at
every single point in an unbroken domain.
Jump discontinuities Inverse functions are functions that 'undo' each other. Formally f(x) and g(x) are inverse functions if f(g(x))=g(f(x))=x.
limit A limit is the value that the output of a function approaches as the input of the function approaches a given value.
Removable Removable discontinuities are also known as holes. They occur when factors can be algebraically canceled from rational functions.
Removable Removable discontinuities are also known as holes. They occur when factors can be algebraically canceled from rational functions.
two-sided limit A two-sided limit is the value that a function approaches from both the left side and the right side.
Additional Resources
PLIX: Play, Learn, Interact, eXplore - One-Sided Limits
Video: Determining Limits and One-Sided Limits Graphically
Practice: One-Sided Limit Types
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Some of carbon isotopes in sedimentary rocks younger. Radiometric dating and most fossils. Free to determine the cell from prehistoric fossils less than 60, bones and other. Also, so the last time.
View the most familiar with dates was developed by over 70. Scientists to be dated using radioisotopes for dating is a fossil or photosynthesizing. | {"url":"https://asta-viadrina.de/why-carbon-dating-is-not-reliable/","timestamp":"2024-11-04T17:18:02Z","content_type":"text/html","content_length":"109798","record_id":"<urn:uuid:0bc2d61e-cc56-4f4a-a2d4-0cc12b0c4a5e>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00273.warc.gz"} |
How Many Pennies are in $100? - Measuring Expert
There are 10,000 pennies in $100.
How many pennies are in $100?
If you had $100 in pennies, you would have 10,000 pennies! That’s a lot of copper. In terms of weight, $100 in pennies would weigh about 22 pounds (or 10 kilograms).
How Many Pennies are in 1000
There are 1000 pennies in a roll. There are 50 rolls in a box. There are 100 boxes in a pallet.
How Many Pennies in 1 Dollar
A single dollar bill is made up of 100 pennies, or four quarters. A quarter is worth 25 cents, or two dimes and a nickel. A dime is worth 10 cents, or two nickels.
And a nickel is worth 5 cents. So if you have 100 pennies, that means you have $1.
How Many Pennies are in 10,000
There are 10,000 pennies in $100. To get this amount, you would need to have 100 one dollar bills and exchange them for pennies at a bank. You could also earn 10,000 pennies by working at a job that
pays you $0.01 per hour for 10,000 hours.
How Many Pennies are in 100,000
There are 100,000 pennies in 100,000 cents. This is because there are 100 cents in 1 dollar, and there are 1000 dollars in 1 thousand. So, 100 multiplied by 1000 equals 100,000.
How Many Pennies are in 50
How Many Pennies are in 50? According to the U.S. Mint, there are 50 pennies in a roll of coins. This means that if you have 50 pennies, they will all fit nicely into a roll.
Of course, this also means that if you have more than 50 pennies, you’ll need more than one roll!
Credit: why.do
Does 1000 Pennies Equal 100 Dollars?
It depends on how you define “equal.” If you mean in terms of total value, then yes, 1,000 pennies is equal to $100. However, if you mean in terms of weight or size, then no, 1,000 pennies does not
equal $100.
Finally, if you mean in terms of purchasing power, then it again depends on a number of factors including inflation and the current economic conditions.
How Many Pennies are in $20?
There are 2,000 pennies in $20. This is because there are 100 pennies in a dollar, and 20 dollars equals 2,000 pennies.
How Much is a 100K Pennies?
If you had 100,000 pennies, it would be the equivalent of $1,000. This is because there are 100 pennies in every dollar. So, if you had 100,000 pennies, it would be the same as having 1,000 dollars.
Does 100 Pennies Make $1?
Yes, 100 pennies make $1. Pennies are worth one cent each, so when you have 100 of them, they add up to $1.
There are 100 pennies in $1, so there are 10,000 pennies in $100.
Rakib Sarwar is a seasoned professional blogger, writer, and digital marketer with over 12 years of experience in freelance writing and niche website development on Upwork. In addition to his
expertise in content creation and online marketing, Rakib is a registered pharmacist. Currently, he works in the IT Division of Sonali Bank PLC, where he combines his diverse skill set to excel in
his career. | {"url":"https://www.measuringexpert.com/how-many-pennies-are-in-100/","timestamp":"2024-11-12T21:31:32Z","content_type":"text/html","content_length":"117977","record_id":"<urn:uuid:1f70084b-a9bb-4a86-8034-c5c4d5b79362>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00663.warc.gz"} |
Special Message from the Teacher
Welcome to the TabletClass Math Algebra 2 course! First, I want to say that I’m very excited to have you as a student. My goal is to give you an enjoyable and high quality learning experience.
Moreover, I want you to know that you can master this material if you work hard and never give up. The secret to being successful in mathematics is your approach to studying the topic- i.e. your
study habits. From years of teaching math I can say that those students with the best study habits almost always earn the top grades. As such, parents and teachers must focus on holding students
accountable for the quality of their work.
Below are critical guidelines for students as they take the course:
1. Never give up- especially when a topic is not understood easily or immediately.
2. Strive to be as neat and organized as possible.
3. Excellent note taking is a must to succeed in math.
4. Show all steps when working problems.
5. Double check your work as you write your solution steps.
6. Always go back and review incorrect problems and discover where the error was made.
7. Master the fundamentals and don’t move forward unless you understand previous material.
Remember, the course material builds on itself so you want to ensure that you don’t skip chapters and sections. Furthermore, you want to correct your weak areas before moving onto the next
topic. Lastly, I want to stress that you can be great in math if you work hard. Even if you have struggled in math before I want you to look at this course as a fresh start in your mathematics
journey- I know in my heart you can ace this course!
Best of luck!
John Zimmerman
TabletClass Math Teacher
Complete and Continue | {"url":"https://tabletclass-academy.teachable.com/courses/tabletclass-math-algebra-21/lectures/9269346","timestamp":"2024-11-06T01:46:40Z","content_type":"text/html","content_length":"283492","record_id":"<urn:uuid:e3608611-0df5-4711-9da9-a2bcc2223366>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00377.warc.gz"} |
Compute the Rank as a Percentage in PieCloudDB
In this article, we'll explore how to compute the rank as a percentage within PieCloudDB, a cloud-based database service designed to manage large datasets efficiently. Understanding how to calculate
the rank as a percentage can help you analyze data trends and make data-driven decisions.
Original Problem Scenario
The initial problem is unclear and could be phrased more understandably. The original code snippet was not provided, but let's assume you want to compute a rank percentage of certain data entries in
Revised Problem Statement
How do I compute the rank of a dataset entry as a percentage in PieCloudDB?
Example Code
Here’s a basic example to illustrate how one might compute ranks as percentages within a hypothetical dataset in PieCloudDB.
SELECT entry_name,
(RANK() OVER (ORDER BY score DESC) - 1) * 100.0 / COUNT(*) AS rank_percentage
FROM dataset_table
ORDER BY rank_percentage DESC;
In this code snippet:
• entry_name represents the column of interest, where you are tracking specific entries.
• score is the field based on which the ranking is calculated.
• The RANK() function assigns a rank to each entry based on its score, ordering from highest to lowest.
• This rank is then converted into a percentage of the total entries using the formula (RANK - 1) * 100 / COUNT(*).
Detailed Explanation
Understanding Ranks and Percentages
1. Rank Calculation: Ranks are useful in identifying the position of an entry compared to others. In our example, the entry with the highest score will get a rank of 1, the second highest will get a
rank of 2, and so on.
2. Percentage Conversion: Converting the rank into a percentage provides a clearer perspective. Instead of knowing that an entry is ranked 5th, saying it is in the top 20% can be more intuitive for
3. Implementation in Queries: The SQL query uses window functions (RANK() and COUNT()) to achieve this in a single step, making it efficient for data retrieval in large datasets.
Practical Example
Let's say you have a dataset of students with their scores in an exam. You want to understand the performance of each student relative to their peers. By applying the above SQL query, you can easily
extract each student's score and its rank percentage, providing insights such as which students are performing in the top 10%, 20%, or even 50%.
Computing the rank as a percentage in PieCloudDB can be a valuable technique for analyzing data. This method allows for intuitive understanding and communication of how individual data points relate
to the dataset as a whole.
Useful Resources
• PieCloudDB Documentation - Official documentation for advanced queries and functionalities.
• SQL Window Functions Guide - Learn more about window functions in SQL.
• Data Analysis with SQL - A comprehensive tutorial on analyzing datasets using SQL queries.
By following the outlined steps and utilizing the example provided, you'll be able to compute ranks as percentages effectively in your own datasets within PieCloudDB. This analysis not only enhances
your understanding of your data but also allows for better insights and decision-making. | {"url":"https://laganvalleydup.co.uk/post/compute-the-rank-as-a-percentage-in-pie-cloud-db","timestamp":"2024-11-05T00:59:56Z","content_type":"text/html","content_length":"82329","record_id":"<urn:uuid:6c480dbe-e514-4e14-88f7-6b917e0b5ce6>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00323.warc.gz"} |
Finding the Time Intervals in Which the Acceleration of a Particle Is Zero Using a Velocity–Time Graph
Question Video: Finding the Time Intervals in Which the Acceleration of a Particle Is Zero Using a Velocity–Time Graph Mathematics • Third Year of Secondary School
The figure shows a velocity time graph of a particle moving in a straight line. When is the particle’s acceleration zero?
Video Transcript
The figure shows a velocity–time graph of a particle moving in a straight line. When is the particle’s acceleration zero?
We’re given a graph that represents the velocity 𝑣 of a particle at time 𝑡. And we’re looking to find some information about the acceleration. So we’re going to begin by linking acceleration with
velocity. We know that the definition of acceleration is rate of change of velocity. And so if we’re given an expression for 𝑣 in terms of time 𝑡, we can differentiate that with respect to time to
find an expression for acceleration. We also know that the derivative represents the slope of a curve.
And so if we consider this graphically, we can say that acceleration is the slope of the velocity–time graph. And we can therefore reword our question and ask ourselves, well, when is the slope of
our graph zero? The slope of the graph looks like a horizontal line. And we see that that occurs over here and over here.
Another way of saying this is that the velocity of the graph remains constant at these points. If we read off of the 𝑡-axis or the horizontal axis, we can see that the slope of our graph is zero from
𝑡 equals four to 𝑡 equals six and from 𝑡 equals 10 to 𝑡 equals 13. We’re not given any units for our time in this question. So we can say that these are in time units.
The acceleration of the particle is zero from 𝑡 equals four to 𝑡 equals six and 𝑡 equals 10 to 𝑡 equals 13. | {"url":"https://www.nagwa.com/en/videos/748143709246/","timestamp":"2024-11-12T10:08:22Z","content_type":"text/html","content_length":"249569","record_id":"<urn:uuid:72766635-0212-4965-b12c-1ec20ab0a2cc>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00820.warc.gz"} |
Pub-stomping Option Markets with ARIMAX [Code Included]
Holy-grail confirmed. Don't believe me? Deploy it yourself, first-hand.
Pubstomp (v.) - the act of coordinating to execute a well-defined strategy against a randomly-assembled team of players on a public server.
Well, we’ve been doing something very similar; except in this case, we’re not playing video games:
To quickly recap; by using data from all 11 S&P 500 sectors, we trained an ARIMAX model with the goal of predicting the overnight direction of the S&P 500. We theorized that due to the leverage and
multiplicative nature of options, the model would only need to be right >50% of the time to generate a long-term profit. In our model analysis stage, we saw figures much better than 50%, so it
encouraged us to dive right into production to see how true-to-reality it was.
As demonstrated, it was definitely as real as we hoped for.
So, in what may prove to be a foolish move in retrospect, I am going to release the full code for this so that you may replicate this yourself first-hand.
But before releasing the code, there are a few finer-points that we should touch on.
How Does This Even Work?
To break-down the intricacies of the model, it will help us to capture the story through plots:
To get a more intuitive understanding, let’s look at the “SP500_returns vs. Energy_returns” plot:
A cross-correlation plot shows the correlation between two different time series at different time lags. For example, in the plot above, the value for 0 on the x-axis represents the correlation of
both time series just outright. So, in this case, the returns of the energy sector are correlated with the returns of the S&P 500 by about 30% (0.30).
The concept of time lags come into play after that first value. The value for 1 on the x-axis represents the correlation of 1 time lag. So in this case, it represents the correlation of the energy
returns on day 1, compared to the S&P 500’s return on day 2. Which in this case is very close to 0%; this implies that the S&P 500’s next day return is not very much influenced by the prior day’s
returns of the Energy sector.
An observation you may have noticed is that in each of the plots, there appears to be a mean-reversion trend across the time lags, before it stabilizes to a constant zero correlation after ~20 days:
So, this is where the power of the model really starts to shine. The AR component of AR.I.MA.X (Auto Regressive), combines all of these correlation values and their mean-reverting nature to help
reach a well-rounded prediction. Then, the I component (Integrated) uses those prediction errors to improve itself and better choose the appropriate weights to each sector.
So, now that we’ve taken a peek under the hood of how we’re getting these predictions, let’s look at how we successfully apply it to real-world markets.
From Textbook to Profit
The core logic of capturing this is simple: based on the direction the model expects the market to open, we long/short the asset before close to sell/buy it at the open.
However, the tricky part is determining how we can get the absolute highest leverage possible. To narrow down our search we needed to examine each tradeable S&P 500 product:
3x Leveraged S&P 500 ETFs
SPXL, the Direxion Daily S&P 500 Bull 3X Shares, simply aims to offer 3x the daily returns of the standard S&P 500. So, if SPY increases by 1%, SPXL aims to return 3%.
Despite what you may immediately think, this is actually the most sub-optimal way of capturing this edge, for a few reasons:
1. While the returns are leveraged, the shares are still priced at ~$97, so if you are starting with a balance of say, $1,000, you will only be able to only purchase about 10 shares per trade.
2. The options for these products are volatility-adjusted. Since it is known that these products have significantly higher volatility by design, they are quoted with higher implied volatilities. For
example, let’s compare the implied volatilites of an ATM call on both SPY and SPXL:
1. SPY ATM Call Implied Volatility - 10%
2. SPXL ATM Call Implied Volatility - 30%
This means that we get no additional boost in profit by buying options on this ETF as opposed to options on the standard S&P 500.
3. No daily expiration options. These products only have weekly expiration options which are inefficient for daily trading since they remain relatively stable due to the preserved time value. We
want the 0-DTE options that either loses its value or significantly increases.
So, leveraged ETFs are out.
S&P 500 Futures
The E-Mini S&P 500 futures are both extremely liquid and provide a great deal of leverage. The futures operate on a tick-model where the price only moves in increments of $0.25 (4,000 to 4,000.25).
Each tick has a profit value of $12.50, so each $1 move in the future results in a profit or loss of $50 ($12.50 x 4).
On average, the overnight return is around +/- 0.45%, which based on the most recent futures price, implies a $20 price movement (4,607 * .0045). This implies a +/- $1,000 average PnL. This is great,
until you see the margin requirements:
The intraday margin would make this a viable choice if we were trading during the day, but this is specifically an overnight strategy, so that means we would have to post upwards of $12,000 of
capital with an expectation of a $1,000 profit or loss.
But are the options any better?
The options suffer the same cost-prohibitiveness since the strikes are only quoted in increments of $5:
Additionally, since the futures are not a leveraged product — if the S&P 500 rises by 1%, the returns of an ATM futures call will be virtually identical to the returns of an ATM call on SPY, since
both products represent the same underlying index.
So, E-Mini futures are also out.
SPY ETF Options
This brings us back to our original strategy of using basic calls and options on SPY.
Not only are 0-DTE options available, but the costs can be extremely low, increasing accessibility to all traders; large and small. In recent times (relatively low volatility), the cost for an ATM
option expiring on the next day is around $87-130. Since we’re just buying the options, this is the total cost and we don’t incur losses greater than that premium.
We still get the multiplicative nature of derivative contracts, and liquidity isn’t even a fore-thought as this is arguably the most liquid option chain in the entire investing universe.
So, SPY options are in!
The Strategy
So, now that we have what we believe to be the most optimal instrument, we can now iron out the most optimal way to use the instruments.
This post is for paid subscribers | {"url":"https://www.quant-galore.com/p/pub-stomping-option-markets-with","timestamp":"2024-11-03T00:55:36Z","content_type":"text/html","content_length":"196525","record_id":"<urn:uuid:545b8763-f0a2-4afb-b529-d7d5e103d86e>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00106.warc.gz"} |
What is the Fatigue Strength in Welding? - Weldingtech.net
What is the Fatigue Strength in Welding?
The factors that affect the fatigue strength of a welded joint include:
• the type of metal,
• the thickness of the metal,
• the welding process,
• and the design of the welded joint.
Fatigue strength is an important consideration in the design of welded structures, such as bridges and offshore platforms.
The fatigue strength of a welded joint is affected by the type of metal used in the joint. The most common metals used in welding are carbon steel, stainless steel, and aluminum. Each of these metals
has different properties that affect the fatigue strength of the welded joint. For example, carbon steel is more susceptible to fatigue than stainless steel or aluminum.
The thickness of the metal also affects the fatigue strength of the welded joint. In general, thicker metals have higher fatigue strengths than thinner metals. However, the welding process can also
affect the thickness of the metal and, as a result, the fatigue strength of the welded joint.
The welding process used to create the welded joint also affects the fatigue strength of the joint. The most common welding processes are arc welding and gas tungsten arc welding. Arc welding is more
commonly used for carbon steel and stainless steel, while gas tungsten arc welding is more commonly used for aluminum.
What is the fatigue strength of a material?
The fatigue strength of a material is the ability of the material to resist failure under repeated or alternating loads. The factors that affect the fatigue strength of a material include the type of
metal, the thickness of the metal, and the welding process.
What is a fatigue test in welding?
A fatigue test in welding is a test that measures the ability of a welded joint to resist failure under repeated or alternating loads. The factors that affect the results of a fatigue test include
the type of metal, the thickness of the metal, and the welding process.
What is the fatigue strength formula?
The fatigue strength formula is a mathematical formula that takes into account the type of metal, the thickness of the metal, and the welding process. The fatigue strength formula can be used to
calculate the maximum load that can be applied to a welded joint without causing failure.
Fatigue life
It is the number of cycles of repeated stress that a material can withstand before failure. The endurance limit is the maximum stress that can be applied to a material without causing failure.
Fatigue loading
It is the application of repeated or alternating loads to a material. The loads can be either static (constant) or dynamic (varying).
Related Links
Fatigue limit
Corrosionpedia – What is a Fatigue Strength? – Definition from Corrosionpedia
Fatigue limit
Fatigue Strength | Definition of Fatigue Strength
Related Videos
Basic Fatigue and S-N Diagrams
Fatigue Failure - Theories of Elastic Failure - Strength of Materials
Basic Fatigue and S-N Diagrams
Fatigue Failure - Theories of Elastic Failure - Strength of Materials | {"url":"https://weldingtech.net/fatigue-strength/","timestamp":"2024-11-14T17:50:57Z","content_type":"text/html","content_length":"82013","record_id":"<urn:uuid:a15c356e-c599-4a7c-9784-3ed415210246>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00130.warc.gz"} |
Math Fact Fluency Races: A Fun and Engaging Math Fact Game for Kids - Saddle Up for 2nd Grade
Math fact fluency is key in the primary grades. By the end of 2nd grade, kids should be proficient with their math facts up to 20. One of the best ways to keep students engaged is by making math fact
practice fun and exciting. This math fact game is a classroom favorite. Read on to learn how to play math fact races and how you can differentiate it for your students.
Math Fact Races Game
Math Fact Fluency Races is a fun math fact game that puts a twist on the traditional game where students go to the board, write a math fact, and see how fast they can solve it. This game is perfect
for 2nd grade students, but it can easily be adapted for younger grades or upper grades.
How to Play the Math Fact Game
To play Math Fact Races, first, split your class up into teams. You can have two teams or more if you have the space in your classroom.
Draw two large circles on the whiteboard. Inside of those circles, write the numbers 0-10 all the way around. Leave space in the middle to write a larger number. The number in the middle is the main
Students will add the main number with a smaller number and solve for the sum around the outside of the circle.
When the teacher says go, the two teams race to complete the circle, adding numbers all the way around. The team that completes all of their math facts the fastest and has them all correct is the
winner of the math fact game.
The students do not have to complete the circle in order. For example, the first student can solve 5+2 and write the sum of 7 on the outside of the circle. Then, they can pass the marker to the next
person and they can do 5+9 and write the sum of 14 on the outside of the circle.
Allowing them to solve for the sums in any order allows for differentiation, as some students may struggle with adding higher numbers. This allows all students to participate without feeling left
After each round, the team that won that round gets a point. Then, the teacher changes the number in the middle and the game starts over.
How to Differentiate the Math Fact Game
This math fact game is so easy to incorporate into your lesson plans. You can add this to your math lesson plans, play as a math warm-up game, or even a fun anytime math game. It is perfect for those
small chunks of time between activities or at the end of the day.
This game can easily be differentiated to practice subtraction, multiplication, or division facts. You can make it easier or more challenging by making the number in the middle smaller or larger.
Digital Math Fact Races
If you’re looking for a ZERO PREP way to play math fact races in your classroom, I have digital versions of this game available in my TPT store! You can choose from a spring-themed set or a
space-themed set of this math fact game.
These digital math fact games will help you cut down on prep time while keeping your students engaged and having fun as they review their math facts. All you have to do is display and play!
Each set includes addition and subtraction facts within 20 as well as 2 versions each. There is a version with the numbers in order and a mixed order version, which makes for easy differentiation.
Whether you choose to play this math fact game on the whiteboard or with the digital versions, it is the perfect math fact practice game to incorporate into your whole group lessons, math warm-ups,
to check student understanding, or even to use during indoor recess!
For more ideas on how to help your students build their fact fluency, check out this blog post.
If you’re looking for more fun and engaging math fact games, fill out the form below to get 5 FREE math fact games delivered straight to your inbox! You’ll get one game delivered straight to your
inbox each day for the next 5 days.
Want to find more engaging activities for your math block? Check out my guided math units for 1st, 2nd, and 3rd grade! Each unit is complete with detailed lesson plans, whole group and small group
activities, interactive notebook activities, task cards, games, math crafts, higher order thinking activities, and more!
Comment below and let me know what your students think of the Math Fact Fluency Races game! | {"url":"https://saddleupfor2ndgrade.com/math-fact-game-fluency-races/","timestamp":"2024-11-08T01:31:58Z","content_type":"text/html","content_length":"137580","record_id":"<urn:uuid:5f9f8e7e-717d-40d3-b50e-d04c05c3e76f>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00209.warc.gz"} |
pare1d0scope koda
generative art | antonino & br | drop on Kodadot.
anchored in a not-so-binary world, the pare1d0scope generates unique patterns of 4-bit squares by applying a generative mix of symmetry, ordering, subdividing, and diagonals adjustments.
the algorithm generates a sequence of the 2^4 possible 4-bits squares, adjusts inner diagonals, then draws them on a defined size canvas after applying a special Polkadot-inspired color palette.
symmetry and ordering combinations produce rarer iterations.
shortcuts: [click] Adjust diagonals of selected 4-bit square iteration, [1-4] Adjust diagonals for all squares, [p] Print png.
auction starts on november 16, 2023, 18:00 on Kodadot | {"url":"http://rabusseau.art/projects/polka_pare/","timestamp":"2024-11-02T15:05:46Z","content_type":"text/html","content_length":"8301","record_id":"<urn:uuid:6cd41f5a-c8ef-4d02-9739-d90c8a57ff6d>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00314.warc.gz"} |
Programming is complicated. Different programs have different abstraction levels, domains, platforms, longevity, team sizes, etc ad infinitum. There is something fundamentally different between the
detailed instructions that goes into, say, computing a checksum and the abstractions when defining the flow of data in any medium-sized system.
I think that the divide between coding the details and describing the flow of a program is so large that a programming language could benefit immensely from keeping them conceptually separate. This
belief has led me to design a new programming language - Glow - that has this separation at its core.
Ai building efforts start at definitions: Ai that can
specify goals and weight them , acquire combine breakdown and refine strategy.
A strategy specifies goals, their desirability and at what likelihoods to take what actions on what (set of) conditions.
Devising strategies can be broken down into:
creating and assessing conditions for actions,
weight of goals, estimates of cost for actions,
estimates of effectiveness of actions, finding related strategies,
taking strategies apart,
combining strategies,
covering contingencies,
evaluating strategies
I would be interested to see the input from which this AI (when implemented) would be able to learn how to play the 5-in-a-row game.
This comment has been removed by the author.
@acetoline No, the project is not abandoned, but thanks for asking :). I tend to post infrequent, overambitiously long posts, so a few weeks silence is normal.
The reason the github activity is low is more silly. I am currently in something between the design and implementation stage, writing Python code with a few pseudocode elements and a lot of prose.
For some reason, I have not considered this semi-code "commit-worthy".
I promise a github update this week.
Hi, I noticed there hasn't been any activity on your blog or github lately. I hope you haven't abandoned the project.
Doesn't sound like a well scalable solution. Don't get overexcited/misled after some early luck in well defined toy worlds. With teaching by manual algorithm entry by techies, you aren't gonna get
very far.
Hopefully, yes, it should be able to solve general problems using more specialized algorithms working together. It will not, however, take a set of specialized algorithms (let's say playing chess,
checkers, poker and backgammon) and produce a general game playing algorithm. That is not how it achieves generality.
It is geared towards very technical users. It takes input tasks as snippets of code and gives a set of inputs that makes the function output true. This is called function inversion and is a fairly
simple way of describing puzzles and technical problems.
If it turns out to be a useful system for solving these types of tasks (a big IF - no one has really been able to achieve that). It would be a very good base on which to build something that can
communicate with non-technical users and interact with our fuzzy world. That is not it's primary purpose, though.
Can this 'AGI' generate general algorithms from a set of relevant non-general algorithms? Will non-technical users be able to teach this AI by describing specific (/non-general) scenarios?
@Jiri Swedes, Norwegians, Danes and many Finns can read Swedish. That makes up a good 0.3% of the earth population :).
Actually, I will remove that. That source code is not for human consumption yet. It is just test cases for analyzing source code, written in an odd Lisp dialect. No actual code relating to
implementing either any of the algorithms I write about or the Scheduler.
One way to build a strong AI is outlined in the http://mind.sourceforge.net/aisteps.html and develops into a simple but gradually expandable AI Mind.
Don't use Swedish in the source, man! 'Nobody' can read that ;-) | {"url":"http://fendrich.se/","timestamp":"2024-11-03T13:29:46Z","content_type":"text/html","content_length":"47682","record_id":"<urn:uuid:7c118daa-1700-417f-a934-0f37da4826c4>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00053.warc.gz"} |
Modelling Height-Diameter Relationship of <i>Pinus Roxburghii </i>in Nepal
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What is Fibonacci trading | Wealthy Traders
What is Fibonacci trading
Fibonacci retracements are a well-known type of technological consideration used by traders to model upcoming possible values in economic bazaars. When used correctly, Fibonacci retracements and
Fibonacci ratios can help traders establish future degrees of help and opposition based on previous price transactions.
It is important to keep in mind that the Fibonacci directions are considered a proof device. According to this circumstance, it is more correct to use the pointer together with other devices of
technological consideration, such as the direction of rate changes, size, and variation of the convergence of moving mediocre (MACD) and moving ordinary. In full, rather than more supporting
pointers, this will be a commercial warning.
What is Fibonacci in trading?
Leonardo Fibonacci is a scientist who appeared in 1170 AD. With his works, I have acquired the Fibonacci order of quantities, and in addition the popular Fibonacci paradisiacal cut. Fibonacci
sequence – this is a few quantities, in which the next quantity is considered simply the sum of 2 previous ones. For example, 0, 1, 1, 2, 3, 5, 5, 8, 13, 21, 21, 34, 55, 55, 89, 144 and so on, while
the order can last indefinitely.
Exactly it is formed in speed of reproduction of 2 abstract bunnies and further increase of population, in case further generations would resume to breed. In the first opinion, it is possible to
present several unclear, that there is an interrelation among arithmetic of the XII century, speed of reproduction of rabbits, and modeling of the future tendency of movement of economic bazaars
together with the support of technological consideration. For what reason are these several quantities so significant for traders?
Fibonacci’s golden ratio
The main interest, as well as the principle, is given to the correspondence among the quantities in order. This is a more significant component of Fibonacci activity. Any quantity in the line,
divided into the preceding quantity, provides 1.618 presence of the subsequent movement downward according to the line. This is commonly known as “Fibonacci’s paradise cut”. For followers of
Fibonacci, there is a great number of samples of observance of this correspondence (or opposite to its quantity 0,618). It has fought a great importance in the concept as a whole that covers us.
For example, if we divide the number of female bees by the number of male bees in the hive, then we have 1.618. For a sunflower, any newest seed is 0.618 expressions from the past. Fibonacci is also
used by people. There are a great number of samples of it, as well as how the paradise section functions in the relationship of our body: for example, the approach of the length of a forearm to the
length of a bunch is 1,618.
Fibonacci’s golden ratio example
In economic bazaars, the Fibonacci Paradise Ratio has the same basis as the previously listed natural actions. If traders apply the paradise cut in their industrial consideration, it usually goes to
3 percent: 38.2% (often rounded up to 38%), 50%, and 61.8% (usually rounded up to 62%). But the presence of needed traders has all chances to apply and the most complex values, such as 23.6%, 161.8%,
423%, 684.4%, etc.
The indicator 38.2% is located by the line of division of the 1st quantity in the line into the quantity, 2 sections to the left. For example, 21, divided into 55, is also 0.382. The figure 23.6% is
located by the division of the 1st quantity in the line into the quantity important 3 sections to the left. For example, 8, divided into 34, also 0.235.
Fibonacci retracement levels
The argument of Fibonacci supporters is as follows: if everything is without exception in nature and society is formed with these Fibonacci proportions, then, surely, in such a case it is also
possible to mention markets? Specialists have a chance to use this aspect if they learn to trade according to Fibonacci using its retracements. Suppose the stock exchange has increased, however, as
well as all bazaars without exception, no one does not move according to the direct direction and begins to decline. Traders will look at the Fibonacci ratios to try to establish where the decline
can stop and the stock exchange will restore its old increase.
Fibonacci retracement rates often together with striking correctness fix the places where the retracement reverses. Adjustment degrees – This is a strong mechanism that can be used in absolutely all
short-term intervals, including day selling and long-term investment. Fibonacci quantities are also of great importance in Elliott’s turbulent belief, a technological consideration device used to
establish bazaar cycles. This mechanism can be used for different asset classes, such as currency, promotions, commodities, and indices.
What is the Fibonacci sequence?
Paradise cut 1.618, the magic quantity, goes to 3 percentages: 23.6%, 38.2%, and 61.8%. These 3 more common percentages, even though certain traders estimate degrees of 50% and 76.4%. 50% is by no
means a Fibonacci number, however, it has turned out to be a very common presence of initial or retracement adjustments. For now, I will concentrate on 50% and the two most common Fibonacci
percentages – 38.2% and 61.8%.
These are put into a plan to try and establish possible secret degrees of help or opposition in a trade. If the stock market goes down to 38.2% from the last rise (the 1st big degree of Fibonacci
adjustment), traders check if a unit of consumers has not emerged. In case this degree of 38.2% is broken, in this case, the next target will be a 50% correction. In case the stock exchange slips
through this degree of 50% adjustment, then traders will watch whether the stock exchange will suspend its decline if it works 61.8% from the last move. For many Fibonacci followers, in case the
stock breaks this 61.8% degree, it means that the trading direction will return to that, together with what someone started.
I can form a Fibonacci retracement by taking the top and trough (or the last 2 places) in the chart and dividing the distance according to the vertical into the previously noted basic Fibonacci
ratios. Already after disclosure of these trader modifications, it is possible to perform horizontal directions, which further will be applied to establish the probable degrees of help and
What is the Fibonacci sequence used for?
The Fibonacci sequence and the Paradise Cut are often found in nature, biology, architecture, and expressive art. They can be noticed in petals of colors, branches of trees, Acid faces, and an
increase in the number of inhabitants. Paradise cut and other Fibonacci correspondences are also often found in economic bazaars and lie at the base of the device “Fibonacci retracement”.
How to use Fibonacci retracements in trading?
• Fibonacci correction directions can be created by dividing the plumb distance among the maximum and minimum quantity points in the basic Fibonacci ratios. Horizontal directions are conducted in
the trader’s chart in the degrees of correction 23.6%, 38.2%, and 61.8%. Certain traders also love to apply the Fifty.0% correspondence. This is in no way a perfect Fibonacci correspondence, but
it can be necessary. Often a significant document is rolled back to about 50%, first of all, rather than extending its initial direction.
• Software provision for charting has adapted the course of Fibonacci directions. Almost all trading platforms allow traders to create Fibonacci directions. In the presence of an uptrend, it is
possible to pick up the “Fibonacci Direction” mechanism, mark a low value, and move the pointer up to a significant value. The pointer will notice in the chart similar major ratios such as 61.8%,
50.0%, and 38.2%.
• Similarly, in the presence of a downtrend, it is possible to pick the Fibonacci Directional mechanism, pick a significant value, and move the cursor down to a low value. The pointer will notice
the main correspondences in the chart. To increase the correctness traders have all chances to use pair tops or pair masses as points of maximum and minimum quantity.
Fibonacci support and resistance
Fibonacci degrees are mainly used to establish the degrees of help and opposition. If a significant document has an upward or downward direction, it is it that usually withdraws somewhat, first of
all, rather than extends the direction. In the presence of this it is often made to return up to the main degree of Fibonacci, for example, 38.2% or 61.8%. These degrees are intended for traders’
signals to enter the latest views during the initial rate change. In the presence of an uptrend, it is possible to open large views (buy) in the presence of a pullback down to the main degree of
help. In the presence of a downtrend, it is possible to disclose short views (realize) in the presence of a pullback of a significant document up to the main degree of counteraction. This mechanism
functions more correctly in general, if the significant document has a direction to increase or decrease.
Examples of the Fibonacci pattern
This sample represents the increase in the value of West Texas Intermediate Black Gold (also called WTI Crude Oil), which is considered a component of commodity trading. Then the exchange stops,
which gives traders a chance to use certain Fibonacci retracements to this event to notice where the help is located. Just as noticeably, the cost is pulling back, but despite the temporary probing,
the 38.2% correction in the $35 area is showing some help as a result. The exchange bounces back and climbs to the newest highs to resume.
Fibonacci trading is not only used in rising markets. In case the stock market has fallen, in this case, Fibonacci fans will use corrections to rebound upwards. Let’s look at a sample trade that has
fallen into the Hundred Points. In case someone rallies in 38.2%, in this case, those who analyze Fibonacci retracements will wait for the competition to exhaust itself. In case this degree is
punctured, in this case, traders will find the turn of the trade to the bottom in the degree of 50%. And, finally, in case this degree is broken, in this case the next target will be a 61.8%
correction of the downward movement, the breakdown of which means that the stock exchange will return to the source of the fall. The following chart shows the decline in GBP/USD vaporization. The
currency pair fell from the area of 1.5200 down to 1.4100, after which it stabilized. Since the exchange stabilized, it was possible to use Fibonacci adjustments for this fall. It is noticeable that
if the stock exchange sharply hit 50%, the resumption ended and the decline was renewed. This sample of this as well as the Fibonacci retracement can help us realize if it is necessary to realize
short views in a downtrend.
Best Fibonacci trading strategies
Fibonacci correction directions are often used within trend trading strategies. If a return is made within a rate change, it is possible to apply Fibonacci degrees to solve the operation during the
main rate change. The concept is that there is a significant possibility that the value of a significant document will fall back from the Fibonacci degree during the initial rate change.
Fibonacci degrees have all the chances to be useful, in case a trader wants to buy a particular significant paper but misses the last increasing direction. In this condition, it is possible to wait
for a pullback. The inclusion of similar Fibonacci ratios, such as 61.8%, 38.2%, and 23.6%, allows traders to establish the probable degrees of pullback and enter into possible trader views.
Fibonacci ratios can be used in many different trading strategies, such as the following:
• Combination of Fibonacci adjustment directions together with the MACD pointer. This policy finds the intersection of the MACD pointer if the value of a significant document touches a significant
Fibonacci degree. If this is done, it is possible to open the trade during a rate change.
• combination of Fibonacci degrees together with the stochastic pointer. This bi-linear pointer can help establish overbought and oversold degrees. The policy finds major signals from the
probability pointer if the value touches a significant Fibonacci degree. These 2 signals together show the chance of revealing the view.
• Fibonacci retracement degrees can be used in different time frames, but the degrees in the longest time frames are clearer. For example, a 38% degree of adjustment in a weekly chart is considered
to be a more significant technological degree than a 38% degree of adjustment in a five-minute chart. Learn more about selecting the right time frames.
Just like all technological consideration devices without exception, Fibonacci correction degrees are more effective when applied within the framework of the most extensive strategy. The use of the
composition of some pointers provides a chance to more specifically set the bazaar directions, increasing the possible income. Equally as a principle, the more supporting conditions, the more
commercial warning.
Not all without exception are considered admirers of the Fibonacci layout and the consideration of the trade. Certain simply believe the degree of self-fulfilling prediction, as they are observed by
a large number of people, and do not observe their special “magical” qualities. But including for skeptics they have all chances to provide an auxiliary degree of comprehension of possible turning
points of the trade, which have all chances to be gloomy in the first opinion. In the presence of the use of industrial pointers in trading, it is always necessary to take into account risk
management strategies. | {"url":"https://wealthytraders.com/what-is-fibonacci-trading/","timestamp":"2024-11-12T08:43:45Z","content_type":"text/html","content_length":"96722","record_id":"<urn:uuid:9564b84e-9c7c-41b3-a2fc-846b33499a65>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00378.warc.gz"} |
Lecture 9: Gravity
Newton’s Embarrassing Secret – Start watching at 9:52 to see the chapters of The Elegant Universe about squaring up Newton’s Law of Universal Gravitation and what we know about the “universal speed
limit” from Einstein’s theory of relativity.
PhET Gravity and Orbits Simulation
You can see how the force of gravity between a star and its planet changes as the masses and distances between the two objects change.
Video Transcript
Hello there! Welcome to lecture 9: gravity!
Gravity is a force we experience all the time in our lives. It allows us to understand concepts such as weight, acceleration, and the motion of planetary objects. Newton’s law of universal
gravitation will allow us to understand how gravity works on both the Earth and other planets, and where the value 9.8 meters per second-squared comes from.
Each of the following concepts will be discussed in this video: apparent weight, the inverse-square law, Newton’s law of universal gravitation, gravitational acceleration, gravitational fields, and
the limits of Newton’s laws.
Apparent weight
Weight is a topic that we’ve discussed in several lectures already. We’ve learned that weight is a force that comes about due to our gravitational attraction with the Earth, and that it’s related to
our mass. While none of that is wrong, it’s also not the full story of what weight is.
As you watch this video, I’d like you to consider where you feel your weight in your body. Where does the sensation of weight come from right now? For me, standing here, I can feel my weight in my
feet. If I were sitting, I’d likely be feeling my weight in my bottom and the backs of my thighs. If I were laying down, I’d feel my weight along my side or my back.
We have weight because of gravity, but our apparent weight comes from the support force that we get from whatever surface we’re in contact with. Our apparent weight is equal to the value of the
support force that is acting on us.
In this video, I jump up and down on a force plate. The force registered by the plate is recorded by Logger Pro. When I stand still, my weight records as being constant. However, when I jump up and
down, my weight changes. When I’m in the air, I’m no longer in contact with the scale and my weight is zero. When I’m coming back to the surface again, my weight increases. This goes to show that
weight is not necessarily constant, even while being located in pretty much the same position on the Earth’s surface.
Any time our motion contains a vertical component of acceleration, whether it be from jumping up and down, riding a roller coaster, or traveling in an elevator, our support force will change, and our
apparent weight will change as well.
Let’s consider riding in an elevator. Any time the elevator moves at a constant speed, there is no acceleration in the vertical direction, and our apparent weight will not change. The net force of
the system is zero. The support force is equal to our mass times gravitational acceleration.
In equation form, we can write this as: our net force (which is equal to our mass times our acceleration) is equal to the support force plus our mass times gravitational acceleration. Recall that
gravitational acceleration is negative 9.8 meters per second-squared.
As the elevator we’re riding in speeds up moving upward, at that time there is a net force pointing up. Our mass hasn’t changed, so the mg term remains the same. The support force becomes greater
than our weight. mg plus the support force equals the resultant force, that net upward force causing the elevator to speed up. This is why our apparent weight increases as we speed up in an elevator
moving upward.
Let’s consider a specific numerical example. Say the occupant of an elevator has a mass of 75 kilograms. Their weight in an unaccelerated condition is negative 9.8 meters per second-squared times 75
kilograms: negative 735 newtons. The elevator accelerates upward at a rate of 4 meters per second-squared. The net force on the person is 75 kilograms times 4 meters per second-squared: 300 newtons.
Mg plus support force equals net force. This means the support force is equal to 300 newtons plus 735 newtons: 1,035 newtons!
If an elevator speeds up moving downward, at that time there is a net force pointing down. The support force becomes less than our weight. mg plus the support force equals a downward pointing force.
This is why our apparent weight decreases as we speed up in an elevator moving downward.
Let’s consider a different numerical example. Our 75 kilogram elevator occupant has an unaccelerated weight of negative 735 newtons. The elevator accelerates downward at a rate of 3 meters per
second-squared. The net force on the person is 75 kilograms times negative 3 meters per second-squared: negative 225 newtons. Mg plus support force equals net force. This means the support force is
equal to -225 newtons plus 735 newtons: 510 newtons!
The extreme condition of this would be a situation where the elevator cable snaps and the elevator moves downward at 9.8 meters per second-squared: free fall. In that case, our apparent weight would
go to zero!
An object in free-fall, moving only under the influence of gravity with no other forces present, will have an apparent weight of zero. If you were to go skydiving, before the parachute deploys, and
before air resistance slows you down, your apparent weight would be zero. Think about using a scale to measure your weight as you fall, there is nothing to give the scale a force reading. In those
conditions you are truly weightless.
For the same reasons, astronauts in Earth orbit: whether they be in a space capsule, the Space Shuttle, or the space station, are also weightless. They are still under the influence of Earth’s
gravitational field, and their acceleration due to gravity is still rather high. The reason that astronauts experience weightlessness is that they are in free-fall around the Earth during their
orbit. To emphasize: astronauts in Earth’s orbit do not experience a zero-gravity condition, only a zero-support force condition.
The inverse-square law
The inverse-square law describes physical properties that decrease when the distance between two objects, or the distance away from a single object, increases. The property and the distance are
inversely related to each other. As distance increases, the physical property decreases. Not only that, but the decrease doesn’t just decrease with distance, but distance-squared. Any change in
distance is going to have a more powerful effect as a result. Mathematically, we can represent the inverse square law as stating that a property is proportional to one divided by the distance
We can see how this looks on a graph by plotting this property. Note that when distance doubles, the intensity of the physical property decreases by one quarter. When the distance is cut in half, the
intensity of the physical property increases by a factor of four.
Many physical properties obey the inverse-square law: light intensity, sound intensity, electromagnetism, and gravitational forces. From a conceptual level, this is because the effect of any single
point of sound, light, electric charge, or mass, dilutes by the distance squared as it moves outward in three-dimensional space.
We’ll see in just a few moments that the inverse-square law plays a role in the effect of gravitational forces. And we’ll also see this again when we learn about electrostatics in lecture 22.
Newton’s law of universal gravitation
Newton’s law of universal gravitation describes how we can quantify the force of gravity acting between any two objects in the universe. The equation states that F equals G m-one m-two over
d-squared. In other words: force equals big G, the universal gravitational constant, times the mass of the first object, times the mass of the second object, divided by the distance between the two
objects, squared.
Note from this equation that the divided by d-squared aspect means this equation obeys the inverse square law. If the distance between two objects were to double, the force would DECREASE by one
fourth. If the distance between two objects were to be cut in half, the force would INCREASE four times.
The denominator of this equation also tells us another interesting thing about gravity; the force of gravity between two objects cannot become exactly equal to zero unless the distance between the
two objects is infinite. Therefore, it can be concluded that all objects of mass that exit in the universe exert gravitational forces on each other. A planet millions of light-years away from you is
exerting a gravitational force on you. However, the value of that force is infinitesimally small. We can effectively treat it as being zero, but it is not exactly zero.
The distance between two objects is more accurately stated as the distance between the center of mass of two objects. Although the density of the Earth is not constant, if we could approximate the
Earth as having a uniform density throughout, we would expect the gravitational force to change as we move along the Earth’s surface. For one thing, the Earth is not a perfect sphere. The distance
between the center of the Earth and the north and south poles is smaller than the distance between the center of the Earth and the equator. Therefore, the force of gravity would be larger at the
poles. In addition, as we move farther away from the center of the Earth, say, by climbing a mountain, the gravitational force would decrease as well. It is important to point out that these
differences are very small, and would not be perceptible unless you had a very accurate scale to stand on to weigh yourself. These effects are furthermore complicated by the fact that the Earth does
not have a uniform density throughout its volume. For the most part, we can treat the gravitational force on the surface of the Earth to be approximately equal, but it is important to note that it is
In fact, astronauts visiting the space station are still under the influence of gravity – that is why the space station is able to orbit the Earth. Without gravity, no force would be able to create a
centripetal force to cause objects to orbit, and they would not be able to move in a circular path. Because the astronauts lack a support force, they experience weightlessness. We will revisit this
subject in the next lecture.
The universal gravitational constant, big G, is 6.67 times 10 to the negative 11 Newton meters-squared per kilogram-squared. The term universal indicates that this number is the same anywhere in the
universe. It’s a very small number, indicating that the force of gravity is relatively weak. In fact, of the four fundamental forces, gravity is the weakest! In order for the force of gravity to be
strong, one or both of the objects must have a lot of mass.
One last interesting thing about gravity: because mass can only come in positive numbers, gravity is only ever an attractive force. When we learn about electricity in lecture 22, we’ll see that
electric charges are capable of both attracting and repelling. However, the force of gravity is only an attractive force, causing two objects to accelerate toward each other.
Let’s do some examples using Newton’s law of universal gravitation.
First, let’s do an example where we’re given numerical values for each quantity and are asked to calculate the gravitational force. Let’s calculate the gravitational force between the Earth and the
sun. The Earth has a mass of 6 times 10 to the 24 kilograms; the sun has a mass of 2 times 10 to the 30 kilograms. The Earth and sun are separated by a distance of 148 times 10 to the 9 meters. We
can plug all of these numbers into the equation for force. F equals 6.67 times 10 to the negative 11 times 6 times 10 to the 24 times 2 times 10 to the 30, divided by 148 times 10 to the 9 meters,
squared, which equals 3.65 times 10 to the 22 Newtons of force. This force keeps the Earth in orbit around the sun.
Now let’s do some examples without numerical quantities where instead we look at what happens to gravitational forces as a result of a change in some quantity. Let’s say we have two planets with
masses of m1 and m2 separated by a distance of d. We can determine what the effect of a change in mass or separation distance will have on the force.
If the mass of one of the planets were to be cut in half, what would the effect be on the force? Force and mass are directly proportional. Therefore if the mass decreases by a factor of two, the
force will decrease by a factor of two as well. The new force would be one half of the original force.
If instead of mass, the distance between the two planets were to change, what would that effect be? If the separation between the two planets is cut in half, what would happen to the force? Force and
distance obey the inverse-square law. If the distance between the two planets decreases by a factor of two, the force will increase by a factor of two-squared: four. The new force would be equal to
four times the value of the original force.
Gravitational acceleration
So far in this class, we have frequently discussed little g, the acceleration due to gravity on the Earth’s surface. We’ve defined little g to be negative 9.8 meters per second-squared. Sometimes,
when we do not need great accuracy in our calculations, we can round little g to be negative 10 meters per second-squared. Where does this number come from?
From Newton’s second law, we know that the net force on an object is equal to its mass times its acceleration. If the net force on an object comes from gravity, then we can use Newton’s second law
and Newton’s law of universal gravitation together. We set G m-one m-two divided by d-squared equal to mass times acceleration. The mass that exists on both sides of the equation is the mass of any
object on Earth: you, me, a butterfly, a tree, or a house. It doesn’t matter. The acceleration due to gravity on any object on the Earth’s surface is equal for all objects on the Earth because the
mass of the object cancels out of both sides of the equation.
The second mass is equal to the mass of the Earth, and the distance is equal to the radius of the Earth. (Assuming the object is at sea level. As we discussed earlier, this value will change if we
climb a mountain or go to the bottom of an ocean, but those effects are pretty small and we’ll ignore them.)
Plugging in the mass of the Earth, which is 5.97 times 10 to the 24 kilograms, and the radius of the Earth, which is 6.37 times 10 to the six meters, we can calculate that little g, the acceleration
due to gravity on the Earth’s surface, is equal to 9.8 meters per second-squared.
What if we wanted to calculate the value of the gravitational acceleration on a different celestial body: the moon, the sun, another planet? In general, g equals G times m divided by d-squared. That
is, the acceleration due to gravity on any celestial body is equal to the universal gravitational constant, times the mass of the celestial body, divided by the radius of the celestial body squared.
Let’s do a couple of examples.
First, let’s calculate the gravitational acceleration on the surface of Mars. Mars has a mass of 6.4 times 10 to the 23 kilograms, and a radius of 3.4 times ten to the 6 meters. We can plug these
values into the equation G times m divided by d-squared. 6.67 times 10 to the negative 11 Newton meters-squared per kilogram-squared times 6.4 times 10 to the 23 kilograms divided by 3.4 times 10 to
the 6 meters, squared, equals 3.7 meters per second-squared, the gravitational acceleration on Mars.
Let’s say Mars were to magically double in mass. What would the effect be on the gravitational acceleration? Note that if we look at the equation for little-g, we see that g is directly proportional
to mass. Therefore, if mass doubles, little-g doubles as well. If Mars were to magically double in mass, its gravitational acceleration would become 7.4 meters per second-squared.
Let’s assume that instead of the mass of Mars changing, the planet expands in size so that the radius doubles. What would that effect have on the gravitational acceleration? In this case, we see that
the relationship between little g and the radius obeys the inverse-square law. Therefore if the radius increases by a factor of two, the gravitational acceleration would decrease by a factor of
two-squared: four! In that case, little g would decrease from 3.7 meters per second-squared to 0.9 meters per second-squared.
One more thing about little g. We can use the equation for little g to determine what the gravitational acceleration would be for a person located at different distances away from the Earth’s center
of mass. 9.81 meters per second-squared is valid at sea level, but what about at the top of mount Everest?
When using the equation in this manner, the mass of the Earth is treated as a constant, but the distance will be equal to the radius of the Earth PLUS whatever distance away the object is from sea
The summit of Mount Everest is located approximately 8,850 meters above sea level. Plugging in to our equation, we get 6.67 times 10 to the negative 11 times 5.97 times 10 to the 24, divided by the
quantity of 6.37 times 10 to the 6 + 8,850 – squared. The result is 9.79 meters per second-squared. Not a big difference from sea level!
Astronauts visiting the space station are still under the influence of gravity. To calculate their gravitational acceleration, simply add the orbital height of the space station to the radius of the
Earth and plug that value in for d.
Gravitational fields
A gravitational field is a model that we can use to describe how objects interact as a result of gravitational forces. We can draw a gravitational field by showing where any object placed around a
massive object would move due to gravity. Let’s draw the gravitational field around the Earth. The field is three-dimensional in reality, but in this video we’ll just show it as two-dimensional.
Any object of mass is going to want to move toward the center of the Earth. We depict the direction of the field using arrows. Therefore, the Earth’s gravitational field is represented by arrows
pointing toward the center of the Earth.
If we look at any given distance away from the center of the Earth, the distance between each of the field lines tells us the relative strength of the force. Close to the center of the Earth, the
arrows are much closer together than they are far away from the center of the Earth. This makes sense based on our understanding of the inverse-square law.
The limits of Newton’s laws
Newton’s laws do a really great job of explaining the motion of so many objects. But there starts to be a discrepancy that becomes apparent when objects move fast – close to the speed of light. In
these cases, Newton’s laws break down and we require another physical theory to take over. Einstein’s theory of general relativity can be used to accurately describe the forces and motions of objects
in these cases.
The theory of general relativity explains the motion of objects due to curves in spacetime, the fabric of the universe. A massive object causes a large curving of spacetime, and anything moving near
that massive object is going to travel along spacetime in a curved direction.
That might be hard to conceptualize, so let’s take a look using a model of the universe. Here, the fabric of spacetime is literally a piece of fabric stretched along a circular frame. When no massive
objects exist to cause any curves in spacetime, marbles that move through space travel in straight lines.
A large piece of mass is placed in the center of the fabric. Viewed from above, it doesn’t seem like much has changed, but viewed from the side, we can see that the fabric is warped. This is similar
to how largely massive objects: stars, planets, and so on, are able to curve spacetime.
Smaller objects can then be put in motion, and we can observe the effect of this spacetime warping. Instead of traveling in straight lines like they did before, the marbles now travel in circular
paths. This describes the orbits of planets around suns; and the orbits of moons and satellites around planets.
Thanks for taking the time to learn about gravity! Until next time, stay well. | {"url":"https://physics.doctor-pasquale.com/lecture-9-gravity/","timestamp":"2024-11-12T03:06:31Z","content_type":"text/html","content_length":"56343","record_id":"<urn:uuid:aaa376ba-7cd6-4b30-a635-f56f7a453627>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00861.warc.gz"} |
What is the perimeter of a triangle with corners at (3 ,4 ), (6 ,7 ), and (4 ,5 )? | HIX Tutor
What is the perimeter of a triangle with corners at #(3 ,4 )#, #(6 ,7 )#, and #(4 ,5 )#?
Answer 1
$\textcolor{b l u e}{\text{No triangle exists}}$
#A=(3,4), B=(6,7), C=(4,5)#
#vec(AC)=mu((3),(3))color(white)(888888)#, for #mu=1/3#
This means the points are collinear ( all lying on a straight line ), so these points do not form a triangle.
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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
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Why is it not divisible by 0? - The Press StoriesWhy is it not divisible by 0? - The Press Stories
QuoraA platform where Internet users can ask questions and have others, experts in the field, answer them.
The Question of the day: “Why is it not divisible by 0?”
The answer is Hadrian’s Knight:
I’m not going to give you the answer you expect because it is actually possible to divide a non-zero real number by 0.
There are two basic approaches you can take to segmentation:
• Application of Inverse Function (Analytic Approach)
• Inverse search for the “multiplication” rule (algebraic approach).
In the first case, there is a singularity at 0. At this point the inverse function simply cannot be used. We can extend it to premises, but nothing helps, a point remains undefined.
A belief that one may sometimes encounter is an extension of continuity or an analytic extension. This applies to certain functions such as x⟼sin(x)/x. But in our case, the left and right limits are
completely different.
In the algebraic approach, the inverse of x for the multiplication rule is the unique element y (if it exists) i.e. xy=1 (neutral for the multiplication rule). If y finds a number like 0×y=1, there
is cause for concern because you are contradicting the fact that 0 absorbs.
Rules depend on context
In short, you cannot divide a number by zero. Finally… in science everything is allowed as long as it’s fair! Indeed, in mathematics and physics, the rules depend on context. If you don’t state the
context, the rule has no meaning.
For example, the sum of the measures of the angles of a triangle does not always add up to 180 degrees. This is only true if we consider a flat space. For a spherical surface, the sum is greater than
180 degrees and for a hyperbolic surface less than 180.
In elementary grades, most of the rules you learn in math and physics can be broken. But it takes more or less creativity and a broader conceptual framework. I gave you the first simple geometric
Another simple example is that a negative number has no square root, or an exponential is always strictly positive. This was no longer true in the final year when the general convention of mixed
numbers was introduced. Other beautiful examples can be found in my answer to the question “What are the most fascinating science facts?”.
What about “x/0” sacrilege? Unfortunately, to successfully break this rule without setting everything on fire, you have to put yourself in a setting that requires a little more imagination. It’s
projective spaces, and more obviously, a real line compressed in time, here’s a little diagram:
This strange point called “infinity” is actually the limit of all real sequences, which are absolutely increasing and infinite. In this set, all numbers have an inverse, and the inverse of 0 is ∞.
You can use the tangent function to move to a region of length 2π from the real line. All that remains is to glue the ends back together to join the infinities.
For those who have studied a bit of mathematics in higher education, addition is not the law of composition, unfortunately not the composition of the body. We also lose order. Truths are
simultaneously less strictly and more than eccentric ∞.
You can do the same in campuses. It gives what is called Riemann sphere:
Bjoern_klipp and GKFX Via Wikimedia Commons
Here, ∞ is what the series going to infinity tends to, regardless of direction. Unless you do math or a bit of advanced physics (say requiring topological elements), these gaps are rarely
But I hope this has shown you once again that scientists are not uncreative psychos. It may not be poetic, because scientists constructively value the logical coherence of their works. There is less
creative freedom than art, but you can still divide by zero! (But not for free.) | {"url":"https://presstories.com/2022/12/04/why-is-it-not-divisible-by-0/","timestamp":"2024-11-06T01:47:11Z","content_type":"text/html","content_length":"58584","record_id":"<urn:uuid:04d9ab27-8bb9-4bf8-87aa-f00759f1af4b>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00486.warc.gz"} |
General solution
From Encyclopedia of Mathematics
of a system of
in a domain
smooth with respect to
are satisfied. (Sometimes it is agreed that the parameters may also take the values
The general solution of
in Cauchy problem for the system with initial conditions
satisfying the condition
in a domain
For an ordinary differential equation of order
the general solution in a domain
from which, by an appropriate choice of the parameters, any solution of (3) can be obtained for arbitrary initial conditions
A function obtained from the general solution for specific values of the parameters is called a particular solution. The family of functions containing all the solutions of the given system
(equation) in some domain cannot always be expressed as an explicit function of the independent variable. This family may turn out to be described by an implicit function, which is called the general
integral, or to be described in parametric form.
If a specific ordinary differential equation (3) can be integrated in closed form (see Integration of differential equations in closed form), then it is often possible to obtain relations of the type
(4), where the parameters arise as integration constants and are arbitrary. (It is therefore often said that the general solution of an
[1] V.V. Stepanov, "A course of differential equations" , Moscow (1959) (In Russian)
[2] N.P. Erugin, "A reader for a general course in differential equations" , Minsk (1979) (In Russian)
[a1] J.K. Hale, "Ordinary differential equations" , Wiley (1980)
[a2] E.L. Ince, "Ordinary differential equations" , Dover, reprint (1956) pp. §§3.6, 3.51, 4.7, A.5
How to Cite This Entry:
General solution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=General_solution&oldid=13722
This article was adapted from an original article by N.Kh. Rozov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article | {"url":"https://encyclopediaofmath.org/index.php?title=General_solution&oldid=13722","timestamp":"2024-11-04T14:04:55Z","content_type":"text/html","content_length":"22677","record_id":"<urn:uuid:f092210d-90f4-404f-bb37-0d25b63d65c0>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00598.warc.gz"} |
Alphabetical Number :: Transum Newsletter
Alphabetical Number
Monday 4th May 2015
It's an old joke but this newsletter is being written on Star Wars Day, 'May The Fourth Be With You!'
The puzzle for this month is not, on the surface, strictly mathematical but, as you’ll see from the answer at the end of this newsletter, there is some mathematical debate as to the correct answer.
It is however a puzzle that can keep you thinking throughout the day and keep your mind active during coffee breaks, jogging sessions or when the output of the TV is not really very engaging.
Here it is. Find the number which when written as a word has all the letters in alphabetical order and then find the first number to contain the letter A.
While you are thinking about that here is some information about the updates on the Transum website made during this last month.
The first activity worth mentioning this month is called Mystic Rose. It’s an old idea made interactive. It initially seems as though the number sequence created by the number of regions in the roses
is simply powers of two but as you get to the 6th term of the sequence there is a surprise in store.
This activity comes with some printable sheets which makes the counting process a lot easier. The sheets can also be used for other investigations such as the two-colour theorem or finding polygons
in the patterns of lines. This activity can produce some stunning display work.
The ‘Learn a times table in five days' page has been brought up to date with a reorganising of the activities and cartoon-like pictures added for all 121 multiplication facts. These pictures,
designed to help a person remember whichever multiplication fact they can’t get into their heads, are collected into an easily accessible click grid for Transum subscribers.
The Tablesmaster results page has also been updated so that a pupil can see the memory-aiding picture for the multiplication fact that took longest to recall. I hope this addition contributes towards
times table learning around the world.
For those of you working in an IB school you may be interested to hear that additional worked solutions have been added to the Exam-Style Questions pages. Most of the worked solutions contain
relevant TI-nSpire screen shots. It is hoped this resource will be just as useful for A-level teachers as the content is so similar.
Finally the answer to the puzzle. Forty is the number that has its letters in alphabetical order and the first number to contain the letter A is either a thousand or one hundred and one. You can see
the discussion this puzzle generated on the 7th October Starter page.
Good luck to everyone involved in this exam season. Just remember that Transum has some less demanding, fun activities for you to enjoy when it is all over.
PS.If it is cold, go and stand in the corner, because it is 90 degrees there!
Do you have any comments? It is always useful to receive feedback on this newsletter and the resources on this website so that they can be made even more useful for those learning Mathematics
anywhere in the world. Click here to enter your comments. | {"url":"https://transum.org/Newsletter/?p=124","timestamp":"2024-11-10T12:55:04Z","content_type":"text/html","content_length":"18244","record_id":"<urn:uuid:612b5b3e-9435-4bec-8862-8bd26082354b>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00320.warc.gz"} |
Copyright (C) 2012-16 Edward Kmett
License BSD-style (see the file LICENSE)
Maintainer Edward Kmett <ekmett@gmail.com>
Stability provisional
Portability Rank2Types
Safe Haskell Safe
Language Haskell98
One commonly asked question is: can we combine two lenses, Lens' a b and Lens' a c into Lens' a (b, c). This is fair thing to ask, but such operation is unsound in general. See lensProduct.
lensProduct :: ALens' s a -> ALens' s b -> Lens' s (a, b) Source #
A lens product. There is no law-abiding way to do this in general. Result is only a valid Lens if the input lenses project disjoint parts of the structure s. Otherwise "you get what you put in" law
view l (set l v s) ≡ v
is violated by
>>> let badLens :: Lens' (Int, Char) (Int, Int); badLens = lensProduct _1 _1
>>> view badLens (set badLens (1,2) (3,'x'))
but we should get (1,2).
Are you looking for alongside?
prismSum :: APrism s t a b -> APrism s t c d -> Prism s t (Either a c) (Either b d) Source #
A dual of lensProduct: a prism sum.
The law
preview l (review l b) ≡ Just b
breaks with
>>> let badPrism :: Prism' (Maybe Char) (Either Char Char); badPrism = prismSum _Just _Just
>>> preview badPrism (review badPrism (Right 'x'))
Just (Left 'x')
We put in Right value, but get back Left.
Are you looking for without? | {"url":"http://hackage-origin.haskell.org/package/lens-4.17/docs/Control-Lens-Unsound.html","timestamp":"2024-11-03T13:06:12Z","content_type":"application/xhtml+xml","content_length":"7299","record_id":"<urn:uuid:d905daed-9006-42bc-8a4b-94d1d8b718c3>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00280.warc.gz"} |
Order Of Operations Worksheets Grade 6 With Answers | Order of Operation Worksheets
Order Of Operations Worksheets Grade 6 With Answers
7Th Grade Math Pemdas Worksheets Rule Order Of Operations Tiktokcook
Order Of Operations Worksheets Grade 6 With Answers
Order Of Operations Worksheets Grade 6 With Answers – You may have become aware of an Order Of Operations Worksheet, but what exactly is it? In this article, we’ll talk about what it is, why it’s
crucial, and exactly how to get a Order Of Operations Worksheets Grade 6 With Answers Hopefully, this information will be practical for you. Your trainees are entitled to an enjoyable, efficient
means to examine the most crucial principles in mathematics. On top of that, worksheets are a great means for pupils to practice new skills and also evaluation old ones.
What is the Order Of Operations Worksheet?
An order of operations worksheet is a type of math worksheet that requires students to perform math operations. These worksheets are separated into 3 main sections: subtraction, multiplication, and
also addition. They additionally consist of the analysis of parentheses and also exponents. Trainees who are still discovering how to do these tasks will discover this kind of worksheet helpful.
The main function of an order of operations worksheet is to aid pupils discover the correct method to solve mathematics equations. They can assess it by referring to an explanation page if a pupil
does not yet comprehend the principle of order of operations. Additionally, an order of operations worksheet can be divided right into several categories, based on its difficulty.
One more vital function of an order of operations worksheet is to teach trainees how to perform PEMDAS operations. These worksheets start with simple troubles associated with the fundamental rules
and also develop to much more complex issues including all of the regulations. These worksheets are a wonderful way to introduce young learners to the excitement of solving algebraic equations.
Why is Order of Operations Important?
One of the most essential things you can discover in math is the order of operations. The order of operations makes sure that the mathematics problems you resolve are consistent.
An order of operations worksheet is a fantastic means to teach trainees the appropriate means to solve mathematics equations. Prior to trainees start using this worksheet, they might require to
examine ideas associated with the order of operations. To do this, they ought to review the idea page for order of operations. This idea web page will certainly provide trainees an overview of the
An order of operations worksheet can assist students establish their skills on top of that and subtraction. Educators can make use of Prodigy as a simple method to distinguish method and supply
engaging content. Prodigy’s worksheets are an ideal way to help pupils discover the order of operations. Educators can begin with the standard principles of addition, multiplication, as well as
division to assist students construct their understanding of parentheses.
Order Of Operations Worksheets Grade 6 With Answers
Order Of Operations Sheet 5 2 Answers 6th Grade Worksheets Pemdas
Mrs White s 6th Grade Math Blog ORDER OF OPERATIONS WHAT DO I DO FIRST
Worksheet Order Of Operations Practice Worksheets Grass Fedjp
Order Of Operations Worksheets Grade 6 With Answers
Order Of Operations Worksheets Grade 6 With Answers supply a fantastic resource for young learners. These worksheets can be easily personalized for particular requirements.
The Order Of Operations Worksheets Grade 6 With Answers can be downloaded free of cost and can be printed out. They can after that be evaluated using addition, division, subtraction, as well as
multiplication. Pupils can likewise make use of these worksheets to examine order of operations and also the use of exponents.
Related For Order Of Operations Worksheets Grade 6 With Answers | {"url":"https://orderofoperationsworksheet.com/order-of-operations-worksheets-grade-6-with-answers/","timestamp":"2024-11-11T14:55:04Z","content_type":"text/html","content_length":"43595","record_id":"<urn:uuid:7cc76f27-7340-4be9-a367-c1313e203815>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00333.warc.gz"} |
Backtracking Algorithm
A backtracking algorithm is a problem-solving algorithm that uses a brute force approach for finding the desired output.
The Brute force approach tries out all the possible solutions and chooses the desired/best solutions.
The term backtracking suggests that if the current solution is not suitable, then backtrack and try other solutions. Thus, recursion is used in this approach.
This approach is used to solve problems that have multiple solutions. If you want an optimal solution, you must go for dynamic programming.
State Space Tree
A space state tree is a tree representing all the possible states (solution or nonsolution) of the problem from the root as an initial state to the leaf as a terminal state.
State Space Tree
Backtracking Algorithm
if x is not a solution
return false
if x is a new solution
add to list of solutions
backtrack(expand x)
Example Backtracking Approach
Problem: You want to find all the possible ways of arranging 2 boys and 1 girl on 3 benches. Constraint: Girl should not be on the middle bench.
Solution: There are a total of 3! = 6 possibilities. We will try all the possibilities and get the possible solutions. We recursively try all the possibilities.
All the possibilities are:
All the possibilities
The following state space tree shows the possible solutions.
State tree with all the solutions
Backtracking Algorithm Applications | {"url":"https://www.programiz.com/dsa/backtracking-algorithm","timestamp":"2024-11-02T21:07:27Z","content_type":"text/html","content_length":"174083","record_id":"<urn:uuid:2373c59b-2e16-4521-b656-3a2c60905210>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00467.warc.gz"} |
Deligne's Finite Fields Riemann Hypothesis uses Math-Induction?? #238; 2nd ed; Correcting Math
On Oct 26, 5:15 am, David Bernier <david...
videotron.ca> wrote: Archimedes Plutonium wrote: David Bernier wrote: There's Deligne's "La conjecture de Weil : I." , downloadable from here: http://www.numdam.org/numdam-bin/item?id=
PMIHES_1974__43__273_0 Also, Barry Mazur's Zbl. revi...
26 Oct 2009 17:50
Help with some exercises
34 NP-Completeness 34.1 Polynomial time From the point of view of language theory, the set of instances for any decision problem Q is simply the set Σ*, where Σ = {0,1}. Since Q is entirely
characterized by those problem instances that produce a 1(yes) answer, we can view Q as a language L over Σ = {0,1}, wh...
24 Oct 2009 00:18
The real deal: Proof of Cook's Theorem in Unary - Thank you Sci.Math for your patience and kindness
MACHINE PROOFED RESOLUTION TO THE P VERSUS NP PROBLEM PRESENTED BY M. MICHAEL MUSATOV WITH A PROMISE TO DONATE ALL $1MM DOLLARS OF THE CLAY PRIZE TO CURE CHILDHOOD CANCER WITH HTTP://
WWW.ALEXSLEMONADE.ORG/ THE P VERSUS NP PROBLEM TWO POSSIBILITIES: 1 OR 2 CHOOSE [P =/=NP] AND [P == NP] OR [P =/=NP...
22 Oct 2009 21:57
Proof of Cook's Theorem in Unary
On Oct 22, 4:48 pm, Tegiri Nenashi <tegirinena...
gmail.com> wrote: On Oct 21, 5:04 pm, cplxphil <cplxp...
gmail.com> wrote: I'm not sure if you're disagreeing. If you are, my response is that you could argue that it preserves the same structure of the decision problem, but expressed as a formal l...
22 Oct 2009 21:57
On The Question of Absolute Undecidability
I found this paper very interesting: http://philmat.oxfordjournals.org/cgi/reprint/14/2/153 In particular, I found the discussion in Section 5.1 very interesting. But I am interested in the
philosophical significance of all of this. What reason do we have, exactly, to think that all the Omega- consequences of ...
21 Oct 2009 20:29
Second Clay Mathematics Award claimed, but how should it be split?
The world of theoretical computer science has been turned upside down by a stunning triple development which has finally solved its most famous problem: whether P=NP. This was one of the seven
problems for which the Clay Mathematics Institute offered a million dollars in their famous Millennium Meeting over thirty ...
25 Oct 2009 19:50
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <title>Gmail</
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15 Oct 2009 22:45 | {"url":"http://www.adras.com/Logic.s94-4.html","timestamp":"2024-11-09T22:58:41Z","content_type":"text/html","content_length":"12530","record_id":"<urn:uuid:8c24b823-3148-46da-9b4f-d36a447951be>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00431.warc.gz"} |
Laurent SCHWARTZ
Famous mathematician.
Laurent Schwartz came from a Jewish background. His father was a surgeon but his family contained other brilliant men such as his uncle, Professor Robert Debre, the founder of Unicef. At school
Schwartz excelled at both mathematics and Latin. He entered the École Normale Supérieure in Paris in 1934. He graduated with the Agrégation de Mathématiques in 1937 and studied for his doctorate in
the Faculty of Science at Strasbourg which he was awarded in 1943. His political activities at this time are described in [1]:-
The intellectual ferment of these years was paralleled by political engagement. Though from a traditionally right-wing background, he was a strong supporter of Leon Blum's Popular Front Government
until he became disillusioned by its failure to support the Spanish Republicans. Similarly, his sympathies for communism were soon dampened by Stalin's show trials, though he then spent ten years as
a Trotskyite, up to 1947. He claimed never to regret this, even though it almost prevented him travelling to America to receive the Fields Medal.
During the war his political activities and Jewish background put him in all manner of delicate situations.
Schwartz spent the year 1944-45 lecturing at the Faculty of Science at Grenoble before moving to Nancy where he became a professor at the Faculty of Science. It was during this period of his career
that he produced his famous work on the theory of distributions described below.
In 1953 Schwartz returned to Paris where he became professor, holding this position until 1959. He taught at the École Polytechnique in Paris from 1959 to 1980. He then spent three years at the
University of Paris VII before he retired in 1983. We say a little below about his remarkable mathematical contributions but before we look at these we recount some of the political activity he took
part in during his career in Paris.
In 1956 he was one of the leaders of protests in France against the Russian invasion of Hungary. Then in the following year he became involved in an event much closer to him personally, the "Audin
Affair" in Algeria [1]:-
Audin, a mathematician and communist based in Algiers, was writing his thesis under Schwartz's supervision. But in June 1957 the 25-year-old father of three and opponent of French rule in Algeria was
abducted by paratroopers, tortured and killed. Schwartz was tireless in his calls for justice, and organised a presentation of the young man's thesis in his absence.
Vocal in his opposition to the French campaign, he signed the famous "Declaration des 121" in favour of military insubordination. The riposte of Pierre Messmer, the Minister for the French Army (and,
by the same token, of the École), was to strip him of his position at the Polytechnique, for reasons of "common sense and honour". To which Schwartz replied that since the Army commanded by Messmer
had sanctioned torture and promoted torturers, such remarks were absurd.
After a brief exile in New York, he regained his post two years later ...
The outstanding contribution to mathematics which Schwartz made in the late 1940s was his work in the theory of distributions. The first publication in which he presented these ideas was
Généralisation de la notion de fonction, de dérivation, de transformation de Fourier et applications mathématiques et physiques which appeared in 1948.
The theory of distribution is a considerable broadening of the differential and integral calculus. Heaviside and Dirac had generalised the calculus with specific applications in mind. These, and
other similar methods of formal calculation, were not, however, built on an abstract and rigorous mathematical foundation. Schwartz's development of the theory of distributions put methods of this
type onto a sound basis, and greatly extended their range of application, providing powerful tools for applications in numerous areas.
In the article on Analysis in Encyclopaedia Britannica François Treves describes Schwartz's work as follows:-
... Schwartz's idea (in 1947) was to give a unified interpretation of all the generalized functions that had infiltrated analysis as (continuous) linear functionals on the space Cç of infinitely
differentiable functions vanishing outside compact sets. He provided a systematic and rigorous description, entirely based on abstract functional analysis and on duality. It is noteworthy that such
an approach had a precedent, in the presentation by André Weil of the integration of locally compact groups ... Because of the demands of differentiability in distribution theory, the spaces of
test-functions and their duals are somewhat more complicated. This has led to extensive studies of topological vector spaces beyond the familiar categories of Hilbert and Banach spaces, studies that,
in turn, have provided useful new insights in some areas of analysis proper, such as partial differential equations or functions of several complex variables. Schwartz's ideas can be applied to many
other spaces of test-functions beside Cç, as he himself and others have shown ...
Harald Bohr presented a Fields Medal to Schwartz at the International Congress in Harvard on 30 August 1950 for his work on the theory of distributions. Harald Bohr [2] described Schwartz's 1948
paper as one:-
... which certainly will stand as one of the classical mathematical papers of our times. ... I think every reader of his cited paper, like myself, will have left a considerable amount of pleasant
excitement, on seeing the wonderful harmony of the whole structure of the calculus to which the theory leads and on understanding how essential an advance its application may mean to many parts of
higher analysis, such as spectral theory, potential theory, and indeed the whole theory of linear partial differential equations ...
Schwartz has received a long list of prizes, medals and honours in addition to the Fields Medal. He received prizes from the Paris Academy of Sciences in 1955, 1964 and 1972. In 1972 he was elected a
member of the Academy. He has been awarded honorary doctorates from many universities including Humboldt (1960), Brussels (1962), Lund (1981), Tel-Aviv (1981), Montreal (1985) and Athens (1993).
Later work by Schwartz on stochastic differential calculus is described by him in the survey article [5], see also [4]. Later political campaigns include those against American involvement in
Vietnam, the Soviet invasion of Afghanistan, and the Russian war against Chechnya.
With such involvement in mathematics and politics one might imagine that Schwartz would not have had time for a major hobby. This however would be entirely wrong for he was an avid collector of
butterflies, with over 20,000 specimens.
Let us end by giving two quotes from Schwartz; the first on politics and the second on mathematics:-
I have always thought that morality in politics was something essential, just like feelings and affinities.
To discover something in mathematics is to overcome an inhibition and a tradition. You cannot move forward if you are not subversive.
Article by: J J O'Connor and E F Robertson | {"url":"http://genealogy.meta-studies.net/PS10/PS10_438.HTML","timestamp":"2024-11-08T06:00:37Z","content_type":"application/xhtml+xml","content_length":"13168","record_id":"<urn:uuid:4a0ba9d9-e766-4a02-8f75-58de02f0ae9d>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00175.warc.gz"} |
FFT1-32-512/4 can process single stream of 32/64/128/256/512 point FFT/IFFT with input and output data in natural order.
The FFT or IFFT radix operations start when START input is sampled high. The core will start reading the input data, asserting the READ signal each time it reads the data. The FFT data output will be
streamed out after fixed latency. The core will indicate data output by asserting the WRITE output.
Core will continue to operate on incoming data stream block of 32/64/128/256/512 samples each while the START signal is high.
SCALE input allows setting of the inter-stage scaling for each of the 9 radix-2 FFT stages. A bit value of 1 in position N indicates that the input data of the stage N are scaled by a factor of 2. | {"url":"https://ipcores.com/fft_32_512.htm","timestamp":"2024-11-11T20:18:30Z","content_type":"application/xhtml+xml","content_length":"57057","record_id":"<urn:uuid:79176c9c-4059-4172-9b70-47935628cc46>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00467.warc.gz"} |
Transition metal
From New World Encyclopedia
(Redirected from Group 5 element)
In common terminology, transition metals (or transition elements) are chemical elements that lie in groups 3 through 12 of the periodic table, in the standard view of the table. The name transition
comes from their position in the table—they form a transition between the main group elements, which occur in groups 1 and 2 on the left side, and groups 13–18 on the right.
Some transition elements occur naturally in their metallic state and have been known since antiquity. Three of these—gold, silver, and copper—have been used extensively in coinage and jewelry.
The use of copper in tools was one of the first historical technological advances. Also, iron, in the form of steel, is used in many structures, from automobiles to bridges. Many transition metals
are useful as catalysts in industrial and laboratory settings, and many of these elements form brightly colored compounds.
The Transition Metals
Group → 3 4 5 6 7 8 9 10 11 12
Period ↓
Sc Ti V Cr Mn Fe Co Ni Cu Zn
Y Zr Nb Mo Tc Ru Rh Pd Ag Cd
La Hf Ta W Re Os Ir Pt Au Hg
Ac Rf Db Sg Bh Hs Mt Ds Rg Uub
Periodic table
Placement of the group of transition elements in the periodic table can be observed by examining the color-coded table shown below.
Chemical Series of the Periodic Table
Alkali metals Alkaline earth metals Lanthanides Actinides Transition metals
Poor metals Metalloids Nonmetals Halogens Noble gases
State at standard temperature and pressure
• Elements numbered in red are gases.
• Elements numbered in green are liquids.
• Elements numbered in black are solids.
Natural occurrence
• Elements without borders have not been discovered/synthesized yet.
• Elements with dotted borders do not occur naturally (synthetic elements).
• Elements with dashed borders naturally arise from decay of other chemical elements.
• Elements with solid borders are older than the
(primordial elements).
□ Note: Although californium (Cf, 98) is not Earth-primordial, it (and its decay products) does occur naturally: its electromagnetic emissions are regularly observed in supernova spectra.
The general definition of transition metals as those that lie in groups 3 through 12 of the periodic table, mentioned above, is simple and has been traditionally used. Although this definition is
still widely used, the characteristic properties of transition metals arise because of the electron configuration of their atoms, which have partially filled "d orbitals." Based on this perspective,
the term transition element has been defined more strictly. The International Union of Pure and Applied Chemistry (IUPAC) defines a transition element as "an element whose atom has an incomplete d
sub-shell, or which can give rise to cations with an incomplete d sub-shell."^[1]
By this definition, zinc, cadmium, and mercury (group 12 elements) are not considered transition metals. This is because the atoms of these elements and their stable ions contain electrons that
completely fill the d orbitals. When these elements form ions, they usually lose electrons from only their outermost s subshell, leaving the d subshell intact. In just a few, exceptional cases, they
have formed unstable ions in which the d subshell is partly filled.^[2] Element 112 (in group 12) may also be excluded, because its electron configuration is likely to be similar to that of other
members of group 12, and its oxidation properties are unlikely to be observed due to its radioactive nature. Thus, this stricter definition of transition metals limits the term to elements in groups
3 to 11.
There are several common characteristic properties of transition elements:
• Almost all of them are solids at room temperature, with high tensile strength (ability to withstand stress), density, and melting and boiling points. The one exception is mercury, which is a
• Most of them are silvery-blue at room temperature. The exceptions are copper and gold.
• They form monatomic ions with a 2+ charge, but can form other ions with a different charge. For example, iron can form Fe^2+ and Fe^3+ ions. In addition, they often have higher oxidation states
in compounds.
• They form complexes known as "coordination compounds," many of which are brightly colored.
• They are often good catalysts. For example, iron is the catalyst for the Haber process, involving the reaction of nitrogen and hydrogen to produce ammonia. Nickel, palladium, or platinum can be
used in the hydrogenation of (addition of hydrogen atoms to) alkenes and alkynes. Platinum is the catalyst in the catalytic converters of automobile exhaust systems.
In addition to these common characteristics, there are some trends in properties as we go through a period, much like those in the main group elements, but with less dramatic changes. Going across
the transition metals of a period, the atomic radius generally tends to decrease, and the first ionization energy (energy required to remove an electron from the neutral atom) increases. Also, as we
go across the period, the metals tend to become softer, and mercury is a liquid at room temperature. Group 11 elements (copper, silver, and gold) are particularly unreactive. These "noble" metals can
occur naturally in their elemental metallic state, and they are sometimes known as coinage metals as they have been useful for minting coins.
Electronic configuration
Main article: electron configuration
The properties of transition metals arise from their defining characteristic of partially filled d orbitals. They are metals because the d orbital electrons are delocalized within the metal lattice,
forming metallic bonds.
Most transition metals have two electrons in their outermost, s subshell. As we consider these elements across a period, the number of d electrons increases by one. Thus, in the fourth period,
scandium (Sc, group 3) has the configuration [Ar]4s^23d^1, and the next element Titanium (Ti, group 4) has the configuration [Ar]4s^23d^2, and so forth. There are, however, some exceptions to this
progression. For instance, in the fourth period, copper has the configuration ([Ar]4s^13d^10) and chromium is ([Ar]4s^13d^5). These exceptions occur because the atoms acquire additional stability
when their subshells are half-filled or fully filled. Copper has a completely filled d subshell, and chromium has a half-filled d subshell. Similar exceptions are more prevalent in the fifth, sixth,
and seventh periods.
When these metals lose electrons to form monatomic ions, they generally lose their s electrons first. Thus, most transition metals form ions with a 2+ charge. Higher oxidation states involve d
electrons as well. Monatomic ions with a charge greater than 3+ are rare, and the higher oxidation states of transition metals occur in compounds with highly electronegative elements such as oxygen.
Variable oxidation states
Unlike ions of most main group metals, monatomic ions of the transition metals may have more than one stable charge, and, in compounds, they can have several higher oxidation states. (Oxidation state
is a measure of the degree of oxidation of an atom in a compound; it is the electrical charge an atom would have, at least hypothetically, if its bonds to all other atoms in the compound were
entirely ionic.)
This variability of oxidation state is because the atoms of transition elements can lose or share d electrons without a high energetic penalty. The atom of manganese, for example, has two 4s
electrons and five 3d electrons, which can be removed or shared with other atoms. Loss or sharing of all of these electrons leads to a 7+ oxidation state. Osmium and ruthenium compounds are commonly
isolated in stable 8+ oxidation states, which is among the highest for isolable compounds.
Moving across a period of transition elements, certain patterns in their oxidation states emerge:
• The number of oxidation states of each element increases up to manganese (group 7), after which they decrease. Later transition metals have a stronger attraction between protons and electrons
(because there are more of them present), requiring more energy to remove the electrons.
• When these elements are in lower oxidation states, they can be found as simple ions. In their higher oxidation states, these elements are usually bonded covalently to electronegative elements
like oxygen or fluorine, forming polyatomic ions such as chromate, vanadate, or permanganate.
Other properties associated with the stability of oxidation states are as follows:
• Ions in higher oxidation states tend to make good oxidizing agents, whereas elements in low oxidation states become reducing agents.
• Going across a period, the 2+ ions start as strong reducing agents and increase in stability.
• Conversely, the 3+ ions start at higher stability and become more oxidizing across the period.
Colored compounds
As noted above, the chemistry of transition metals is characterized by the partially filled d orbitals allowing for multiple oxidation states. Another consequence of their electron configuration is
that these elements can form stable complexes, or coordination compounds. In such a complex, the transition metal atom or ion forms weak covalent bonds to other small molecules or ions known as "
ligands." In some cases, the oxidation state of the transition metal may be zero or a negative number.
Transition metal compounds are often highly colored and coordination by ligands plays a large part in determining the compound's color. In the absence of ligands, the d orbitals of an atom all have
the same energy, but when surrounded by ligands, the energies of the d orbitals change and are no longer equal. This phenomenon is described by the cystal field theory. For many compounds of this
type, the resulting difference in energy of the d orbitals is in the energy range of visible light. As a result, they strongly absorb particular wavelengths of visible light and appear vividly
colored. Many different colors can be observed, and the color can vary even between different ions of the same element. A striking example is the different ions of vanadium (V): VO[2]^+ is yellow in
solution, VO^2+ is blue, V^3+(aq) is green and V^2+(aq) is purple.
The color of a complex depends on:
• the nature of the metal ion, specifically the number of electrons in the d orbitals;
• the arrangement of the ligands around the metal ion; and
• the nature of the ligands surrounding the metal ion. (The stronger the ligand, the greater the energy difference between the different d orbitals.)
Interestingly, though zinc can form complexes, they are colorless because the 3d orbitals of zinc are completely filled. The full d orbitals prevent the complex from absorbing visible light when the
energies of the d orbitals are altered by ligands. As zinc is in group 12, it is not considered a transition metal by the newer IUPAC definition.
See also
1. ↑ transition element. IUPAC Gold Book. Retrieved January 9, 2009.
2. ↑ Cotton, F. Albert, G. Wilkinson, C.A. Murillo, and M. Bochmann. 1999. Advanced Inorganic Chemistry, 6th ed. New York: Wiley. ISBN 0471199575.
ISBN links support NWE through referral fees
• Cotton, F. Albert, G. Wilkinson, C.A. Murillo, and M. Bochmann. 1999. Advanced Inorganic Chemistry, 6th ed. New York: Wiley. ISBN 0471199575
• Crabtree, Robert H. 2005. The Organometallic Chemistry of the Transition Metals. Hoboken, NJ: Wiley. ISBN 978-0471662563
• Greenwood, N. N., and A. Earnshaw. 1997. Chemistry of the Elements, 2nd ed. Oxford: Butterworth-Heinemann. ISBN 0750633654
Periodic tables
Standard table | Vertical table | Table with names | Names and atomic masses (large) | Names and atomic masses (small) | Names and atomic masses (text only) | Inline F-block | Elements to 218 |
Electron configurations | Metals and non metals | Table by blocks | List of elements by name
Groups: Â Â 1 - Â 2 - Â 3 - Â 4 - Â 5 - Â 6 - Â 7 - Â 8 - Â 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18
Periods: Â 1Â - Â 2Â - Â 3Â - Â 4Â - Â 5Â - Â 6Â - Â 7Â - Â 8
Series:  Alkalis -  Alkaline earths -  Lanthanides -  Actinides -  Transition metals -  Poor metals -  Metalloids -  Nonmetals -  Halogens -  Noble gases
Blocks: s-block -  p-block -  d-block -  f-block -  g-block
New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons
CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia
contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite this article click here for a list of acceptable citing formats.The history of earlier contributions by
wikipedians is accessible to researchers here:
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If f (x) is an even function, then write whether f′ (x) is even... | Filo
If f (x) is an even function, then write whether is even or odd ?
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Question Text If f (x) is an even function, then write whether is even or odd ?
Updated On Sep 19, 2022
Topic Continuity and Differentiability
Subject Mathematics
Class Class 12
Answer Type Text solution:1 Video solution: 1
Upvotes 99
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Source code for fmask.landsatangles
#!/usr/bin/env python
# This file is part of 'python-fmask' - a cloud masking module
# Copyright (C) 2015 Neil Flood
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 3
# of the License, or (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
Functions relating to estimating the per-pixel sun and satellite angles for
a given Landsat image. These are rough estimates, using the generic
characteristics of the Landsat 5 platform, and are not particularly accurate,
but good enough for the current purposes.
Historically, the USGS have not supplied satellite zenith/azimuth angles, and have only
supplied scene-centre values for sun zenith/azimuth angles. Since the satellite
view geometry is important in correctly tracking a shadow when matching shadows
to their respective clouds, the Fmask algorithm requires good estimates of all these
angles. The routines contained here are used to derive per-pixel estimates of
these angles.
As of mid-2016, the USGS are planning to supply sufficient information to calculate
these angles directly from orbit ephemeris data. When that comes about, it seems likely
that the need for the routines here will diminish, but any data downloaded from USGS
prior to then will still require this approach, as the associated angle metadata will
not be present.
The core Fmask code in this package is adaptable enough to be configured for either
The general approach for satellite angles is to estimate the nadir line by running it
down the middle of the image data area. The satellite azimuth is assumed to be
at right angles to this nadir line, which is only roughly correct. For the whisk-broom
sensors on Landsat-5 and Landsat-7, this angle is not 90 degrees, but is affected by
earth rotation and is latitude dependent. For Landsat-8, the scan line is at
right angles, due to the compensation for earth rotation, but the push-broom is
made up of sub-modules which point in slightly different directions, giving
slightly different satellite azimuths along the scan line. None of these effects
are included in the current estimates. The satellite zenith is estimated based on the
nadir point, the scan-line, and the assumed satellite altitude, and includes the
appropriate allowance for earth curvature.
Because this works by searching the imagery for the non-null area, and assumes that
this represents a full-swath image, it would not work for a subset of a full image.
The sun angles are approximated using the algorithm found in the Fortran code with
6S (Second Simulation of the Satellite Signal in the Solar Spectrum). The subroutine
in question is the POSSOL() routine. I translated the Fortran code into Python for
inclusion here.
from __future__ import print_function, division
import datetime
import numpy
from osgeo import osr
from rios import applier
from rios import fileinfo
[docs]def findImgCorners(img, imgInfo):
Find the corners of the data within the given template image
Return a numpy array of (x, y) coordinates. The array has 2 columns, for X and Y.
Each row is a corner, in the order:
top-left, top-right, bottom-left, bottom-right.
Uses RIOS to pass through the image searching for non-null data,
and find the extremes. Assumes we are working with a full-swathe Landsat
Each list element is a numpy array of (x, y)
infiles = applier.FilenameAssociations()
outfiles = applier.FilenameAssociations()
otherargs = applier.OtherInputs()
infiles.img = img
otherargs.tl = None
otherargs.tr = None
otherargs.bl = None
otherargs.br = None
otherargs.nullVal = imgInfo.nodataval[0]
if otherargs.nullVal is None:
otherargs.nullVal = 0
applier.apply(findCorners, infiles, outfiles, otherargs)
corners = numpy.array([
return corners
[docs]def findCorners(info, inputs, outputs, otherargs):
Called from RIOS
Checks non-null area of image block. Finds extremes, records coords
of extremes against those already in otherargs.
Note that the logic is very specific to the orientation of the usual Landsat
descending pass imagery. The same logic should not be applied to swathes
oriented in other, e.g. for other satellites.
(xblock, yblock) = info.getBlockCoordArrays()
nonnull = (inputs.img != otherargs.nullVal).all(axis=0)
xNonnull = xblock[nonnull]
yNonnull = yblock[nonnull]
if len(xNonnull) > 0:
topNdx = numpy.argmax(yNonnull)
topXY = (xNonnull[topNdx], yNonnull[topNdx])
leftNdx = numpy.argmin(xNonnull)
leftXY = (xNonnull[leftNdx], yNonnull[leftNdx])
bottomNdx = numpy.argmin(yNonnull)
bottomXY = (xNonnull[bottomNdx], yNonnull[bottomNdx])
rightNdx = numpy.argmax(xNonnull)
rightXY = (xNonnull[rightNdx], yNonnull[rightNdx])
# If these are more extreme than those already in otherargs, replace them
if otherargs.tl is None or topXY[1] > otherargs.tl[1]:
otherargs.tl = topXY
if otherargs.tr is None or rightXY[0] > otherargs.tr[0]:
otherargs.tr = rightXY
if otherargs.bl is None or leftXY[0] < otherargs.bl[0]:
otherargs.bl = leftXY
if otherargs.br is None or bottomXY[1] < otherargs.br[1]:
otherargs.br = bottomXY
[docs]def findNadirLine(corners):
Return the equation of the nadir line, from the given corners of the swathe.
Returns a numpy array of [b, m], for the equation
y = mx + b
giving the y coordinate of the nadir as a function of the x coordinate.
# Find the top and bottom mid-points.
topMid = (corners[0] + corners[1]) / 2.0
bottomMid = (corners[2] + corners[3]) / 2.0
slope = (topMid[1] - bottomMid[1]) / (topMid[0] - bottomMid[0])
intercept = topMid[1] - slope * topMid[0]
coeffs = numpy.array([intercept, slope])
return coeffs
[docs]def satAzLeftRight(nadirLine):
Calculate the satellite azimuth for the left and right sides of the nadir line.
Assume that the satellite azimuth vector is at right angles to the nadir line
(which is not really true, but reasonably close), and that there are only
two possibilities, as a pixel is either to the left or to the right of the nadir
Return a numpy array of [satAzLeft, satAzRight], with angles in radians,
in the range [-pi, pi]
slope = nadirLine[1]
# Slope of a line perpendicular to the nadir
slopePerp = -1 / slope
# Azimuth for pixels to the left of the line
azimuthLeft = numpy.pi / 2.0 - numpy.arctan(slopePerp)
# Azimuth for pixels to the right is directly opposite
azimuthRight = azimuthLeft - numpy.pi
return numpy.array([azimuthLeft, azimuthRight])
[docs]def localRadius(latitude):
Calculate a local radius of curvature, for the given geodetic latitude.
This approximates the earth curvature at this latitude. The given
latitude is in degrees. This is probably overkill, given some of the other
approximations I am making....
latRadians = numpy.radians(latitude)
# Earth axis lengths
a = osr.SRS_WGS84_SEMIMAJOR
invFlat = osr.SRS_WGS84_INVFLATTENING
f = 1 / invFlat
eSqd = 2 * f - f**2
# Radius of curvature
R = a / numpy.sqrt(1 - eSqd * numpy.sin(latRadians)**2)
return R
[docs]def sunAnglesForExtent(imgInfo, mtlInfo):
Return array of sun azimuth and zenith for each of the corners of the image
extent. Note that this is the raster extent, not the corners of the swathe.
The algorithm used here has been copied from the 6S possol() subroutine. The
Fortran code I copied it from was .... up to the usual standard in 6S. So, the
notation is not always clear.
cornerLatLong = imgInfo.getCorners(outEPSG=4326)
(ul_long, ul_lat, ur_long, ur_lat, lr_long, lr_lat, ll_long, ll_lat) = cornerLatLong
pts = numpy.array([
[ul_long, ul_lat],
[ur_long, ur_lat],
[ll_long, ll_lat],
[lr_long, lr_lat]
longDeg = pts[:, 0]
latDeg = pts[:, 1]
# Date/time in UTC
dateStr = mtlInfo['DATE_ACQUIRED']
timeStr = mtlInfo['SCENE_CENTER_TIME'].replace('Z', '')
ymd = [int(i) for i in dateStr.split('-')]
dateObj = datetime.date(ymd[0], ymd[1], ymd[2])
julianDay = (dateObj - datetime.date(ymd[0], 1, 1)).days + 1
juldayYearEnd = (datetime.date(ymd[0], 12, 31) - datetime.date(ymd[0], 1, 1)).days + 1
# Julian day as a proportion of the year
jdp = julianDay / juldayYearEnd
# Hour in UTC
hms = [float(x) for x in timeStr.split(':')]
hourGMT = hms[0] + hms[1] / 60.0 + hms[2] / 3600.0
(sunAz, sunZen) = sunAnglesForPoints(latDeg, longDeg, hourGMT, jdp)
sunAngles = numpy.vstack((sunAz, sunZen)).T
return sunAngles
[docs]def sunAnglesForPoints(latDeg, longDeg, hourGMT, jdp):
Calculate sun azimuth and zenith for the given location(s), for the given
time of year. jdp is the julian day as a proportion, ranging from 0 to 1, where
Jan 1 is 1.0/365 and Dec 31 is 1.0.
Location is given in latitude/longitude, in degrees, and can be arrays to
calculate for multiple locations. hourGMT is a decimal hour number giving the time
of day in GMT (i.e. UTC).
Return a tuple of (sunAz, sunZen). If latDeg and longDeg are arrays, then returned
values will be arrays of the same shape.
latRad = numpy.radians(latDeg)
# Express jdp in radians
jdpr = jdp * 2 * numpy.pi
# Now work out the solar position. This is copied from the 6S code, but
# is also documented in the 6S manual. The notation
a = numpy.array([0.000075, 0.001868, 0.032077, 0.014615, 0.040849])
meanSolarTime = hourGMT + longDeg / 15.0
localSolarDiff = (a[0] + a[1] * numpy.cos(jdpr) - a[2] * numpy.sin(jdpr) -
a[3] * numpy.cos(2 * jdpr) - a[4] * numpy.sin(2 * jdpr)) * 12 * 60 / numpy.pi
trueSolarTime = meanSolarTime + localSolarDiff / 60 - 12.0
# Hour as an angle
ah = trueSolarTime * numpy.radians(15)
b = numpy.array([0.006918, 0.399912, 0.070257, 0.006758, 0.000907, 0.002697, 0.001480])
delta = (b[0] - b[1] * numpy.cos(jdpr) + b[2] * numpy.sin(jdpr) -
b[3] * numpy.cos(2. * jdpr) + b[4] * numpy.sin(2. * jdpr) -
b[5] * numpy.cos(3. * jdpr) + b[6] * numpy.sin(3. * jdpr))
cosSunZen = (numpy.sin(latRad) * numpy.sin(delta) +
numpy.cos(latRad) * numpy.cos(delta) * numpy.cos(ah))
sunZen = numpy.arccos(cosSunZen)
# sun azimuth from south, turning west (yeah, I know, weird, isn't it....)
sinSunAzSW = numpy.cos(delta) * numpy.sin(ah) / numpy.sin(sunZen)
sinSunAzSW = sinSunAzSW.clip(-1.0, 1.0)
# This next bit seems to be to get the azimuth in the correct quadrant. I do
# not really understand it.
cosSunAzSW = (-numpy.cos(latRad) * numpy.sin(delta) +
numpy.sin(latRad) * numpy.cos(delta) * numpy.cos(ah)) / numpy.sin(sunZen)
sunAzSW = numpy.arcsin(sinSunAzSW)
sunAzSW = numpy.where(cosSunAzSW <= 0, numpy.pi - sunAzSW, sunAzSW)
sunAzSW = numpy.where((cosSunAzSW > 0) & (sinSunAzSW <= 0), 2 * numpy.pi + sunAzSW, sunAzSW)
# Now convert to azimuth from north, turning east, as is usual convention
sunAz = sunAzSW + numpy.pi
# Keep within [0, 2pi] range
sunAz = numpy.where(sunAz > 2 * numpy.pi, sunAz - 2 * numpy.pi, sunAz)
return (sunAz, sunZen)
[docs]def makeAnglesImage(templateimg, outfile, nadirLine, extentSunAngles, satAzimuth, imgInfo):
Make a single output image file of the sun and satellite angles for every
pixel in the template image.
imgInfo = fileinfo.ImageInfo(templateimg)
infiles = applier.FilenameAssociations()
outfiles = applier.FilenameAssociations()
otherargs = applier.OtherInputs()
controls = applier.ApplierControls()
infiles.img = templateimg
outfiles.angles = outfile
(ctrLat, ctrLong) = getCtrLatLong(imgInfo)
otherargs.R = localRadius(ctrLat)
otherargs.nadirLine = nadirLine
otherargs.xMin = imgInfo.xMin
otherargs.xMax = imgInfo.xMax
otherargs.yMin = imgInfo.yMin
otherargs.yMax = imgInfo.yMax
otherargs.extentSunAngles = extentSunAngles
otherargs.satAltitude = 705000 # Landsat nominal altitude in metres
otherargs.satAzimuth = satAzimuth
otherargs.radianScale = 100 # Store pixel values as (radians * radianScale)
applier.apply(makeAngles, infiles, outfiles, otherargs, controls=controls)
[docs]def makeAngles(info, inputs, outputs, otherargs):
Called from RIOS
Make 4-layer sun and satellite angles for the image block
(xblock, yblock) = info.getBlockCoordArrays()
# Nadir line coefficients of y=mx+b
(b, m) = otherargs.nadirLine
# Distance of each pixel from the nadir line
dist = numpy.absolute((m * xblock - yblock + b) / numpy.sqrt(m**2 + 1))
# Zenith angle assuming a flat earth
satZenith = numpy.arctan(dist / otherargs.satAltitude)
# Adjust satZenith for earth curvature. This is a very simple approximation, but
# the adjustment is less than one degree anyway, so this is accurate enough.
curveAngle = numpy.arctan(dist / otherargs.R)
satZenith += curveAngle
# Work out whether we are left or right of the nadir line
isLeft = (yblock - (m * xblock + b)) > 0
(satAzimuthLeft, satAzimuthRight) = otherargs.satAzimuth
satAzimuth = numpy.where(isLeft, satAzimuthLeft, satAzimuthRight)
# Interpolate the sun angles from those calculated at the corners of the whole raster extent
(xMin, xMax, yMin, yMax) = (otherargs.xMin, otherargs.xMax, otherargs.yMin, otherargs.yMax)
sunAzimuth = bilinearInterp(xMin, xMax, yMin, yMax, otherargs.extentSunAngles[:, 0], xblock, yblock)
sunZenith = bilinearInterp(xMin, xMax, yMin, yMax, otherargs.extentSunAngles[:, 1], xblock, yblock)
angleStack = numpy.array([satAzimuth, satZenith, sunAzimuth, sunZenith])
angleStackDN = angleStack * otherargs.radianScale
outputs.angles = numpy.round(angleStackDN).astype(numpy.int16)
[docs]def bilinearInterp(xMin, xMax, yMin, yMax, cornerVals, x, y):
Evaluate the given value on a grid of (x, y) points. The exact value is given
on a set of corner points (top-left, top-right, bottom-left, bottom-right).
The corner locations are implied from xMin, xMax, yMin, yMax.
p = (y - yMin) / (yMax - yMin)
q = (x - xMin) / (xMax - xMin)
# Give the known corner values some simple names
(tl, tr, bl, br) = cornerVals
# Calculate the interpolated values
vals = tr * p * q + tl * p * (1 - q) + br * (1 - p) * q + bl * (1 - p) * (1 - q)
return vals
[docs]def getCtrLatLong(imgInfo):
Return the lat/long of the centre of the image as
(ctrLat, ctrLong)
cornerLatLong = imgInfo.getCorners(outEPSG=4326)
(ul_long, ul_lat, ur_long, ur_lat, lr_long, lr_lat, ll_long, ll_lat) = cornerLatLong
ctrLat = numpy.array([ul_lat, ur_lat, lr_lat, ll_lat]).mean()
ctrLong = numpy.array([ul_long, ur_long, lr_long, ll_long]).mean()
return (ctrLat, ctrLong) | {"url":"https://www.pythonfmask.org/en/latest/_modules/fmask/landsatangles.html","timestamp":"2024-11-02T08:35:34Z","content_type":"text/html","content_length":"69855","record_id":"<urn:uuid:af75b4a9-a01a-48ac-aeac-dbf8181547a3>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00898.warc.gz"} |
DMS Combinatorics Seminar
Time: Nov 09, 2023 (02:45 PM)
Location: ZOOM
Speaker: Dan Cranston (Virginia Commonwealth University)
Title: Kempe Equivalent List Colorings
Abstract: An \(\alpha,\beta\)-Kempe swap in a properly colored graph interchanges the colors on some component of the subgraph induced by colors \(\alpha\) and \(\beta\). Two \(k\)-colorings of a
graph are \(k\)-Kempe equivalent if we can form one from the other by a sequence of Kempe swaps (never using more than \(k\) colors). Las Vergnas and Meyniel showed that if a graph is \((k-1)\)
-degenerate, then each pair of its \(k\)-colorings are \(k\)-Kempe equivalent. Mohar conjectured the same conclusion for connected \(k\)-regular graphs. This was proved for \(k=3\) by Feghali,
Johnson, and Paulusma (with a single exception \(K_2\dbox K_3\), also called the 3-prism) and for \(k\ge 4\) by Bonamy, Bousquet, Feghali, and Johnson.
In this paper we prove an analogous result for list-coloring. For a list-assignment \(L\) and an \(L\)-coloring \(\vph\), a Kempe swap is called \(L\)-valid for \(\vph\) if performing the Kempe swap
yields another \(L\)-coloring. Two \(L\)-colorings are called \(L\)-equivalent if we can form one from the other by a sequence of \(L\)-valid Kempe swaps. Let \(G\) be a connected \(k\)-regular graph
with \(k\ge 3\). We prove that if \((L)\) is a \(k\)-assignment, then all \(L\)-colorings are \(L\)-equivalent (again excluding only \(K_2\box K_3\). When \((k\ge 4\), the proof is completely
self-contained, implying an alternate proof of the result of Bonamy et al.
This is joint work with Reem Mahmoud. | {"url":"https://www.auburn.edu/cosam/events/2023/11/dms_combinatorics_seminar.htm","timestamp":"2024-11-06T06:16:19Z","content_type":"application/xhtml+xml","content_length":"33381","record_id":"<urn:uuid:75a19a82-6df9-4270-afd3-e0a5f41f3a8a>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00337.warc.gz"} |
The Best Problems Are Your Own Problems
In our years of teaching and being around students (as I'm sure any fellow teacher that is reading this can attest to), we often get asked the question: "how should I study?" or "how do I get better
at this or that?". In fields like math and physics, these questions are hard to answer because most definitions of "being good" at these things involves "being good" at solving problems. And the
thing about solving problems is that it's a very personal, and intimate affair.
Sure, there are skills and bits of knowledge that you either will, or won't, have at any given time, but gaining those is the "easy" part. The hard part comes when you're facing a problem you
haven't seen before and are at a complete loss as to what to do next. And that's where the personal, intimate part comes. You have to fight your inner demons, you have to find something to try, you
have to know how your brain most effectively gets out of these ruts.
If we (society) had a well-tested and generally applicable formula for how humans can move from being stuck to un-stuck, then we'd all be Fields medalists, cancer would be cured, and we'd be driving
cars that get us from point A to point B quickly, safely, without intervention, while powered by plastic bags and emitting only pure oxygen, H20, and the smell of freshly cut pine. But alas, we
don't have such a formula, and therefore no one can tell you precisely and with certainty how you can get better at problem solving.
There is, however, one extremely powerful method that you can use to repeatedly put yourself in a position where you can learn about how your brain works, how it gets itself out of ruts, and how it
makes progress.
Create Your Own Problems
Over our collective years teaching math and physics to undergrads and grads at various levels, there's been one pretty consistent pattern that has been noticed. Those who create their own problems,
and then solve (or at least try to solve) them, get better, faster, at problem solving than those who don't. The benefits of doing so are indescribable and not limited to simply doing better on
problem sets and/or exams. It's a great technique for eventually transitioning into research-level work, if that's your desired end-game. Before elaborating on the benefits, though, let's make
clearer what exactly we mean.
How To Create Your Own Problems
Typically, "creating your own problems" involves taking problems that have been given to you and simply changing them (after you solve the original problem, if you can). Were you given an integral
that has something like "1 + x^2" in it somewhere? If so, can you replace the 1 with a general constant "a" and solve this more general integral? Can you take your 1-dimensional kinematics question
in physics and place it on an inclined plane instead? Or can you add friction to the problem? Can you do both?
This version of "creating your own problems" is probably my personal favorite, for many reasons. First, it usually allows you to "check your work" by taking the limit of your new problem that
recovers your original problem. In the first example above, if we can solve the integral for a general "a", then we can check that our answer agrees with the original problem's answer when a=1.
Similarly, if we take the angle of our inclined plane to be 0, or the coefficient of friction to be 0, we should recover the answer to the original 1-dimensional kinematics question.
Sometimes a really magical thing happens: you take this limit and your answer does not agree with what you expect. At this point there are a few options. One option is that you solved the first
problem incorrectly. Another option is that you solved the new problem incorrectly. A third option is that you solved both incorrectly (hopefully you don't solve both incorrectly, but in such a way
that the new answer still "flows" to the old answer in the limit!). And the fourth, truly magical option is that you solved both correctly, but your new, generalized problem is actually subtly not
continuously related to your first problem.
One example of this fourth option is adding friction to physics problems — where the dynamics of a frictional system with arbitrarily small coefficients of friction can, sometimes, actually be
fundamentally different than a frictionless system. Another example is adding a general parameter to an integral that might introduce a divergence. The integral might converge to different things
in different regions of your new parameter, and if you're not careful this might be really confusing for a while.
Which brings us to the question of how to deal with the four options we just mentioned above. Our answer is: we don't know. You just kind of have to think really hard. Go back to the original
version of the problem and make damn sure you solved it correctly. Once you're very confident you did that, do the same for your new version. If you still haven't found any mistakes, then start
considering option 4 (the magical one). Can't find the subtle "regime change" that you may have introduced? Well, go back and check your work on parts 1 and 2 again.
Here's why this is so great: while you're doing all the stuff just mentioned in the previous paragraph, you're getting way better at solving stuff. You're getting to know how your brain works and
how it struggles. You're mastering concepts, your way. And, since at least one of these problems is one that you came up with, it's probably going to be more fun going through this struggle than if
it were just some textbook problem.
You might not know it, but another side-effect of going through all this is that it's preparing you for doing research as well.
Research Prep
Creating your own problems in this way is, in our opinion at least, the best possible research prep you can possibly do. In fact, it literally is research, just on problems that are likely not
Imagine you're a high-schooler learning integrals. If you take an integral and find a way to make it harder, then solve it, you probably have learned a lot but you probably haven't solved any truly
original problem. And that's okay.
Now suppose that you're an undergrad and you take a problem on your topology problem set and make it a little harder (after you solve it, of course). Again, you probably learned a lot, which is
great, but you probably haven't found anything publishable.
But now imagine you're a grad student, and your years of practicing "creating your own problems" has put you in a mindset where every problem and every proof you see, you're thinking about possible
small little extensions. You're reading a paper and into your mind pops a little idea about some lemma you just read and how it could be extended. You let it jostle around in your brain for a week
and you start to get more confident that you might be able to find some in-roads. Now, my friend, you are doing research, and extending that lemma very well could give you something publishable.
And nowhere along this journey did you consciously decide to "start doing research" — you were literally doing research the whole time, it's just that eventually you got to the point where your
research hadn't been done before by anybody else. And that's a pretty neat feeling.
Creating The Right Kind Of Problems
Most research is not done by thinking about some brilliant new idea in a vacuum and then expounding upon it. 99.9995% of the time, research comes from reading someone else's work (or your own work
from an earlier time), and finding some direction to generalize it and make it 2-10% harder than it was before.
Sometimes, though, when you take a solved problem and try to make it different and/or harder, you sometimes make it way too hard. Or worse, maybe you make it impossible (and impossible problems are
very annoying). Being able to identify this situation, and more importantly, being able to get yourself back out of this situation, is a crucial skill to have. Why is it so hard now? What other
info might you need in order to make it less hard? How can you backtrack a little without sacrificing too much of the interestingness of the problem?
This is the type of thinking that's involved in a lot of research, and fortunately, if you've been creating your own problems for years, you'll already be familiar with it.
It's also fascinating (and fun) to take a problem that you've solved, extend it in a way that you think is reasonable, and then find yourself utterly stuck. It updates your intuition about how
problems of that type behave, since you initially thought it was going to be a tractable extension. I have no way of measuring just how valuable of a learning experience this is, but it certainly
feels like a lot of learning (in the deepest sense of that word) gets done in this process.
In Short
The same way that a doctor might prescribe "exercise" as the single best and most generally applicable intervention that one can take to improve their health, we truly believe (but should not be
trusted as much as you should trust your doctor!) that creating your own problems is the single best thing anyone can do to up their math and/or problem solving game. It puts you in a position to
start wrestling the demons in your brain as often as possible, and learning how to tame them. It is also the single best preparation for research that there is — because it literally is research,
just not on original problems (at first).
So, if you discover a problem that you particularly enjoyed working on, even if it's not original, let us know about it! | {"url":"https://cohomologous.com/blogs/news/the-best-problems-are-your-own-problems","timestamp":"2024-11-05T15:08:30Z","content_type":"text/html","content_length":"251802","record_id":"<urn:uuid:96b6ce4e-7e89-48ce-8630-4280f595e578>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00272.warc.gz"} |
Roy Wagner: Catalogue data in Spring Semester 2021
Name Prof. Dr. Roy Wagner
Field History and Philosophy of Mathematical Sciences
Geschichte u. Philo. d. Math.Wiss.
ETH Zürich, RZ J 6
Address Clausiusstrasse 59
8092 Zürich
Telephone +41 44 632 84 34
E-mail roy.wagner@gess.ethz.ch
URL https://hpm.ethz.ch/people/person-detail.MjI4ODY5.TGlzdC8yNDY4LC0yNDgyNTI2NTg=.html
Department Humanities, Social and Political Sciences
Relationship Full Professor
Number Title ECTS Hours Lecturers
851-0181-00L A New History of Greek Mathematics 3 credits 2V R. Wagner
Abstract This course will review parts of the history of ancient Greek mathematics, evaluate its characteristic features, attempt to explain them, and reflect on their relation to contemporary
Learning The students will have an overview knowledge of Greek mathematics, and will be able to reflect on it in historical terms and in relation to modern mathematics.
Content We will follow extracts from Reviel Netz's upcoming monograph entitled "A new history of Greek mathematics".
851-0182-00L From Economy to Mathematics and Back: A History of Interactions 3 credits 2S R. Wagner
Abstract This course will review several historical episodes where economy shaped mathematics, and where mathematics re-shaped economy.
Learning Students will understand how different fields of knowledge can interact in various historical situations. They will also be able to describe various episodes in the history of
objective mathematics and economy.
The first part of the course will study how practices related to money and commerce affected the development of mathematics in antiquity and the middle ages. The second part will study
Content how mathematical entities shaped the study of various economic problems in the 19th and 20th century. We will review methodologies based on Marxist historiography, sociology of science
and contemporary science studies.
Research Colloquium Philosophy for Master Students and PhD (FS 2021)
862-0004-12L For MAGPW and PhD students of D-GESS only. 2 credits 1K L. Wingert, M. Hampe, R. Wagner
Personal registration required to Prof. Wingert.
Abstract Ph.D. students, post docs, members of staff, and senior colleagues from other philosophy departments will report on their work in progress. Furthermore, promissing new philosophical
articles and parts of new philosophical books will be studied.
Learning Ideas and arguments dealing with systematic problems especially in epistemology, ethics, political philosophy, and the philosophy of mind will be scrutinized and elaborated. | {"url":"https://www.vorlesungen.ethz.ch/Vorlesungsverzeichnis/dozent.view?dozide=10048358&semkez=2021S&ansicht=2&lang=en","timestamp":"2024-11-12T16:25:38Z","content_type":"text/html","content_length":"11077","record_id":"<urn:uuid:3f536a50-2f3d-4e73-a074-6c8e0dd7b801>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00607.warc.gz"} |
Surplus Handling - electowikiSurplus HandlingSurplus Handling
In a sequential Multi-Member System which uses a Quota Method to ensure the Hare Quota Criterion is satisfied, there is an ambiguity about which voters should be in the quota when there are more than
needed. This amount is referred to as a surplus and the various methods to deal with this situation are referred to as surplus handling.
Surplus allocation
In allocation-based systems, the surplus can be transferred to other candidates with some form of surplus allocation. The number of surplus votes is known, but none of the various allocation methods
is universally preferred. Alternatives exist for deciding which votes to transfer, how to weight the transfers, who receives the votes and the order in which surpluses from two or more winners are
Random subset
Some surplus allocation methods select a random vote sample. Sometimes, ballots of one elected candidate are manually mixed. In Cambridge, Massachusetts, votes are counted one precinct at a time,
imposing a spurious ordering on the votes. To prevent all transferred ballots coming from the same precinct, every ${\displaystyle n}$th ballot is selected, where ${\displaystyle {\begin{matrix}{\
frac {1}{n}}\end{matrix}}}$ is the fraction to be selected.
Reallocation ballots are drawn at random from those transferred. In a manual count of paper ballots, this is the easiest method to implement; it is close to Thomas Hare's original 1857 proposal.
Reallocation ballots are drawn at random from all of the candidate's votes. This method is more likely than Hare to be representative, and less likely to suffer from exhausted ballots. The starting
point for counting is arbitrary. Under a recount, the same sample and starting point is used in the recount (i.e., the recount must only be to check for mistakes in the original count, and not a
second selection of votes).
Hare and Cincinnati have the same effect for first-count winners, since all the winners' votes are in the "last batch received" from which the Hare surplus is drawn.
The Wright system is a reiterative linear counting process where on each candidate's exclusion the quota is reset and the votes recounted, distributing votes according to the voters' nominated order
of preference, excluding candidates removed from the count as if they had not nominated.
For each successful candidate that exceeds the quota threshold, calculate the ratio of that candidate's surplus votes (i.e., the excess over the quota) divided by the total number of votes for that
candidate, including the value of previous transfers. Transfer that candidate's votes to each voter's next preferred hopeful. Increase the recipient's vote tally by the product of the ratio and the
ballot's value as the previous transfer (1 for the initial count.)
The UK's Electoral Reform Society recommends essentially this method.^[1] Every preference continues to count until the choices on that ballot have been exhausted or the election is complete. Its
main disadvantage is that given large numbers of votes, candidates and/or seats, counting is administratively burdensome for a manual count due to the number of interactions. This is not the case
with the use of computerised distribution of preference votes.
This is a variation on the original Hare method that used random choices. It allows votes to the same ballots to be repeatedly transferred. The surplus value is calculated based on the allocation of
preference of the last bundle transfer. The last bundle transfer method has been criticized as being inherently flawed in that only one segment of votes is used to transfer the value of surplus votes
denying voters who contributed to a candidate's surplus a say in the surplus distribution. In the following explanation, Q is the quota required for election.
1. Separate all ballots according to their first preferences.
2. Count the votes.
3. Declare as winners those hopefuls whose total is at least Q.
4. For each winner, compute surplus as total minus Q.
5. For each winner, in order of descending surplus:
1. Assign that candidate's ballots to hopefuls according to each ballot's preference, setting aside exhausted ballots.
2. Calculate the ratio of surplus to the number of reassigned ballots or 1 if the number of such ballots is less than surplus.
3. For each hopeful, multiply ratio * the number of that hopeful's reassigned votes and add the result (rounded down) to the hopeful's tally.
6. Repeat 3–5 until winners fill all seats, or all ballots are exhausted.
7. If more winners are needed, declare a loser the hopeful with the fewest votes, recompute Q and repeat from 1, ignoring all preferences for the loser.
Example: If Q is 200 and a winner has 272 first-choice votes, of which 92 have no other hopeful listed, surplus is 72, ratio is 72/(272−92) or 0.4. If 75 of the reassigned 180 ballots have hopeful X
as their second-choice, and if X has 190 votes, then X becomes a winner, with a surplus of 20 for the next round, if needed.
The Australian variant of step 7 treats the loser's votes as though they were surplus votes. But redoing the whole method prevents what is perhaps the only significant way of gaming this system –
some voters put first a candidate they are sure will be eliminated early, hoping that their later preferences will then have more influence on the outcome.
Another method, known as Senatorial rules, or the Gregory method (after its inventor in 1880, J.B. Gregory of Melbourne) eliminates all randomness. Instead of transferring a fraction of votes at full
value, transfer all votes at a fractional value.
In the above example, the relevant fraction is ${\displaystyle \textstyle {\frac {72}{272-92}}={\frac {4}{10}}}$. Note that part of the 272 vote result may be from earlier transfers; e.g., perhaps Y
had been elected with 250 votes, 150 with X as next preference, so that the previous transfer of 30 votes was actually 150 ballots at a value of ${\displaystyle \textstyle {\frac {1}{5}}}$. In this
case, these 150 ballots would now be retransferred with a compounded fractional value of ${\displaystyle \textstyle {\frac {1}{5}}\times {\frac {4}{10}}={\frac {4}{50}}}$.
An alternative means of expressing Gregory in calculating the Surplus Transfer Value applied to each vote is
${\displaystyle {\text{Surplus Transfer Value}}=\left({{{\text{Total value of Candidate's votes}}-{\text{Quota}}} \over {\text{Total value of Candidate's votes}}}\right)\times {\text{Value of
each vote}}}$
The Unweighted Inclusive Gregory Method is used for the Australian Senate.^[2]
Fractional Surplus Handling
In Cardinal voting systems the problem of surplus handing is simplified because the vote aggregation is arithmetic. This means that the surplus voters do not need to be allocated to other candidates.
Instead, they can have their ballot weight reduced proportionally to the surplus and the tabulation process can continue unaffected. This method is better than allocation because it is completely
deterministic and unbiased. This down-weighting of ballots can be applied to all ballots or to a subset depending on the desired effects and the tabulation system. | {"url":"https://electowiki.org/wiki/Fractional_Surplus_Handling","timestamp":"2024-11-13T05:23:16Z","content_type":"text/html","content_length":"64969","record_id":"<urn:uuid:d0a175f8-3398-4d41-a0db-d0a647fc9466>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00006.warc.gz"} |
The Direct Method of Fundamental Solutions and the Inverse Kirsch-Kress Method for the Reconstruction of Elastic Inclusions OR Cavities
Alves, Carlos J. S.; Martins, Nuno F. M.
Journal of Integral Equations and Applications, 21(2) (2009), 153-178
In this work we consider the inverse problem of detecting inclusions or cavities in an elastic body, using a single boundary measurement on an external boundary. We discuss the identifiability
questions on shape reconstruction, presenting counterexamples for Robin boundary conditions or with additional unknown Lame parameters. Using the method of fundamental solutions (MFS) we adapt a
method introduced twenty years ago by Andreas Kirsch and Rainer Kress [20] (in the context of an exterior problem in acoustic scattering) to this inverse problem in a bounded domain. We prove density
results that justify the reconstruction of the solution from the Cauchy data using the MFS. We also establish some connections between this linear part of the Kirsch-Kress method and the direct MFS,
through matrices of boundary layer integrals. Several numerical examples are presented, showing that with noisy data we were able to retrieve a fairly good reconstruction of the shape (or of its
convex hull) with this MFS version of the Kirsch-Kress method. | {"url":"https://cemat.tecnico.ulisboa.pt/document.php?project_id=4&member_id=103&doc_id=1296","timestamp":"2024-11-14T17:56:35Z","content_type":"text/html","content_length":"9208","record_id":"<urn:uuid:b0c8b63b-4d2e-4e95-a9f1-c408d86eef73>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00291.warc.gz"} |
Some examples of discrete group actions on aspherical manifolds
Davis, M.W. and Leary, I.J. (2003) Some examples of discrete group actions on aspherical manifolds. Farrell, F.T. and Luck, W. (eds.) In High-Dimensional Manifold Topology: Proceedings of the School
Ictp. World Scientific. pp. 139-150 . (doi:10.1142/9789812704443_0006).
Record type: Conference or Workshop Item (Paper)
We construct two classes of examples of virtually torsion-free groups G acting properly cocompactly on contractible manifolds X. In the first class of examples, the universal space for proper actions
has no model with finitely many orbits of cells (and so the given manifold X cannot have this equivariant homotopy type). The reason is that the centralizers of some finite subgroups of G do not have
finite-type classifying spaces.
In the second class of examples, X is a CAT(0) manifold upon which G acts by isometries, and hence X is a model for the universal space for proper G actions. In these examples, the fixed-point sets
for some finite subgroups of G are not manifolds and the centralizers of these subgroups are not virtual Poincare duality groups.
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Published date: 2003
Venue - Dates: School on High-Dimensional Manifold Topology 2001 ICTP Trieste, Trieste, Italy, 2001-05-21 - 2001-06-08
Organisations: Pure Mathematics
Local EPrints ID: 199381
URI: http://eprints.soton.ac.uk/id/eprint/199381
ISBN: 981-238-223-2
PURE UUID: 42c19ff6-9053-4d37-b844-d9a2e9b0ce14
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Date deposited: 18 Oct 2011 14:38
Last modified: 15 Mar 2024 03:36
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Editor: F.T. Farrell
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Architecture-aware optimisation: train ImageNet and more without hyperparameters — LessWrong
A deep learning system is composed of lots of interrelated components: architecture, data, loss function and gradients. There is a structure in the way these components interact - however, the most
popular optimisers (e.g. Adam and SGD) do not utilise this information. This means there are leftover degrees of freedom in the optimisation process - which we currently have to take care of via
manually tuning their hyperparameters (most importantly, the learning rate). If we could characterise these interactions perfectly, we could remove all degrees of freedom, and thus remove the need
for hyperparameters.
Second-order methods characterise the sensitivity of the objective to weight perturbations using implicit architectural information via the Hessian, and remove degrees of freedom that way. However,
such methods can be computationally intensive and thus not practical for large models.
I worked with Jeremy Bernstein on leveraging explicit architectural information to produce a new first-order optimisation algorithm: Automatic Gradient Descent (AGD). With computational complexity no
greater than SGD, AGD trained all architectures and datasets we threw at it without needing any hyperparameters: from a 2-layer FCN on CIFAR10 to ResNet50 on ImageNet. Where tested, AGD achieved
comparable test accuracy to tuned Adam and SGD.
Anyone interested in the derivation, PyTorch code, or experiments might be interested in any of the following links, or the summary figure below.
Solid lines show train accuracy and dotted lines show test accuracy. Left: In contrast to our method, Adam and SGD with default hyperparameters perform poorly on a deep fully connected network (FCN)
on CIFAR-10. Middle: A learning rate grid search for Adam and SGD. Our optimiser performs about as well as fully-tuned Adam and SGD. Right: AGD trains ImageNet to a respectable test accuracy.
Hopefully, the ideas in the paper will form the basis of a more complete understanding of optimisation in neural networks - as discussed in the paper, there are a few applications that need to be
fully fleshed out. The derivation relies on an architectural perturbation bound (bounding the sensitivity of the function to changes in weights) based on a fully connected network with linear
activations and no bias terms - however, empirically it works extremely well. Our experiments therefore did not use bias terms, nor affine parameters.
However, the version of AGD in the experimental GitHub supports 1D parameters like bias terms and affine parameters (implemented in the most obvious way, although requiring further theoretical
justification), and preliminary experiments indicate good performance. Preliminary experiments on GPT2-scale language models on OpenWebText2 are also promising.
If anyone has any feedback or suggestions, please let me know!
AGD can train any architecture, dataset and batch size combination (as far as we have tested), out-of-the-box. I would argue that this is a qualitative change to the current methods, where you have
to find the right learning rate for every batch size, architecture and dataset combination, in order to converge in an optimal or near-optimal time. I think this is a reasonable interpretation of
"train ImageNet without hyperparameters". That said, there is a stronger sense of "hyperparameter-free" where the optimum batch size and architecture size would decide on the compute-optimal scaling.
And, an even stronger sense where the architecture type is selected.
In other words, we have the following hierarchy of lack of hyperparameterness,
1. learning rate must be selected, sometimes with schedulers etc. or via heuristics, to guarantee convergence for any architecture, dataset, batch size ...
2. pick and architecture, dataset and batch size and it will converge (hopefully) in a near-optimal time
3. compute-optimal batch size and architecture size is automatically found for a dataset
4. given a dataset, we are given the best architecture type (e.g. resnet, CNN etc.)
I would argue that we currently are in stage 1. If AGD (or similar optimisers) do actually work like we think, we're now in stage 2. In my mind, this is a qualitative change.
So, I think calling it "another learning-rate tuner" is a little disingenuous - incorporating information about the architecture seems to move in a direction of eliminating a hyperparameter by
removing a degree of freedom, rather than a "learning rate tuner" whichI think of as a heuristic method usually involving trial-and-error, without any explanation for why that learning rate is best.
However, if there are similar papers out there already that you think do something similar, or you think I'm wrong in any way, please send them over, or let me know!
New Comment
2 comments, sorted by Click to highlight new comments since:
So, this is another learning-rate tuner. What are the prospects for the many other kinds of hyperparameters? Even stuff like arch size still require the equivalent of hyperparameter tuning to decide
on the compute-optimal scaling. | {"url":"https://www.lesswrong.com/posts/Lia5RfipxFr2chrD3/architecture-aware-optimisation-train-imagenet-and-more","timestamp":"2024-11-09T10:01:24Z","content_type":"text/html","content_length":"160816","record_id":"<urn:uuid:3865ccfc-f3fd-45b2-83dd-d38c373dcfee>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00753.warc.gz"} |
GB/T 4352-2022 Related PDF English (GB/T 4352-2007, GB/T 4352-1984)
GB/T 4352-2022 (GB/T4352-2022, GBT 4352-2022, GBT4352-2022) & related versions
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│GB/T 4352-2022│ English │170│Add to Cart│0-9 seconds. Auto delivery.│Fuel consumption for trucks in operation│GB/T 4352-2022│ Valid │GBT 4352-2022│
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GB/T 4352-2022 GB NATIONAL STANDARD OF THE PEOPLE’S REPUBLIC OF CHINA ICS 43.020 CCS R 06 Replacing GB/T 4352-2007 Fuel Consumption for Trucks in Operation ISSUED ON: DECEMBER 30, 2022 IMPLEMENTED
ON: DECEMBER 30, 2022 Issued by: State Administration for Market Regulation; Standardization Administration of the People’s Republic of China. Table of Contents Foreword ... 3 1 Scope ... 5 2
Normative References ... 5 3 Terms and Definitions ... 5 4 Classification of Truck Operating Conditions and Correction Coefficients ... 6 5 Fuel Consumption for Truck in Operation ... 8 Appendix A
(Informative) Calculation Example of Fuel Consumption of a Truck in Operation with a Maximum Gross Mass of more than 3500kg ... 11 Appendix B (Informative) Calculation Example of Fuel Consumption of
a Truck with a Maximum Gross Mass no more than 3500kg ... 14 Fuel Consumption for Trucks in Operation 1 Scope This Document specifies the classification of truck operating conditions and correction
factors, as well as the calculation method of fuel consumption for operation. This Document is applicable to the calculation of the fuel consumption of trucks running on highways and urban roads that
use gasoline or diesel as the single fuel. The fuel consumption quota management of road transport enterprises shall be used as a reference. 2 Normative References The provisions in following
documents become the essential provisions of this Document through reference in this Document. For the dated documents, only the versions with the dates indicated are applicable to this Document; for
the undated documents, only the latest version (including all the amendments) is applicable to this Document. GB/T 19233 Measurement methods of fuel consumption for light-duty vehicles JT/T 719
Limits and measurement methods of fuel consumption for commercial vehicle for cargos transportation 3 Terms and Definitions For the purposes of this Document, the terms and definitions given in JT/T
719 apply. 3.1 Fuel consumption for truck in operation The amount of fuel a truck consumes during operation. NOTE: The unit is L. 3.2 Basic fuel consumption of truck When a truck with a total mass of
more than 3500kg is under the comprehensive working conditions given in JT/T 719, and a truck with a total mass of no more than 3500kg is under the comprehensive working conditions given in GB/T
19233, the fuel consumption per 100 km, if they drive with curb mass (no load). NOTE: The unit is L/100km. 3.3 Fuel consumption of fully loaded truck When a truck with a total mass of more than
3500kg under the comprehensive working conditions given in JT/T 719, and a truck with a total mass of no more than 3500kg under the comprehensive working conditions given in GB/T 19233, the fuel
consumption per 100km if they drive with total mass (full load). NOTE: The unit is L/100km. 3.4 Changes in fuel consumption per unit load of truck For every 1000kg (1 ton) increase in the loading
capacity of a truck, the fuel consumption increased by driving 100km. NOTE: The unit is L/(t·100km). 3.5 Fuel consumption correction coefficient of road The ratio of the fuel consumption of a truck
running on a certain type of road to the fuel consumption of a Type 1 road (other operating conditions are the same). 3.6 Fuel consumption correction coefficient of temperature The ratio of the fuel
consumption when a truck is running in a certain monthly average temperature range to the fuel consumption when the monthly average temperature range is 5°C to 28°C (inclusive) (other operating
conditions are the same). 3.7 Fuel consumption correction coefficient of traffic congestion The ratio of the fuel consumption of a truck in a certain average speed range to the fuel consumption of an
average speed of 30km/h to 40km/h (inclusive) (other operating conditions are the same) when the truck is operating on urban roads. 4 Classification of Truck Operating Conditions and Correction
Coefficients 4.1 Road category and fuel consumption correction coefficient of road Road category and fuel consumption correction coefficient of road (Kr) is according to Table 1. 4.4 Fuel consumption
correction coefficient of other influential factors The correction coefficient Kx of other factors that affect the fuel consumption of trucks in operation (such as the running-in period of trucks,
seasonal rainy seasons and ice and snow roads in the operating area, loading of dangerous goods, loading of over-limited goods, road construction, etc.), the unit shall be decide by the truck users.
5 Fuel Consumption for Truck in Operation 5.1 Values for basic fuel consumption of truck and fuel consumption of fully loaded truck 5.1.1 Trucks more than 3500kg The value of basic fuel consumption
is the comprehensive fuel consumption of the vehicle under the test conditions specified in JT/T 719 and at no load; and the unit is L/100km. The value of full-loaded fuel consumption is the
comprehensive fuel consumption obtained under the test conditions specified in JT/T 719, or the comprehensive fuel consumption given in the announcement issued by the competent department of
transportation for the qualified types of road transport vehicles; and the unit is L/100km. 5.1.2 Trucks no more than 3500kg The value of the basic fuel consumption is the comprehensive fuel
consumption obtained under the test cycle conditions specified in GB/T 19233, or the light vehicle fuel consumption label query; and the unit is L/100km. The value of full-loaded fuel consumption is
the comprehensive fuel consumption obtained under the test cycle conditions specified in GB/T 19233 when the vehicle is fully-loaded; and the unit is L/100km. 5.2 Changes in fuel consumption per unit
load of truck 5.2.1 Calculation When the basic fuel consumption and full-loaded fuel consumption are given by the automobile manufacturer, the changes in fuel consumption per unit load of the truck
is calculated according to Formula (1). Where: Qb – changes in fuel consumption per unit load of truck, in L/(t•100km); Qi - the fuel consumption of the truck in operation under the ith operating
mode, in L; Si - the driving mileage of the truck under the ith operating mode, in km; ΔWi - the load mass of the truck under the ith operating mode, in t; Kri – the fuel consumption correction
coefficient of the road of the truck under the ith operating mode, see Table 1; Kti - the fuel consumption correction coefficient of the temperature of the truck under the ith operating mode, see
Table 2; Kvi - the fuel consumption correction coefficient of the traffic congestion of the truck under the ith operating mode, see Table 3; Kxi - the fuel consumption correction coefficient of other
influential factors of the truck under the ith operating mode, which is specified by the vehicle user itself; Qai - the additional fuel consumption of the truck under the ith operating mode, the
specific value is specified by the vehicle user itself, in L. NOTE: The additional fuel consumption of truck is the main energy-consuming equipment of truck that are not used to drive vehicles, such
as the fuel consumption of air conditioners, refrigeration units for refrigerated trucks, and truck-mounted loading and unloading machinery; the unit is L. The total fuel consumption of trucks in
different operating modes is calculated according to Formula (3). Where: Q - total fuel consumption of trucks in different operating modes, in L. 5.4 Calculation example of the fuel consumption of
truck in operation See Appendix A for the calculation example of fuel consumption of truck in operation with a maximum gross mass more than 3500kg. See Appendix B for the calculation example of fuel
consumption of trucks in operation with a maximum gross mass of no more than 3500kg. Appendix A (Informative) Calculation Example of Fuel Consumption of a Truck in Operation with a Maximum Gross Mass
of more than 3500kg An ordinary truck has a maximum gross mass of 9.29t, a curb mass of 4.29t, and a rated load mass of 5t. It travels 30km with a full load on a slightly hilly Class-III highway
between cities with an average monthly temperature of -6°C. After unloading, it returns to the original place with no load. The operating period is the evening rush hour in the city, there is
congestion, the average driving speed is 22km/h; the hot air air-conditioner is turned on during driving; and the fuel consumption of the air conditioner is calculated as 0.1L for one-way operation.
Find the total fuel consumption of the truck in operation. Method 1: When the truck manufacturer gives the basic fuel consumption and full-load fuel consumption Calculate as follows. a) The basic
fuel consumption of truck Qk provided by truck manufacturers is 16.1 (L/100km); the fuel consumption of the full-loaded truck Qm is 20.4 (L/100km) after checking the announcement of the qualified
vehicle model for the road transportation issued by the competent department of transportation. b) According to the Formula (1), calculate the changes in fuel consumption per unit load of truck Qb.
c) Calculate the fuel consumption of the truck in operation according to the Formula (2). According to the known conditions, the correction coefficient of the Type-2 roads is 1.10; the correction
coefficient at the monthly average temperature of -6°C is 1.06; the correction coefficient of traffic congestion at an average driving speed of 22km/h is 1.15; and the correction coefficient with no
other influential factors is 1.00; the hot air air- conditioner is turned on during driving, and the fuel consumption of the air conditioner is 0.1L for one-way operation; so the fuel consumption of
the truck in operation is as follows: Appendix B (Informative) Calculation Example of Fuel Consumption of a Truck with a Maximum Gross Mass no more than 3500kg A truck with a maximum gross mass of
3.4t, a curb mass of 1.9t, and a rated load mass of 1.5t is driving 30km with a full load on a Class-III highway between cities at a monthly average temperature of -3°C, and returns to its original
place with no load after unloading. The operating period is the evening rush hour in the city, there is congestion; the average driving speed is 22km/h; the hot air air-conditioner is turned on
during driving, and the fuel consumption of the air conditioner is calculated as 0.1L for one-way operation. Find the total fuel consumption of the truck in operation. Method 1: When the truck
manufacturer gives the basic fuel consumption and full-loaded fuel consumption Calculate as follows. a) The basic fuel consumption of trucks Qk is 9.2 (L/100km), which is obtained through checking
the light-duty truck fuel consumption label, and the full-loaded fuel consumption of trucks Qm provided by truck manufacturers is 11.2 (L/100km). b) Calculate the changes in fuel consumption per unit
load truck Qb according to the formula (1). c) Calculate the fuel consumption of the truck in operation according to the Formula (2). According to the known conditions, the correction coefficient of
the Type-2 roads is 1.10; the correction coefficient at the monthly average temperature -3°C is 1.03; the correction coefficient of traffic congestion at an average driving speed of 22km/h is 1.15;
and the correction coefficient with no other influential factors is 1.00; when the hot air air- conditioner is turned on during driving, the fuel consumption of air-conditioner is calculated as 0.1L
for one-way operation; so the fuel consumption of the truck in operation is as follows: ......
GB/T 4352-2007 Fuel consumption for trucks in operation ICS 43.020 R06 National Standards of People's Republic of China Replacing GB/T 4352-1984 Truck operation of the fuel consumption Posted
2007-12-18 2008-06-01 implementation Administration of Quality Supervision, Inspection and Quarantine of People's Republic of China Standardization Administration of China released Foreword This
standard replaces GB/T 4352-1984 "Run truck fuel consumption." This standard and GB/T 4352-1984 compared to the main changes are as follows. --- On truck operating conditions of the road type
classification has been revised (see 4.2); --- Increased truck speed operation mode weighting coefficients (see 4.3); --- The constant increase of fuel for automobile manufacturers to provide truck
Curb Weight (unloaded) and the total mass (full load) under consumption Regulations (see 5.1); --- Increasing the basic truck loaded with fuel consumption and fuel consumption calculation method (see
5.2); --- Increasing the calculation method of truck fuel consumption of the additional mass change (see 5.3); --- For other effects, run truck fuel consumption factors increase the rainy period of
regional regulations (see 5.4.4); --- For truck operation fuel consumption calculation method has been revised (see 5.5); --- Cancel the original standard car Kongshi basic fuel consumption (before
version 2.3), the additional fuel consumption of basic goods turnover (Before version 2.5), weight change basic additional fuel consumption and vehicle weight data table (before version 2.6 and 4.1
Table 2). Appendix A of this standard is the data appendix. This standard is proposed and managed by the People's Republic of China Ministry of Transportation. This standard was drafted. Traffic
Research Institute of Highway, Chang'an University. The main drafters of this standard. Kyung, Yong, Liu Li, Cai Fengtian, Wang Shengchang, Wangxu Bin, Wang Yunlong. This standard replaces the
previous standard published case. --- GB/T 4352-1984. Truck operation of the fuel consumption 1 Scope This standard specifies the truck classification and the calculation of operating conditions and
operation of the fuel consumption correction coefficient. This standard applies to driving on the highway and urban road use gasoline or diesel fuel to run the truck fuel consumption Calculations. 2
Normative references The following documents contain provisions which, through reference in this standard and become the standard terms. For dated references, subsequent Amendments (not including
errata content) or revisions do not apply to this standard, however, encourage the parties to the agreement are based on research Whether the latest versions of these documents. For undated reference
documents, the latest versions apply to this standard. GB/T 12545.2 commercial vehicle fuel consumption test method JTGB 01 highway engineering standard 3 Terms and Definitions The following terms
and definitions apply to this standard. 3.1 Number of truck fuel consumption during operation, in liters (L). 3.2 In the basic operating conditions, the truck when Curb Weight (unloaded) with fuel
consumption per hundred kilometers number of liters per 100 units of public Lane (L/100km). 3.3 In the basic operating conditions with the truck to the total mass (fully loaded) with fuel consumption
per hundred kilometers number in liters per hundred kilometers (L/100km). 3.4 In the basic operating conditions, the actual total mass of the truck (including load weight, curb weight and trailer
curb weight) than truck production Each additional enterprise gives Truck curb weight (or decrease) 1t, with 100km of the increase (or decrease) the amount of fuel consumed per unit Liters per ton of
one hundred kilometers (L/100km · t). 3.5 The ratio of fuel consumption car run on the road and on certain Class 1 roads (the same other operating conditions) fuel consumption. 3.6 Fuel consumption
when the car is running at a monthly average temperature range and average monthly temperature in the range of 5 ℃ to 28 ℃ when (the other running strip Same member) fuel consumption ratio. ......
│ Standard ID │ GB/T 4352-2022 (GB/T4352-2022) │
│ Description (Translated │ Fuel consumption for trucks in operation │
│ English) │ │
│ Sector / Industry │ National Standard (Recommended) │
│ Classification of Chinese │ R06 │
│ Standard │ │
│Classification of International│ 43.020 │
│ Standard │ │
│ Word Count Estimation │ 14,158 │
│ Date of Issue │ 2022-12-30 │
│ Date of Implementation │ 2022-12-30 │
│ Older Standard (superseded by │ GB/T 4352-2007 │
│ this standard) │ │
│ Drafting Organization │ Highway Research Institute of the Ministry of Transport, Offcn Gaoyuan (Beijing) Automobile Inspection Technology Co., Ltd., Anhui Transportation Comprehensive Law │
│ │ Enforcement Supervision Bureau, China Energy Conservation Association │
│ Administrative Organization │ National Road Transport Standardization Technical Committee (SAC/TC 521) │
│ Proposing organization │ Ministry of Transport of the People's Republic of China │
│ Issuing agency(ies) │ State Administration for Market Regulation, National Standardization Management Committee │
│ Standard ID │ GB/T 4352-2007 (GB/T4352-2007) │
│ Description (Translated │ Fuel consumption for trucks in operation │
│ English) │ │
│ Sector / Industry │ National Standard (Recommended) │
│Classification of Chinese │ R06 │
│ Standard │ │
│ Classification of │ 43.020 │
│ International Standard │ │
│ Word Count Estimation │ 8,895 │
│ Date of Issue │ 2007-12-18 │
│ Date of Implementation │ 2008-06-01 │
│Older Standard (superseded│ GB/T 4352-1984 │
│ by this standard) │ │
│ Drafting Organization │ Ministry of Transportation Highway Research Institute │
│ Administrative │ Ministry of Communications │
│ Organization │ │
│Regulation (derived from) │ China National Standard Approval Announcement2007 No.13 (Total No.113) │
│ Proposing organization │ People's Republic of China Ministry of Transportation │
│ Issuing agency(ies) │ Administration of Quality Supervision, Inspection and Quarantine of People's Republic of China; Standardization Administration of China │
│ Summary │This standard specifies the truck classification and calculation of operating conditions and fuel consumption correction coefficient is running. This standard applies to │
│ │ the use of gasoline or diesel driving on highways and city roads as fuel truck running children 's calculation of fuel consumption. │
│ Standard ID │ GB/T 4352-1984 (GB/T4352-1984) │
│ Description (Translated English) │ Fuel consumption for trucks in operation │
│ Sector / Industry │ National Standard (Recommended) │
│ Classification of Chinese Standard │ R06 │
│Classification of International Standard│ 43.02 │
│ Word Count Estimation │ 6,687 │
│ Date of Issue │ 1984/4/30 │
│ Date of Implementation │ 1985/1/1 │
│ Regulation (derived from) │ China Announcement of Newly Approved National Standards No. 13, 2007 (No. 113 overall) │
│ Proposing organization │State Economic Commission, State Planning Commission, the People Republic of China Ministry of Communications│
│ Issuing agency(ies) │ National Bureau of Standards │ | {"url":"https://www.chinesestandard.net/Related.aspx/GBT4352-2022","timestamp":"2024-11-07T09:45:37Z","content_type":"application/xhtml+xml","content_length":"41744","record_id":"<urn:uuid:56076fe4-fe49-4bfe-b17f-92d8eb119bde>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00843.warc.gz"} |
Undergraduate Research
The Mathematics Department is one of the top math departments in the nation for undergraduate mentored research. CURM, a national organization dedicated to assisting university math departments in
undergraduate research, was founded here (see CURM home page). In recent years, hundreds of students have participated in undergraduate research mentoring.
Undergraduate students can pursue research in various exciting topics. Many of these undergraduate research projects have led to publication and an opportunity to travel and present at various
conferences. A list of a few recent publications by BYU undergraduates can be found here.
Why Undergraduate Research?
• Provide out-of-classroom learning experiences and apply class room knowledge to solve new problems.
• Develop and foster an analytical approach to doing research
• Gain motivation and create new knowledge
• Excellent experience and preparation for graduate school
• Develop oral and written communication skills
• Promote interactions with faculty and graduate students
• Make better informed decisions about your future career
Funding for Undergraduate Research
Pay: $14/hr — Students can work up to 20 hrs/week. To apply, please talk to a professor you are interested in working with. See below for a summary of projects professors are working on with
students. Contact info for professors can be found here.
Finding a Research Mentor
Mark Allen
My research involves modeling spread of disease or wildfires with differential equations. I have several possible undergraduate research projects that involve fractional derivatives. In many
applications, modeling with a fractional derivative (like a 0.5 or 1.5) derivative is more accurate than modeling with integer order derivatives (like the first and second derivative). In order to
start these research projects, a student should have already taken Ordinary Differential Equations (Math 334).
Nickolas Andersen
I am primarily interested in analytic number theory, especially the theory of modular forms and L-functions. Student projects combine computational and theoretical methods to prove new results in
number theory. I am also interested in formalizing proofs using the Lean proof assistant. Students must have completed Math 290 (with Math 371 and/or Math 352 recommended) and be interested in coding
in Mathematica and/or Sage (no prior experience with those languages is necessary).
Lennard Bakker
We study problems in an area of dynamical systems known as Celestial Mechanics. This includes analysis of a binary asteroid model, restricted N+k problems, and the general N-body problem. Initial
training includes fundamentals such as the circular restricted three-body problem (that NASA uses to design space missions) and the theory of Hamiltonian systems. After initial training undergraduate
students are given a problem in which numerical investigations are combined with analytic theory to understand the nature of solutions. Recent problems have involved various aspects of motion of
binary asteroids. Students must have successfully taken Math 213, Math 215 (or have some coding skills), Math 314, and Math 334.
Blake Barker
Math FIRE lab (mathematical fire and industry research experience lab): We use machine learning, scientific computing, and modeling to advance knowledge about wildfires in ways that can aid wildfire
managers. We are interested in problems like wildfire risk analysis, perimeter prediction, and ecological effects of burn severity. Before working with the group, students need to take a course on
linear algebra, ODEs, and have some experience programming with Python.
Zach Boyd
I work in applied math/data science/math modeling, especially with the tools of network science. I have possible undergraduate projects across a broad range of application areas, such as global
supply chains, genealogy, social drinking, brain networks, and network structure detection, to name a few. In terms of “mathematical purity,” I touch on some very pure topics, such as graph theory or
functional analysis, but spend lots of my time close to the data doing modeling, algorithm design, data exploration, and so forth. There are no strict prerequisites to work with me, although the more
you know in advance the more agile you will be. Particularly good preparatory topics include linear algebra, computer programming (e.g. Python), and network science. Data science/machine learning,
dynamical systems, statistics, and real analysis can also open more topics to work on with me. If you already have a particular project you want to work on, I am open to talking about it, or I can
provide topic ideas.
Jennifer Brooks
My group conducts research in complex analysis. Specifically, we study zeros of complex harmonic polynomials. It is helpful if students who join the group have taken Math 341 and Math 352, but I
encourage any interested student to come talk to me.
David Cardon
My research is currently in the area of complex analysis. I study operators on entire functions with only real zeros that preserve reality of the zeros. This topic is motivated by the Riemann
hypothesis. Students must complete of all of Math 341 (real analysis), Math 352 (complex analysis), Math 371 (abstract algebra) and begin working with me at least a year before graduation
Gregory Conner
Over the last few years I’ve had several undergraduate students work with me on research projects in low-dimensional wild homotopy groups. Topics range from geometric — understanding how
“fractal-like” objects in the plane can be deformed in to others, to algebraic — understanding infinitely stranded braid groups, to analytic — understanding how to prove very delicate continuity
arguments on wild subsets of our universe. These undergraduate research projects have all turned into masters’ theses at BYU and have lead each of the students into a high-quality mathematics Ph.D.
program such as Vanderbilt, Tennessee and BYU.
John Dallon
I am doing research modeling properties of collagen lattices and cell motion. Students must have completed Math 334 and have some computational skills.
Michael Dorff
Minimal surfaces and complex-valued functions:
We investigate minimal surfaces in R^3. In some ways, minimal surfaces can be thought of as soap films that form when a wire-frame is dipped in soap solution–they tend to minimize the surface area
for a given boundary condition. Images of minimal surfaces can easily be displayed by using computers, and this lends itself nicely to student explorations. We will use results about analytic
functions from complex analysis (Math 332) to investigate minimal surfaces. To help introduce students to this topic and begin to do research, we have received a grant to write two chapters in a book
on this topic along with exploratory problems using applets.
Darrin Doud
Undergraduate research with Dr. Doud can include topics such as modular forms with connections to Galois representations, diophantine equations, elliptic curves, and LLL-reduced lattices. A
prerequisite for all of this research is Math 371, and several topics would require Math 372.
Scott Glasgow
Undergrads in this program either work in Mathematical Finance, including Extremal Events in Insurance and Finance, or in certain components of mathematical physics—symmetries, conservation laws,
integrability. These topics require interest in probability theory, differential equations, and/or complex variables, and students will have had success in courses 334, 343, and/or 332.
Chris Grant
Denise Halverson
Mark Hughes
My research is in low-dimensional topology, where I study things like knots, surfaces, and 4-dimensional spaces called manifolds. Recently I have been working with undergraduates on a particular
representation of knots called petal diagrams, which provides a connection between knot theory and the algebra of the symmetric group. Familiarity with some abstract algebra is helpful with this
research. I’m also interested in studying knots and topological objects using machine learning. I’ve been working with students to apply deep learning models (including generative deep learning and
deep reinforcement learning) to answering difficult questions in knot theory. This research requires calculus, linear algebra, and some experience with programming (preferably in Python).
Stephen Humphries
I have mentored many students in various Abstract Algebra subjects including: Group theory, Difference sets, Representation Theory, Combinatorics, semi-simple rings.
I am happy to consider doing mentored research with anyone who has obtained a good grade in 371.
Tyler Jarvis
Project 1: This project is focused on numerical algebraic geometry and multivariable root-finding. Students must have completed Math 341 and CS 235 and preferably have completed CS 240, Math 320-321
Project 2 :This project is concerned with physiological signals. It includes analyzing spectrometer and bioimpedance signals to identify blood analytes noninvasively. Student must have completed Math
320-321 and preferably have completed CS 235 and Math 322-323
Paul Jenkins
We study problems in number theory related to modular forms and their coefficients. Students who have successfully mastered the concepts in Math 371 and 352 will be better prepared to do research in
these areas. Problems in computational elementary number theory are also available. More information on papers written by students in this group is available here. Interested students are invited to
attend meetings of the Computational Number Theory research group at 10 AM on Thursdays during fall and winter semesters.
Mark Kempton
I work in the area of spectral graph theory, which examines how matrices and their eigenvalues can help us understand graphs and networks. Specific projects include: understanding the mixing rate of
non-backtracking random walks on graphs; studying quantum state transfer phenomena, especially using isospectral reductions; studying Kemeny’s constant and effective resistance in graphs; finding
bounds for eigenvalues of the Laplacian and normalized Laplacian. I am always willing to talk to students interested in getting involved in research. Requirements to work in this area are Math 213,
with Math 290 strongly recommended. Extra experience with linear algebra is also nice.
Xian-Jin Li
1. Research on spectral theory of automorphic forms:
In 1956, A. Selberg introduced trace formulas into the classical theory of automorphic forms, a theory whose origins lie in the work of Riemann, Klein, and Poincar\’e. The theory of automorphic forms
is intimately connected with questions from the theory of numbers, and is one of the most powerful tools in number theory. The discrete spectrum of the non-Euclidean Laplacian for congruence
subgroups is one of the fundamental objects in number theory. My research interests are Selberg’s trace formula, Selberg’s eigenvalue conjecture, and the multiplicity of the discrete eigenvalues.
2. Research on Beurling-Selberg’s extremal functions:
In 1974, A. Selberg used the Beurling-Selberg extremal function to give a simple proof of a sharp form of the large sieve. By using the large sieve, E. Bombieri proved in 1965 a remarkable theorem on
the distribution of primes in arithmetical progressions that may sometimes serve as a substitute for the assumption of the generalized Riemann hypothesis. The large sieve is closely related to
Hilbert’s inequality. An open problem is to prove a weighted version of H. L. Montgomery and R. C. Vaughan’s generalized Hilbert inequality. A weighted large sieve can be derived from the weighted
Hilbert inequality, and is fundamentally more delicate than the large sieve. It has important arithmetic applications. My research interest is to attack the open problem on the weighted Hilbert
inequality. “
Pace Nielsen
My current projects are focused on abstract algebra. To work with me, I usually require Math 371.
Nathan Priddis
My research is inspired the the physics of string theory. Mostly I study a phenomenon called Mirror Symmetry, which basically is that in string theory, there is a choice along the way, that shouldn’t
make any difference. But it does, and so you get two different kinds of mathematical objects, that should be the same. Mirror symmetry is a way to see how these objects are the same. My research
requires a solid understanding of abstract algebra, and I will ask you to learn some things about algebraic geometry.
Jared Whitehead
1. We use Bayesian statistics to determine the location and magnitude of historical (prior to 1950) earthquakes in Indonesia using historical records of the resultant shaking and tsunami that
resulted. This is a very interdisciplinary project that has students participating from 3-4 departments on campus at any time. Primary pre-requisites are a basic knowledge of Python programming, and
some basic understanding of probability and linear algebra.
2. Another project is determining parameters of high dimensional dynamical systems from sparse observations of the system. This project is more theoretical currently, but has application to
experimental fluid dynamics (with colleagues from Mechanical Engineering), weather prediction, and climate modeling. Pre-requisites are familiarity with Python programming, and at least one course
(preferably more) in differential equations.
Vianey Villamizar
Project 1. This project is concerned with the development of 3-D grid generators with nearly uniform cell volume and surface spacing, respectively. The proposed algorithm will be based on recently
developed 2-D quasi-linear elliptic grid generators with similar features. It requires knowledge of boundary value problems of partial differential equations (Math 347), numerical iterative methods
for linear and non-linear systems, interpolation techniques (Math 311), and good programming skills.
Project 2. We propose to obtain numerical solution for the Helmholtz equation in locally perturbed half-plane with Robin-type boundary conditions. This problem is motivated by a system sea-coast
where each media is represented by a half-plane. Knowledge about partial differential equations (Math 347), numerical solution of partial differential equation (Math 511), and numerical methods in
general is desirable. | {"url":"https://math.byu.edu/undergraduate-research","timestamp":"2024-11-05T04:10:21Z","content_type":"text/html","content_length":"112659","record_id":"<urn:uuid:98d8d9d6-d1ae-45df-91f2-d4dd4c82a3d6>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00012.warc.gz"} |
All-familiar map on steroids: a set of functions that generalize map.
filtermap(f, X): map and filter a collection in one go. Most useful when the mapped function shares some computations with the filter predicate.
Returns same as map(f, X), dropping elements where f(x) is nothing. Return Some(nothing) from f to keep nothing in the result.
filtermap(x -> x % 3 == 0 ? x^2 : nothing, 1:10) == [9, 36, 81]
Analogous to filter_map in Rust
These functions are similar to Iterators.flatmap and Iterators.flatten, but operate on arrays in a more performant and generic manner.
flatmap(f, X): apply f to all elements of X and flatten the result by concatenating all f(x) collections.
flatmap(fₒᵤₜ, fᵢₙ, X): apply fₒᵤₜ to all elements of X, and apply fᵢₙ to the results. Basically, [fᵢₙ(x, y) for x in X for y in fₒᵤₜ(x)].
flatmap(f, X) is similar to mapreduce(f, vcat, X) and SplitApplyCombine.mapmany(f, A), but more efficient and generic.
Defining differences include:
• better result type inference
• keeps array types, eg StructArray
• works with empty collections
• supports arbitrary iterators, not only arrays
Analogous to flat_map in Rust, and SelectMany in C#
flatten(X): flatten a collection of collections by concatenating all elements, equivalent to flatmap(identity, X).
mapview(f, X):
• like map(f, X), but works lazily, doesn't materialize the result returning a view instead.
• like Iterators.map(f, X), but with better collection support, type stability, etc.
Works on different collections and arbitrary iterables. Collection types are preserved when possible for ranges, arrays, dictionaires. Passes length, keys and others directly to the parent. Does its
best to determine the resulting eltype without evaluating f. Supports both getting and setting values (through Accessors.jl).
X = [1, 2, 3]
mapview(x -> x + 1, X) == [2, 3, 4] # a view of X, doesn't take extra memory
X = Dict(:a => 1, :b => 2, :c => 3)
mapview(x -> x + 1, X) == Dict(:a => 2, :b => 3, :c => 4) # same with Dict
X = [1, 2, 3]
mapview(x -> x + 1, (x for x in X)) # and with iterator
julia> X = [1, 2, 3.]
julia> Y = mapview(exp10, X)
3-element FlexiMaps.MappedArray{Float64, 1, typeof(exp10), Vector{Float64}}:
# setindex! works for all functions/optics supported by Accessors
julia> Y[2] = 10^10
# when invertible, push! also works
julia> push!(Y, 10000)
julia> X
4-element Vector{Float64}:
maprange(f, start, stop; length): length values between start and stop, so that f(x) is incremented in uniform steps. Uses mapview in order not to materialize the array.
maprange(identity, ...) is equivalent to range(...). Most common application - log-spaced ranges:
maprange(log, 10, 1000, length=5) ≈ [10, 31.6227766, 100, 316.227766, 1000]
Other transformations can also be useful:
maprange(sqrt, 16, 1024, length=5) == [16, 121, 324, 625, 1024] | {"url":"https://juliapackages.com/p/fleximaps","timestamp":"2024-11-14T18:27:05Z","content_type":"text/html","content_length":"98708","record_id":"<urn:uuid:d157f19d-4026-44d3-92d6-64aea8bb39c5>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00834.warc.gz"} |
Calculating the dispersion relation of dirac lagrangian in curved spacetime
871 views
I am trying to calculate the dispersion relation for a fermion in a gravitational field. So far, I have computed the equation of motion, but I am stuck trying to figure out a determinant I just can't
get.... I am having trouble calculating the final determinant.
My derivation is below:
Equation of motion:
$$\left(i\gamma^a\partial_a - m -\frac{1}{2} \gamma^a\gamma^5B_a\right)\Psi = 0$$
If we take $\Psi = u(\vec{p_a})e^{-ip_ax^a}$ as our ansatz we get the result \left(i\gamma^a(-ip_a) -m -\frac 12\gamma^a\gamma^5B_a \right)u(\vec{p_a}) &= 0 \\ \left(\gamma^ap_a -m -\frac 12\gamma^a\
gamma^5B_a \right)u(\vec{p_a}) &= 0 We multiply this by expression by $\left(\gamma^ap_a +m -\frac 12\gamma^a\gamma^5B_a \right)$ and expand to get $$\bigg[\gamma^b\gamma^ap_ap_b -m^2 + m(\gamma^ap_a
- \gamma^bp_b) - \frac{m}{2}(\gamma^b\gamma^5B_b-\gamma^a\gamma^5B_a) - \gamma^b\gamma^a\gamma^5B_aP_b ~~ - otag$$ $$-~~ \gamma^a\gamma^5\gamma^bB_bP_a + \frac 14 \gamma^b\gamma^5\gamma^a\gamma^
5B_aB_b\bigg]u(\vec{p}_a) = 0$$ $$\bigg[p^ap_a -m^2 + \frac 12[\gamma^a,\gamma^b]\gamma^5B_aP_b - \frac 14B^aB_a\bigg]u(\vec{p}_a) = 0$$ This is a matrix times spinor equal to zero, meaning the
determinant of the matrix must be zero (since the spinor being zero is of no interest to us). Therefore:
$$ \text{det}\bigg[(p^ap_a -m^2 - \frac 14B^aB_a){\mathcal{\large\mathbb{1}}}+ \frac 12[\gamma^a,\gamma^b]\gamma^5B_aP_b\bigg] = 0 $$
Anyone have any tips on calculating such a monster? Or even a different way of finding the relation?
This post imported from StackExchange Physics at 2014-03-06 21:59 (UCT), posted by SE-user Nathan Moynihan
I think you may choose a frame where the spatial part of $p$ is zero (so only $p^0 $ is non-zero) and use the Weyl Basis. The interesting matrices $[\gamma^0, \gamma^i]\gamma^5$ are block-diagonal,
so it is easy to find the determinant (Each block is a matrix $\lambda ~ \mathbb{Id} + \vec \mu . \vec \sigma$, with determinant $\lambda^2-\vec \mu^2$). Then, you have to express the final result in
a Lorentz-invariant way, using $p^2, B^2, (p.B)^2$
This post imported from StackExchange Physics at 2014-03-06 21:59 (UCT), posted by SE-user Trimok | {"url":"https://www.physicsoverflow.org/5355/calculating-dispersion-relation-lagrangian-curved-spacetime","timestamp":"2024-11-07T21:40:13Z","content_type":"text/html","content_length":"103432","record_id":"<urn:uuid:c5212093-5f8f-4f39-99c4-4dfc35967412>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00624.warc.gz"} |
1995 IMO Problems
Problems of the 1995 IMO.
Day I
Problem 1
Let $A,B,C,D$ be four distinct points on a line, in that order. The circles with diameters $AC$ and $BD$ intersect at $X$ and $Y$. The line $XY$ meets $BC$ at $Z$. Let $P$ be a point on the line $XY$
other than $Z$. The line $CP$ intersects the circle with diameter $AC$ at $C$ and $M$, and the line $BP$ intersects the circle with diameter $BD$ at $B$ and $N$. Prove that the lines $AM,DN,XY$ are
Problem 2
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $\[\frac{1}{a^3(b+c)} + \frac{1}{b^3(c+a)} + \frac{1}{c^3(a+b)} \geq \frac{3}{2}.\]$
Problem 3
Determine all integers $n>3$ for which there exist $n$ points $A_1,\ldots,A_n$ in the plane, no three collinear, and real numbers $r_1,\ldots,r_n$ such that for $1\le i<j<k\le n$, the area of $\
triangle A_iA_jA_k$ is $r_i+r_j+r_k$.
Day II
Problem 4
The positive real numbers $x_0, x_1, x_2,.....x_{1994}, x_{1995}$ satisfy the relations
$x_0=x_{1995}$ and $x_{i-1}+\frac{2}{x_{i-1}}=2{x_i}+\frac{1}{x_i}$
for $i=1,2,3,....1995$
Find the maximum value that $x_0$ can have.
Problem 5
Let $ABCDEF$ be a convex hexagon with $AB=BC=CD$ and $DE=EF=FA$, such that $\angle BCD=\angle EFA=\frac{\pi}{3}$. Suppose $G$ and $H$ are points in the interior of the hexagon such that $\angle AGB=\
angle DHE=\frac{2\pi}{3}$. Prove that $AG+GB+GH+DH+HE\ge CF$.
Problem 6
Let $p$ be an odd prime number. How many $p$-element subsets $A$ of ${1,2,\ldots,2p}$ are there, the sum of whose elements is divisible by $p$?
See Also | {"url":"https://artofproblemsolving.com/wiki/index.php?title=1995_IMO_Problems&oldid=221678","timestamp":"2024-11-09T07:41:17Z","content_type":"text/html","content_length":"48952","record_id":"<urn:uuid:ac280d8f-0be6-4660-a004-bf409cdbc222>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00130.warc.gz"} |
Journey Through the Infinite Dimensions: An Introduction to Hilbert Spaces
Exploring the mathematical concept of Hilbert spaces and their applications in quantum mechanics, signal processing, and more.
Hilbert spaces are a cornerstone of modern mathematics and physics, playing a crucial role in various branches of science and engineering. Named after German mathematician David Hilbert, these spaces
offer a powerful and elegant framework for understanding the world around us. In this blog post, we'll dive into the concept of Hilbert spaces, unravel their mathematical foundations, and explore
their applications in quantum mechanics, signal processing, and beyond.
What is a Hilbert space?
A Hilbert space is a complete inner product space, which is a mathematical structure that generalizes the familiar concept of Euclidean space. It allows us to work with infinite-dimensional spaces
while still maintaining the essential properties of finite-dimensional spaces. The defining characteristics of a Hilbert space are:
• A vector space: A set of objects, called vectors, that can be added and multiplied by scalars (real or complex numbers) while satisfying certain axioms (e.g., associativity, distributivity, and
the existence of zero and inverse elements).
• An inner product: A function that takes two vectors as input and returns a scalar, satisfying specific properties (e.g., linearity, conjugate symmetry, and positive definiteness).
• Completeness: Every Cauchy sequence of vectors in the space converges to a limit within the space.
2. Mathematical foundations
To understand Hilbert spaces, let's first take a closer look at the mathematical concepts underlying them:
• Vector spaces: Vector spaces are fundamental constructs in linear algebra, abstracting the notion of direction and magnitude. Examples include the familiar n-dimensional Euclidean space and
function spaces.
• Inner product: The inner product, often denoted as <u, v>, is a generalization of the dot product in Euclidean spaces. It allows us to define notions such as angle and orthogonality between
• Completeness and the Cauchy criterion: A space is complete if every Cauchy sequence (i.e., a sequence of vectors where the distance between successive elements tends to zero) converges to a limit
within the space. Completeness ensures that the space is "well-behaved" and does not have any "holes."
Examples of Hilbert spaces
Hilbert spaces come in many forms, ranging from finite-dimensional to infinite-dimensional. Some common examples include:
• Finite-dimensional Euclidean spaces (e.g., R^n and C^n): These spaces are the simplest examples of Hilbert spaces, with the standard dot product serving as the inner product.
• L^2 spaces: These spaces consist of square-integrable functions defined over a specific domain, with the inner product being the integral of the product of the functions.
• Sequence spaces: Spaces of infinite sequences with the inner product defined as the sum of the product of corresponding elements.
Applications in quantum mechanics
Hilbert spaces play a central role in quantum mechanics, where they are used to represent the state of a quantum system. The wave function, a fundamental concept in quantum mechanics, is an element
of a Hilbert space. Properties such as superposition, entanglement, and measurement can be elegantly described within the framework of Hilbert spaces.
Applications in signal processing
Hilbert spaces provide a powerful tool for analyzing and processing signals in signal processing. For instance, the L^2 space is commonly used to represent signals, allowing for the application of
Fourier analysis and other mathematical techniques. Additionally, Hilbert spaces enable the formulation of optimal filtering and estimation problems.
We research, curate and publish daily updates from the field of AI.
Consider becoming a paying subscriber to get the latest! | {"url":"https://everydayseries.com/untitled/","timestamp":"2024-11-04T18:56:36Z","content_type":"text/html","content_length":"47984","record_id":"<urn:uuid:f8246416-e65d-4007-acf3-e9b05be58124>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00326.warc.gz"} |
Tri Tiling
Problem AM
Tri Tiling
In how many ways can you tile a $3\times n$ rectangle with $2\times 1$ dominoes?
Here is a sample tiling of a $3\times 12$ rectangle.
Input consists of several test cases followed by a line containing -1. Each test case is a line containing an integer $0 \leq n \leq 30$. For each test case, output one integer number giving the
number of possible tilings.
Sample Input 1 Sample Output 1 | {"url":"https://purdue.kattis.com/courses/CS311-CP2/2024-Spring/assignments/ps6tpj/problems/tritiling","timestamp":"2024-11-06T02:26:23Z","content_type":"text/html","content_length":"27362","record_id":"<urn:uuid:7bd40ccd-c1b2-49c5-aa1c-45bb56916960>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00325.warc.gz"} |
Error with the Freefem script; composite finite element spaces
I am experimenting with a Freefem script, which demonstrates the composite finite element spaces, as in the example solving Stokes equations given at Composite finite element spaces NEW!.
The script runs properly when the script in “using solve or problem” is used. But when the script in the section “using varf and matrix” is used it gives an error:
Error line number 17, in file stokes-in-diff-meshes.edp, before token =syntax error
current line = 17
Compile error : syntax error
line number :17, =
error Compile error : syntax error
line number :17, =
code = 1 mpirank: 0
I have thought that the error is due to any bad hidden character - however, I edit the text with pure text editor (vim) and it does not look to be the case.
I run Freefem 4.6, installed with FreeFEM_4.6_Ubuntu_withPETSc_amd64.deb in a linux ubuntu machine.
Any help is greatly appreciated.
For convenience I have included the script that I run (copied from Composite finite element spaces NEW!).
Thank you.
1. int nn = 30; // number of edges in each direction
2. mesh ThP = square(nn,nn,[2pix,2piy],flags=3); // Pressure mesh
3. mesh ThU = trunc(ThP,1,split=2); // Velocity mesh
4. fespace Uh(ThU,[P1,P1]); // Velocity space
5. fespace Ph(ThP,P1); // Pressure space
6. macro grad(u) [dx(u),dy(u)] //
7. macro Grad(u1,u2) [grad(u1), grad(u2)] //
8. macro div(u1,u2) (dx(u1)+dy(u2)) //
9. // definition of the boundary condition
10. func g1 = sin(x)*cos(y);
11. func g2 = -cos(x)*sin(y);
12. // definition of the right-hand side
13. func f1 = 0;
14. func f2 = -4*cos(x)*sin(y);
15. Uh [u1,u2],[v1,v2];
16. Ph p,q;
17. fespace Xh=Uh*Ph;
18. varf Stokes (<[u1,u2],[p]>, <[v1,v2],[q]>) = int2d(ThU)((Grad(u1,u2):Grad(v1,v2))) +
19. int2d(ThU)(-div(u1,u2)*q -div(v1,v2)*p) +
20. int2d(ThP)(-1e-10pq) +
21. int2d(ThU)([f1,f2]'*[v1,v2]) +
22. on(1,2,3,4, u1=g1, u2=g2);
23. matrix M = Stokes(Xh,Xh);
24. real[int] b = Stokes(0,Xh);
25. real[int] sol = M^-1*b;
26. [u1,p] = sol; // dispatch the solution
27. plot([u1,u2], cmm=“u”);
28. plot(p, cmm=“p”);
You need a newer FreeFEM version.
Thank you for the suggestion.
The latest deb package installing the version 4.6 - which does not support composite FEs, I tried to compile the source following the instructions in Installation guide. Unfortunately, errors occur
during the installation. For example:
• the step ./3rdparty/getall -a fails with many errors; one of them like
Error download pkg/patch.tar.gz
Error download pkg/arpack96.tar.gz
Download 2 times failed from http://pkgs.freefem.org/patch.tar.gz of patch.tar.gz
Try (2 times) other site: http://104.46.50.187/pkg/patch.tar.gz
• the following step make -j1 fails also, with one of errors like
HTTP request sent, awaiting response… HTTP request sent, awaiting response… 404 Not Found
404 Not Found
2024-10-10 09:58:18 ERROR 404: Not Found.
2024-10-10 09:58:18 ERROR 404: Not Found.
I am following the installation guide. I do not have errors when I installed required packages, but only when I configure/install freefem.
Thank you for any help.
Switch to the develop branch instead of using the master branch.
I think you need to try from
Installing the deb binary from github solves the issue.
Thank you to both of you for the help. | {"url":"https://community.freefem.org/t/error-with-the-freefem-script-composite-finite-element-spaces/3541","timestamp":"2024-11-10T21:39:32Z","content_type":"text/html","content_length":"33951","record_id":"<urn:uuid:6dd45d23-55dc-497e-85e4-3eeae85f4f70>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00508.warc.gz"} |
Library Coq.FSets.FSetAVL
FSetAVL : Implementation of FSetInterface via AVL trees
This module implements finite sets using AVL trees. It follows the implementation from Ocaml's standard library,
All operations given here expect and produce well-balanced trees (in the ocaml sense: heights of subtrees shouldn't differ by more than 2), and hence has low complexities (e.g. add is logarithmic in
the size of the set). But proving these balancing preservations is in fact not necessary for ensuring correct operational behavior and hence fulfilling the FSet interface. As a consequence, balancing
results are not part of this file anymore, they can now be found in
Four operations (
) have been slightly adapted in order to have only structural recursive calls. The precise ocaml versions of these operations have also been formalized (thanks to Function+measure), see
. The structural variants compute faster in Coq, whereas the other variants produce nicer and/or (slightly) faster code after extraction.
This is just a compatibility layer, the real implementation is now in MSetAVL | {"url":"https://coq.inria.fr/doc/V8.19.0/stdlib/Coq.FSets.FSetAVL.html","timestamp":"2024-11-14T15:04:40Z","content_type":"application/xhtml+xml","content_length":"9893","record_id":"<urn:uuid:8520672d-bf3a-48b8-8682-6fa6d490f428>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00598.warc.gz"} |
What's the difference between LibSVM and LibLinear
LIBSVM and LIBLINEAR are two popular open source machine learning libraries.
• LIBSVM implements the Sequential minimal optimization (SMO) algorithm, for kernelized support vector machines (SVMs), supporting classification and regression.
• LIBLINEAR implements linear SVMs and logistic regression models
For a large dataset, use liblinear. Libsvm performs very slow at 10k samples.
Hope this answer helps. | {"url":"https://intellipaat.com/community/2931/whats-the-difference-between-libsvm-and-liblinear","timestamp":"2024-11-07T04:20:53Z","content_type":"text/html","content_length":"98040","record_id":"<urn:uuid:affbdefc-a47d-4c0f-a1c0-1af8578d4017>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00408.warc.gz"} |
Mathematics Of Sudoku Wikipedia Printable Sudoku 5X5 Printable | Sudoku Printables
Mathematics Of Sudoku Wikipedia Printable Sudoku 5X5 Printable
Mathematics Of Sudoku Wikipedia Printable Sudoku 5X5 Printable – If you’ve ever had trouble with sudoku, you’re aware that there are many different kinds of puzzles to choose from and, at times, it’s
difficult to decide which one you’ll need to solve. However, there are different ways to solve them, and you’ll discover that solving a printable version will prove to be an ideal way to get started.
The rules to solve sudoku are similar to the rules for solving other types of puzzles, however, the exact format differs slightly.
What Does the Word ‘Sudoku’ Mean?
The word ‘Sudoku’ is taken from the Japanese words suji and dokushin which translate to ‘number’ and ‘unmarried person and ‘unmarried person’, respectively. The goal of the game is to fill each box
with numbers so that every digit from one to nine appears only one time on each horizontal line. The term Sudoku is an emblem belonging to the Japanese puzzle manufacturer Nikoli, which originated in
The name Sudoku comes in the Japanese word”shuji Wa Dokushin Ni Kagiru, which means ‘numbers must be single’. The game is composed of nine 3×3 squares and nine smaller squares. It was initially
referred to as Number Place, Sudoku was an educational puzzle that encouraged mathematical development. Although the origins of the game are unknown, Sudoku is known to have deep roots in ancient
number puzzles.
Why is Sudoku So Addicting?
If you’ve played Sudoku then you’re aware of how addictive it can be. A Sudoku addict won’t be able to get rid of thinking about the next puzzle they’ll solve. They’re constantly planning their next
challenge, and other aspects of their life seem to fall by the wayside. Sudoku is a game that can be addictive however it’s essential for players to maintain the addicting power of the game under
control. If you’ve developed a craving for Sudoku here are a few methods to reduce your dependence.
One of the most popular methods of determining if your addiction to Sudoku is to watch your behaviour. The majority of people carry books and magazines with them, while others simply scroll through
social news posts. Sudoku addicts carry newspapers, books, exercise books and smartphones wherever they go. They can be found for hours solving puzzles, and they don’t want to stop! Some discover it
is easier to complete Sudoku puzzles than standard crosswords. They simply can’t stop.
The Daily Sudoku Printable Sudoku 5×5
What is the Key to Solving a Sudoku Puzzle?
A good strategy for solving the printable Sudoku is to practice and experiment with various approaches. The best Sudoku puzzle solvers don’t follow the same formula for every single puzzle. The trick
is to test and practice several different approaches until you find the one that works best for you. After some time, you’ll be able to solve sudoku puzzles without difficulty! However, how do you
learn to solve the printable Sudoku game?
In the beginning, you must grasp the basic idea behind suduko. It’s a game of analysis and deduction and requires you to view the puzzle from different angles to identify patterns and then solve it.
When solving Suduko puzzles, suduko puzzle, do not try to guess the numbers, instead, you should scan the grid for opportunities to spot patterns. You can apply this strategy to squares and rows.
Related For Sudoku Puzzles Printable | {"url":"https://sudokuprintables.net/the-daily-sudoku-printable-sudoku-5x5/mathematics-of-sudoku-wikipedia-printable-sudoku-5x5-printable/","timestamp":"2024-11-05T00:43:36Z","content_type":"text/html","content_length":"26721","record_id":"<urn:uuid:e4a03e88-86ab-4179-9c25-ca3e70b2efea>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00662.warc.gz"} |
Statistical Modeling
Science topic
Statistical Modeling - Science topic
Explore the latest questions and answers in Statistical Modeling, and find Statistical Modeling experts.
Questions related to Statistical Modeling
Hello, I am currently writing my bachelor's thesis and I am trying to investigate, based on BD2MS2 selectorate theory, whether the ratio of government expenditure to the winning coalition/selectorate
value can provide an explanation as to why some leaders under economic sanctions are able to maintain office better than others. For this, I need a statistical model that will allow me to test the
correlation between a dependent variable (has the leader remained in power regardless of the sanctions imposed against him) and an independent variable that varies over time (as I said before, gov't
spending in relation to w/s for the duration of sanctions). I would also like to compare this correlation at least with the country's score on the polity scale and its gdp per capita, to see if using
the selectorate theory provides any better results. Does anyone know what the best statistical model to do this would be? I must add that I am not the most versed in complicated statistical models
but I am a fast learner, so any suggestion would help. Thank you so much!
Relevant answer
To recommend the best statistical model, I need more details about your specific research question, data characteristics, and objectives. Common models include:
1. Linear Regression: For predicting a continuous outcome based on one or more predictors.
2. Logistic Regression: For binary outcomes, predicting the probability of a particular class.
3. ANOVA: For comparing means across multiple groups.
4. Structural Equation Modeling (SEM): For examining complex relationships among variables.
5. Mixed-Effects Models: For data with hierarchical structures.
Please provide more context for tailored advice! | {"url":"https://www.researchgate.net/topic/Statistical-Modeling","timestamp":"2024-11-04T05:50:51Z","content_type":"text/html","content_length":"1050258","record_id":"<urn:uuid:5ddeaed7-21c8-4d1d-a8e0-0e0d385710a0>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00642.warc.gz"} |
higher education in france
The weighted grade is equal to the sum of the product of the weights (w) in percent (%) times the grade (g): Weighted grade = w1×g1+ w2×g2+ w3×g3+… When the weights are not in percent (hours or
points…), you should also divided by the sum of the weights: A weighted average, on the other hand, considers one or more numbers in the range to be worth more or have a greater weight than the other
numbers. As you can see, in the above table there are five tasks each one with its own “priority” and “completion percentage”. We have now added all of the headers to our software gradebook. Next,
each weight is multiplied by the grade received. First of all open the Weighted Average Calculator in any browser. Student Grade Calculator makes it easy for teachers to immediately calculate the
weighted grade for up to 40 students. 5. Nothing is easier than that if using a final grade calculator. Weighted Average in Excel Calculation. How to use Weighted Average Calculator? : Compute
Weighted Grades in Excel 2016. Finding a Weighted Average in Excel. The first thing that usually comes to mind is to calculate the classic average score using the standard Excel function with the
same name. This is because Excel doesn’t provide a function in the Pivot Table that automatically calculates the weighted average.The steps below will walk through the process. Comments. We now have
a few different types of grade books that can handle most of the … So if homework is worth 25% of your grade, the weight would be 0.25. taskhill asked on 2012-03-08. Each of these weights can be
converted into decimals and added together they should equal 1. And that’s it! All of these values should be added to find the final grade. Use the functions at step 3 and step 4 to calculate the
weighted average of these scores in Excel. An example use is as a weighted grade calculator.Works easily with copy-paste from a spreadsheet (Excel, etc. The first column of input fields are to enter
the weight. Excel tips: use sumproduct to calculate weighted averages. We can use the SUM function in Excel to calculate the number below the fraction line (6). For example, if you received a 95 and
an 80, then type '95' in A2 and '80' in A3. Exercise 1 - Weighted Scoring Sheet (Excel) Author: Giacomo Rambaldi Last modified by: martens Created Date: 6/10/2006 7:39:23 AM Other titles: Sheet1 …
Use this weighted mean calculator to calculate the weighted arithmetic average of a set of data. 4. Excel Formula Training. Type your grades in column A. This is only one possible way of creating a
software gradebook. Take apart the template and see how it works (password is ‘test’). For example, you have 5 papers and 2 tests. To calculate the weighted average of a data with a Pivot Table, we
can add a column to our source data as an intermediate calculation. Weighted grades are used in college, university and even high school courses by educators in order to determine how tests,
assignments, projects and other factors should count towards the final grade. For more information about the SUMPRODUCT and SUM functions, see the course summary. Weighted Average in Excel (with
excel template) Let us now do the same example as above in Excel. The below table shows the data from a “Project Task Completion Plan” table. This concludes part 1 of our article on creating a
weighted gradebook in Excel. In this video, we'll show how to calculate weighted grade-point averages for a group of students. Grades in the blue column, weights in the red column. Microsoft Excel; 5
Comments. Stay tuned for part 2 where we will improve our gradebook by adding formulas for automatically calculating our weighted grade averages. Calculating a weighted average is possible in Excel
using the SUMPRODUCT formula. Note: the SUMPRODUCT function performs this calculation: (20 * 1) + (40 * 2) + (90 * 3) = 370. Students can use this tracker template to record how they are doing in
each class and calculate their grade point average. 1 Solution. Use Excel’s formula auditing feature (found under ‘FORMULAS’ on the ribbon) to audit the mega array formula that is beneath ‘Grade%’ in
sheet ‘Class#1’. In this MS Excel tutorial from ExcelIsFun, the 197th installment in their series of digital spreadsheet magic tricks, you'll learn how to use the SUM and VLOOKUP functions to create
a grade book based on a specified total score with weights assigned to different categories. Instructions in this article apply to Excel 2019, 2016, 2013, 2010, 2007; Excel for Microsoft 365, Excel
Online, Excel for Mac, Excel for iPad, Excel for iPhone, and Excel for Android. To get the Weighted Average, you divide by the Total of the weights. Follow the steps below to use this online tool.
This free Gradebook Template for Excel started out as a very basic grade book spreadsheet, but it has evolved into something that is very useful, flexible, and powerful (and still free). Because, you
can learn a lot about Excel by auditing formulas! Formula to calculate weighted grades. Video: Compute Weighted Grades in Excel 2016. 2. Excel Formula Training. In the template provided, you will see
two tables. In the example above, the calculator outputs a money-weighted rate of return of 9.90%. The first step is to input the different grading categories and their weight. Grade Student in Excel
With This Grading Calculator Student Grade Calculator. Student grade tracker and gpa calculator. Type 'Grade' in cell A1, 'Weight' in B1 and 'Total Worth' in C1. Learn how to calculate weighted grade
quickly and effectively. Weighted Grades in Excel. Formulas are the key to getting things done in Excel. Edited by Djinu, Alexander Avdeev, Eng. How to calculate weighted average in excel (sum and.
You may also look at the following articles to learn more – Guide To Harmonic Mean Formula; Examples of Expected Return Formula null; Determine the weight of each data point. If we had just averaged
the Test scores, the value would be 75.5, a significant difference. Formulas are the key to getting things done in Excel. My grades are weighted and I used sumproduct() to calculate the weighted
average of my grades. Multiply the weight by each value. You're watching VisiHow. These inputs correspond to the light gray cells in the excel calculator, as shown below. In this accelerated
training, you'll learn how to use formulas to manipulate text, work with dates and times, lookup values with VLOOKUP and INDEX & MATCH, count and sum with criteria, dynamically rank … Here we discuss
how to calculate the Weighted Mean along with practical examples. Weighted grade calculation manually . Here is an example. Student Grade Calculator for Excel: Student Grade Calculator for Excel
makes easy work of grading students. Questions and Answers. The free template file is a simplified example of how you would incorporate the weighted average function into your own excel template to
keep track of each students grades. Example Calculation. g = grade. ). Student grade tracker and GPA calculator. In this accelerated training, you'll learn how to use formulas to manipulate text,
work with dates and times, lookup values with VLOOKUP and INDEX & MATCH, count and sum with criteria, dynamically rank … Hi, I am creating an excel sheet to track my grades in my class, so that I can
calculate my grade in the class as I go. Guide to Weighted Average formula, here we discuss its uses along with practical examples and also provide you Calculator with downloadable excel template. I
find Excel to be really useful in calculating my grades, and there are only a few simple formulas that need to be used! Now, you have a good idea about how to average numbers in Excel. Learn what
formula you should use to calculate weighted grade. How to Calculate Weighted Averages for Grades in Excel 1. Let's say you received a 90% on your first assignment and it was worth 10% of the class
grade. The tests are each worth 25% of the student's grades. 3. 4 Parts: Steps. Weighted Grade Formula. Calculating a weighted average requires knowing what the weight assigned to each grade is.
Weighted Average Calculator. (Note that if the period is less than one year, it will display the actual rate of return.) Grade Calculator Enter your grades and press the Calculate button. It quickly
weights the students grades on a per-assignment basis. An Example of Calculating Weighted Average in Excel. Gradebook template for excel free teacher grade book. Weighted Average is an average in
which each observation in the data set is assigned or multiplied by weight before summing to a single average value. After opne the calculator, you can see there are many input fields. Calculating
weighted average: method, formula & example video. The shortcut to creating weighted grades using excel 2007.
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How to Find Horizontal Asymptotes: Rational FunctionHow to Find Horizontal Asymptotes: Rational Function
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How to Find Horizontal Asymptotes: Rational Function
What are Asymptotes in a Rational Function?
Definition of asymptotes: In mathematics, asymptotes are lines that a curve approaches but never quite reaches. In the context of functions, asymptotes represent values that the function gets close
to as the input approaches a certain number.
Types of asymptotes in functions: There are mainly two types of asymptotes – vertical and horizontal. Vertical asymptotes occur where the function is undefined, while horizontal asymptotes show the
value the function approaches as x approaches positive or negative infinity.
Importance of asymptotes in graphing: Asymptotes play a crucial role in graphing functions as they help in understanding the behavior of functions towards certain inputs. They provide valuable
information about the trends and limits of the function.
Related Article: How many People can solve a Rubik’s Cube? Rubik Cube
How to Identify Vertical Asymptotes?
Understanding vertical asymptotes: Vertical asymptotes arise in functions when the denominator of a rational function becomes zero at certain points, leading to vertical lines that the graph
approaches but does not cross.
Finding vertical asymptotes in a rational function: To find vertical asymptotes in a rational function, set the denominator equal to zero and solve for the values of x that make the denominator zero.
These values will be the locations of the vertical asymptotes.
Steps to identify vertical asymptotes: Identify the values of x that make the denominator equal to zero. These values will be the vertical asymptotes of the function. Plotting these asymptotes on a
graph helps in understanding the behavior of the function.
Methods to Find Horizontal Asymptotes
Definition of horizontal asymptotes: Horizontal asymptotes are horizontal lines that a function approaches as x tends to positive or negative infinity. They represent the long-term behavior of a
Techniques to find horizontal asymptotes: To find horizontal asymptotes, compare the degrees of the numerator and denominator of a rational function. If the degree of the numerator is less than the
degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, divide the leading coefficients to find the horizontal asymptote.
Examples of finding horizontal asymptotes: For a rational function where the degree of the numerator is less than the degree of the denominator, the horizontal asymptote will be the x-axis (y = 0).
In cases where the degrees are equal, dividing the leading coefficients gives the value of the horizontal asymptote.
Related Article: How many People can solve a Rubik’s Cube? Rubik Cube
Comparing Horizontal and Vertical Asymptotes
Differences between horizontal and vertical asymptotes: Vertical asymptotes are vertical lines that represent the places where the function is undefined, while horizontal asymptotes are horizontal
lines that the function approaches as x goes to infinity.
Relationship between horizontal and vertical asymptotes: Horizontal and vertical asymptotes provide insights into the behavior of the function at different points. While vertical asymptotes denote
discontinuities, horizontal asymptotes show the long-term trends of the function.
How to analyze functions using both types of asymptotes: By considering both horizontal and vertical asymptotes, one can gain a comprehensive understanding of how a function behaves, both locally
around specific points and globally as x approaches infinity.
Advanced Concepts in Horizontal Asymptotes
Exploring oblique asymptotes: In some cases, rational functions may have oblique asymptotes, also known as slant asymptotes. These occur when the degree of the numerator is exactly one more than the
degree of the denominator.
Identifying end behavior in rational functions: The end behavior of a rational function is determined by its horizontal asymptotes. Understanding the long-term trends of the function near infinity
helps in sketching accurate graphs.
Factors affecting the presence of horizontal asymptotes: The presence of horizontal asymptotes in rational functions depends on the degrees of the numerator and denominator. The relationships between
these degrees dictate whether horizontal asymptotes exist and their values.
How to Find Horizontal Asymptotes: Rational Function
What is a Horizontal Asymptote in a Rational Function?
Definition of horizontal asymptote
A horizontal asymptote in a rational function is a horizontal line that the graph of the function approaches as x tends towards positive or negative infinity. This line indicates the behavior of the
function at the extremes of its domain.
Characteristics of horizontal asymptotes
Horizontal asymptotes can be identified by analyzing the degrees of the numerator and denominator of the rational function. They play a crucial role in understanding the long-term behavior of the
Importance of horizontal asymptotes in graphing
Understanding horizontal asymptotes is essential in graphing rational functions accurately. They help in visualizing how the function behaves as x approaches infinity or negative infinity.
How to Identify Horizontal Asymptotes of Rational Functions
Finding horizontal asymptotes algebraically
To find horizontal asymptotes algebraically, compare the degrees of the numerator and denominator of the rational function. If the degree of the numerator is less than the degree of the denominator,
the horizontal asymptote is y = 0.
Using limits to determine horizontal asymptotes
Calculating the limit of the function as x approaches infinity or negative infinity helps in identifying horizontal asymptotes. If the limit exists and is a real number, it represents the horizontal
Graphical representation of horizontal asymptotes
Graphing the rational function visually can also help in determining the horizontal asymptotes. They appear as the horizontal lines that the function approaches but never crosses.
Key Differences Between Horizontal and Vertical Asymptotes
Definition of vertical asymptote
Unlike horizontal asymptotes, vertical asymptotes occur where the denominator of a rational function is equal to zero, causing a vertical line that the function approaches but never crosses.
Comparison of end behaviors related to horizontal and vertical asymptotes
Horizontal asymptotes indicate the function’s behavior at infinity, whereas vertical asymptotes show discontinuities in the function. They have distinct effects on the graph’s end behavior.
Distinguishing features in the graph of the function
The graph of a function may have multiple vertical asymptotes but typically only one horizontal asymptote. Vertical asymptotes are associated with abrupt changes in the function’s value.
Strategies to Find Horizontal Asymptotes in College Algebra
Techniques to identify horizontal asymptotes in rational functions
In college algebra, students learn various methods to identify horizontal asymptotes, such as degree analysis and limit calculations.
Applying degree analysis to determine horizontal asymptotes
Analyzing the degrees of the numerator and denominator helps in determining the behavior of a rational function towards infinity, aiding in finding horizontal asymptotes.
Practical examples of finding horizontal asymptotes
Solving real-world problems and practicing with different rational functions helps students in mastering the skill of finding horizontal asymptotes accurately.
Challenges in Identifying Horizontal Asymptotes
Dealing with complex rational functions
Complex rational functions with multiple terms or higher-degree polynomials can pose challenges in identifying horizontal asymptotes due to the complexity of the function.
Factors affecting the identification of horizontal asymptotes
Factors such as the presence of slant asymptotes or ambiguous cases can complicate the process of identifying horizontal asymptotes in certain rational functions.
Strategies to overcome common mistakes in finding horizontal asymptotes
Overcoming common errors in finding horizontal asymptotes involves thorough practice, understanding the underlying concepts, and seeking help when encountering difficulties.
Q: What is a horizontal asymptote of a rational function?
A: A horizontal asymptote of a rational function is a horizontal line that the function approaches as the input values become very large or very small.
Q: How can I find the horizontal asymptote of a rational function?
A: To find the horizontal asymptote of a rational function, compare the degrees of the numerator and the denominator and determine how they affect the function’s behavior as x approaches positive or
negative infinity.
Q: When does a rational function have a horizontal asymptote?
A: A rational function has a horizontal asymptote when the degree of the numerator is less than or equal to the degree of the denominator.
Q: How do vertical and horizontal asymptotes differ in a rational function?
A: Vertical asymptotes are values of x where the function is undefined, while horizontal asymptotes are lines that the function approaches as x goes to infinity or negative infinity.
Q: What is the relationship between the leading terms of a rational function and its horizontal asymptote?
A: The horizontal asymptote of a rational function is determined by the ratio of the leading coefficients of the highest degree terms in the numerator and denominator.
Q: Can a rational function cross its horizontal asymptote?
A: A rational function will never cross its horizontal asymptote; it will approach the asymptote as x approaches infinity or negative infinity.
Q: How can I identify horizontal asymptotes in the graph of a rational function?
A: To identify horizontal asymptotes in the graph of a rational function, analyze the end behavior of the function as x approaches positive or negative infinity. | {"url":"https://webuncovered.com/how-to-find-horizontal-asymptotes-rational-function/","timestamp":"2024-11-01T23:57:38Z","content_type":"text/html","content_length":"79508","record_id":"<urn:uuid:b0beedaa-77e6-4074-8b3f-fec23accf422>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00441.warc.gz"} |
NEHRP Clearing
NEHRP Clearinghouse
displaying 1 - 3 results in total 3
• Mehta, K. C.
Proceedings of the Workshop on Wind Climate Held at Asheville, North Carolina on November 12-13, 1979.
National Science Foundation, Washington, DC. Engineering and Applied Science.; Electric Power Research Inst., Palo Alto, CA., January 1979, 249 p.
Keywords: ; Climate; Wind (Meteorology); Wind direction; Data; Mathematical models; Atmospheric motion; Acquisition; Hazards; Meetings; Data processing; Weather forecasting; Wind velocity;
• Journal of Research of the National Institute of Standards and Technology, July/August 1994. Volume 99, Number 4. Special Issue: Extreme Value Theory and Applications. Proceedings of the
Conference on Extreme Value Theory and Applications, Volume 2. Held at Gaithersburg, Maryland, in May 1993.
May 1993, 302 p.
Keywords: Risk analysis; Seismic risk; Corrosion; Floods; Ozone; Loads (Forces); Wind velocity; Extreme value theory; Sequences (Mathematics); Failure analysis; Bayesian analysis; Spacecraft
electronic equipment; Uses; Fatigue limit; Meetings; Ocean waves; Radiation damage; Microelectronics; Aerosols; Weibull density functions; Extreme-value problems; Ground motion; Multivariate
analysis; Extremum values
• Freeman, B. E.
A New Wind Energy Site Selection Methodology.
National Science Foundation, Washington, D.C. Applied Science and Research Applications., October 1975, 17 p.
Identifying Number(s): SAI-75-662-LJ
Keywords: Planning; Wind (Meteorology); Wind power; Site selection; Mathematical models; Data acquisition; Site surveys; SIGMET computer program; Wind power generation; Wind velocity | {"url":"https://nehrpsearch.nist.gov/search_result/?keyword_raw=Wind+velocity","timestamp":"2024-11-05T23:23:34Z","content_type":"text/html","content_length":"6252","record_id":"<urn:uuid:8495b05c-1fe2-4e3e-9a58-2288a84b5947>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00777.warc.gz"} |
QIRX V3: Frequencies
This page deals with frequencies.
There are three possibilities to tune to a frequency. All of them are operated by the mouse. QIRX does not offer the frequency selection by keyboard.
• VFO Tuning: VFO is a commonly used shortcut for "Variable Frequency Oscillator". Here it simply means that your SDR can be tuned to any frequency you like, within its possible range, by adjusting
the digits withthe mouse. This is the usual and recommended way of selecting a frequency. It works very fast and accurately, because all digits can be operated by using the mouse wheel.
The Device Frequency indicator on the top and the spectrum plot are updated automatically, if necessary.
The Step(kHz) indicated number does NOT affect this kind of tuning, even if checked.
Hint: A right click into a digit zeroes all digits to the right of it. This is often desirable and works on all mouse-editable fields, not only the VFO indicator.
• Device Tuning: This operates directly on the device, i.e. the device frequency is changed. The device frequency is in the center of the frquency plot, in case no x-zoom is applied. The VFO
frequency and the spectrum plot are updated. This frequency selection method is NOT recommended. It is mainly provided to have an indication of the frequency which the device is currently tuned
No rule without exception: When - for whatever reason - in ADS-B mode the wrong frequency is indicated, then the Device Tuning is the only way to get the necessary 1090MHz tuned.
• Click into spectrum: A click into the spectrum plot tunes to the selected frequency. The "Step(kHz)" indication - when selected - dictates the steps of the mouse movement in the spectrum. In this
way it is possible to exactly hit narrow-band frequencies. As an additional indication the selected RF bandwidth is drawn as two dashed vertical lines on the right and left of the selected
frequency line.
This selection method is also possible in the waterfall spectrum.
The frequency axis can be zoomed by shifting the slider "Zoom X". It influences the way the frequencies are displayed in the spectrum.
• Un-Zoomed: The "Zoom X" slider is positioned completely left. The spectrum displays the full range according to the selected sampling rate. For instance, with the RSP1A and a sampling rate of
2.048Msps a range of 2.048MHz is displayed. The spectrum is attenuated at the borders, because the RSP1A offers a bandwidth of 1.536MHz.
When the VFO is tuned, the green selection bar moves until it approaches the border, then it stays and the spectrum together with its scale moves.
• Zoomed: The "Zoom X" slider is moved. The spectrum is zoomed around the green selection bar. When tuning the VFO, the green selection bar stays in place, and the spectrum together with its scale
Zooming only very slightly is a convenient way to select that not the selction bar should move, but the spectrum and its scale.
Different scenarios require different frequency resolutions in the spectrum plot. Examples:
• AM Sidebands: Inspections of the AM sideband bandwidth can give a hint about the necessary bandwidth for a certain station.
• SSB Tuning: Visualization of the SSB waterfall spectrum gives an indication where to position the suppressed carrier for a proper reception.
• Aircraft Doppler Shifts: When e.g. a strong VOLMET airband broadcast transmitter is in range, the gap between the central carrier and the start of the sidebands can show the Doppler-shifted
carrier of aircraft flying by. This requires a high resolution spectrum, because the shift is small.
The screenshot shows such a Doppler echo (i.e. the crossing line) with a high frequency resolution. Each vertical division has a width of 50Hz, the FFT length was more than 2 Million points, each
frequency bin got a width of 1Hz.
Spectrum Resolution Calculation
For the calculation of a suitable frequency resolution, two parameters have to be considered, the sampling rate and the FFT length.
• Sampling Rate: For the spectrum plot, the "Software Sampling Rate" is necessary. Sometimes the hardware offers sampling rates not very suitable for software applications. For instance, DAB
demodulations needs I/Q data having been sampled with 2.048Msps, which not every hardware is able to deliver. The Airspy can send data sampled with 4.096Msps, which have to be "decimated" by a
factor of two before processing. "Decimation" means filtering and downsampling. You find the two sampling rates in use on the "Connection" tab of the Frontend section on the GUI. If you are in
doubt whether a certain sampling rate can be used in your scenario, please counsult the Setup Dialog on this website.
• FFT Length: "FFT" means "Fast Fourier Transform" and indicates the algorithm used to transform the I/Q data from the time domain to the frequency domain. The frquency spectrum shows the result of
the FFT.
"FFT Length" indicates the number of I/Q data used to perform the FFT. This number determines - together with the Sampling Rate - the frequency width of a single point of the FFT outcome (usually
called a "bin"). The simple formula is:
Frequency Resolution fRes = Sampling Rate / FFT Length.
In our high-res example with the Doppler Shifts we get 2,048,000[1/sec]/2,097,152[bin] = 0.977/sec/bin ~ 1Hz/bin.
For convenience, this calculation is also performed in the software and the result is indicated as an inset into the spectrum plot.
• FFT Length Selection: The FFT length can be selected from the corresponding dropdown box.
There is no such thing as a free lunch. Usually, one does not want to set the frequency display to an extremely high resolution like the one above in the Doppler shift example. The reason is simple:
The higher the FFT length, the longer it takes to collect the I/Q data to fill the memory buffer for the FFT. In our above example it already takes one second to fill the FFT buffer once. This
results in some disadvantages:
• Slow Display: The spectrum display is slowed down. Of course, this holds also for the waterfall display.
• No Realtime: As a result, one loses the responsiveness of the spectrum. The longer the FFT length, the worse is the realtime behaviour of the display.
The tradeoff between high timely resolution (responsiveness) and high frequency resolution (high FFT length) is a well-known fundamental property of every Fourier Transform.
FFT Window
For its spectrum display, QIRX offers the selection of different "FFT Windows". One of their uses is to allow a single peak in the display to be confined in a narrow region, and not do decay slowly
in case that peak does not hit the exact center of a FFT bin. I will not go into further details here, in case you have more interest in the topic you might consult National Instrument's
Application Note 041 "The Fundamentals of FFT-Based Signal Analysis and Measurement"
, describing the topic to some detail.
Here, we are interested in the practical use of these "FFT Windows". They come into play if you are keen on separating two neighboring peaks in a high-resolution spectrum, like the one in the picture
with the un-collapsed drop-down box. All of these windwos, except the "None" have the (adverse) effect that they widen the peak, meaning that a narrow single peak will occupy more than one frequency
bin in the spectrum.
Then, why not stick with the "None" altogether? Because another property comes into play, the "sidelobes". These (also unwanted) properties mean that a peak widens on decaying into its neighboring
bins. And the "None" widens very much.
But how many bins are occupied by using a FFT Window? The answer is given in the inset of the spectrum. It is the
property, indicating the number of FFT bins a single peak will occupy in the spectrum. "NENBW" means "Normalized Equivalent Noise Bandwidth".
Here is a short list of the recommended use for the offered FFT Windows:
• None: Used for: Nothing, just for comparison how much sidelobes it produces.
• Hann: Excellent allround FFT Window. NENBW is 1.5, rounded to two in the inset. Good choice for e.g. Doppler effect measurements, mentioned above. Not recommended for accurate level measurements.
• Hamming: Like Hann, a very good "Allrounder", often used in other applications as well. NENBW is 1.3, rounded to 1. Best separation between two neighboring peaks, due to its low NENBW. Not to be
used for accurate level measurements.
• BlackmanHarris7: Lowest sidelobes of all offered FFT Windows, meaning low-level peaks not too near by can be resolved.
• HFT70: "Flat Top" Window with low sidelobes. Due to its "flat top" it is used for accurate level measurements, e.g. using the calibrated scales for the RSPs or the RTL-SDRs with a R820T tuner.
The flexibility outlined in the above description applies for the spectrum display on the GUI. As QIRX works FFT-based for its demodulators, similar considerations have to be made for them. However,
usually there is no need to be able to adjust e.g. the FFT length in a wide range. As a result, the FFT lengths applied in the demodulators are fixed values.
For the demodulator FFTs, the "Hann" window is used.
• "Standard" Demodulators: AM, NFM, WFM: The FFT length used is 65535, with a sampling rate of 2,048,000sps a frequency resolution of about 32Hz is achieved. This is sufficient for SSB tuning, and
corresponds to the frequency resolution of RTL-SDR dongles.
• DAB: The FFT length used is 2.048, resulting in a frequency resolution of 1kHz (sampling rate of 2.048Msps), adapted to DAB's OFDM specification with a carrier separation of 1kHz. In case of the
selection of a higher sampling rate by the user, the samples are down-converted to a rate of 2,048,000sps before processing further.
• ADS-B: The decoder is not affected by this consideration, as it works directly on the I/Q data, sampled in QIRX at 2Msps. | {"url":"https://qirx.softsyst.com/QIRX3_Tuning","timestamp":"2024-11-09T06:58:58Z","content_type":"text/html","content_length":"39138","record_id":"<urn:uuid:4938d94e-59ca-434e-a975-ece7b8e5cc17>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00750.warc.gz"} |
to Astronomical Units
Russian archin to Astronomical Units Converter
Enter Russian archin
Astronomical Units
β Switch toAstronomical Units to Russian archin Converter
How to use this Russian archin to Astronomical Units Converter π €
Follow these steps to convert given length from the units of Russian archin to the units of Astronomical Units.
1. Enter the input Russian archin value in the text field.
2. The calculator converts the given Russian archin into Astronomical Units in realtime β using the conversion formula, and displays under the Astronomical Units label. You do not need to click
any button. If the input changes, Astronomical Units value is re-calculated, just like that.
3. You may copy the resulting Astronomical Units value using the Copy button.
4. To view a detailed step by step calculation of the conversion, click on the View Calculation button.
5. You can also reset the input by clicking on button present below the input field.
What is the Formula to convert Russian archin to Astronomical Units?
The formula to convert given length from Russian archin to Astronomical Units is:
Length[(Astronomical Units)] = Length[(Russian archin)] / 210345712463.28653
Substitute the given value of length in russian archin, i.e., Length[(Russian archin)] in the above formula and simplify the right-hand side value. The resulting value is the length in astronomical
units, i.e., Length[(Astronomical Units)].
Calculation will be done after you enter a valid input.
Consider that a traditional Russian fabric is measured to be 5 Russian archins in length.
Convert this length from Russian archins to Astronomical Units.
The length in russian archin is:
Length[(Russian archin)] = 5
The formula to convert length from russian archin to astronomical units is:
Length[(Astronomical Units)] = Length[(Russian archin)] / 210345712463.28653
Substitute given weight Length[(Russian archin)] = 5 in the above formula.
Length[(Astronomical Units)] = 5 / 210345712463.28653
Length[(Astronomical Units)] = 2.37704e-11
Final Answer:
Therefore, 5 russian archin is equal to 2.37704e-11 AU.
The length is 2.37704e-11 AU, in astronomical units.
Consider that a historical Russian building's doorway is 3 Russian archins tall.
Convert this height from Russian archins to Astronomical Units.
The length in russian archin is:
Length[(Russian archin)] = 3
The formula to convert length from russian archin to astronomical units is:
Length[(Astronomical Units)] = Length[(Russian archin)] / 210345712463.28653
Substitute given weight Length[(Russian archin)] = 3 in the above formula.
Length[(Astronomical Units)] = 3 / 210345712463.28653
Length[(Astronomical Units)] = 1.42622e-11
Final Answer:
Therefore, 3 russian archin is equal to 1.42622e-11 AU.
The length is 1.42622e-11 AU, in astronomical units.
Russian archin to Astronomical Units Conversion Table
The following table gives some of the most used conversions from Russian archin to Astronomical Units.
Russian archin (russian archin) Astronomical Units (AU)
0 russian archin 0 AU
1 russian archin 0 AU
2 russian archin 1e-11 AU
3 russian archin 1e-11 AU
4 russian archin 2e-11 AU
5 russian archin 2e-11 AU
6 russian archin 3e-11 AU
7 russian archin 3e-11 AU
8 russian archin 4e-11 AU
9 russian archin 4e-11 AU
10 russian archin 5e-11 AU
20 russian archin 1e-10 AU
50 russian archin 2.4e-10 AU
100 russian archin 4.8e-10 AU
1000 russian archin 4.75e-9 AU
10000 russian archin 4.754e-8 AU
100000 russian archin 4.7541e-7 AU
Russian archin
A Russian archin is a historical unit of length used in Russia. One Russian archin is approximately equivalent to 28 inches or about 0.7112 meters.
The archin was used in various contexts, including land measurement and textile work, and its length could vary slightly depending on the historical period and region.
Russian archins were employed in trade, construction, and textile industries. While not in common use today, the unit provides historical insight into Russian measurement practices and standards.
Astronomical Units
An astronomical unit (AU) is a unit of length used in astronomy to measure distances within our solar system. One astronomical unit is equivalent to approximately 149,597,870.7 kilometers or about
92,955,807.3 miles.
The astronomical unit is defined as the mean distance between the Earth and the Sun.
Astronomical units are used to express distances between celestial bodies within the solar system, such as the distances between planets and their orbits. They provide a convenient scale for
describing and comparing distances in a way that is more manageable than using kilometers or miles.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Russian archin to Astronomical Units in Length?
The formula to convert Russian archin to Astronomical Units in Length is:
Russian archin / 210345712463.28653
2. Is this tool free or paid?
This Length conversion tool, which converts Russian archin to Astronomical Units, is completely free to use.
3. How do I convert Length from Russian archin to Astronomical Units?
To convert Length from Russian archin to Astronomical Units, you can use the following formula:
Russian archin / 210345712463.28653
For example, if you have a value in Russian archin, you substitute that value in place of Russian archin in the above formula, and solve the mathematical expression to get the equivalent value in
Astronomical Units. | {"url":"https://convertonline.org/unit/?convert=russian_archin-astronomical_unit","timestamp":"2024-11-02T13:59:14Z","content_type":"text/html","content_length":"91755","record_id":"<urn:uuid:4bd1bbd9-708f-46f9-8f86-eb86817e033a>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00552.warc.gz"} |
Precalculus - Online Tutor, Practice Problems & Exam Prep
So we've worked with real numbers like 3 and imaginary numbers like 2i separately, but you're often going to see expressions that have these two numbers together, so something like 3+2i. And these
are actually called complex numbers when you have both a real number and an imaginary number added together. Now, complex numbers are going to be really important for us throughout this course and
have a ton of different uses. And while they might sound a little complicated at first, I'm going to walk you through what they are and how we use them step by step. So let's get started. So a
complex number has a standard form of a+bi. So in this complex number, a+bi, a is called the real part of the number, and b is called the imaginary part because it's multiplying i, our imaginary
unit. Now it's important to know that b by itself is the imaginary part. It's not the whole term bi. So when I'm identifying the real and the imaginary part of the number I have up here, this 3+2i, 3
is going to be the real part of my number. And then 2 is going to be the imaginary part, just the 2 by itself.
Now, let's look at a couple of different examples of complex numbers and identify the real and imaginary parts of each of them. So first, I have this 4 − 3i. So looking at this number, the real part,
a, is going to be this 4 because it's out there by itself. It's not multiplying my imaginary unit. This is going to be my real part, a. Then b, so I want to look for what is multiplying i, my
imaginary unit. And in this case, it is negative 3. Now it's important to look at everything that's multiplying our imaginary unit. So if it's a negative number, if it's a square root, if it's a
combination of a number and a square root, I want to get everything that's multiplying my imaginary unit. So in this case, b is going to be a negative 3. That's what's multiplying my imaginary unit
Let's look at another example. So here I have 0+7i. Now if I look for the real part of my number, what is not multiplying my imaginary unit, I have this as 0. So that means that, a, my real part is
going to be 0. Then, b, my imaginary part, the part that's multiplying my imaginary unit i, in this case is going to be positive 7. Now you might look at this number and think, couldn't you just
write that number as 7i? That zero isn't really doing anything. And you're right. I could just write this as 7i. But we still need to know that if we're looking at this as a complex number, it still
has a real part. It's just 0.
So let's look at another example. So I have 2+0i over here. So what do you think the real part of this number is? Well, since this 2 is out here by itself, it's not multiplying my imaginary unit. 2
is going to be the real part of my number, a. Then looking at b, so the imaginary part, the part that is multiplying my imaginary unit, in this case, is just 0. So, again, you might be looking at
this number thinking, isn't that just a real number? Couldn't I just write this as 2? And you're right. Again, I could just write this as 2. But remember, if we're looking at this as a complex
number, it still has an imaginary part. It's just 0.
So that's all for this one, and I'll see you in the next video. | {"url":"https://www.pearson.com/channels/precalculus/learn/patrick/1-equations-and-inequalities/complex-numbers?chapterId=24afea94","timestamp":"2024-11-10T22:41:16Z","content_type":"text/html","content_length":"614502","record_id":"<urn:uuid:34668911-bc90-4d5d-bc24-bd6bbc59effd>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00541.warc.gz"} |
tf.scan | TensorFlow v2.15.0.post1
scan on the list of tensors unpacked from elems on dimension 0. (deprecated argument values)
The simplest version of scan repeatedly applies the callable fn to a sequence of elements from first to last. The elements are made of the tensors unpacked from elems on dimension 0. The callable fn
takes two tensors as arguments. The first argument is the accumulated value computed from the preceding invocation of fn, and the second is the value at the current position of elems. If initializer
is None, elems must contain at least one element, and its first element is used as the initializer.
Suppose that elems is unpacked into values, a list of tensors. The shape of the result tensor is [len(values)] + fn(initializer, values[0]).shape. If reverse=True, it's fn(initializer, values
This method also allows multi-arity elems and accumulator. If elems is a (possibly nested) list or tuple of tensors, then each of these tensors must have a matching first (unpack) dimension. The
second argument of fn must match the structure of elems.
If no initializer is provided, the output structure and dtypes of fn are assumed to be the same as its input; and in this case, the first argument of fn must match the structure of elems.
If an initializer is provided, then the output of fn must have the same structure as initializer; and the first argument of fn must match this structure.
For example, if elems is (t1, [t2, t3]) and initializer is [i1, i2] then an appropriate signature for fn in python2 is: fn = lambda (acc_p1, acc_p2), (t1, [t2, t3]): and fn must return a list,
[acc_n1, acc_n2]. An alternative correct signature for fn, and the one that works in python3, is: fn = lambda a, t:, where a and t correspond to the input tuples.
The callable to be performed. It accepts two arguments. The first will have the same structure as initializer if one is provided, otherwise it will have the same structure as
fn elems. The second will have the same (possibly nested) structure as elems. Its output must have the same structure as initializer if one is provided, otherwise it must have the
same structure as elems.
elems A tensor or (possibly nested) sequence of tensors, each of which will be unpacked along their first dimension. The nested sequence of the resulting slices will be the first
argument to fn.
initializer (optional) A tensor or (possibly nested) sequence of tensors, initial value for the accumulator, and the expected output type of fn.
parallel_iterations (optional) The number of iterations allowed to run in parallel.
back_prop (optional) Deprecated. False disables support for back propagation. Prefer using tf.stop_gradient instead.
swap_memory (optional) True enables GPU-CPU memory swapping.
infer_shape (optional) False disables tests for consistent output shapes.
reverse (optional) True scans the tensor last to first (instead of first to last).
name (optional) Name prefix for the returned tensors.
A tensor or (possibly nested) sequence of tensors. Each tensor packs the results of applying fn to tensors unpacked from elems along the first dimension, and the previous accumulator value(s), from
first to last (or last to first, if reverse=True).
TypeError if fn is not callable or the structure of the output of fn and initializer do not match.
ValueError if the lengths of the output of fn and initializer do not match.
elems = np.array([1, 2, 3, 4, 5, 6])
sum = scan(lambda a, x: a + x, elems)
# sum == [1, 3, 6, 10, 15, 21]
sum = scan(lambda a, x: a + x, elems, reverse=True)
# sum == [21, 20, 18, 15, 11, 6]
elems = np.array([1, 2, 3, 4, 5, 6])
initializer = np.array(0)
sum_one = scan(
lambda a, x: x[0] - x[1] + a, (elems + 1, elems), initializer)
# sum_one == [1, 2, 3, 4, 5, 6]
elems = np.array([1, 0, 0, 0, 0, 0])
initializer = (np.array(0), np.array(1))
fibonaccis = scan(lambda a, _: (a[1], a[0] + a[1]), elems, initializer)
# fibonaccis == ([1, 1, 2, 3, 5, 8], [1, 2, 3, 5, 8, 13]) | {"url":"https://tensorflow.google.cn/versions/r2.15/api_docs/python/tf/scan","timestamp":"2024-11-05T13:11:08Z","content_type":"text/html","content_length":"53322","record_id":"<urn:uuid:23f809a5-2dc7-43cb-b37c-da37ccc0db8d>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00119.warc.gz"} |
Vertex Algebras and Quantum Groups
Schedule for: 16w5070 - Vertex Algebras and Quantum Groups
Beginning on Sunday, February 7 and ending Friday February 12, 2016
All times in Banff, Alberta time, MST (UTC-7).
Sunday, February 7
16:00 - 17:30 Check-in begins at 16:00 on Sunday and is open 24 hours (Front Desk - Professional Development Centre)
Dinner ↓
17:30 - 19:30 A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
20:00 - 22:00 Informal gathering (Corbett Hall Lounge (CH 2110))
Monday, February 8
Breakfast ↓
- Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
- Introduction and Welcome by BIRS Station Manager (TCPL 201)
Henning Haahr Andersen: Tilting modules for quantum groups at roots of unity ↓
09:00 In this talk I will survey some of the basic properties of the category of finite dimensional tilting modules for the quantized enveloping algebra of a simple Lie algebra. At a generic
- parameter this category is semisimple and consists of all finite dimensional modules. But at roots of unity the category is non-semisimple and has a rich structure. We shall highlight some of
09:50 its main properties and also point to several applications. At the end we shall discuss some recent developments and a couple of open questions.
(TCPL 201)
- Coffee Break (TCPL Foyer)
Daniel Nakano: Cohomology and Support Theory for Quantum Groups ↓
Quantum groups are a fertile area for explicit computations of cohomology and support varieties because of the availability of geometric methods involving complex algebraic geometry. Ginzburg
and Kumar have shown that for l>h (l is order of the root of unity and h is the Coxeter number), the cohomology ring identifies with the coordinate algebra of the nilpotent cone of the
10:30 underlying Lie algebra g=Lie(G). Bendel, Pillen, Parshall and the speaker have determined the cohomology ring when l is less than or equal to h and have shown that in most cases this identifies
- with the coordinate algebra of a G-invariant irreducible subvariety of the nilpotent cone. The latter computation employs vanishing results on partial flag variety G/P via the
11:20 Grauert-Riemenschneider theorem. Support varieties have been determined for tilting modules (by Bezrukavinov), induced/Weyl modules (by Ostrik and Bendel-Nakano-Pillen-Parshall), and simple
modules (by Drupieski-Nakano-Parshall). The calculations for tilting modules and simple modules employed the deep fact that the Lusztig Character Formula holds for quantum groups when l>h. In
this talk, I will survey several of the main results of the topic and indicate the combinatorial and geometric techniques necessary to make such calculations. Open problems will also be
(TCPL 201)
- Lunch (Vistas Dining Room)
Guided Tour of The Banff Centre ↓
- Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.
(Corbett Hall Lounge (CH 2110))
Group Photo ↓
- Meet in foyer of TCPL to participate in the BIRS group photo. Please don't be late, or you will not be in the official group photo! The photograph will be taken outdoors so a jacket might be
14:20 required.
(TCPL Foyer)
- Coffee Break (TCPL Foyer)
Evgeny Mukhin: Trivial systems with non-trivial Bethe ansatz ↓
15:30 Bethe ansatz is a physics motivated method which is used to diagonalize matrices which appear as Hamiltonians of various integrable systems. In particular, it can be applied to the case where
- the matrices have size 1x1. Interestingly, it leads to a variety of non-trivial questions with important applications. In this talk I will review the basics of the Bethe ansatz on the example
16:20 of the Gaudin model and discuss the results and conjectures related to the 1x1 case.
(TCPL 201)
Fyodor Malikov: Strong homotopy algebras of chiral differential operators ↓
- We shall discuss how a desire to work over singular varieties leads to infinity versions of Picard-Lie algebroids and their vertex/chiral algebra analogues.
(TCPL 201)
Dinner ↓
- A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
Tuesday, February 9
- Breakfast (Vistas Dining Room)
Chongying Dong: On orbifold theory ↓
09:00 Let $V$ be a simple vertex operator algebra and $G$ a finite automorphism group of $V$ such that $V^G$ is regular. It is proved that every irreducible $V^G$-module occurs in an irreducible
- $g$-twisted $V$-module for some $g\in G.$ Moreover, the quantum dimensions of each irreducible $V^G$-module is determined and a global dimension formula for $V$ in terms of twisted modules is
09:50 obtained.
(TCPL 201)
- Coffee Break (TCPL Foyer)
Terry Gannon: The theory of C2-cofinite VOAs ↓
10:30 Rational VOAs are by now quite well understood: their representation theory is captured by a modular tensor category; their characters define a vector-valued modular form for $SL(2,Z)$; etc.
- The class of C2-cofinite (logarithmic) VOAs is the natural generalisation of rationality, but their theory is still much less clear. This talk reviews and contributes to this theory. It is
11:20 joint work with Thomas Creutzig.
(TCPL 201)
- Lunch (Vistas Dining Room)
Drazen Adamovic: Conformal embeddings and realizations of certain simple W-algebras ↓
We shall first recall explicit realizations of certain affine and superconformal vertex algebras from [D. Adamovic, Transform. Groups (2015)] and study their relations with vertex operator
14:00 algebras appearing in LCFT. Then we shall consider a generalization motivated by the construction of conformal embeddings of affine vertex algebras in W-algebras. We shall also present a
- decomposition of a large family of non-rational affine W-algebras as modules for affine vertex operator algebras at admissible and negative levels. A particular emphasis will be put on the
14:50 application of affine fusion rules and intertwining operators in the determination of branching rules. The second part of this talk is based on a joint paper with V. Kac, P. Moseneder-Frajria,
P. Papi and O. Perse.
(TCPL 201)
- Coffee Break (TCPL Foyer)
Open Problem Session ↓
- Speakers: K. Nagatomo, S. Kanade, X. He, A. Zeitlin, J. van Ekeren (short talk) and T. Creutzig (short talk)
(TCPL 201)
- Dinner (Vistas Dining Room)
Wednesday, February 10
- Breakfast (Vistas Dining Room)
Valerio Toledano Laredo: Yangians, quantum loop algebras and elliptic quantum groups ↓
The Yangian Yg and quantum loop algebra Uq(Lg) of a complex semisimple Lie algebra g share very many similarities, and were long thought to have the same representations, though no precise
09:00 relation between them existed until recently. I will explain how to construct a faithful functor from the finite-dimensional representations of Yg to those of Uq(Lg). The functor is entirely
- explicit, and governed by the monodromy of the abelian difference equations determined by the commuting fields of the Yangian. It yields a meromorphic, braided Kazhdan-Lusztig equivalence
09:50 between finite-dimensional representations of the Yg and of U_q(Lg). A similar construction yields a faithful functor from representations of U_q(Lg) to those of the elliptic quantum group E_
{q,t}(g) corresponding to g. This allows in particular a classification of irreducible finite-dimensional representations of E_{q,tau}(g), which was previously unknown. This is joint work with
Sachin Gautam (Perimeter Institute).
(TCPL 201)
- Coffee Break (TCPL Foyer)
Naihuan Jing: Vertex operators and Giambelli identities ↓
10:30 We use the Jacobi-Trudi identity to incorporate several well-known families of symmetric functions to uniformly treat generalized Schur symmetric functions and their vertex operator
- realization. Under the general set-up, we prove that Gambelli identity also holds, thus derive several scattered results under one umbrella. In particular, this includes Weyl's character
11:20 formulas of classical simple Lie algebras and the shifted Schur symmetric functions studied by Olshanski-Okounkov. This is joint work with Natasha Rozhkovskaya.
(TCPL 201)
Haisheng Li: $q$-Virasoro algebra and affine Lie algebras ↓
In this talk, I will discuss a natural connection of a certain $q$-Virasoro algebra with affine Lie algebras and vertex algebras. To any abelian group $S$ with a linear character, we associate
11:30 an infinite-dimensional Lie algebra $D_{S}$. When $S=\Z$ with $\chi$ defined by $\chi(n)=q^{n}$ with $q$ a nonzero complex number, $D_{S}$ reduces to the $q$-Virasoro algebra $D_{q}$ which was
- introduced in \cite{BC}. We also introduce a Lie algebra $\g_{S}$ with $S$ as an automorphism group and we prove that $D_{S}$ is isomorphic to the $S$-covariant algebra of the affine Lie
12:30 algebra $\widehat{\g_{S}}$. Then we relate restricted $D_{S}$-modules of level $\ell\in \C$ with equivariant quasi modules for the vertex algebra $V_{\widehat{\g_{S}}}(\ell,0)$. Furthermore, we
show that if $S$ is a finite abelian group of order $2l+1$, $D_{S}$ is isomorphic to the affine Kac-Moody algebra of type $B^{(1)}_{l}$. This talk is based on a joint work with Hongyan Guo,
Shaobin Tan and Qing Wang.
(TCPL 201)
- Lunch (Vistas Dining Room)
- Free Afternoon (Banff National Park)
- Dinner (Vistas Dining Room)
Thursday, February 11
- Breakfast (Vistas Dining Room)
- Vidas Regelskis: Towards classification of trigonometric reflection matrices (TCPL 201)
- Shashank Kanade: Simple current extensions beyond semi-simplicity (TCPL 201)
- Coffee Break (TCPL Foyer)
- Simon Wood: The rationality of N=1 minimal models through symmetric polynomials (TCPL 201)
- Anton Zeitlin: Towards the continuous Kazhdan-Lusztig correspondence (TCPL 201)
- Lunch (Vistas Dining Room)
Iana Anguelova: Towards quantum chiral algebras ↓
Chiral algebras are extensively studied in many areas of both mathematics and physics, due to the wealth of examples from various classes of algebras generated by chiral fields (although
precise axiomatic/mathematical definition of the concept is lacking in it full generality). Super vertex algebras constitute a class of chiral algebras, corresponding to the chiral part of a
14:00 conformal quantum field theory on the complex plane, and their theory is well established. Nevertheless there is a variety of important examples of algebras generated by chiral fields that
- cannot be described by the concept of super vertex algebra. The most challenging case concerns the quantum vertex operators and the quantum chiral algebras they generate. This area of research,
14:50 which by now is quite large and growing, was started with the fundamental problem posed by Igor Frenkel: to formulate and develop a theory of quantum vertex algebras incorporating as examples
the Frenkel-Jing quantum vertex operators realizing the quantum affine algebras. This problem is still ultimately unsolved despite the comparative progress lately. In this talk we will discuss
some of the issues that are encountered on the way to defining a suitable theory of quantum chiral algebras. As a guiding principle for the the mathematical description of any class of chiral
algebras we will discuss the notable instances of certain special isomorphisms between chiral algebras of that class (such as the boson-fermion correspondences).
(TCPL 201)
- Coffee Break (TCPL Foyer)
- Yaping Yang: Cohomological Hall algebras and affine quantum groups (TCPL 201)
- Azat Gainutdinov: VOA and quasi-Hopf algebras (TCPL 201)
- Alex Weekes: Highest weights for some algebras constructed from Yangians (TCPL 201)
- Kazuya Kawesetsu: W-algebras with non-admissible levels and the Deligne exceptional series (TCPL 201)
- Dinner (Vistas Dining Room)
Friday, February 12
07:00 - Breakfast (Vistas Dining Room)
Andy Linshaw: Orbifolds and cosets via invariant theory ↓
09:00 - The orbifold and coset constructions are standard ways to create new vertex algebras from old ones. It is believed that orbifolds and cosets will inherit nice properties such as strong finite
09:50 generation, C_2-cofiniteness, and rationality, but few general results of this kind are known. I will discuss how these problems can be studied systematically using ideas from classical
invariant theory. This is based on joint work with T. Creutzig.
(TCPL 201)
10:00 - Coffee Break (TCPL Foyer)
Nicolas Guay: Twisted Yangians of types B-C-D and their irreducible finite dimensional modules ↓
10:30 - I will introduce new twisted Yangians associated to symmetric pairs of types B, C and D which are similar to the twisted Yangians of type A introduced by G. Olshanski around twenty-give years
11:20 ago and which have been quite well studied. After a discussion of a number of their properties, I will present classification results for their irreducible finite dimensional modules. This is
joint work with Vidas Regelskis and Curtis Wendlandt.
(TCPL 201)
Checkout by Noon ↓
11:30 - 5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the
12:00 guest rooms by 12 noon.
(Front Desk - Professional Development Centre)
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Wikipedia articles that are too technical.
Wikipedia articles that are too technical.
August 30, 2007 7:36 PM Subscribe
Wow, a link to a number of things that I am interested in. Thanks, loquacious!
posted by turing_test at 7:39 PM on August 30, 2007
Kuujjuarapik, you have to hit "article" in the tabs at the top of the Wikipedia page. The links go to the discussion portion of the article.
posted by barchan at 7:44 PM on August 30, 2007
Ok. That did it. That's the straw that made me stop giving money to wikimedia.
For all the good they still do (the things I search for are consistently well-covered) the hall-monitors have taken over.
What alien mind virus has made such a decent idea into some sort of finite-space analog where quality is second fiddle to conformity?
posted by abulafa at 7:47 PM on August 30, 2007 [5 favorites]
I don't quite get the point as regards the math articles. Yes, the page about "cohomological dimension" is technical. Too technical for most people who might stumble across it. But not too technical
for anyone with the slightest reason to want to know what cohomological dimension is! The math articles on wikipedia are, by and large, one of the site's finest features; I use them all the time when
I'm in a coffeeshop and need a definition or a theorem statement.
posted by escabeche at 7:47 PM on August 30, 2007 [2 favorites]
I've often looked at math and science articles on wikipedia and have understood maybe a third of what's on the page, and I think I'm a pretty bright guy.
I think it's amazing that there are so many technical, detailed explanations on there, and I don't think they should be removed but I do think more attention should be paid to the 'cohomological
dimensions for dummys' sections of the articles.
posted by empath at 7:51 PM on August 30, 2007
empath: Some topics simply have no "for dummies" explanation - it's silly to demand laymen's introductions to every arcane topic under the sun. It would be nice, but it's certainly no reason to
condemn and article.
posted by phrontist at 7:57 PM on August 30, 2007
The point is that I don't think there
any sensible way of talking about cohomological dimension that doesn't presuppose that you are not, say, at least a first-year graduate student in pure math. It's not about being smart or willing to
read carefully; it requires having spent years climbing the very grand heap of prior ideas in order to get to the place where cohomological dimension sits -- not all that near the top.
(on preview, what phrontist said.)
posted by escabeche at 7:58 PM on August 30, 2007
I wonder why the links go to the articles' talk pages, rather than to the articles themselves.
It seems like sound policy to make Wikipedia articles as accessible as possible, and that many of the articles on this list could be improved. I'm glad to see editors paying attention to this.
This page
explains Wikipedia's philosophy re accessibility, and it seems pretty much like common sense to me:
Every reasonable attempt should be made to ensure that material is presented in the most widely accessible manner possible. If an article is written in a highly technical manner, but the material
permits a more accessible explanation, then editors are strongly encouraged to rewrite it.
I don't think this is cause for alarm.
posted by washburn at 8:01 PM on August 30, 2007
For all the good they still do (the things I search for are consistently well-covered) the hall-monitors have taken over.
I'm not familiar with the editing nuances of wikiworld, but it seems like these flags maybe don't get revisited when the articles in question get revised. For example, the complaint about
(an object whose basic description is pretty simple) seems to have been addressed rather clearly.
posted by kittyprecious at 8:07 PM on August 30, 2007
Reading about stuff like cohomological dimensions is something that makes me hope for the future. It's like how they came up with the complex numbers many many years before anyone figured out you
could use them to figure out electric circuits, before anyone was even trying to figure out electric circuits - what are they going to figure out how to do with the cohomological dimensions?
posted by TheOnlyCoolTim at 8:09 PM on August 30, 2007
you have to hit "article" in the tabs at the top of the Wikipedia page. The links go to the discussion portion of the article.
Ah. Thanks.
Yesh, these must be too technical for me if I can't get to the article without a helpdesk ticket.
posted by YoBananaBoy at 8:14 PM on August 30, 2007
The one that turned me was the discussion of the
Bridge Pattern
. An anonymous editor's critique: "Why are there all these code samples?"
A moderator responds favorably, belying a misunderstanding of the value of seeing the same concept illustrated across many languages. You learn nuance and best practice that way, and wikipedia was
once a fine place to figure out comparative programming.
Sure, give me an overview and justification, great. But give me the detail that editors are willing to provide, validate, and maintain.
posted by abulafa at 8:20 PM on August 30, 2007
From the list, the link to the
Banzai Pipeline
entry caught my eye. In question is the use of jargon employed in describing Pipeline's particular wave mechanics:
When hit by a north swell, the peak becomes a true A-frame, with Pipe closing out a bit and peeling off left, and the just-as-famous Backdoor going right. As the size at Pipe increases, over 12
feet usually, Second Reef starts cracking, with longer walls, and more size. At an extreme size Third Reef starts to bomb out.
Seriously, that got me stoked. But I think this entry is on the wrong list - it needs to be moved to "Wikipedia articles that need more technical info, brah."
posted by krippledkonscious at 8:27 PM on August 30, 2007 [1 favorite]
it seems like these flags maybe don't get revisited when the articles in question get revised
Usually "serious" flags add those boxes at the top of the article. Like "biased" or "doesn't cite sources". (Maybe it changes the page template.) This flag is just a category, and I think people just
ignore categories.
posted by smackfu at 8:28 PM on August 30, 2007
Some topics simply have no "for dummies" explanation
I disagree with this sentiment, both generally and in detail. One of the most profound things an old prof of mine once told me was that if you can't explain the gist of a topic to an interested
layman in a sentence or two, then you really don't understand it yourself.
There are plenty of examples of people who can do this well. Feynmann was a master at it: read his
Six Easy Pieces
. See Hawking's
A Brief History of Time
. See Holldobler and Wilson's
The Ants
. I could name a dozen more covering all the fields of scientific inquiry.
Is it hard to do this well? Sure, but that doesn't mean it isn't worth a try. I do not support dumbing down the articles one bit, but brief introductions in plain language help even experts orient
themselves to a topic.
posted by bonehead at 8:29 PM on August 30, 2007 [1 favorite]
One of the most profound things an old prof of mine once told me was that if you can't explain the gist of a topic to an interested layman in a sentence or two, then you really don't understand it
I do think that's profound, but I also think it's false. I review popular math books all the time. Some of them are really first-rate (John Derbyshire's book on the Riemann hypothesis is a good
example.) They don't try to explain the gist of the topic to laymen in a sentence or two; they use a whole book. And still, they don't really come close to a gist. At best, you get a milligist.
I hope I don't seem cranky about this, but I really do believe that you can't learn very much mathematics without concerted study.
posted by escabeche at 8:38 PM on August 30, 2007
Sometimes it takes a whole book to give a dummy's explanation. Simon Singh is really good at this. See his books on the Big Bang and Fermat's Last Theorem.
But he does it by explaining each concept as he goes along, and Wikipedia already has that... you just have to follow the links.
posted by smackfu at 8:39 PM on August 30, 2007
This is silly. For example, could someone please explain to me how an article about the
Boltzmann Equation
could be any less technical without omitting important information? The intro is fine for us liberal arts majors, we just stop reading when we get to the funny looking symbols and letters.
posted by chlorus at 8:45 PM on August 30, 2007
The highly technical things I know about "Contemporary Art Production" ain't listed... WTF Wikipedia???
posted by R. Mutt at 8:48 PM on August 30, 2007
I found the articles to be largely accurate (perhaps missing a nuance here & there) and far from incomprehensible, or "too technical". If I had the time, I'd sign up as an editor, merely to correct
some of the more glaring (minor) errors that I noticed. I have a mental list of about 387 things I'd prefer to see corrected, in the collective interests of other lay readers like me.
posted by UbuRoivas at 9:08 PM on August 30, 2007
All this is is a list of articles for which some Wikipedia user has put the "This article is too technical" infobox on the article's discussion page. That's
It's not a Wikipedia-official list, or a particular damnation -- it's just a list of articles that someone (and not the same person every time) thought was too technical and would therefore like
someone who knows the subject to take a look and see if it could benefit from simplifying.
(The reason that the talk pages are linked is because the "too technical" cleanup tag goes on the talk page, so that people reading the article itself helpfully remain ignorant of the claim.)
posted by mendel at 9:25 PM on August 30, 2007
Wait - the articles aren't actually made unavailable because someone flagged it as "too technical," right?
This is just a plea for someone to ... wait, bollux up a perfectly informative page into a "biphenyl degradation for dummies?"
I dunno - would including links explaining the background for certain terms/ideas required to "understand" a particular wiki page be sufficient to remove the "too technical" flag? Using the
example, rudimentary ideas that are required to understand the body of the article
From definitions of an
organic compound
chemical formula
, or even
crude oil
to methods such as
, salient information about it's handling by providing a definition for
, and even related products like
liquid crystals
. It also has links to explain common chemical reactions like
coupling reactions
to more specific reactions like the
and the
Maybe this particular post wasn't such a great one to flag as "too technical."
... and have understood maybe a third of what's on the page, and I think I'm a pretty bright guy
What were limitations to you're understanding the other 2/3rds of a page?
posted by porpoise at 9:30 PM on August 30, 2007
Oh... can I flag post on some random over-exposed celebrity as "too technical" because I find the the subject matter alien and I lack the associated cultural knowledge to appreciate why that
celebrity matters?
posted by porpoise at 9:33 PM on August 30, 2007
There are 200 pages in this section of this category.
Miss Shirley, hold my calls.
posted by spock at 10:07 PM on August 30, 2007
I'm still with bonehead, others here and with the originators of this flag. In the majority of cases, it is certainly possible to at least
some text that attempts to summarize the scope of the article and it appears that many of the articles with this flag either don't attempt to do so, or do it inadequately. That's not the same thing
as saying that Wikipedia editors need to
water down
their content in any way, and it's certainly not a suggestion that any layperson reading such a summary would come away with a full grasp of the subject.
And porpoise, although your question may have been rhetorical/sarcastic I think the answer is actually yes (sort of). It's still specialist knowledge that requires specialist training.
posted by christopherious at 11:12 PM on August 30, 2007
These are some of Wikipedia's finest articles. They are written not for a general audience, but for the average person seeking a definition of the term. What the fuck is wrong with that?
Here's an examle:
Cytochrome P450 reductase
; as someone who has taken one semester of microbi and one of biochem, this is at the limit of what I can comprehend
prima facie.
I may have to follow a few links, but I don't have to do a search to know what NADPH is. I actually learned something from this article. I needed to read up on Cytochrome P450, but what of it? I have
lost 20 minutes and gained a fuller understanding of the composition and nature of electron supply chains, the way reducing potential is used for energy inside the cell, steroidogenesis and hepatic
Thanks Wikipedia! Stay too technical.
posted by [expletive deleted] at 2:10 AM on August 31, 2007
I can understand the argument that some things are very difficult to, and doesn't neccessarily have to be explained in laymans terms. The example with cohomological dimensions, and that only people
who would have a chance of understanding what the article was about, would read up on it in the first case, is easy to understand.
But in the cases where you have a topic that has a greater likelyhood of interesting the ordinary me, I find it annoying when the article is filled with technical words, all the way through, and
neither in the overview nor anywhere else is there given room for 'ordinary language'. Medical text on wikipedia is very prone to this juxtaposition between a likelyhood of being of interest to a
great deal of ordinary people, but having been written only with others, proficient in the language of the profession, in mind.
posted by Catfry at 2:50 AM on August 31, 2007
It's a bogus category. I see most articles there are not too complex. And two complex is subjective. In fact they have categories for "needs expert attention". If you feel an artcile istoo complex,
it probably means it needs an expert to trim it down.
posted by jeffburdges at 3:29 AM on August 31, 2007
It's not a Wikipedia-official list,
??? This is Wikipedia. Everything is just a list put together by some random users.
posted by smackfu at 5:53 AM on August 31, 2007
And of course, since it's Wikipedia, you can remove any of the articles that you think don't belong in this category.
posted by smackfu at 5:54 AM on August 31, 2007
I was actually just thinking of this the other day. One of the coolest things about wikipedia is that as you get into more technical issues, you get more technical writing.
I disagree with this sentiment, both generally and in detail. One of the most profound things an old prof of mine once told me was that if you can't explain the gist of a topic to an interested
layman in a sentence or two, then you really don't understand it yourself.
You ought to be able to explain it, but a sentence or two? I mean I don't know what your area of expertise is, but how could you explain a non-deterministic finite state automata in a sentence or
two? Or context free grammar? You could maybe explain those things in a few paragraphs, but not one or two sentances.
I found the articles to be largely accurate (perhaps missing a nuance here & there) and far from incomprehensible, or "too technical". If I had the time, I'd sign up as an editor, merely to correct
some of the more glaring (minor) errors that I noticed. I have a mental list of about 387 things I'd prefer to see corrected, in the collective interests of other lay readers like me.
Dude, you don't need to sign up to edit! The next time you see something you want to correct, correct it! Just press the 'edit' tab at the top. The only reason to sign in is if you want to keep track
of the work you're doing, otherwise it goes under your IP.
posted by delmoi at 6:36 AM on August 31, 2007
I use them all the time when I'm in a coffeeshop and need a definition or a theorem statement.
To drop into casual conversation, or perhaps to spice up that poem you're about to recite?
posted by Kirth Gerson at 7:44 AM on August 31, 2007 [3 favorites]
I saw no mention of fellatio, so why do so few folks get it right?
posted by davy at 9:17 AM on August 31, 2007
if you can't explain the gist of a topic to an interested layman in a sentence or two, then you really don't understand it yourself.
There are plenty of examples of people who can do this well. Feynmann was a master at it: read his Six Easy Pieces. See Hawking's A Brief History of Time.
I think these books are longer than a sentence or two.
posted by yohko at 9:20 AM on August 31, 2007
"If you can't explain the gist of a topic to an interested layman in a sentence or two, then you really don't understand it yourself."
Here's one: somebody please explain in a sentence or two the gist of Shiite theology. Not Muslim theology generally, not the political notion of who should rule the Muslim community, but those
theological concepts that separate Shia from Sunni.
posted by davy at 9:45 AM on August 31, 2007
Note that I'm not holding you to a limit on the length of the sentences nor am I forbidding subordinate claues.
posted by davy at 9:46 AM on August 31, 2007
subordinate claues
Or subordinate clauses either. (I'm starting to think I need to clean my keyboard
, sorry.)
posted by davy at 9:47 AM on August 31, 2007
I got into an argument in a taproom with a buddy of mine and wikipedia settled it for us.
We were shooting pool and talking about enzymes that regulate glucocorticoid action in the brain.
See we knew 11-Beta Hydroxysteroid Dehydrogenase was the name of a family of enzymes that catalyzes the conversion of inert 11 keto-products to active cortisol, or vice versa and regulates acccess of
glucocorticoids to the steroid receptors but he was saying coenzymes composed of ribosylnicotinamide 5'-diphosphate coupled to adenosine 5'-phosphate by pyrophosphate linkages were used as a cofactor
and I said no, it must be nicotinamide adenine dinucleotide phosphate because it’s a coenzyme composed of ribosylnicotinamide 5'-phosphate coupled by pyrophosphate linkage to the 5'-phosphate
adenosine 2',5'-bisphosphate.
As turns out, they’re both cofactors - Thanks Wikipedia!
posted by Smedleyman at 1:15 PM on August 31, 2007 [1 favorite]
The central theological concept that separates the Sunnis and the Shiites is whether religious leadership is to be determined by egalitarian means and statecraft or through bloodline (of the prophet
Mahammad), heirarchy and divine inspiration, respectively.
Of course - given the iteration of heirarchy in Shiite sects (Twelver Shiism, Sevener Shiism, the Zaydis, the Alawites, the Druzes) it’s tough to get your Shiite straight, so your point is taken.
Like saying “Martin Luther” in explaining the difference between Catholics and Protestants.
But I think the issue is making a complex point clear rather than overall brevity.
posted by Smedleyman at 2:00 PM on August 31, 2007
The behavior I find most amusing, as a former Wikipedian, is this tendency ... well, I'm not sure how to label it, but essentially, Wikipedians love to flag something as needing work of one kind
or another — they never love to actually do the work they're flagging the article for.
I beg to differ.
As someone that has participated in both sides of that system, I see the value of flagging an article for later followup.
The simplest argument in favor of this system is the same that applies to open-source software development: just because you can't — or don't have the time to — code (write encyclopedia articles)
doesn't mean you can't help development by participating in the absolutely critical peer review process.
I can get terribly distracted but even I realize that if I'm hunting for something specific: information on a software development tool, say, and I find a semi-terrible article that nevertheless
points me in the right direction, it's not a good idea for purposes of time management to stop and spend an hour fixing everything wrong with the article. But I can make a note so that someone who
does have the time knows where to start, and so that someone having trouble reading the article knows it's not simply a problem with their reading comprehension.
I've flagged articles, I've outright edited articles, I've done work based on others' flags, and I've gone back and implemented my own suggestions later. I'm proud of each of those instances because
in each case I've contributed in a tiny way to improving a public resource. Better than scratching dirty words in the walls and throwing cigarette butts all over the street, anyway.
And with that, I'm done with both Wikipedia and Metafilter for the day and off to do some real work.
posted by vsync at 2:51 PM on August 31, 2007
MetaFilter: it’s tough to get your Shiite straight
posted by Kirth Gerson at 3:07 PM on August 31, 2007
The one that turned me was the discussion of the Bridge Pattern.
Ya, that is a good example.. The graphic doesn't even have a representation of a bridge pattern. If they mean that the graphic itself
the bridge pattern (seems to be the case), they should say that
(like, with a box around the whole thing labeled 'design pattern').
On top of that, the connection symbols used in the diagram have no meaning to me, and certainly no meaning at all to a general audience.
And another, from the article:
One thing all shapes can do is draw themselves.
And I'm only getting started..
From the
design pattern
Design patterns gained popularity in computer science after the book Design Patterns: Elements of Reusable Object-Oriented Software was published in 1994. ... The scope of the term remained a
matter of dispute into the next decade.
Perhaps this is the root of the problem. There seem to be a lot of "new" concepts in software engineering that only serve to muddy the actual issues. I guess that is a common property in every young
field - it takes time for the language to settle.
On the other hand, software engineering is in a unique position.. In software you can always layer another level of abstraction onto what has gone before, and you can always claim that the new level
is actually something
, rather than just some guys latest pet way of describing the same old thing. I mean, software is inherently just more and more layers of abstraction anyway, so.. If that mechanism is at work here,
it is in the interest of the person promoting the new term to muddy the water, so that the overlap isn't obvious.
Nah, that second possibility must be wrong, 'cause the article says:
the practical application of design patterns is a phenomenon
Phenomenal! Too bad they haven't settled on a definition yet.
posted by Chuckles at 2:03 PM on September 1, 2007
One of the most profound things an old prof of mine once told me was that if you can't explain the gist of a topic to an interested layman in a sentence or two, then you really don't understand it
As a matter of personal philosophy, I totally agree. However, to add a little objectivity, one might say that this is more provable as it applies to an entire field, rather than an individual
practitioner. Which is, I guess, just an abstracted way of interpreting my screed on software engineering :P
posted by Chuckles at 2:14 PM on September 1, 2007
One of the most profound things an old prof of mine once told me was that if you can't explain the gist of a topic to an interested layman in a sentence or two, then you really don't understand it
Well, if it were as simple as that, then we'd all understand everything, wouldn't we? Clearly even those easy explanations for the layman don't really make everything completely clear... In a way
it's a misguided hope of our capacity as teachers, and a stupid expectation to have of our students, to think that issues of real complexity, and honestly, long, hard
, can be communicated so neatly.
That's not to say you can never open a topic up, show someone why it's interesting, or give them a peek into what you study, but I dunno if that can be called "the gist", and even then it really
depends on the topic, and what about it is so interesting.
I would say that the ability to explain complex topics in simple terms is probably not indicative of how well you understand the complex topic to start with. Some people are just good at explaining
things straightforwardly. Sometimes they also have a very good grasp of the higher order difficulties, but sometimes, they are simply thinking the whole time in a more boxy configured straightforward
model that's easier to translate to lay terms. And sometimes the people who can't explain in lay terms have trouble because they're still fundamentally lacking a real sense of the big picture, but
sometimes it's because they have so many details and complications that to them, telling the boxy straightforward model is missing the entire point of the investigation and a complete waste of time,
that's nothing to do with their research.
posted by mdn at 6:38 PM on September 1, 2007
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type_sepa.h File Reference
Detailed Description
type definitions for separators
Tobias Achterberg
Definition in file type_sepa.h.
Go to the source code of this file.
#define SCIP_DECL_SEPACOPY(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
#define SCIP_DECL_SEPAFREE(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
#define SCIP_DECL_SEPAINIT(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
#define SCIP_DECL_SEPAEXIT(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
#define SCIP_DECL_SEPAINITSOL(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
#define SCIP_DECL_SEPAEXITSOL(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
#define SCIP_DECL_SEPAEXECLP(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa, SCIP_RESULT* result, SCIP_Bool allowlocal)
#define SCIP_DECL_SEPAEXECSOL(x) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa, SCIP_SOL* sol, SCIP_RESULT* result, SCIP_Bool allowlocal)
Macro Definition Documentation
#define SCIP_DECL_SEPACOPY ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
copy method for separator plugins (called when SCIP copies plugins)
• scip : SCIP main data structure
• sepa : the separator itself
Definition at line 47 of file type_sepa.h.
#define SCIP_DECL_SEPAFREE ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
destructor of separator to free user data (called when SCIP is exiting)
• scip : SCIP main data structure
• sepa : the separator itself
Definition at line 55 of file type_sepa.h.
#define SCIP_DECL_SEPAINIT ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
initialization method of separator (called after problem was transformed)
• scip : SCIP main data structure
• sepa : the separator itself
Definition at line 63 of file type_sepa.h.
#define SCIP_DECL_SEPAEXIT ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
deinitialization method of separator (called before transformed problem is freed)
• scip : SCIP main data structure
• sepa : the separator itself
Definition at line 71 of file type_sepa.h.
#define SCIP_DECL_SEPAINITSOL ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
solving process initialization method of separator (called when branch and bound process is about to begin)
This method is called when the presolving was finished and the branch and bound process is about to begin. The separator may use this call to initialize its branch and bound specific data.
• scip : SCIP main data structure
• sepa : the separator itself
Definition at line 82 of file type_sepa.h.
#define SCIP_DECL_SEPAEXITSOL ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa)
solving process deinitialization method of separator (called before branch and bound process data is freed)
This method is called before the branch and bound process is freed. The separator should use this call to clean up its branch and bound data.
• scip : SCIP main data structure
• sepa : the separator itself
Definition at line 93 of file type_sepa.h.
#define SCIP_DECL_SEPAEXECLP ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa, SCIP_RESULT* result, SCIP_Bool allowlocal)
LP solution separation method of separator
Searches for cutting planes that separate the current LP solution. The method is called in the LP solving loop, which means that a valid LP solution exists.
• scip : SCIP main data structure
• sepa : the separator itself
• result : pointer to store the result of the separation call
• allowlocal : should the separator allow local cuts?
possible return values for *result (if more than one applies, the first in the list should be used):
• SCIP_CUTOFF : the node is infeasible in the variable's bounds and can be cut off
• SCIP_CONSADDED : an additional constraint was generated
• SCIP_REDUCEDDOM : a variable's domain was reduced
• SCIP_SEPARATED : a cutting plane was generated
• SCIP_NEWROUND : a cutting plane was generated and a new separation round should immediately start
• SCIP_DIDNOTFIND : the separator searched, but did not find domain reductions, cutting planes, or cut constraints
• SCIP_DIDNOTRUN : the separator was skipped
• SCIP_DELAYED : the separator was skipped, but should be called again
Definition at line 116 of file type_sepa.h.
#define SCIP_DECL_SEPAEXECSOL ( x ) SCIP_RETCODE x (SCIP* scip, SCIP_SEPA* sepa, SCIP_SOL* sol, SCIP_RESULT* result, SCIP_Bool allowlocal)
arbitrary primal solution separation method of separator
Searches for cutting planes that separate the given primal solution. The method is called outside the LP solution loop (e.g., by a relaxator or a primal heuristic), which means that there is no valid
LP solution.
• scip : SCIP main data structure
• sepa : the separator itself
• sol : primal solution that should be separated
• result : pointer to store the result of the separation call
• allowlocal : should the separator allow local cuts?
possible return values for *result (if more than one applies, the first in the list should be used):
• SCIP_CUTOFF : the node is infeasible in the variable's bounds and can be cut off
• SCIP_CONSADDED : an additional constraint was generated
• SCIP_REDUCEDDOM : a variable's domain was reduced
• SCIP_SEPARATED : a cutting plane was generated
• SCIP_NEWROUND : a cutting plane was generated and a new separation round should immediately start
• SCIP_DIDNOTFIND : the separator searched, but did not find domain reductions, cutting planes, or cut constraints
• SCIP_DIDNOTRUN : the separator was skipped
• SCIP_DELAYED : the separator was skipped, but should be called again
Definition at line 140 of file type_sepa.h.
Typedef Documentation
◆ SCIP_SEPA
locally defined separator data
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Counting filtered data
Hi - I have a question. I want to count the number of rows NOT BLANK after I filter the rows. Currently, the counting formula counts all of the rows even the ones that are filtered out. This seems
rather simple but I could not seem to figure it out.
Thanks in advance for your help!
• You need to use the COUNTIF formula and use your filtered options as range & criteria in the COUNTIF function.
Hope it helped!
• Thanks for your help but this did not work.
This picture shows how it should work.
Notice that the header column in row 5 has the formula. The result is 2 indicating that when the filter is set to "Level 2", then there are two rows under the Engineering header that meet that
The problem is, of course, that it returns the value of 2 always. When I change the filter to Level 1, it returns this.
Note that the header value stays at 2 but there is more than 2 rows. Same with Level 3 below.
While it returns the value of 2 and there are 2 rows, it is still counting the Level 2 rows.
This is my problem. I need the number in row 5 Sub Process # to reflect the number of child rows for each filter.
• That's not exactly quite I thought when I read your first post.
So If I understand you correctly, you want the formula to change when you change the filter option right?
I don't have much answer to provides right now, because your formula is independant from any filter options (that are just a way to display stuff from the sheet basically).
What comes first to mind is having an helper cell that is displaying the filter option (not sure how to do it automatically though).
Then change your CONTAINS formula like this:
=COUNTIFS(CHILDREN([Audit Level]@row), CONTAINS($[Helper Column]$1, @cell))
Hope it helped!
• Hello! I just found this and I'm trying to do something similar to get a rolling count of different phrase occurrences in a column.
Is there a way to integrate a filter into a formula? I wasn't sure what @David Joyeuse, you meant with your very first response.
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C++ Program to Find Sum of n Natural Numbers using For loop
Sum of n Natural Numbers using For loop
Write a C++ Program to Find Sum of n Natural Numbers using For loop. Here’s simple C++ Program to Find Sum of n Natural Numbers using For loop in C++ Programming Language.
Normally, when we work with Numbers, we use primitive data types such as int, short, long, float and double, etc. The number data types, their possible values and number ranges have been explained
while discussing C++ Data Types.
Here is source code of the C++ Program to Find Sum of n Natural Numbers using For loop. The C++ program is successfully compiled and run(on Codeblocks) on a Windows system. The program output is also
shown in below.
SOURCE CODE : :
/* C++ Program to Find Sum of n Natural Numbers using For loop */
using namespace std;
int main()
int i,n,sum=0;
cout<<"\nHow many numbers u want :: ";
cout<<"\nSum of first [ "<<n<<" ] Numbers are = "<<sum<<"\n";
return 0;
OUTPUT : :
/* C++ Program to Find Sum of n Natural Numbers using For loop */
How many numbers u want :: 10
Sum of first [ 10 ] Numbers are = 55
Process returned 0
Above is the source code for C++ Program to Find Sum of Natural Numbers using For loop which is successfully compiled and run on Windows System.The Output of the program is shown above .
If you found any error or any queries related to the above program or any questions or reviews , you wanna to ask from us ,you may Contact Us through our contact Page or you can also comment below in
the comment section.We will try our best to reach up to you in short interval.
Thanks for reading the post….
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Although ,this method fits well for smaller nos. it’s very hectic to sum upto large number e.g., upto 1,000,000. To reduce time complexity a better approach is being used . This approach uses simple
mathematical formula to calculate sum upto n terms .
Happy coding !!!
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Ordinal Numbers And Months Of The Year Puzzle - OrdinalNumbers.com
Ordinal Numbers And Months Of The Year Puzzle
Ordinal Numbers And Months Of The Year Puzzle – It is possible to enumerate an unlimited number of sets by making use of ordinal numbers as an instrument. It is also possible to use them to
generalize ordinal numbers.
One of the fundamental ideas of math is the ordinal number. It is a number that indicates the position of an item within an array. Ordinal numbers can be expressed as a number that ranges between
zero and twenty. Ominal numbers are used for a variety of purposes but are most commonly utilized to signify the order of items on the list.
Ordinal numbers can be represented using charts, words, numbers and various other techniques. They can also serve to illustrate how a set of or pieces are set up.
The majority of ordinal numbers are classified into one of the following two categories. Transfinite ordinals will be represented in lowercase Greek letters. The finite ordinals will be represented
as Arabic numbers.
A properly-organized collection must include at least one ordinal, according to the axiom. For instance, the highest possible grade will be given to the class’s initial member. The winner of the
contest was the student with the highest grade.
Combinational ordinal figures
Multiple-digit numbers are also known as compound ordinal numbers. They are created by multiplying an ordinal figure by its last digit. These numbers are typically used to determine ranking and
dating. They don’t use a distinctive ending as cardinal numbers do.
Ordinal numbers indicate the order in which elements are located in a collection. They can be used to identify the elements in a collection. You can find both regular and suppletive numbers to
ordinal numbers.
Regular ordinals are created by prefixing a cardinal number with the -u suffix. Next, the number is typed in a word, and a hyphen follows it. There are additional suffixes available.For instance, the
suffix “-nd” is utilized for numerals that end with 2, and “-th” is utilized for numbers ending in 4 and 9.
By affixing words with the -u or–ie suffix results in suffixtive ordinals. This suffix can be used for counting. It’s also larger than the standard one.
Limits of Ordinal
The limit on ordinal quantities that do not have zeros is an ordinal quantity that isn’t zero. Limit ordinal numbers come with the disadvantage of having no limit on the number of elements they can
have. You can make them by joining empty sets with no the maximum element.
Infinite transfinite-recursion concepts employ a limit ordinal number. The von Neumann model declares that each infinite cardinal numbers is also an ordinal number.
A number of ordinal units with a limit are equivalent to the sums of all the ordinals below it. Limit ordinal numbers can be quantified using math and can be expressed in a series or natural numbers.
The ordinal numbers are used to arrange the information. These numbers are used to explain the nature of the object’s position numerically. They are utilized in set theory and arithmetic contexts.
Although they have the same structure as natural numbers, they are not part of the same class.
The von Neumann method uses a well-ordered list. Consider that fy fy is one of the subfunctions of an g’ function that is specified as a singular function. If fy is only one subfunction (ii) the
function g’ must meet the requirements.
In the same way in a similar manner, it is similar to the Church Kleene ordinal is a limit ordeal. The Church-Kleene ordinal defines an ordinal that is a limit as a properly arranged set of smaller
ordinals, and it has a non-zero ordinal.
Stories that make use of ordinary numbers as examples
Ordinal numbers are used to indicate the order of things between objects or entities. They are crucial to organize, count as well as ranking reasons. They are used to indicate the sequence of events
as well as to illustrate the position of objects.
The ordinal number is typically identified by the letter “th”. Sometimes, however, the letter “nd” could be substituted. There are a lot of ordinal numbers in the titles of books.
Ordinal numbers may be expressed as words even though they are often employed in list format. They may be expressed with numbers or acronyms. These numbers are simpler to understand than cardinal
Ordinary numbers are available in three distinct flavors. They can be learned more by playing games, practice, or other activities. You can improve your arithmetic skills by learning more about them.
Try coloring exercises to provide a fun and easy method of improving. A handy sheet of marking is a great way to record your results.
Gallery of Ordinal Numbers And Months Of The Year Puzzle
Months Of The Year Ordinal Numbers Worksheet
Months Of The Year Ordinal Numbers And Colors Worksheet
Months Of The Year And Ordinal Numbers Worksheet
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Re: The effect of symmetry sets on TLC performance
On Thursday, December 3, 2015 at 5:05:30 PM UTC+2, Leslie Lamport wrote:
To fingerprint a state, TLC should construct a single new state that
is a permutation of that state and fingerprint the permuted state.
The time to construct that permuted state should be linear in the size
of the state.
That's perfectly fine, but it should also be significantly less (in practice) than the time to compute (by next-step), or the optimization might not pay off.
A specification is symmetric in a set S iff for every behavior b
allowed by the specification and every permutation p of S, the
behavior obtained by applying p to every state of b is also a behavior
allowed by the specification. (Applying p to a state means replacing
each element s of S by p(s).)
I believe mine is symmetric in both sets.
I interpret what you have written to meant that your specification
allows only intial states in which foo = a iff bar = x. Such a
specification is not symmetric in either {a, b, c} or {x, y, z}.
Ah, no, that's not what I meant. It allows any initial state, but no matter the mapping between values in the initial state, it is always preserved, so states with different mappings will never be
reached. I think I have an effective clarification: consider a model with a single variable `foo` that can obtain the symmetric values `{a, b, c}`. Now introduce a constant, Map, which maps the set
to {x, y, z} in any arbitrary way. Then, introduce another variable, `bar` and the following conjunction to the next state formula:
/\ bar' = Map(foo')
I think this model is semantically symmetrical in both sets, but from any given initial condition, only 3 permutations out of 9 are reachable for each state. TLC, however (I think) will construct all
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Re: st: RE: interpreting the significance level of spearmans rank correl
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]
Re: st: RE: interpreting the significance level of spearmans rank correlation
From Maarten buis <[email protected]>
To [email protected]
Subject Re: st: RE: interpreting the significance level of spearmans rank correlation
Date Sat, 3 Jun 2006 16:07:18 +0100 (BST)
Unfortunately the interpretation isn't that simple: either you say that
you have chosen to reject the null hypothesis using a procedure that
incorrectly rejects the null in 5% of the times that that procedure is
used, or you say that the probability of finding the results you have
found if the null hypothesis were true is less than 5%. The probability
of finding the data given the hypothsis is not the same as the
probability of the hypothesis given the data, just as the probability
that an American is the president of the United States is not the same
as the probability that the president of the United States is an
If you want to make the statement that a hypothesis is true with a 95%
probability you'll have to go Bayesian.
--- Patric Mayer <[email protected]> wrote:
> so, in my example, I can say that I found a significant correlation
> of 0.8804. (and this is true with a probability of 95%)?
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z214
+31 20 5986715
Send instant messages to your online friends http://uk.messenger.yahoo.com
* For searches and help try:
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* http://www.stata.com/support/statalist/faq
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Combination Generator
Related Articles
Roughly speaking, a combination is a selection of letters inside a String. For example, consider the String "abcde". We want to select 3 letters out of it. How many combinations do we have ?
Answer : 10. The full list is :
Divide and Conquer
We can keep breaking down the problem into smaller sub-problems, until the sub-problems have obvious solution. This technique of problem solving is known as "divide and conquer".
Problem : Find all 3-letters combinations from "abcde"
Sub-problems :
1. Find the combination that contains the letter "a"
2. Find the combination that doesn't contains the letter "a"
The second sub-problem is identical to :
Find all 3-letters combinations from "bcde", that would produce the list :
And the first sub-problem is identical to :
Find all 2-letters combinations from "bcde", then add an "a" in front of each combination
Let's write it in details :
all 2-letters combinations of "bcde" = ["bc","bd","be","cd","ce","de"]
add an "a" in front of each of them = ["abc","abd","abe","acd","ace","ade"]
Combining two sub-problems will give the full solutions :
["abc","abd","abe","acd","ace","ade"] + ["bcd","bce","bde","cde"]
A recursive implementation follows directly from the above algorithm.
Runnable Demonstration
You may skip this section if you feel you understand the algorithm well enough.
We will trace a smaller problem, find all 3-letters combination from "abcd"
Level 1 expand, divide into 2 sub-problems
1. combination("a","bcd",2)
2. combination("" ,"bcd",3)
Level 2 expand
1. combination("a","bcd",2)
1.1 combination("ab","cd",1)
1.2 combination("a" ,"cd",2)
2. combination("","bcd",3)
2.1 combination("b","cd",2)
2.2 combination("" ,"cd",3) // dead end, cannot pick 3 letters from tail "cd"
Level 3 expand
1. combination("a","bcd",2)
1.1 combination("ab","cd",1)
1.1.1 combination("abc","d",0) // k=0, print "abc"
1.1.2 combination("ab" ,"d",1)
1.2 combination("a","cd",2)
1.2.1 combination("ac","d",1)
1.2.2 combination("a" ,"d",2) // dead end, cannot pick 2 letters from tail "d"
2. combination("","bcd",3)
2.1 combination("b","cd",2)
2.1.1 combination("bc","d",1)
2.1.2 combination("b" ,"d",2) // dead end, cannot pick 2 letters from tail "d"
2.2 combination("" ,"cd",3) // dead end, cannot pick 3 letters from tail "cd"
Level 4 expand
1. combination("a","bcd",2)
1.1 combination("ab","cd",1)
1.1.1 combination("abc","d",0) // k=0, print "abc"
1.1.2 combination("ab" ,"d",1)
1.1.2.1 combination("abd","",0) // k=0, print "abd"
1.1.2.2 combination("ab" ,"",1) // dead end, cannot pick 1 letter from tail ""
1.2 combination("a","cd",2)
1.2.1 combination("ac","d",1)
1.2.1.1 combination("acd","",0) // k=0, print "acd"
1.2.1.2 combination("ac" ,"",1) // dead end, cannot pick 1 letter from tail ""
1.2.2 combination("a" ,"d",2) // dead end, cannot pick 2 letters from tail "d"
2. combination("","bcd",3)
2.1 combination("b","cd",2)
2.1.1 combination("bc","d",1)
2.1.1.1 combination("bcd","",0) // k=0, print "bcd"
2.1.1.2 combination("bc" ,"",1) // dead end, cannot pick 1 letter from tail ""
2.1.2 combination("b" ,"d",2) // dead end, cannot pick 2 letters from tail "d"
2.2 combination("" ,"cd",3) // dead end, cannot pick 3 letters from tail "cd"
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Data Smart : Summary
Data Science is a very loose word and can mean different things in different situations. However one thing is certain, the principles used in tacking problems are from diverse fields. Drew Conway has
this Venn diagram on his blog :
In such a diverse field one does not know where to start and how to start. Someone has made a nice Metromap too. All said and done, this is a field that has considerable entry barriers. One needs to
spend at least a few years to get the basics right to understand some basic algorithms.
Where does this book fit in? This book is apt for people who want to see what’s going on behind various algorithms without the math. The book touches upon a dozen topics in data mining and explains
the main principles of each of those topics via Excel. By restricting to Excel, the author enables a wider audience to get a glimpse of the various concepts. The ideal way to to read this book is by
working out the various case studies that are mentioned in the book. I could not motivate myself to do the analysis in Excel, so replicated the analysis in R. In this document I have listed down some
of the code to work through the book, that essentially replicates the results of the analysis done via Excel. But first a brief summary of the chapters in the book.
Chapter 1 is on Excel and can be speed read as I cannot imagine someone reading this book without ever working on Excel. Chapter 2 discusses k-means clustering. It uses an offer-purchases dataset to
segment the customers in to various clusters for better marketing. The k-means needs a distance metric and there are many to choose from based on the situation. The book shows that for the specific
dataset used, correlation based distance or cosine similarity score is a better metric than Euclidean distance.
Chapter 3 is on Naive Bayes, a simple method that surprisingly performs better than many other algorithms. In fact the reason for its ubiquity stems from its simplicity; it does not overfit the
data.Naive Bayes principle is applied on a set of tweets to classify them as business-related or junk. Obviously there is not much of math in this book as expected. So, the results from this chapter
will motivate anyone to understand the reason why Naive Bayes works and understand why bias-variance tradeoff works very differently in a classification setting than a regression setting.
Chapter 4 is about optimization, the quintessential skillset that any data scientist needs to have. Using a case study, the author introduces Linear Programming, Integer programming, Mixed Integer
programming and ways to convert a nonlinear optimization problem in to Linear Optimization problem. The good thing about this book and this chapter in particular is that there is a good sense of
humor that the author brings along while explaining principles. That makes the book an immensely readable book.
Chapter 5 discusses graph analysis and uses the same dataset from one of the previous chapters to do an unsupervised learning. k-neighborhood and Modularity maximization procedures are used to group
the customers in to communities. Even though Gephi is used for Visualization, igraph is powerful enough to give all the visualization features to an R user. Chapter 6 is about regression. The book
uses a sample dataset to explain the concepts of regression and logistic regression.All the creation of dummy variables, setting up the objective function etc. are done in Excel and the reader is
made to understand the basic steps behind regression modeling.
Chapter 7 gives the reader an insight in to wisdom of crowds type models. The models discussed are Random Forest and Boosting. A reader who reaches until this point of the book is abundantly
convinced that Excel is too painful use boosting techniques, where every model built on a bootstrapped sample has to be recorded as a macro and one has to run it manually to get estimates. In any
case, the chapter does a wonderful job of explaining the nuts and bolts of Boosting.
Chapter 8 gives a crash course on exponential smoothing. It starts off with simple exponential smoothing and then moves on to Holt’s trend-corrected exponential smoothing and finally ending with
multiplicative Holt-Winters exponential smoothing. The basic limitation of these models is that there is no probabilistic framework around them. Hyndman has written a book on Exponential smoothing
where he casts all the models in a State space framework that makes the models far more richer.
Chapter 9 talks about outlier detection and introduces three methods: indegree method, k-distance method , local outlier factor method. Chapter 10 introduces some basic commands in R and then works
out the k-means model, the regression model, the random forests model, forecasting model and outlier detection methods in R. Chapter 11 is the concluding chapter in the book that talks about some
soft skills that a data scientist should have in order to be effective in an organization. | {"url":"https://www.rksmusings.com/2014/04/29/data-smart-summary/","timestamp":"2024-11-14T08:07:23Z","content_type":"text/html","content_length":"14541","record_id":"<urn:uuid:f2afab84-9e35-4db7-a9c0-045134cd7324>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00852.warc.gz"} |
Genie in a Model | Highbrow
Genie in a Model
Episode #6 of the course An introduction to data science by Roger Peng
Today, you’ll learn about using models to find associations and make predictions.
This lesson is typically the part of the statistics textbook or course where people tend to hit a wall. In particular, there’s often a lot of math. Math is good, but gratuitous math is not good. We
are not in favor of that. It’s important to realize that often it is useful to represent a model using mathematical notation because it is a compact notation and can be easy to interpret once you get
used to it. Also, writing down a statistical model using mathematical notation, as opposed to just natural language, forces you to be precise in your description of the model and in your statement of
what you are trying to accomplish, such as estimating a parameter.
Associational Analyses
Associational analyses are ones where we are looking at an association between two or more features in the presence of other potentially confounding factors. There are three classes of variables that
are important to think about in an associational analysis.
1. Outcome. The outcome is the feature of your dataset that is thought to change along with your key predictor. Even if you are not asking a causal or mechanistic question, so you don’t necessarily
believe that the outcome responds to changes in the key predictor, an outcome still needs to be defined for most formal modeling approaches.
2. Key predictor. Often for associational analyses there is one key predictor of interest (there may be a few of them). We want to know how the outcome changes with this key predictor. However, our
understanding of that relationship may be challenged by the presence of potential confounders.
3. Potential confounders. This is a large class of predictors that are both related to the key predictor and the outcome. It’s important to have a good understanding of what these are and whether
they are available in your dataset. If a key confounder is not available in the dataset, sometimes there will be a proxy that is related to that key confounder that can be substituted instead.
Once you have identified these three classes of variables in your dataset, you can start to think about formal modeling in an associational setting.
Prediction Analyses
In the previous section we described associational analyses, where the goal is to see if a key predictor x and an outcome y are associated. But sometimes the goal is to use all of the information
available to you to predict y. Furthermore, it doesn’t matter if the variables would be considered unrelated in a causal way to the outcome you want to predict because the objective is prediction,
not developing an understanding about the relationships between features.
With prediction models, we have outcome variables—features about which we would like to make predictions—but we typically do not make a distinction between “key predictors” and other predictors. In
most cases, any predictor that might be of use in predicting the outcome would be considered in an analysis and might, a priori, be given equal weight in terms of its importance in predicting the
outcome. Prediction analyses will often leave it to the prediction algorithm to determine the importance of each predictor and the functional form of the model.
For many prediction analyses, it is not possible to literally write down the model that is being used to predict because it cannot be represented using standard mathematical notation. Many modern
prediction routines are structured as algorithms or procedures that take inputs and transform them into outputs. The path that the inputs take to be transformed into outputs may be highly nonlinear,
and predictors may interact with other predictors on the way. Typically, there are no parameters of interest that we try to estimate; in fact, many algorithmic procedures do not have any estimable
parameters at all.
The key thing to remember with prediction analyses is that we usually do not care about the specific details of the model. In most cases, as long as the method “works,” is reproducible, and produces
good predictions with minimal error, then we have achieved our goals.
With prediction analyses, the precise type of analysis you do depends on the nature of the outcome (as it does with all analyses). Prediction problems typically come in the form of a classification
problem where the outcome is binary. In some cases the outcome can take more than two levels, but the binary case is by far the most common.
In the next lesson, you’ll learn about the differences between making an inference and a prediction.
Recommended book
“Storytelling with Data: A Data Visualization Guide for Business Professionals” by Cole Nussbaumer Knaflic
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The course gives an introduction to the field of mathematical logic by presenting the syntax and semantics of propositional logic and of the richer language of predicate logic. The goal is to
describe and investigate the above logics by finitary methods, and to train students in formalizing specifications and in verifying properties of systems.
Originally logic was used by the Greek Sophists to demonstrate the correctness of their argument in formal debates. The ambiguity of human languages asked for formulation of logic in a symbolic
formal language. Only towards the end of the 19th century logic has been formulated in the language of mathematics, and in particular of algebra, making it a useful tool to solve mathematical
problems. In the same period the language used to prove theorems from mathematics begun suffering the same problems of natural language, showing many paradoxes. Logic was proposed as the foundational
language of mathematics, but several limitation where soon discovered. More recently logic has become the language of computer science, just as calculus is the language of many engineering
In this course we will study propositional and predicate logic, their proof theory, their limitation, as well as some of their applications in computer science.
Inleiding Informatica
The following book will be used for the course: Michael R. A. Huth and Mark D. Ryan Logic in Computer Science: Modelling and Reasoning about Systems, Cambridge University Press, 2004 (ISBN
Table of Contents
1. Introduction and motivation
2. A brief history of mathematical logic
Part I : Propositional Logic
3. Syntax
4. Proof theory
a. Natural deduction
5. Semantics
6. Normal forms
7. SAT solvers
Part II: Predicate Logic
8. Syntax
9. Proof theory
a. Natural deduction
10. Undecidability
11. Expressiveness
12. A Theorem prover
Slides will be provided to the students for download.
Students will be evaluated on the basis of a written examination, complemented with take-home assignments.
Practice class
Yes, a weekly practice class is a mandatory component of the course. | {"url":"https://studiegids.universiteitleiden.nl/courses/30321/logica","timestamp":"2024-11-10T22:34:55Z","content_type":"text/html","content_length":"13118","record_id":"<urn:uuid:d2b8691e-3a57-4a96-a90e-ac474e873026>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00862.warc.gz"} |
A supplemental units package for Unitful.jl, adding units for all currently active currencies, some stocks and commodities, along with tools to perform conversions based on exchange market rates.
This package is currently under development and is not yet registered.
Several assets such as cash, stock, and commodity are created as Unitful objects. A new dimension is created for each asset, along with its reference unit. Being an extension of Unitful.jl, asset
units play nicely along with Unitful's quantities, units, and dimensions.
An ExchangeMarket type is defined as Dict{AssetsPair,Rate}, in which AssetsPair is a tuple of Strings corresponding to the base and quote assets, and Rate contains a positive Unitful.Quantity with
the corresponding quote-ask rate for the pair.
Based on a given ExchangeMarket instance, a conversion can be made from the "quote" asset to the "base" asset. This conversion is implemented as an extended dispatch for Unitful.uconvert.
All defined assets are listed in src/pkgdefaults.jl. Some currency symbols are also defined and are listed in src/currencysymbols.jl.
This package is compatible with Julia ≥ 1.2 and Unitful ≥ 1.0.
Since it has not been registered yet, it can be installed directly from the github repo in the Julia REPL, by typing ] and adding the url for the repo:
pkg> add https://github.com/rmsrosa/UnitfulAssets.jl
Let us see some examples using UnitfulAssets.jl.
As an example, consider a T-shirt with a Julia logo that requires as raw material 1.6 square-meters of 150GSM (grams-per-square-meter) cotton fabric at USD$15 per 44 in x 8 yards bolt; two ounces in
dyes at USD$20 per pound; one ounce of dye fixer at US$8 per five pounds; and 48 yards in stitching thread at USD$19 per 1000 yards. Then, we may calculate the cost of the raw material as follows.
julia> using Unitful, UnitfulAssets
julia> fabric = 15u"USD"/8u"yd"/44u"inch"
0.04261363636363636 USD inch⁻¹ yd⁻¹
julia> dyes = 20u"USD/lb"
20 USD lb⁻¹
julia> fixer = 8u"USD"/5u"lb"
1.6 USD lb⁻¹
julia> thread = 19u"USD"/1000u"yd"
0.019 USD yd⁻¹
julia> cost_per_t_shirt = 1.6u"m^2" * fabric + 2u"oz" * dyes + 1u"oz" * fixer + 48u"yd" * thread;
julia> println("\nThe cost of raw material per t-shirt is of $cost_per_t_shirt")
The cost of raw material per t-shirt is of 6.447611931829924 USD
Thus, the cost of the raw material is about USD$ 6.45 per T-shirt.
Suppose, now, that we have a small business to manufacture the T-shirts above. Besides the raw material expenses, we need eletricity for the sewing machine and the workplace, workers, rent,
insurance, and so on. With that in mind, we assume we have a fixed overhead cost of USD$ 24000 per year for rent and the essential utilities, insurance and things like that; eletricity expenses for
the sewing machine at USD$ 0.13 per kilowatt-hour; and labor at USD$ 10.50 per worker per hour.
In order to implement that, we add two nondimensional units, namely tshirt and worker, then we define the price constants above and two functions that give us the total cost and total material used.
We do this as follows.
julia> using Unitful, UnitfulAssets
julia> module ProductionUnits
using Unitful
using Unitful: @unit
@unit tshirt "tshirt" TShirt 1 false
@unit worker "worker" Worker 1 false
julia> Unitful.register(ProductionUnits);
julia> fabric = 15u"USD"/8u"yd"/44u"inch"
0.04261363636363636 USD inch⁻¹ yd⁻¹
julia> dyes = 20u"USD/lb"
20 USD lb⁻¹
julia> fixer = 8u"USD"/5u"lb"
1.6 USD lb⁻¹
julia> thread = 19u"USD"/1000u"yd"
0.019 USD yd⁻¹
julia> """
Return the amount of each raw material needed to manufacture `n` T-shirts.
The argument `n` must be given in `tshirt` units.
Returns a tuple with the following quantities, respectively:
* The necessary amount of cotton fabric.
* The necessary amount of dye.
* The necessary amount of fixer.
* The necessary amount of thread.
raw_material(n::Unitful.Quantity) = (1.6u"m^2" * n / u"tshirt", 2u"oz" * n / u"tshirt", 1u"oz" * n / u"tshirt", 48u"yd" * n / u"tshirt")
julia> eletricity_price = 0.13u"USD/kW/hr"
0.13 USD hr⁻¹ kW⁻¹
julia> labor_price = 10.50u"USD/worker/hr"
10.5 USD hr⁻¹ worker⁻¹
julia> fixed_cost = 24000u"USD/yr"
24000 USD yr⁻¹
julia> """
manufacturing_cost(n::Unitful.Quantity, t::Unitful.Quantity, tlim::Unitful.Quantity=40u"hr/worker/wk")
Return the cost of manufacturing `n` T-shirts during a time period `t`.
The argument `n` must be given in `tshirt` units, and `t`, in time units.
The optional argument `tlim` is the time limit of work per worker, which defaults to `40u"hr/worker/wk"`.
Return a tuple with the following quantities, respectively:
* The cost of the production, in US Dollars.
* The cost per T-shirt.
* The number of labor hours required to produce `n` t-shirts.
* The minimum number of workers considering the limit given by `tlim`.
* The eletricity required for the whole manufacturing process.
function production_cost(n::Unitful.Quantity, t::Unitful.Quantity, tlim::Unitful.Quantity=40u"hr/worker/wk")
labor_hours = 2u"hr/tshirt" * n
eletricity_spent = 2u"kW * hr/tshirt" * n
total_cost = n * raw_material_price + labor_hours * labor_price + eletricity_spent * eletricity_price + fixed_cost * t
cost_per_tshirt = total_cost / n
min_num_workers = Int(ceil(labor_hours/tlim/t)) * u"worker"
return total_cost, cost_per_tshirt, labor_hours, min_num_workers, eletricity_spent
Now, if we want to see the cost and everything else needed to produce 50 T-shirts per week, we do
julia> production_cost(50u"tshirt", 1u"wk")
(1845.3395288296892 USD, 36.906790576593785 USD tshirt⁻¹, 100 hr, 3 worker, 100 hr kW)
julia> raw_material(50u"tshirt")
(80.0 m², 100 oz, 50 oz, 2400 yd)
So, it costs about USD$ 36.91 per T-shirt in this case.
If we want to reduce the cost per T-shirt, we increase production, aiming for 2000 T-shirts per month, with workers working 44 hours per week:
julia> production_cost(2000u"tshirt", 30u"d", 44u"hr/worker/wk")
(57386.47643039496 USD, 28.693238215197482 USD tshirt⁻¹, 4000 hr, 22 worker, 4000 hr kW)
julia> raw_material(2000u"tshirt")
(3200.0 m², 4000 oz, 2000 oz, 96000 yd)
With that, we are able to reduce the cost per T-shirt to about USD$ 28.69.
1. Add benefit costs for each worker, so that the number of workers properly affects the cost.
2. Add a linear revenue function proportional to the number of T-shirts sold, with proportionality constant being the selling price per T-shirt.
3. Add an affine profit function, which is the difference between the revenue function and the cost function.
4. Find the break-even point, which is the number of T-shirts where profit vanishes, i.e. neiher profit nor loss is incurred.
Here we use the package DifferentialEquations.jl.
Suppose we have a £1,000 in a savings account in a British bank, with an expected variable interest rate for the next ten years given by
and suppose we want to estimate how much we will have after ten years. This can be implemented as follows.
julia> using Unitful, UnitfulAssets, DifferentialEquations
julia> rate(t) = (1.5 + 5(t * u"1/yr")^2 * ( 1 + (t * u"1/yr")^3)^-1)*u"percent/yr"
rate (generic function with 1 method)
julia> f(u,rate,t) = rate(t) * u
f (generic function with 1 method)
julia> tspan = Tuple([0.0,10.0]*u"yr")
(0.0 yr, 10.0 yr)
julia> u₀ = 1000.0u"GBP"
1000.0 GBP
julia> prob = ODEProblem(f,u₀,tspan,rate)
ODEProblem with uType Quantity{Float64,GBPCURRENCY,Unitful.FreeUnits{(GBP,),GBPCURRENCY,nothing}} and tType Quantity{Float64,𝐓,Unitful.FreeUnits{(yr,),𝐓,nothing}}. In-place: false
timespan: (0.0 yr, 10.0 yr)
u0: 1000.0 GBP
julia> savings = solve(prob);
julia> println("After $(savings.t[end]), we expect to have $(savings.u[end])")
After 10.0 yr, we expect to have 1303.6211777402004 GBP
Thus, we expect to have about £1,303.62 in our savings account, after ten years.
For exchanging/trading assets, we provide a few dispatches of a function generate_exchmkt to generate a ExchangeMarket instance from a single Tuple, an Array or a Dict with AssetsPair and Rate
instances. Consider, for example, the following exchange market:
julia> using Unitful, UnitfulAssets
julia> exch_mkt_27nov2020 = generate_exchmkt([
("EUR","USD") => 1.19536, ("USD","EUR") => 0.836570,
("EUR","GBP") => 1.11268, ("GBP","EUR") => 0.898734,
("USD","CAD") => 1.29849, ("CAD","USD") => 0.770125,
("USD","BRL") => 5.33897, ("BRL","USD") => 0.187302
Dict{UnitfulAssets.AssetsPair,UnitfulAssets.Rate} with 8 entries:
AssetsPair("USD", "BRL") => Rate(5.33897 BRL USD⁻¹)
AssetsPair("USD", "EUR") => Rate(0.83657 EUR USD⁻¹)
AssetsPair("EUR", "GBP") => Rate(1.11268 GBP EUR⁻¹)
AssetsPair("GBP", "EUR") => Rate(0.898734 EUR GBP⁻¹)
AssetsPair("USD", "CAD") => Rate(1.29849 CAD USD⁻¹)
AssetsPair("EUR", "USD") => Rate(1.19536 USD EUR⁻¹)
AssetsPair("CAD", "USD") => Rate(0.770125 USD CAD⁻¹)
AssetsPair("BRL", "USD") => Rate(0.187302 USD BRL⁻¹)
Then, the conversions between these currencies can be done as follows:
julia> uconvert(u"BRL", 100u"USD", exch_mkt_27nov2020)
533.8969999999999 BRL
This means that I need about 533.90 BRL to buy 100 USD.
If I have dollars and I want to buy about 500 BRL, we do it the other way around:
julia> uconvert(u"USD", 500u"BRL", exch_mkt_27nov2020)
93.651 USD
Now, if, instead, I have 500 BRL and I want to see how many dollars I can buy with it, I need the same exchange rate as in the first conversion, but in a inverse relation, which is accomplished with
the option argument mode=-1, so that
julia> uconvert(u"USD", 500u"BRL", exch_mkt_27nov2020, mode=-1)
93.65102257551551 USD
Another situation is when we don't have a currency pair in the given exchange market, such as ("EUR", "CAD"), which is not in exch_mkt_27nov2020. In this case we can use an intermediate currency, if
available. In the example market, USD works. The exchange with an intermediate currency is achieved with mode=2:
julia> uconvert(u"CAD", 100u"EUR", exch_mkt_27nov2020, mode=2)
155.21630064 CAD
Now, if we have 150 CAD and want to see how many Euros we can buy with it, we use mode=-2:
julia> uconvert(u"EUR", 150u"CAD", exch_mkt_27nov2020, mode=-2)
96.63933451674102 EUR
There are also a few dispatches of generate_exchmkt to create ExchangeMarket instances from JSON files downloaed from fixer.io and currencylayer.com forex conversion sites. Further conversion
providers should be added in the future. In any case, one can easily add a dispatch for the API of one's choice.
Now, considering again the example above of continuously varying interest rate, suppose that I am actually in Brazil and I want to see the evolution of my savings in terms of Brazillian Reais.
Suppose, also, that this happened ten years ago, so we can use some real exchange rates. In this case, I use an exchange rate time series, as follows.
julia> BRLGBP_timeseries = Dict(
"2011-01-01" => generate_exchmkt(("BRL","GBP") => 0.38585),
"2012-01-01" => generate_exchmkt(("BRL","GBP") => 0.34587),
"2013-01-01" => generate_exchmkt(("BRL","GBP") => 0.29998),
"2014-01-01" => generate_exchmkt(("BRL","GBP") => 0.25562),
"2015-01-02" => generate_exchmkt(("BRL","GBP") => 0.24153),
"2016-01-03" => generate_exchmkt(("BRL","GBP") => 0.17093),
"2017-01-02" => generate_exchmkt(("BRL","GBP") => 0.24888),
"2018-01-02" => generate_exchmkt(("BRL","GBP") => 0.22569),
"2019-01-04" => generate_exchmkt(("BRL","GBP") => 0.21082),
"2020-01-04" => generate_exchmkt(("BRL","GBP") => 0.18784)
julia> uconvert.(u"BRL", 1000u"GBP", values(BRLGBP_timeseries), mode=-1)'
1×10 LinearAlgebra.Adjoint{Quantity{Float64,BRLCURRENCY,Unitful.FreeUnits{(BRL,),BRLCURRENCY,nothing}},Array{Quantity{Float64,BRLCURRENCY,Unitful.FreeUnits{(BRL,),BRLCURRENCY,nothing}},1}}:
2591.68 BRL 2891.26 BRL 4018.0 BRL 4743.38 BRL … 4140.27 BRL 3912.06 BRL 4430.86 BRL 5323.68 BRL
Notice the optional argument mode=-1, so it uses the inverse rate for the conversion. As explained above, this is different than using the rate for the pair ("GBP", "BRL") since we don't want to buy
GBP with BRL, and neither do we want the direct rate for ("BRL", "GBP") since we don't want to buy a specific amount of BRL with GBP. Instead, we want to find out how much BRL we can buy with a given
amount of GBP, so we use the inverse of the rate ("BRL", "GBP").
Exercise: In the Production cost problem, suppose the raw materials come from a foreign country (or countries). Add an exchange market for properly taking into account the dependency of the
production cost, the profit, and the break even point on the foreing currency(ies).
Since the type Rate has been defined with of value of type Number, it is possible to work with any subtype of Number, such as Decimal, FixedDecimals and Rational rates. For example, the following
code generates an ExchangeMarket instance with Rational rates:
julia> exch_mkt_from_dict_and_rationals = generate_exchmkt(Dict([
("EUR","USD") => 119536//100000, ("USD","EUR") => 836570//1000000
Dict{UnitfulAssets.AssetsPair,UnitfulAssets.Rate} with 2 entries:
AssetsPair("USD", "EUR") => Rate(83657//100000 EUR USD⁻¹)
AssetsPair("EUR", "USD") => Rate(7471//6250 USD EUR⁻¹)
For Decimal rates, it is similar:
julia> using Decimals
julia> exch_mkt_from_dict_and_decimals = generate_exchmkt(Dict([
("EUR","USD") => Decimal(1.19536), ("USD","EUR") => Decimal(0.836570)
Dict{UnitfulAssets.AssetsPair,UnitfulAssets.Rate} with 2 entries:
AssetsPair("USD", "EUR") => Rate(0.83657 EUR USD⁻¹)
AssetsPair("EUR", "USD") => Rate(1.19536 USD EUR⁻¹)
Similarly for FixedDecimal rates:
julia> using FixedPointDecimals
julia> exch_mkt_from_dict_and_fixeddecimals = generate_exchmkt(Dict([
("EUR","USD") => FixedDecimal{Int,4}(1.19536), ("USD","EUR") => FixedDecimal{Int,4}(0.836570)
Dict{UnitfulAssets.AssetsPair, UnitfulAssets.Rate} with 2 entries:
AssetsPair("EUR", "USD") => Rate(1.1954 USD EUR⁻¹)
AssetsPair("USD", "EUR") => Rate(0.8366 EUR USD⁻¹)
At some point, I changed the rate from a plain number, such as Rate(1.19536), to a Unitful.Quantity, such as Rate(1.19536 USD EUR⁻¹). With that, the associated unit does not need to be formed each
time during the conversion from one assets to the other. It becomes simply a multiplication in Unitful. This is especially useful when broadcasting, significantly speeding up the conversion of arrays
of currency quantities.
For instance, the example in Continuously varying interest rate in a foreign bank got more than a 100-fold reduction in speed. These were the respective results in the same machine, using
BenchmarkTools, first with the plain rate:
julia> @btime uconvert.(u"BRL", 1000u"GBP", values(BRLGBP_timeseries), mode=-1)'
2.695 ms (1262 allocations: 71.54 KiB)
and the second with the UnitfulQuantity rate:
julia> @btime uconvert.(u"BRL", 1000u"GBP", values(BRLGBP_timeseries), mode=-1)'
21.419 μs (282 allocations: 14.82 KiB)
The predefined list of assets is obtained from SNV - Standards Connect the World, more specifically from the xls file in Current currency & funds code list, which is converted to a csv file and then
to a julia script that calls the macro to generate the assets.
The list is supposed to contain all currencies currently active in the world. It also contains some bonds and commodity metals, such as gold and platinum. The full list of currencies, bonds and
metals defined in this package are given in src/pkgdefaults.jl.
More assets can be added by the user.
Some currency symbols are also defined as Unitful units, namely the US Dollar symbol US\$, equivalent to USD; the Canadian dollar CA\$,equivalent to CAD; the sterling £, equivalent to GBR; the euro
€, equivalent to EUR; and the Brazilian Real R$, equivalent to BRL.
Both the euro and the sterling pound symbols are used as units, so that one may use directly 10u"€" and 1u"£". Both are unicode characters that can be obtained in the REPL or in some proper Julia
environment by tab completion \euro+[TAB] and \sterling+[TAB].
The dollar sign, however, is a reserved sign in Julia, so we do not use it as a unit symbol, but we do use it as an abbreviation. The unit definitions for US\$, CA\$, and R$ are, respectively,
USdollar, CAdollar, and Real, so for instance we have
julia> 1u"USdollar"
1 US$
The list of units with their symbols defined in this package is given in src/currencysymbols.jl
Many symbols are used for different currencies, so we do not attempt to define all symbols here. For instance, the yen sign ¥ is used both for China's Renminbi, with code CNY, also known as Yuan, as
well as for Japan's Yen, with code JPY.
If one desires to include the Yen sign for, say China, then one should create a module and not forget about registering the module with Unitful:
module NewUnits
using Unitful
using UnitfulAssets
@unit ¥ "¥" YuanSign 1.0u"CNY" true
In this case,
One can even have the same sign for the Chinese yuan and the Japanese yen as abbreviation but with different symbols:
module NewUnits
using Unitful
using UnitfulAssets
@unit yuan "¥" YuanSign 1.0u"CNY" true
@unit yen "¥" YenSign 1.0u"JPY" true
In this case, we have
julia> 1u"yen"
1 ¥
julia> 1u"yuan"
1 ¥
I have been doing this mostly for learning purposes, but also hoping that it will turn out to be a useful package for the community.
There are still a number of things to be added:
1. See whether it is possible to display currencies as, say USD$ 10.50, instead of 10.50 USD.
2. See whether it is possible to display 10-fold multiples of a currency in a better way than say kEUR, MEUR, GMEUR, and so on. It would be great to have USD$ 10k, USD$ 10M, and USD$ 10B.
3. Add tools to read exchange markets from web sources other than fixer.io and currencylayer.com.
4. Add an option to directly obtain the exchange/trade rates from the web sources using a given API.
5. Move README examples to a proper Documenter-generated site.
After I started writing this package, I found out about bhgomes/UnitfulCurrency.jl, which, however, has been archived for unknown reasons.
Based on bhgomes/UnitfulCurrency, I modified my initial approach of currency pairs to be Rate("EUR", "USD"), instead of a six-length string "EURUSD", for instance.
bhgomes/UnifulCurrency, however, has a single dimension for all currencies, which has the side-effect of allowing to uconvert different quantities without an exchange market rate, on a one-to-one
basis. Moreover, all currencies are reference units for the same dimension, which might have further side-effects, although I am not sure.
There is no documentation in bhgomes/UnitfulCurrency, and the README is short. It seems, though, that the exchange markets in bhgomes/UnitfulCurrency are defined for each pair, which is different
than our approach, in which an exchange market contains a dictionary of currency pairs, allowing for more flexibility, in my point of view.
Later I also found out about the github organization JuliaFinance, which has the packages JuliaFinance/Assets.jl and JuliaFinance/Currencies.jl, among others. There are some nice concepts there,
distinguishing currencies from assets and cash. Take this excerpt for instance:
"When a currency is thought of as a financial instrument (as opposed to a mere label), we choose to refer to it as "Cash" as it would appear, for example, in a balance sheet. Assets.jl provides a
Cash instrument together with a specialized Position type that allows for basic algebraic manipulations of Cash and other financial instrument positions".
However, JuliaFinance/Assets.jl is not based on Unitful, so none of the examples above can be easily implemented.
Inspired now by JuliaFinance, and upon realizing that what I have implemented are actually assets, not just currencies, I decided to rename my package to UnitfulAssets.jl. Originally, it was named
This package is licensed under the MIT license (see file LICENSE in the root directory of the project). | {"url":"https://juliapackages.com/p/unitfulassets","timestamp":"2024-11-04T02:20:28Z","content_type":"text/html","content_length":"165079","record_id":"<urn:uuid:589c9adf-08dd-4aac-9f9e-7d95e080299c>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00799.warc.gz"} |
Part A: Statistics as a Problem-Solving Process (25 minutes) - Annenberg Learner
Private: Learning Math: Data Analysis, Statistics, and Probability
Classroom Case Studies, Grades K-2 Part A: Statistics as a Problem-Solving Process (25 minutes)
A data investigation should begin with a question about a real-world phenomenon that can be answered by collecting data. After the children have gathered and organized their data, they should analyze
and interpret the data by relating the data back to the real-world context and the question that motivated the investigation in the first place. Too often, classrooms focus on the techniques of
making data displays without engaging children in the process. However, it is important to include children, even very young children, in all aspects of the process for solving statistical problems.
The process studied in this course consisted of four components:
Children often talk about numbers out of context and lose the connection between the numbers and the real-world situation. During all steps of the statistical process, it is critical that students
not lose sight of the questions they are pursuing and of the real-world contexts from which the data were collected.
When viewing the video segment, keep the following questions in mind: See Note 2 below.
• Think about each component of the statistical process as it relates to what’s going on in the classroom: What statistical question are the students trying to answer? How were the data collected?
How are the data organized, summarized, and represented? What interpretations are students considering?
• How does the teacher keep her students focused on the meaning of the data and the data’s connection to a real-world context?
• Thinking back to the big ideas of this course, what are some statistical ideas that these students are beginning to develop?
In this video segment, the teacher, Ellen Sabanosh, applies the mathematics she learned in the Data Analysis, Statistics, and Probability course to her own teaching situation by asking her students
to analyze and interpret the data they collected earlier. (Each child was given two boxes of raisins; the children then counted and recorded the number of raisins in each box.) The children will now
compile their data into a class line plot and discuss the distribution of the data.
Problem A1
Answer the questions you reflected on as you watched the video:
a. What statistical question are the students trying to answer?
b. How did the students collect their data?
c. How did they organize, summarize, and represent their data?
d. What interpretations are the students considering?
e. How does the teacher keep her students focused on the meaning of the data and the data’s connection to a real-world context?
f. What statistical ideas are these students beginning to develop?
Problem A2
As the students examined the data, Ms. Sabanosh asked several times, “What do you notice?” or “What else do you notice?” What are some reasons for asking open-ended questions at these points in the
Problem A3
Ms. Sabanosh gave each student two boxes of raisins for data collection. The students counted the number of raisins in each box separately and recorded both data values on the line plot. What were
some advantages and disadvantages, mathematically and pedagogically, of her decision to give each student two boxes of raisins?
Problem A4
Ms. Sabanosh asked the students to analyze the data when only about half the data had been compiled onto the class line plot. How might early analysis of partial data, such as in this episode,
support students’ evolving statistical ideas?
Note 2
The purpose of the video segments is not to reflect on the methods or teaching style of the teacher portrayed. Instead, look closely at how the teacher brings out statistical ideas while engaging her
students in statistical problem solving. You might want to review the four-step process for solving statistical problems. What are the four steps? What characterizes each step?
Problem A1
a. The question is, “How many raisins are in a box?”
b. The students collected the data by counting the number of raisins in each of the boxes of raisins they were given.
c. Students organized and represented their data by placing blue dots on a class line plot, and they summarized their data by finding the mode.
d. Students interpreted their data by reasoning that smaller numbers meant that they had bigger raisins.
e. The teacher asked the students to interpret their results by relating them back to the context.
f. Some statistical ideas the students touched on are the nature of data, quantitative variables, variation, range, mode as a summary measure of a data set, sampling, and making and interpreting a
line plot.
Problem A2
Asking open-ended questions gives students more opportunities to engage in statistical problem solving and to construct their understanding of statistical ideas.
Problem A3
The main advantage is that giving students two boxes of raisins enlarged the sample, making the results slightly more representative of the population than if students had only been given one box.
However, the overall sample size is still relatively small. One disadvantage in giving students two boxes of raisins is that the teacher and students had to carefully determine ways to organize their
work environment so that each box was counted and recorded separately.
Problem A4
The early analysis of partial data encouraged students to begin thinking and making predictions about how the data might evolve. | {"url":"https://www.learner.org/series/learning-math-data-analysis-statistics-and-probability/classroom-case-studies-grades-k-2/statistics-as-a-problem-solving-process-25-minutes/","timestamp":"2024-11-09T15:44:18Z","content_type":"text/html","content_length":"112072","record_id":"<urn:uuid:a8b07bbc-3ca1-45ed-ae4a-14a781509576>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00124.warc.gz"} |
MassKinetics Tutorial
1. Introduction
Here we will show you in detail how to use the MassKinetics program in a simple case. In this tutorial various MassKinetics window names and menu items are printed red italic bold; parameters to be
selected by underlined bold characters. Detailed description of the theory, terminology, parameters, approximations used in MassKinetics can be found in our recent review (L. Drahos and K. Vékey, J.
Mass Spectrom. 36, 237 (2001)).
We take the example published few years ago in a tutorial article in JMS on ion energetics (K. Vékey, J. Mass Spectrom. 31, 445-463 (1996)) – this is also a good place to start understanding
fundamentals of mass spectrometry. First we show you how to set up a given experiment, next we show you how you can calculate various features for this model reaction. The ‘Tips and Tricks’ section
of our homepage gives you ideas how to use MassKinetics for more advanced calculations. Tips for application of MassKinetics to chemical problems can be found in the ‘Examples’ and ‘References’
sections of this homepage.
Please note that we are in the process of developing and testing the program, and there are likely to be many errors and bugs in it. If you find one, please inform us, preferably sending us the
project file ('mkp' extension) and a short explanation of the bug.
First, you have to start the program (by double clicking on its icon) and accept the license agreement. After that you get to the main window of MassKinetics:
If it is your first application, you have to create a new project (green arrow), otherwise you may open an existing one (red arrow). You may save your MassKinetics project any time, and you may
change its name by "save as". In general, if you want to select or modify an item in the dialog box you have to click or double click on it – then you will either be able to type in the proper value,
or you will be led to a new dialog box which you have to fill out properly.
If you want to learn, how to create a new MassKinetics project, continue with the next section. If you want to learn, how to modify an existing project and use it for various model calculations, go
to the Tips & Tricks section.
2. Create a new project: CID fragmentation (buthyl radical and buthene loss) of buthylbenzene
After you create a new project (green arrow in the previous diagram) you will be able to click on the Setup menu (blue arrow) to define your experiment. This brings up a dialog box and takes you to
the "Comments" tab of this dialog:
In the Comments window you can type (now, or any time later) comments about your MassKinetics project. To specify/modify the MassKinetics project, you have to go through Molecular System, Numerical
Parameters, MS Experiment, Calculation and Results tabs. You can do it in any sequence you prefer, and you can return to a previous one at will. You may save the setup file at any point. To do so you
have to click OK button (red arrow), than in the file menu click "save" or "save as". In fact, it is advisable to save the setup as you progress, possibly using different names (e.g. Test1, Test2
etc.). Clicking on the Molecular System (blue arrow) you get to the "General" section of the most complex page:
Here you select (red arrow) the required reaction type ("parallel reaction"). In future versions of MassKinetics you will have several more options, now you proceed to the Reactions tab (blue arrow).
Here you define critical (~ activation) energy (E0, given in eV units) and the transition state for each reaction channel. To specify or modify values (here and elsewhere) you have to click or double
click on them. After that you can either type in the correct value, or a new dialog box will appear, which you can fill out. Click on the critical energy of the first reaction (corresponding to
propene elimination, blue arrow), and type in 1.0 (E0 in eV units). E0 of the second process (prolyl radical loss, 1.7 eV) is filled out similarly (light blue arrow). To specify the transition states
you have to double-click on them (red and yellow arrows), than another dialog box appears:
You can characterize the Transition State window using the pre-exponential (or frequency) factor. To do so, select the Pre-Exponential Factor (red arrow), and fill out the lg(Ape) value (the
logarithm of pre-exponential factor, blue arrow). For propene elimination it is 11.0, for propyl radical elimination it is 14.0. A more accurate alternative is using transition state frequencies –
see ‘Tips and Tricks’ how to do that. Beside the pre-exponential factor you have to define reaction degeneracy as well (green arrow) – in the example it is 1 (the default value) for both reactions.
When you finished defining the transition state click OK button to accept it, than you return to the Reactions section. When you have defined both transition states you select the Molecules tab:
In the table here you specify the molecular parameters and initial state of the compounds. The first column (red arrow) gives the name of the ion – it is only for your information, and you can rename
them as you wish by clicking on it and typing the new name. Rename Fragment A as ‘propene’, Fragment B as ‘propyl radical’. The second column (blue arrow) gives the molecular mass. For the precursor
(molecular) ion you have to specify it (in Daltons, for buthylbenzene it is 134), for the fragments it is irrelevant. The third column (green arrow) defines the Frequency Model – a list of molecular
normal frequencies (used in RRKM calculations), necessary only for the precursor ion. Double clicking on it will give you a new dialog box:
In the "Set Frequency Model" dialog box you can specify the frequency model by clicking on the "Load Frequency File" button (red arrow), which prompts you to select the required frequency file:
The MassKinetics Demo contains the frequency file of buthylbenzene (Buthylbenzene.frq) in the MassKinetics folder, for other compounds you will have to prepare that in advance. The frequency file is
text file (you can create it using any text editor program) containing all molecular normal frequencies separated by Enter. Note that this file has to have an .frq or txt extension Note that
buthylbenzene has altogether 66 (3N-6) molecular frequencies. After selecting the frequency file you click "Open" Button, which takes you back to the "Set Frequency Model" box, where you can accept
the frequency file clicking the OK button, which takes you back to the Molecules window:
The next column (red arrow) here is the initial concentration (Conc.) – at the time of ion formation the initial concentration of the molecular ion is unity, while it is zero for all other species
(these are the default values). The Int. Energy column (blue arrow) specifies the initial internal energy (necessary to specify only for the precursor). When you double click on it a new window
In the Internal Energy Distribution window you can either specify a fixed, single value, or a thermal distribution. The latter is often a good approximation – the mean internal energy is defined
using certain temperature. For buthylbenzene in EI ionization you may define internal energy distribution to correspond to 1000 K. You click on "Thermal at:" than type in the temperature (1000) which
is given in K (red arrows). Accept it by clicking on OK, than you get back to the Molecules window:
The last column in this dialog box (green arrow) is the initial kinetic energy (Kin. Energy), double clicking on it takes you to the Initial Kinetic Energy Distribution window: This is very similar
to the previous one. For buthylbenzene you can specify fixed at 1 eV (red arrows) and accept it (OK). This takes you back to the Molecules window. You continue to the Radiation tab (red arrow):
For the buthylbenzene example we do not consider radiative transitions, so leave the 'Radiative Energy Transfer (RET) is Considered' checkbox (blue arrow) unchecked, which is the default. (Note that
it is not necessary to open/close the Radiation dialog box, but it is worth checking, if it is correctly set. Proceed to the Collisions tab (green arrow):
In the collision window you can define collision parameters. The checkbox (red arrow) should be checked (default setting) to consider collisional energy transfer. In the right hand side you can
define the name and mass of the collision gas (click/type Ar and 40), the cross section of the collision (25) in square angstroms, efficiency (the fraction of the center of mass collision energy
converted into internal energy (0.06, i.e. 6%), and the shape of CET function (collision energy transfer) – at present only exponential is available. You can proceed than to the next dialog box,
Numerical Parameters:
This box defines the numerical accuracy of the calculations. You have to experiment with the various tolerance limits yourself. You can change the pre-set values by click/type. In most cases you can
leave the Int. Energy Change, Kin. Energy Change and Frequency Bin (red arrows) as they are (1%, 1% and 25 cm^-1). You have to set the Maximum Internal Energy in eV units (to 10.0), and the Number of
Energy Bins (to 300) by click/type (blue arrows). Note that the speed of calculations is inversely related to the square of the number of energy bins. After you finish with this dialog box, you can
go to MS Experiment, which defines the mass spectrometric experiment you want to model:
In the right hand side (red arrow) you have the possible experimental events (for a detailed description see L. Drahos and K. Vékey, J. Mass Spectrom. 36, 237 (2001) ), on the left (blue arrow) your
experimental setup. You can select one item by clicking on it. If you select one on the right hand side you can move it to the left column by clicking the Add button. If you select one on the left,
you can Delete, or Edit it or move it up or down the list (change the sequence. To edit an item you either click on Edit, or double click on the event.
EI ionization followed by CID in a typical triple quadrupole mass spectrometer can be defined using the following parameters: acceleration to 50 eV through 0.01 m distance, 0.50 m long distance to
the collision region with selection of the molecular ion (1^st quad), 0.20 m long collision cell (2^nd quad), 0.50 m long distance through the 3^rd quad to the detector. In the collision region the
pressure of the collision gas is ~ 0.05 Pa (ca. 0.5 torr).
To set up such an experiment select/add events in the following sequence:
1. ion formation (pre-selected)
2. electrostatic acceleration
3. field free flight (through the 1^st quad)
4. ion selection (of m/z 134)
5. collision cascade/collision cell
6. ion selection (through 3^rd quad) followed by detection
When you have selected the proper experimental sequence, these will appear on the left hand side of this dialog box, as indicated in the figure above.
Now double-click on each item to define the specific parameters. Double-click on electrostatic acceleration, which takes you to the following dialog box:
Here you should click on flight length, and specify 0.01 (m); red arrow. Specify the potential difference as 99 eV, (blue arrow) and finish by accepting it (OK), which brings you back to the MS
Experiment dialog box. (Note that this defines kinetic (and therefore the lab-frame collision) energy to 100 eV.) Continue by double-clicking on field free flight (now representing the 1^st quad):
Now you click on flight length, and specify 0.5 (m), and accept it (OK). The next item is ion selection, double clicking brings you to:
You select the Molecular ion ‘buthilbenzene (M)’, accept it (OK), than continue with collision cascade/collision cell:
Here you select flight length, and specify 0.2 (m). Leave the Collisions box (red arrow) selected (you do want to study collisions). Specify the collision gas pressure (0.1, in Pa units, green
arrow). Finally tick the Collisions may change the kinetic energy box (blue arrow). Note that this is the proper approximation, you may want to fix the kinetic energy in specific model calculations
only. Finish by accepting these values (OK), than select the last item (ion selection followed by detection) by double clicking:
Here you have to check flight length, set it to 0.5 (m) and accept it (OK). Now you have finished defining your experiment, and you can continue with the Calculations tab (red arrow):
Here you specify single calculation (blue arrow), and you can switch to the Results tab (red arrow):
Here you can specify what sort of data you want to obtain for results. Let’s assume that you want to know the concentration of the molecular and fragment ions (relative to the initial amount you
specified at Molecular System/Molecules/Conc.); the mean number of collisions; the effective temperature (as defined in the kinetic method) and the survival yield (molecular ion abundance relative to
the sum of all ions). You also want to get the internal energy distribution of the molecular ion at the time of ion formation and before and after the collision cell. Finally, you want to know how
does the mean internal energy change along the mass spectrometer.
In the Results dialog box you select Type to Reactant (blue arrow), Item to buthyilbenzene (green arrow) and check Avg. Number of Collisions and Concentration in the Parameters to Calculate box
(yellow arrow). Next you set Item to propene (first fragment), and check Concentration in the Parameters to Calculate box:
You continue in an analogous manner setting Item to propyl radical, and check Concentration in the Parameters to Calculate box again. Next you set Type to Molecular System (blue arrow), and check
Effective Temperature and Survival Yield in the Parameters to Calculate box (red arrow):
The next step is to ask for the internal energy distribution curves for the molecular ion. To do so, first set Type to Reactant, Item to buthylbenzene (Molecular Ion) and than click on the Add_2D tab
(green arrow), which prompts you to fill out the following dialog box:
Here you set Graph Type to Int. Energy Distribution (red arrow), and set Show Internal Energy Distribution when to "Flight length" "equals", and click/type in "0" (blue, green and yellow arrows,
respectively), than accept this selection by OK. You proceed in a similar manner to obtain the internal energy distribution immediately before the collision cell by clicking the Add_2D tab and
setting again Graph Type to Int. Energy Distribution. Now you have to set Show Internal Energy Distribution when to "Flight Length" "bigger than" "0.5" – which distance corresponds to the beginning
of the collision cell (measured from the ion source). Click Add_2D tab again, and set Graph Type to Int. Energy Distribution, and Show Internal Energy Distribution when to "Flight Length" "bigger
than" "0.7" – which distance corresponds to the end of the collision cell (measured from the ion source). You are still in the Type = Reactant, Item = Molecular Ion case, and you click on the Add_2D
tab again:
You set Graph Type to "Custom", y axis to "Avg. Internal Energy" and x axis to "Flight Length", and accept this choice by clicking OK. Now you have finished the Setup, so you should accept it by
clicking OK at the bottom. This takes you back to the main window:
You should save it by clicking on the icon (blue arrow above) or by clicking on File/Save or File/Save as. Before you do so you may write comments in the Comments dialog box (which you can access
from the Setup box).
Next you can prompt your computer to do the actual calculation, by clicking on Calculate (green arrow).
Calculation takes a few seconds only, you can monitor progress by the blue bar at the bottom right corner. When the calculations are finished, you will get the results in the main window:
You can arrange them as in other Windows applications. The results show a fairly low survival yield (0.277) and a high effective temperature (2150 K), which is mainly the result of the high collision
energy. There are only few collisions (1.24 on average). The concentrations of the molecular ion, propene loss and propyl radical loss are 1.34%, 3.42% and 0.0782%. These are all very small numbers –
which indicates that most of the ions decompose either in the ion source or during flight through the 1^st quadrupole. Those information can be found in the Calculation Result child window:
The first Figure shows the internal energy distribution of ions in the ion source (i.e. at 1000 K, as defined):
The next Figure shows the internal energy distribution of ions before the collision cell:
This indicates that most ions above ca. 1.5 eV internal energy decomposed during mass analysis (in accordance with the low ion yields) and only low internal energy ions enter the collision cell. The
next Figure shows the internal energy distribution at the end of the collision cell:
It shows a higher energy tail in the energy distribution curve, a consequence of collisional activation. (Note that ions which get to internal energy levels above ca. 2 eV decompose so fast, that
they will not be apparent in this energy diagram). The last Figure shows the mean internal energy of the molecular ions as they move through the mass spectrometer:
If you want to copy the diagrams you have to click Edit/Copy, this copies the current diagram onto the clipboard, and you can paste that into other programs (e.g. Word, Powerpoint, etc.) If you want
to export the curve into text file, where you can manipulate them easily, click on the right mouse button over the graph and select Save Data as... menu item. | {"url":"http://proteomics.ttk.hu/masskinetics/","timestamp":"2024-11-11T07:17:22Z","content_type":"text/html","content_length":"153182","record_id":"<urn:uuid:d3789628-939d-4b6e-9ac6-33c4b5ef52c6>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00090.warc.gz"} |
Walks + Hits per Inning Pitched Calculator
What is the WHIP of a pitcher with 12 walks and 32 hits in 6 innings pitched?
Recently Searched:
Formula Explanation of Walks + Hits per Inning Pitched Calculator:
The formula for calculating WHIP is: (Walks + Hits) / Innings Pitched. This formula essentially measures the average number of base runners a pitcher allows per inning.
Detailed Explanation of Walks + Hits per Inning Pitched Calculator:
WHIP is a measure of the average number of base runners a pitcher allows per inning, calculated as (Walks + Hits) / Innings Pitched. This means that WHIP rewards pitchers for allowing fewer walks and
Importance of Walks + Hits per Inning Pitched Calculator:
WHIP is an important statistic in baseball as it is a key component of many other statistics and is a primary measure of a pitcher's effectiveness. A low WHIP means a pitcher is allowing fewer base
runners, which gives their team a better chance to win.
Historical Use of Walks + Hits per Inning Pitched Calculator:
Walks + Hits per Inning Pitched (WHIP) has been used as an official MLB statistic since the 1980s. It is a measure of a pitcher's ability to prevent base runners.
Historical Context:
WHIP has been used in baseball since the 1980s and is a measure of a pitcher's ability to prevent base runners.
Limitations of Walks + Hits per Inning Pitched Calculator:
While WHIP is a useful statistic, it does not take into account the quality of the defensive players behind the pitcher, which can significantly affect the number of hits allowed.
Example of Walks + Hits per Inning Pitched Calculator:
If a pitcher allows 2 walks and 3 hits in 6 innings pitched, their WHIP would be calculated as follows: (2 (walks) + 3 (hits)) / 6 (innings pitched).
Famous Examples of Walks + Hits per Inning Pitched Calculator:
Pedro Martinez holds the record for the lowest single-season WHIP at 0.737 in 2000. Ed Walsh holds the record for the lowest career WHIP at 0.999.
Frequently Asked Questions:
What is a good WHIP?
In professional baseball, a WHIP under 1.30 is generally considered good, and a WHIP under 1.00 is considered excellent.
Why is WHIP important?
WHIP is important because it measures a pitcher's effectiveness at preventing base runners, which is the primary goal of a pitcher.
Who has the lowest career WHIP?
Ed Walsh holds the record for the lowest career WHIP at 0.999.
Similar Calculators
Sources Used:
Walks + Hits per Inning Pitched (WHIP)
Read more | {"url":"https://sportcalcs.com/calculators/whip","timestamp":"2024-11-05T22:47:52Z","content_type":"text/html","content_length":"39836","record_id":"<urn:uuid:097825b8-3d6a-4c6c-b503-902b4a04f1d6>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00284.warc.gz"} |
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complete analytics with interactive assessments. Download App Store & Play Store learning Apps & enjoy 100% functionality with subscriptions! | {"url":"https://mcqlearn.com/math/g7/volume-of-pyramid-mcqs.php","timestamp":"2024-11-08T19:06:49Z","content_type":"text/html","content_length":"67602","record_id":"<urn:uuid:3e0ffe87-f20e-402a-aa0d-69b93fe25136>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00621.warc.gz"} |
Convex sets with the lipschitz fixed point property are compact
Let K be a noncompact convex subset of a normed space X. It is shown that if K is not totally-bounded then there exists a Lipschitz self map f of K with inf||x - f(x)||: x ∈ K} > 0, while if K is
totally-bounded then such a map does not exist, but still K lacks the fixed point property for Lipschitz mappings. It follows that a closed convex set in a normed space has the fixed point property
for Lipschitz maps if and only if it is compact. © 1985 American Mathematical Society.
Publication Title
Proceedings of the American Mathematical Society
Recommended Citation
Lin, P., & Sternfeld, Y. (1985). Convex sets with the lipschitz fixed point property are compact. Proceedings of the American Mathematical Society, 93 (4), 633-639. https://doi.org/10.1090/ | {"url":"https://digitalcommons.memphis.edu/facpubs/4451/","timestamp":"2024-11-08T20:50:12Z","content_type":"text/html","content_length":"32080","record_id":"<urn:uuid:b801cc84-a40c-430c-bbe1-3c839a8e9f61>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00336.warc.gz"} |
- Elementary
Math help
6th grade math knowledge map info
In this video, Salman Khan of Khan Academy demonstrates multiplying and dividing negative numbers.
In this video, Salman Khan of Khan Academy demonstrates adding and subtracting negative numbers.
This page explains how to do basic addition and gives examples for practice of sums.
K-8 interactive lessons
AAA Math features a comprehensive set of interactive arithmetic lessons. Unlimited practice is available on each topic which allows thorough mastery of the concepts. A wide range of lessons
(Kindergarten through Eighth grade level) enables learning or review to occur at each individual's current level. Immediate feedback prevents practicing and learning incorrect methods, which is a
common result of traditional homework and worksheets. Practice can continue as long as desired in a non-threatening format which helps build self-esteem and confidence.
Learning games, educational comics, reading activities, and more.
A functional scientific calculator with the look and feel of a real calculator for teaching how to use a calculator over the web.
A list of divisibility rules and examples of how to apply them. | {"url":"https://www.tutor.com/resources/math/elementary/numbers-facts","timestamp":"2024-11-06T18:57:36Z","content_type":"application/xhtml+xml","content_length":"70596","record_id":"<urn:uuid:bb2368b3-b674-436c-9f69-ff639e043d9f>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00173.warc.gz"} |
Baths 2 by 2 - these sizes are also capable of a lot
Basics of bath ergonomics
In fact, there is only one specific room in the bathhouse; all the rest can be considered as analogues of well-known residential premises. Therefore, here we will only talk about the steam room.
So, what is a steam room and how is the space organized in it?
Most often we are dealing with a steam room , either Russian or Finnish . They are different. They differ not only in temperature and humidity conditions, but also in the methods of achieving them.
This means that the same oven most likely (not always, but often) will not be enough to reproduce both modes. ventilation shelf designs differ .
In addition, the volume of the room is heated non-uniformly; can be distinguished . The dimensions of these zones and the temperature in them depend on the convection of heat flows, and it is
determined by the location of the ventilation holes.
But you will find a lot of material about this on our website; we have covered each topic in detail for both types of baths. If we talk about ergonomics, then its subject will be human convenience,
determined by the anatomical characteristics of a person.
Or we can say this: ergonomics solves the question of how to adapt furniture and other surroundings to our anatomy. Because sitting, lying down, bending over, squatting, etc. It’s convenient for us
only if our dimensions and capabilities are taken into account.
This diagram shows how people usually sit or lie in a bathhouse. You can see that the minimum width of the seat should be at least 40 cm, and 60 cm deep is enough to sit comfortably leaning against
the wall. The seat depth of 90 cm is already enough to sit on it with your legs tucked under you.
So, the Finns would have made three tiers of shelves with a width of 40 cm per “step”. Consequently, the depth of their shelves would take up only 3x40 = 120 cm. Its length would vary depending on
the size of the room and the number of people in the steam room.
Why would they do this? Because in a sauna it is customary to sit on a shelf, and not lie down. They sit and sweat, that’s the whole bath procedure. The temperature reaches 70-90 degrees, humidity -
They pour very little water onto the stones, the steam is thick, like from a kettle, and the ventilation works in such a way that there is always something to breathe - oxygen constantly arrives from
the ventilation and is quickly heated by the stove.
In a Russian bathhouse, shelves 40 cm wide are not suitable . Because it is customary to lie on it. And the other person should float while lying down. The minimum usable width is 60 cm .
But it’s better to start from the size between the paired’s arms, which are freely lying along the body. Only in this case will he really be comfortable lying down. ADVICE! Measure these dimensions
for the widest of the frequent visitors to your bathhouse and make shelves according to it.
A Russian shelf is a lounger, often two-level, the first level of which can be used as a step for a person floating, or can be a seat. Therefore, it can be narrow - 30-40 cm in depth. And the second
level is just wide, under a lying person. Its length, of course, should be appropriate - 180-220 cm.
Shelves in a Russian bath
You may be attracted to options with footrests, but here you need to proceed from the specifics of your bath; try to calculate this option yourself.
On a note! There are many other materials on our website that clarify various nuances regarding steam rooms. You may be interested in learning about the structure of the Russian steam room, its
design, the layout of the bath space as a whole, the optimal dimensions of the steam room, as well as its finishing - lining, processing, insulation, the features of electrical wiring and flooring.
Necessary furniture for a bath
Rest room (dressing room)
The dressing room should look spacious, and the furniture should be arranged so as not to block the passage to another room.
If this is a separate room, then there are no restrictions on the choice of furniture material. And if it is combined with a shower room, preference should be given to moisture-resistant raw
materials with a minimum of textiles.
Often, wooden furniture decorated in country, chalet, and Provence styles is placed in the bathhouse.
For small rooms, a folding table, benches or stools, as well as wooden kitchen corners are suitable.
If there is space, you can put a leather sofa with armchairs and a glass table in the relaxation room, and a rocking chair near the fireplace.
Steam room
The main furniture of the steam room is shelves.
They are made from wood, mostly hardwood. They do not contain resins, which heat up at high temperatures and can cause burns.
The following lumber is well suited for creating shelves:
The shelves should be such that it is comfortable to sit on them.
The recommended sizes are as follows:
• length - from 1.4 to 2 m;
• width - 40-150 cm;
• distance from the floor to the bottom shelf - 20 cm;
• from the top shelf to the ceiling - at least 1 m.
The shelves can be arranged in different ways:
1. Steps. Along the wall in two or three tiers.
2. In the shape of the letter G. The first and last bench are attached to one wall, the middle one to the side. Plus the coupe principle - two shelves go above each other, the top one rises.
The photo above shows examples of different fastenings for shelves in a steam room.
The relationship between area and number of people soaring
The owner of the bathhouse usually has an idea of how many people in the steam room would be most acceptable for him, but usually it is still from 2 to 5 people , then something like a “public
bath” begins. At the same time, this does not impose any real restrictions on the number of guests in your bathhouse - if there are more of them, then they will steam in “shifts.”
In essence, the steam room is designed for the usual number of steamers. But taking into account the fact that the steam room should not be too large - not only for reasons of economy. It is
important to find a balance between the power of the stove, the volume of the room, ventilation (in a sauna), and the quality and quantity of steam (in a Russian bath).
The results of the calculations are transferred to the steam room project.
If we summarize all of the above, it turns out that the minimum size of a bathhouse for 4 people, consisting of three rooms, should be 360x380 centimeters. If you decide to combine a steam
compartment with a washing room. Then the minimum dimensions of the bath should be 210x400 centimeters.
The video included in this article will give you additional insight into its topic.
Optimal steam room sizes
For 2 people
The size of a steam room for 2 people also depends on how exactly they are going to steam. For example, they can only sit on a shelf, then the steam room can generally be tiny. You remember that for
a person sitting, 40-60 cm in depth is enough.
IMPORTANT! The distance from the stove to the shelf can be found in the instructions for the latter, but we will assume that it will not be less than half a meter.
There should also be a gap between the stove and the wall, and the wall itself should be protected by a heat insulator, let’s give it all 10-15 cm. Therefore, 60-75 cm should be added to the
dimensions of the stove, considering that this space is occupied. Let's assume that the oven is 50 by 70 cm. Therefore, it will occupy a “spot” of 110 by 130 or 125 by 145 cm.
The shelves will occupy 40-60-90 cm in seat depth; if they are in two levels, then we multiply them by 2, if three - by 3. They are rarely made the same, so add up the values that you have in
Another option is when there are two people in the steam room, one lies down, the second parries him. Then a shelf 70-90 cm wide and foot rests 30 cm wide are sufficient. A step is needed because the
shelf being steamed should be 5-10 cm higher than the top edge of the stove.
So we calculate that for two people sitting, the width of the shelves will be 80 cm, if there are two levels. For one lying and one floating - 100 cm. Plus the “spot” of the stove (depending on how
it is positioned).
ON A NOTE! They try not to leave empty space on the floor of the steam room. It is better to make the shelves wider if there is a lot of unfilled space.
The third option is when people are just lying down , then the size of the steam room increases. For each person lying down you need 200-220 cm in length and 70-90 cm in width.
Below we show two example diagrams, try making your own based on them:
The optimal size of the steam room is for 2 people sitting.
The same for those lying down.
Note that in the latter case, if the person is not too tall, he can be safely hovered from the bottom step if he lies perpendicular to the position drawn here.
For 2-3 people
If you are hesitating, not knowing how many people you will most often have in the steam room, and are calculating in your mind the size of the steam room for 2-3 people, then we advise you not to do
the “one and a half option” - there seems to be room for a third, but it is not full-fledged and everyone will have to make room a little. Why is this necessary? Make a competent calculation of the
size of the steam room for 3 people, do not add anything - you will get a normal steam room that will not increase your costs too much.
For 3 people
Will one of those in the steam room steam the other? Or will all three sit as if in a sauna?
Based on the fact that one person sitting needs at least 70 cm in width, therefore, two people sitting next to each other are 140 cm, three people are 210 cm. You can arrange the shelves in a corner
so that two people sit on the long side and one on the short side.
If you make a very wide shelf, then three steamers can be located on it as shown in the diagrams below:
The optimal size of the steam room is for 3 people.
In this situation, the top shelf is more intended for lying with bent legs. If you want to stretch out to your full height, then the following scheme is more suitable for this:
Dimensions of the steam room for 3 people.
ADVICE! If you try to arrange the figures perpendicularly, then this shelf length of 180 cm will not suit everyone, so be guided by the height of the tallest of the regular visitors to your
Please note that in these diagrams there is practically no space allocated for the stove; more precisely, it is almost identical to its own area. Only stoves for which the instructions allow such
close placement of the shelves can be installed this way . For example, these could be electric furnaces.
IMPORTANT! But this does not apply to ordinary iron ones! To make shelves close to such a stove, they must be separated by at least a brick screen or a screen made of heat insulator. Or the entire
oven should be in a stone or brick lining.
For 4 people: drawing
By reading the text above, you have already learned how to calculate the amount of space for a seated person. He needs an area of 40x70 cm so as not to feel cramped and on a narrow perch.
Distribute these 280 cm (4x70) shelf lengths yourself in a way that is convenient for you. But remember that this is seated only .
The area that we allocate for one person lying down is 200 (220) cm x 60 (90) cm (in the first case, focus on the tallest, in the second - on the fullest visitor to the steam room, although 90 cm is
recommended by all lovers of the Russian bath). It is clear that you are unlikely to be able to install four sunbeds with such parameters.
Consequently, the more people are planned to be allowed into the steam room at the same time, the greater the likelihood that they will only be able to sit there. But in the case of 4 visitors, there
is one good option: two steamers and two steamers . Then you will have two sunbeds 90 cm wide. But in this case, the size of the steam room for 4 people will be large.
Optimal dimensions of a steam room for 4 people: drawing.
For seated visitors, a shelf 150 cm long for a couple of people and a total width of 80 cm is enough. Place such shelves parallel to each other (as shown above for wide shelves) or in a corner.
For 4-5 people
Below you see two schemes designed for a maximum of 5 people in a steam room. Of course, one or two people can steam there, but the capacity is considered to be maximum.
It is clear from the diagrams that in the first case we again show the structure of the sauna - no indentations from the stove are visible, but look how compact it turned out! 2x2 is the standard
size of a steam room, but here it’s even smaller and can fit 5 people!
Steam room size for 4-5 people.
There is an upper wide shelf of 90 cm, on which people sit with their legs tucked up and perpendicular to the shelves of 60 cm of the same level. Plus two levels below, highlighted in other shades of
In the second case, we can already talk about a Russian bathhouse, if the stove is enclosed and there is an indentation. The shelves are wide, you can comfortably lie down on them; if they are high,
you can pull out benches from below. The size of the room, of course, has become larger, but this is inevitable.
Washing room parameters
Washing area with shower for four visitors.
1. Based on the design of the bathhouse, tanks with cold and hot water or a shower stall and a small pool can be installed in the washing room.
2. In any case, the minimum dimensions for washing are determined. For four users, a standard room without a pool and shower must have sides of at least 200x210 cm.
3. The stove can be placed in two rooms at once. Its firebox can be in the sink, and the heater can be in the steam compartment. A stove tank for heated water should also be located in the washing
4. The sauna stove must be large enough to heat the steam room and prepare the required volume of boiling water. Thus, a compact heater with metal walls is capable of heating a steam room with a
volume of 18 m3 and heating up to 70 liters of water. This is quite enough to serve four users simultaneously.
5. The steam room should be separated from the washing room by a solid partition with a door.
6. You can install windows in the sink. They must be placed at a height of at least 140 cm from the floor level. It is better if it is not the wall opposite the entrance to the room. Otherwise,
drafts will be created. Window units should not be too large. The optimal size is 50x70 cm.
7. The door to the washing room can be installed to an almost standard size - 180x80 cm. The threshold must be made high so that drafts do not pass through the floors.
8. If you are not bothered by the additional price of the equipment, then you can place showers in the sink. At a minimum, each of them will occupy an area of 90×90 cm.
9. If you want to build a pool, keep in mind that the washing volume will increase.
Useful video
But this video simply talks about the structure of a Russian steam room, but it tells it so kindly that we simply couldn’t resist bringing it to your attention | {"url":"https://banny-mir.ru/en/proekty/parilka-2h2.html","timestamp":"2024-11-10T05:14:03Z","content_type":"text/html","content_length":"60986","record_id":"<urn:uuid:be39ee9a-b949-44fb-a72c-3f98824d796e>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00788.warc.gz"} |
Page 3 - Question - Constellations/ Space travel
May 14, 2021
Wait! What? OK, galaxies are thousands, if not millions of light years apart. Stars are typically a few light years apart. Two ships at almost c to meet in a week would have left planets two light
weeks apart. Stars that close are either part of a binary system, or they are really disrupting one another’s Oort clouds, and even their Kuiper belts. Heaven help the small planets.
But, anyway, a week’s travel would not be enough time to accelerate to 0.99c within that week.
But, even if you started sufficiently far apart and have a really long time to try this, it would take such a humongous rocket and prodigious amount of fuel, that it would be impractical. So, this
becomes no more than a thought experiment, and I don’t know the answer.
Jun 1, 2020
I understand that we are travelling relative to CMBR.
But I read that there is no absolute velocity in the universe.
Velocity is only relative, thus "Relativity".
And I read that no moving observer using any machine they carry with them can determine their own absolute velocity.
So what gives? Any ideas?
I just noticed this question...
I’m no expert, but as I see it, it helps to separate velocities between speeds through space and speeds due to expansion (co-moving) of space. Imagine giant clocks in every galaxy of equal size and
mass. They would all tick at the same rate as the MW clock. The CMB has those same clocks. The light from those galaxies and the CMB travel through space and are redshifted.
An absolute velocity would require an absolute reference point. If the universe had a center, then absolute velocities would exist, but there is no center.
Ironically, however, the speed of light is an absolute, which gave us relativity. This speed is measured to be the same regardless of one’s inertial frame. This reveals that other moving reference
frames will present to us their time dilation, and they say the same about our clock rates.
Aug 14, 2020
I just noticed this question...
I’m no expert, but as I see it, it helps to separate velocities between speeds through space and speeds due to expansion (co-moving) of space. Imagine giant clocks in every galaxy of equal size
and mass. They would all tick at the same rate as the MW clock. The CMB has those same clocks. The light from those galaxies and the CMB travel through space and are redshifted.
An absolute velocity would require an absolute reference point. If the universe had a center, then absolute velocities would exist, but there is no center.
Ironically, however, the speed of light is an absolute, which gave us relativity. This speed is measured to be the same regardless of one’s inertial frame. This reveals that other moving
reference frames will present to us their time dilation, and they say the same about our clock rates.
Yep! The speed of light is the absolute of momentum. Now what does that mean for position? Would all positioning be a matter of relativity? No absolute of position? I have an absolute answer, but I'm
looking for relative opinions.
How far can we travel through space, until the constellations are no longer recognizable?
The key is which constellation? Unless you are burning up by a star or being pulled into a black hole. You can see constellations, too many to count
How far can we travel through space, until the constellations are no longer recognizable?
I think we want to travel the edge of the universe but it is so difficult because this universe expanding faster than light speed
Aug 14, 2020
I think we want to travel the edge of the universe but it is so difficult because this universe expanding faster than light speed
The traveler under powered, accelerative, flight, local universe-wise, could match the observed acceleration of nonlocal expansion . . . and exceed it locally (achieving point and point, point to
point, contraction of the local universe which is exactly what any traveler wants).
No traveler ever closes, really, with the frame infinities of the collapsed constant horizon of c, much less reaching .99c. Not unless the traveler is accelerated to it in the black hole of a Large
Hadron Collider-like closed systemic environment by a leveraged external driver. Otherwise, it, the traveler's assumed position and velocity, is nothing more than that light-time history which is
relatively observable to any distant observer distant from a traveler (in a future light cone relative to the observer) no longer anywhere near the observed position or velocity. That observer, in
reality, has no fishing line tether ruling the traveler's ability to contract space and thus time between point and point, point to point, which is positionally inverted eigenvector(?), or an
inverted square matrix(?), and has no local relationship to velocity or the speed of light (which the traveler always traveling a warp space of
distances will always measure the speed of light 300,000kps (if not being locally mashed flat, ship and all, by some black hole super-acceleration)).
(I've often imagined the possibility of 32 feet per second per second per second.... which when closed up in horizon would simply mean nothing more than 32 feet may not be an absolute measurement of
its own space in the universe at large.)
Last edited:
Since the Universe, by definition, is everything there is, you cannot be outside of it. Since there is only one Universe, the term "universes" is illogical.
Having said that,
Isaac Asimov once described what he referred to as the Observable Universe. Consider that the Universe as we know it is expanding. Also consider that the further away a give point is, the faster
it is moving relative to the observer.
And easy way to demonstrate this is to imagine three points, A, B, and C., in a straight line, equidistant apart. From A to B is 1 billion miles, from B to C is 1 billion miles. Then, from A to C
is 2 billion miles. If A is moving away from B at 1000m/s, and B is moving away from C at 1000m/s, then C is moving away from B at 1000m/s,, but moving away from A at 2000m/s. The further away a
give point is, the faster it is moving relative to the observer.
At some point distant from the observer, objects are moving at c relative to the observer, and objects more distant are moving at faster than c relative to the observer. Therefore, any object
moving at more than c relative to the observer can no longer be seen by the observer because that light can never travel faster than the velocity of that object relative to the observer.
Since the distance between objects in an expanding Universe is proportional to time, due to the speed of light, the further an object is from an observer, the older it is compared to the light
that the observer sees from it.
The most distant object we can see will be at the very edge of the Observable Universe. Therefore, since there is no way to tell what is past the edge of the Observable Universe, it is irrelevant
to us.
Forgive my remedial question…but if our universe is, indeed, expanding, then it must be then increasing its size/volume. How can our universe get any larger if there is nothing else past the edge of
our universe. Surely, as we expand, we must be absorbing whatever else is utilizing the space we have yet to expand to, no? Even if there is nothing else taking up any space beyond our universe, then
would it not be correct in thinking of the vast emptiness as an infinite or otherwise area of volume much like our universe, though with nothing (matter of whatever variety) occupying that space? An
empty void is still a tangible space that can be realized.
Nov 19, 2021
The Universe expands equally in all directions as seen from every location within it. There is no edge to it. The Universe is a three dimensional analog to the two dimensional expanding surface of a
balloon. There is no center to a balloon's surface and it expands equally as seen from every spot on it.
How far can we travel through space, until the constellations are no longer recognizable?
To the far end of the universe which is the linear/90 degree opposite of where you started from. So long as it is at the very least equal distance to where you started from. Of course, that
presupposes the constellations are three dimensional non mirror images. | {"url":"https://forums.space.com/threads/constellations-space-travel.29641/page-3","timestamp":"2024-11-12T19:32:00Z","content_type":"text/html","content_length":"187687","record_id":"<urn:uuid:0838b493-5648-413d-b400-f6cc2669ac31>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00524.warc.gz"} |
What is the key advantage of using a Trie for string storage compared to other data structures - ITEagers
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Each semiannual sample represents roughly one-sixth of the establishments for the full six-panel sample plan. Each sample is used in conjunction with the previous five semiannual samples in order to
create a combined sample of approximately 1.1 million establishments. This includes only the most recent data for federal and state government. In this cycle, data collected in May 2020 are combined
with data collected in November 2019, May 2019, November 2018, May 2018, and November 2017.
Of the approximately 1.1 million establishments in the 50 states, the District of Columbia, Guam, Puerto Rico, and the Virgin Islands combined in the initial sample, approximately 1,028,000 were
viable establishments (that is, establishments that are not outside the scope or out of business). Of the viable establishments, approximately 709,000 responded and 319,000 did not, yielding a
69-percent response rate. The response rate in terms of weighted sample employment is 66.3 percent.
Preparing data for estimation
Sample data must be correctly prepared prior to computation of occupational employment and wage estimates and estimates of their variance. Data for sampled nonrespondents are imputed and benchmarking
factors are computed before estimation. This is necessary for sampled data from the current panel to be reweighted to correctly reflect industrial employment levels recorded in the U.S. Bureau of
Labor Statistics Quarterly Census of Employment and Wages (QCEW).
Nonresponse is a chronic problem in virtually all large-scale surveys because it may introduce a bias in estimates if the nonrespondents tend to differ from respondents in terms of the characteristic
being measured. To partially compensate for nonresponse, the missing data for each nonrespondent are imputed using plausible data from responding units with similar characteristics.
Data for sampled nonrespondents are imputed and benchmarking factors are computed before estimation. This is necessary for sampled data from the current panel to be reweighted to accurately reflect
industrial employment levels recorded in the U.S. Bureau of Labor Statistics Quarterly Census of Employment and Wages (QCEW).
Establishments that do not report occupational employment data are called “unit” nonrespondents. Establishments that report employment data but fail to report some or all of the corresponding wages
are called “partial” nonrespondents. Missing data for unit nonrespondents are imputed through a two-step imputation process. Missing data for partial nonrespondents are only imputed through the
second step of the process only.
Step 1) Impute an occupational employment staffing pattern
For each unit nonrespondent, a staffing pattern is imputed using a nearest-neighbor “hot deck” imputation method. The procedure links a responding donor establishment to each nonrespondent. The
nearest-neighbor hot deck procedure searches within defined cells for a donor that most closely resembles the nonrespondent by geographic area, industry, and employment size. Ownership is also used
in the hospital, education, gambling, and casino hotel industries. The procedure initially searches for a donor whose reported employment is approximately the same as the nonrespondent’s frame
employment within the same 5- or 6-digit NAICS (North American Industry Classification System) or NAICS aggregation, state, and ownership. If more than one otherwise equally qualified donor is found,
a donor from a more recent panel will be selected over a donor from an older panel. If the search is unsuccessful, the pool of donors is enlarged in incremental steps by expanding geographic area
and industry until a suitable donor is found. Limits are placed on the number of times a donor can be used.
After a donor has been found, its occupational staffing pattern is used to prorate the nonrespondent’s frame employment by occupation. The prorated employment is the nonrespondent’s imputed
occupational employment.
Step 2) Impute an employment distribution across wage intervals
For each “unit” nonrespondent in step 1 or for each “partial” nonrespondent, impute an employment distribution across wage intervals for occupations without complete wage data. This distribution,
called the wage employment distribution, is imputed as follows:
· Identify the imputation cell for each of the nonrespondent’s occupations. Imputation cells are initially defined by MSA (Metropolitan Statistical Area) / BOS (Balance of State), NAICS 5/6 or
NAICS aggregation, and size class from the most recent panel only. For schools, hospitals, gambling establishments, and casino hotels, cells are further divided by ownership.
· Determine if the imputation cell has enough respondents to compute wage employment distributions. If not, incrementally enlarge the cell until there are enough respondents.
· Use the distributions above to prorate the nonrespondent’s imputed occupational employment across wage intervals. (Or, for partial respondents, use the distributions above to prorate the
reported occupational employment across wage intervals.)
Special procedures
Within the past 3-year cycle, the OEWS had critical nonrespondents that could not be imputed using current OEWS methods. The OEWS employed special imputation procedures that used nonrespondents’
prior staffing patterns. The occupational employment was benchmarked to the current year and the wage distribution was imputed using procedures very similar to the current partial imputation method.
Reweighting for the combined sample
Employment and wage rate estimates are computed using a rolling 6-panel (3-year) sample. Establishments from each panel’s sample are initially assigned weights as if one panel were being used to
represent the entire population. When the samples are combined, each sampled establishment must be reweighted so that the aggregated sample across six panels represents the entire population.
Establishments selected with certainty in the 6-panel cycle are given a weight equal to 1. Noncertainty units are reweighted stratum by stratum. This revised weight is called the 6-panel combined
sample weight. The original single-panel sampling weights are computed so that responses in a stratum could be weighted to represent the entire stratum population. In one common scenario, 6-panel
samples are combined, and all six panels have sample units for a particular stratum. A summation of the single-panel weights would over-represent the population by a factor of 6. Because we do not
want to over-represent the stratum population, the 6-panel combined sample weight of each establishment is set equal to 1/K times its single-panel sampling weight. In general, when 6-panel samples
are combined, a count of the number of panels with at least one unit selected for a given stratum is assigned to K.
Benchmarking to QCEW employment
A sum of ratio-adjusted weighted reported occupational employment is used to calculate estimates of occupational employment. The auxiliary variable for the estimator is the average of the latest May
and November employment totals from the BLS Quarterly Census of Employment and Wages (QCEW). For the May 2020 estimates, the auxiliary variable is the average of May 2020 and November 2019
employment. To balance the states’ need for estimates at differing levels of geography and industry, the ratio estimation process is carried out through a series of four hierarchical employment ratio
adjustments. The ratio adjustments are also known as benchmark factors (BMFs).
The first of the hierarchical benchmark factors is calculated for cells defined by state, MSA/BOS, NAICS 3/4/5/6, and employment size class (4 size classes: 1-19, 20-49, 50-249, 250+). For
establishments in the hospital and education industries (NAICS 622 and 611), the first hierarchical factor is calculated for cells defined by state, MSA/BOS, NAICS 3/4/5/6, employment size class (4
size classes: 1-19, 20-49, 50-249, 250+), and ownership (state government, local government, or privately owned). If a first-level BMF is out of range, it is reset to a maximum (ceiling) or minimum
(floor) value. First-level BMFs are calculated as follows:
h = MSA/BOS by NAICS 3/4/5/6
H = state by NAICS 3/4/5/6
s = employment size classes (1-19, 20-49, 50-249, 250+)
S = aggregated employment size classes (1-49, 50+)
o = ownership (state government, local government, or privately owned)
M = average of May and November QCEW employment
$w i$ = six-panel combined sample weight for establishment i
$x i$[ ]= total establishment employment
$BMF min$ = a parameter, the lowest value allowed for BMF
$BMF max$ = a parameter, the highest value allowed for BMF
$β hs = M hs ∑ i ∈ hs w i x i , β hS = ( M hS / ∑ i ∈ hS w i x i ), β h = ( M h / ∑ i ∈ h w i x i )$
$β hso = M hso ∑ i ∈ hso w i x i , β hSo = ( M hSo / ∑ i ∈ hSo w i x i ), β ho = ( M ho / ∑ i ∈ ho w i x i ), then$
$BM F 1, hs = β hso , if all β hso within h are bounded by BM F
min , BM F max , β hs , if all β hs within h are bounded by BM F min , BM F max , β hSo , if all β hSo within h are bounded by BM F min , BM F max , β hS , if all β hS within h are bounded by BM F
min , BM F max , β ho , if all β ho within h are bounded by BM F min , BM F max , β h , if all β h within h are bounded by BM F min , BM F max , BM F min , if β h <BM F min , BM F max , if β h >BM F
Second-level BMFs are calculated for cells defined at the state, NAICS 3/4/5/6 level by summing the product of combined 6-panel weight and first-level BMF for each establishment in the cell. For
establishments in the hospital, education, gambling, and casino hotel industries (NAICS 622, 611, 7132 and 72112), the first hierarchical of the second-level BMK factor is calculated at the state,
NAICS 3/4/5/6, and ownership level. Second-level BMFs account for the portion of universe employment that is not adequately covered by weighted employment in first-level benchmarking. Inadequate
coverage occurs when “MSA/BOS | NAICS 3/4/5/6 | size class” cells have no sample data or when a floor or ceiling is imposed on first-level BMFs. Second-level benchmarks are calculated as follows:
$β Ho = M Ho ∑ hs ∈ H ∑ i ∈ hs w i x i BM F 1, hs$
$β H = M H ∑ hs ∈ H ∑ i ∈ hs w i x i BM F 1, hs , then$
$BM F 2,H = β Ho , if all β Ho within H are bounded by BM F min , BM F max , β H , if all β
H within H are bounded by BM F min , BM F max , BM F min , if β H <BM F min , BM F max , if β H >BM F max$
Third-level BMFs $(BM F 3,H )$ are calculated at the State, 3-digit NAICS cell level by summing the product of combined 6-panel weight, first-level BMF, and second-level BMF for each establishment in
the cell. The third-level BMF also benchmarks by ownership for the hospital, education, gambling, and casino hotel industries. Fourth-level BMFs$(BM F 4,H )$ are calculated at the State, 2-digit
NAICS cell level by summing the product of final weight, first-level BMF, second-level BMF, and third-level BMF for each establishment in the cell. The fourth-level BMK factor does not benchmark by
ownership. As with second-level BMFs, third- and fourth-level BMFs are computed to account for inadequate coverage of the universe employment.
A final benchmark factor, $BM F i$$BMF i$$BMF i$, is calculated for each establishment as the product of its four hierarchical benchmark factors $( BM F i = BM F 1 * BM F 2 * BM F 3 * BM F 4$). A
benchmark weight value is then calculated as the product of the establishment’s six-panel combined sample weight and final benchmark factor.
Estimation methodology
OEWS produces estimates of occupational employment totals, mean wage rates, and wage rate percentiles. Variance estimates are produced via jackknife random group and Taylor series linearization
Occupational employment estimates
Benchmark factors and the combined 6-panel weights are used to compute estimates of occupational employment. Estimates are produced for cells defined by geographic area and industry group. The total
employment for an occupation in a cell is estimated by taking the product of the reported occupational employment, the 6-panel combined sample weight, and the final benchmark factor for each
establishment in the cell, and summing the product across all establishments in the cell. This sum is the estimate of total occupational employment in the cell.
The equation below is used to calculate occupational employment estimates for an estimation cell defined by geographic area, industry group, and size class.
$X ^ ho = ∑ i ∈ h w
i BM F i x io$
o = occupation
h = estimation cell
$w i$$w i$$w i$ = six-panel combined sample weight for establishment i
= final benchmark factor for establishment i
$x io$$x io$ = employment for occupation o in establishment i
$X ^ ho$ = estimated employment for occupation o in cell h
Wage rate estimation
Two externally derived parameters are used to calculate wage rate estimates. They are:
· the mean wage rates for each of the 12 wage intervals and
· wage updating factors (also known as aging factors)
Wage rates of workers are converted to 1 of 12 consecutive, nonoverlapping wage bands. Individual wage rates are used for federal government and U.S. Postal Service workers. State governments may
report their data as either individual wage rates or interval wage rates.
An illustration
An establishment employs 10 secretaries at the following wage rates:
$9/hour 1 secretary
$10/hour 1 secretary
$12/hour 2 secretaries
$13/hour 2 secretaries
$14/hour 2 secretaries
$16/hour 1 secretary
$17/hour 1 secretary
Wage rates for secretaries, however, are used in the OEWS survey as follows:
Wage interval A (under $9.25/hour) 1 secretary
Wage interval B ($9.25-$11.99/hour) 1 secretary
Wage interval C ($12.00-$15.49/hour) 6 secretaries
Wage interval D ($15.50-$19.74/hour) 2 secretaries
The remaining wage intervals have 0 secretaries.
Because wage rates are grouped into intervals, we must use grouped data formulas to calculate estimates of mean and percentile wage rates. Assumptions are made when using grouped data formulas. For
the mean wage rate formula, we assume that we can calculate the average wage rate for workers in each interval. For the percentile wage rate formula, we assume that workers are evenly distributed in
each interval.
Wage data from the May 2020, November 2019, May 2019, November 2018, May 2018, and November 2017 panels were used to calculate May 2020 wage rate estimates. Wage data from different panels, however,
are not equivalent in real-dollar terms due to inflation and changing compensation costs. Consequently, wage data collected prior to the current survey reference period have to be updated or aged to
approximate that period.
Determining a mean wage rate for each interval
The mean hourly wage rate for all workers in any given wage interval cannot be computed using grouped data collected by the OEWS survey. This value is calculated externally using data from the BLS
National Compensation Survey (NCS). With the exception of the highest wage interval, mean wage rates for each panel are calculated using the most recent NCS data available. The hourly mean wage rate
of the highest wage interval is calculated differently from the others. A weighted average of the previous 3 years’ means is used, instead of just the current year’s mean. Note that the mean hourly
wage rate for interval L (the upper, open-ended wage interval) is calculated without wage data for pilots. This occupation is excluded because pilots work fewer hours than workers in other
Wage aging process
Aging factors are developed from the Bureau’s Employment Cost Index (ECI) survey. The ECI survey measures the rate of change in wages and salaries for 10 major occupational groups on a quarterly
basis. Aging factors are used to adjust OEWS wage data from past survey reference periods to the current survey reference period. The procedure assumes that there are no major differences by
geography, industry, or detailed occupation within the occupational division. The 12th, open-ended, interval is not aged.
Mean hourly wage rate estimates
For data from private sector, local government, and certain state government establishments, the mean hourly wage is calculated as the total weighted hourly wages for an occupation divided by its
weighted survey employment. Estimates of mean hourly wages are calculated using a standard grouped data formula that was modified to use ECI aging factors as:
$R ^ o = ∑ z = t -
5 t ∑ i ∈ z w i BM F i y ^ io X ^ o$
$R ^ ο$$R ^ o$$R ^ o$ = mean hourly wage rate for occupation o
o = occupation
z = panel (or year)
t = current panel
= six-panel combined sample weight for establishment i
= final benchmark factor applied to establishment I
$y ^ io$$y ^ io$ = unweighted total hourly wage estimate for occupation o in establishment $i = u zo ∑ r c zr , (i ∈ z)$
r = wage interval
$X ^ o$$X ^ o$ = estimated employment for occupation o
$x ior$$x ior$ = reported employment for occupation o in establishment i in wage interval r (note that establishment i reports data
for only one panel z or one year z)
$u zo$ = ECI aging factor for panel (or year) z and occupation o
$c zr$$c zr$ = mean hourly wage for interval r in panel (or year) z
In this formula, represents the mean hourly wage of interval r in panel (or year) z. The mean is computed externally using data from the Bureau’s NCS survey.
For wage rate data from federal and certain state government establishments, the hourly wages for an occupation within an establishment are summed to get total wages. Employment for that occupation
within that establishment is also summed to get total employment. The total wages and total employment across all establishments in the occupation for the estimation level of interest are summed.
$Mean Wage = Total Interval Wages + Total
Individual Wages Total Interval Employment + Total Individual Employment$
Percentile hourly wage rate estimates
The p-th percentile hourly wage rate for an occupation is the wage where p percent of all workers earn that amount or less and where (100-p) percent of all workers earn that amount or more. The wage
interval containing the p-th percentile hourly wage rate is located using a cumulative frequency count of estimated employment across all wage intervals. After the targeted wage interval is
identified, the p-th percentile wage rate is then estimated using a linear interpolation procedure. This statistic is calculated by first distributing federal, state, local government, and private
sector workers inside each wage interval. Federal and certain state government workers are distributed throughout the wage intervals according to their wage rates, while certain state government,
local government, and private sector workers are distributed uniformly within each wage interval. Next, workers are ranked from lowest paid to highest paid. Finally, the product of the total
employment for the occupation and the desired percentile is calculated to determine the worker that earns the p-th percentile wage rate.
$p R o = L r + j f r ( U r - L r )$
$pR o$ = p-th percentile hourly wage rate for occupation o
r = wage interval that encompasses $pR o$
$L r$$L r$ = lower bound of wage interval r
$U r$, = upper bound of wage interval r
$f r$ = number of workers in interval r
j = difference between the number of workers needed to reach the p-th percentile wage rate and
the number of workers needed to reach the wage rate
Annual wage rate estimates
These estimates are calculated by multiplying mean or percentile hourly wage rate estimates by a “year-round, full time” figure of 2,080 hours (52 weeks x 40 hours) per year. These estimates,
however, may not represent mean annual pay should the workers work more or less than 2,080 hours per year.
Alternatively, some workers are paid on an annual basis but do not work the usual 2,080 hours per year. For these workers, survey respondents report annual wages. Hourly wage rates cannot be derived
from annual wage rates with any reasonable degree of confidence because the OEWS survey does not collect the actual number of hours worked. Only annual wages are reported for some occupations.
Occupational employment variance estimation
A subsample replication technique called the “jackknife random group” is used to estimate variances of occupational employment. In this technique, each sampled establishment is assigned to one of G
random groups. G subsamples are created from the G random groups. Each subsample is reweighted to represent the universe.
G estimates of total occupational employment $(X ^ hjog )$ (one estimate per subsample) are calculated. The variability among the G employment estimates is a good variance estimate for occupational
employment. The two formulas that follow are used to estimate the variance of occupational employment for an estimation cell defined by geographic area and industry group.
$v X ^ hjo = ∑ g =
1 G X ^ hjog - X ̅^ hjo 2 G(G - 1)$
h = estimation cell defined by geographic area and industry group
j = employment size class (1-19, 20-49, 50-249, 250+)
o = occupation
$v( X ^ hjo )$ = estimated variance of $X ^ hjo$$X ^ hjo$$X ^ hjo$
G = number of random groups
= estimated employment of occupation o in cell h and size class j
$X ^ hjog$= estimated employment of occupation o in cell h, size class j, and subsample g
$X ̅^ hjo$$X ̅^ hjo$ = estimated mean employment for occupation o in cell h and size class j based on the
G subsamples (Note: a finite population correction factor is applied to the terms and )
The variance for an occupational employment estimate in cell h is obtained by the equation:
$v X ^ ho = ∑ j ∈ h
v X ^ hjo$
This sums the variances $v X ^ hjo$ across all size classes j in the cell.
Occupational mean wage variance estimates
Because the OEWS wage data are placed into intervals (grouped), the exact wage of each worker is not used. Therefore, some components of the wage variance are approximated using factors developed
from NCS data. A Taylor Series Linearization technique is used to develop a variance estimator appropriate for OEWS mean wage estimates. The primary component of the mean wage variance, which
accounts for the variability of the observed sample data, is estimated using the standard estimator of variance for a ratio estimate. This component is the first term in the formula that follows:
$v R ^ o = 1 X ^ o 2 ∑ h n ho 1 - f ho n ho - 1 ∑ i ∈ h BM F i w
i 2 q io - q ̅ho 2 + ∑ r θ or 2 σ cr 2 + 1 X ^ o 2 ∑ r ∑ i = 1 n o BM F i w i x ior 2 σ er 2 + 1 X ^ o ∑ r θ or σ ωr 2$
= estimated mean wage for occupation o
$v R ^ o$ = estimated variance of
= estimated occupational employment for occupation o
h = stratum (area/industry/size class)
$n ho$ = number of sampled establishments that reported occupation o in stratum h
$f ho$ = sampling fraction for occupation o in stratum h
= six-panel combined sample weight for establishment i
$n o$ = number of sampled establishments that reported occupation o
$BM F i$ = final benchmark factor applied to establishment i
$q io$$q io$ = $y ^ io - R ^ o x io$ for occupation o in establishment i
= estimated total occupational wage in establishment i for occupation o
= reported employment in establishment i for occupation o
$q ̅ho$ = mean of the quantities for occupation o in stratum h
$θ or$ = proportion of employment within interval r for occupation o
= reported employment in establishment i within wage interval r for occupation o
= Within wage interval r, these are estimated using the NCS and, respectively, represent the variability of
the wage value imputed to each worker, the variability of wages across establishments, and the variability
of wages within establishments.
Reliability of the estimates
Estimates developed from a sample will differ from the results of a census. An estimate based on a sample survey is subject to two types of error: sampling and nonsampling error. An estimate based on
a census is subject only to nonsampling error.
Nonsampling error
This type of error is attributable to several causes, such as errors in the sampling frame; an inability to obtain information for all establishments in the sample; differences in respondents'
interpretation of a survey question; an inability or unwillingness of the respondents to provide correct information; errors made in recording, coding, or processing the data; and errors made in
imputing values for missing data. Explicit measures of the effects of nonsampling error are not available.
Sampling error
When a sample, rather than an entire population, is surveyed, estimates differ from the true population values that they represent. This difference, the sampling error, occurs by chance and its
variability is measured by the variance of the estimate or the standard error of the estimate (square root of the variance). The relative standard error is the ratio of the standard error to the
estimate itself.
Estimates of the sampling error for occupational employment and mean wage rates are provided for all employment and mean wage estimates to allow data users to determine if those statistics are
reliable enough for their needs. Only a probability-based sample can be used to calculate estimates of sampling error. The formulas used to estimate OEWS variances are adaptations of formulas
appropriate for the survey design used.
The particular sample used in the OEWS survey is one of a large number of many possible samples of the same size that could have been selected using the same sample design. Sample estimates from a
given design are said to be unbiased when an average of the estimates from all possible samples yields the true population value. In this case, the sample estimate and its standard error can be used
to construct confidence intervals, or ranges of values that include the true population value with known probabilities. To illustrate, if the process of selecting a sample from the population were
repeated many times, if each sample were surveyed under essentially the same unbiased conditions, and if an estimate and a suitable estimate of its standard error were made from each sample, then:
1. Approximately 68 percent of the intervals from one standard error below to one standard error above the estimate would include the true population value. This interval is called a 68-percent
confidence interval
2. Approximately 90 percent of the intervals from 1.6 standard errors below to 1.6 standard errors above the estimate would include the true population value. This interval is called a
90-percent confidence interval.
3. Approximately 95 percent of the intervals from 2 standard errors below to 2 standard errors above the estimate would include the true population value. This interval is called the 95-percent
confidence interval.
4. Almost all (99.7 percent) of the intervals from 3 standard errors below to 3 standard errors above the estimate would include the true population value.
For example, suppose that an estimated occupational employment total is 5,000, with an associated estimate of relative standard error of 2.0 percent. Based on these data, the standard error of the
estimate is 100 (2 percent of 5,000). To construct a 90-percent confidence interval, add and subtract 160 (1.6 times the standard error) from the estimate: (4,840; 5,160). Approximately 90 percent of
the intervals constructed in this manner will include the true occupational employment if survey methods are nearly unbiased.
Estimated standard errors should be taken to indicate the magnitude of sampling error only. They are not intended to measure nonsampling error, including any biases in the data. Particular care
should be exercised in the interpretation of small estimates or of small differences between estimates when the sampling error is relatively large or the magnitude of the bias is unknown. | {"url":"https://www.bls.gov/opub/hom/oews/calculation.htm","timestamp":"2024-11-02T21:16:40Z","content_type":"text/html","content_length":"186429","record_id":"<urn:uuid:e294391a-ad00-4260-9061-9e1f222f9261>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00104.warc.gz"} |
Normal subgroups are not transitive
The property “is a normal subgroup of” is not transitive.
If A is a subgroup of B, and B is a subgroup of C, then A is a subgroup of C. But the corresponding statement about normal subgroups is false. And there’s a simple example that shows it is false.
We need to find a group C with subgroups A and B such that A is normal in B, B is normal in C, but A is not normal in C.
The subgroup A must have at least two elements, otherwise A would just be the group identity and would then be a normal subgroup of C. The order of a subgroup divides the order of the group, so B
must have at least twice as many elements as A, and C must have twice as many elements as B. So the smallest possible example would be a group with 8 elements and subgroups of order 2 and 4.
We’re in luck, because there’s a group of order 8 that will work, D[8]. This is the group of symmetries of a square under flips and rotations. Let A be the subgroup of flips about the vertical axis
of symmetry. Let B the symmetries you can find by combinations of such flips and 180 degree rotations. You can show that A is normal in B, and B is normal in C.
Now let c be a 90 degree clockwise turn and let a be a flip. You can show that cac^−1 is not a flip or the identity, so A is not a normal subgroup of C.
Related post: A 3,000 page proof (classification of finite simple groups)
2 thoughts on “Normal subgroups are not transitive”
1. Now suppose S is the only normal subgroup of H and H is a normal subgroup of G, is S a normal subgroup of G?
2. Very helpful post! Now mentioned on stackexchange. | {"url":"https://www.johndcook.com/blog/2011/09/07/normal-subgroups/","timestamp":"2024-11-09T06:08:48Z","content_type":"text/html","content_length":"53008","record_id":"<urn:uuid:daed2c6f-f1f8-4f8c-ac42-2364b954a853>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00045.warc.gz"} |
Geographic Position Encoders | Business Blog Articles & Reviews - BB.AIGeographic Position Encoders
Geographic Position Encoders
Understanding techniques for encoding geographic coordinates in a neural network
Photo by CHUTTERSNAP on Unsplash
An inductive bias in machine learning is a constraint on a model given some prior knowledge of the target task. As humans, we can recognize a bird whether it’s flying in the sky or perched in a tree.
Moreover, we don’t need to examine every cloud or take in the entirety of the tree to know that we are looking at a bird and not something else. These biases in the vision process are encoded in
convolution layers via two properties:
Weight sharing: the same kernel weights are re-used along an input channel’s full width and height.Locality: the kernel has a much smaller width and height than the input.
We can also encode inductive biases in our choice of input features to the model, which can be interpreted as a constraint on the model itself. Designing input features for a neural network involves
a trade-off between expressiveness and inductive bias. On one hand, we want to allow the model the flexibility to learn patterns beyond what we humans can detect and encode. On the other hand, a
model without any inductive biases will struggle to learn anything meaningful at all.
In this article, we will explore the inductive biases that go into designing effective position encoders for geographic coordinates. Position on Earth can be a useful input to a wide range of
prediction tasks, including image classification. As we will see, using latitude and longitude directly as input features is under-constraining and ultimately will make it harder for the model to
learn anything meaningful. Instead, it is more common to encode prior knowledge about latitude and longitude in a nonparametric re-mapping that we call a positional encoder.
Introduction: Position Encoders in Transformers
To motivate the importance of choosing effective position encoder more broadly, let’s first examine the well-known position encoder in the transformer model. We start with the notion that the
representation of a token input to an attention block should include some information about its position in the sequence it belongs to. The question is then: how should we encode the position index
(0, 1, 2…) into a vector?
Assume we have a position-independent token embedding. One possible approach is to add or concatenate the index value directly to this embedding vector. Here is why this doesn’t work well:
The similarity (dot product) between two embeddings—after their position has been encoded—should be independent of the total number of tokens in the sequence. The two last tokens of a sequence
should record the same similarity whether the sequence is 5 or 50 words long.The similarity between two tokens should not depend on the absolute value of their positions, but only the relative
distance between them. Even if the encoded indices were normalized to the range [0, 1], two adjacent tokens at positions 1 and 2 would record a lower similarity than the same two tokens later in the
The original “Attention is All You Need” paper [1] proposes instead to encode the position index pos into a discrete “snapshot” of k different sinusoids, where k is the dimension of the token
embeddings. These snapshots are computed as follows:
where i = 1, 2, …, k / 2. The resulting k-dimensional position embedding is then added elementwise to the corresponding token embedding.
The intuition behind this encoding is that the more snapshots are out of phase for any two embeddings, the further apart are their corresponding positions. The absolute value of two different
positions will not influence how out of phase their snapshots are. Moreover, since the range of any sinusoid is the interval [-1, 1], the magnitude of the positional embeddings will not grow with
sequence length.
I won’t go into more detail on this particular position encoder since there are several excellent blog posts that do so (see [2]). Hopefully, you can now see why it is important, in general, to think
carefully about how position should be encoded.
Geographic Position Encoders
Let’s now turn to encoders for geographic position. We want to train a neural network to predict some variable of interest given a position on the surface of the Earth. How should we encode a
position (λ, ϕ) in spherical coordinates—i.e. a longitude/latitude pair—into a vector that can be used as an input to our network?
By Peter Mercator, Public Domain.
Simple approach
One possible approach would be to use latitude and longitude values directly as inputs. In this case our input feature space would be the rectangle [-π, π] × [0, π], which I will refer to as lat/lon
space. As with position encoders for transformers, this simple approach unfortunately has its limitations:
Notice that as you move towards the poles, the distance on the surface of the Earth covered by 1 unit of longitude (λ) decreases. Lat/lon space does not preserve distances on the surface of
the Earth.Notice that the position on Earth corresponding to coordinates (λ, ϕ) should be identical to the position corresponding to (λ + 2π, ϕ). But in lat/lon space, these two coordinates are very
far apart. Lat/lon space does not preserve periodicity: the way spherical coordinates wrap around the surface of the Earth.
To learn anything meaningful directly from inputs in lat/long space, a neural network must learn how to encode these properties about the curvature of the Earth’s surface on its own—a challenging
task. How can we instead design a position encoder that already encodes these inductive biases? Let’s explore some early approaches to this problem and how they have evolved over time.
Early Position Encoders
Discretization-based (2015)
The first paper to propose featurizing geographic coordinates for use as input to a convolutional neural network is called “Improving Image Classification with Location Context” [3]. Published in
2015, this work proposes and evaluates many different featurization approaches with the goal of training better classification models for geo-tagged images.
The idea behind each of their approaches is to directly encode a position on Earth into a set of numerical features that can be computed from auxiliary data sources. Some examples include:
Dividing the U.S. into evenly spaced grids in lat/lon space and using a one-hot encoding to encode a given location into a vector based on which grid it falls into.Looking up the U.S ZIP code that
corresponds to a given location, then retrieving demographic data about this ZIP code from ACS (American Community Survey) related to age, sex, race, living conditions, and more. This is made into a
numerical vector using one-hot encodings.For a chosen set of Instagram hashtags, counting how many hashtags are recorded at different distances from a given location and concatenating these counts
into a vector.Retrieving color-coded maps from Google Maps for various features such as precipitation, land cover, congressional district, and concatenating the numerical color values from each into
a vector.
Note that these positional encodings are not continuous and do not preserve distances on the surface of the Earth. In the first example, two nearby locations that fall into different grids will be
equally distant in feature space as two locations from opposite sides of the country. Moreover, these features mostly rely on the availability of auxiliary data sources and must be carefully
hand-crafted, requiring a specific choice of hashtags, map features, survey data, etc. These approaches do not generalize well to arbitrary locations on Earth.
WRAP (2019)
In 2019, a paper titled “Presence-Only Geographical Priors for Fine-Grained Image Classification” [4] took an important step towards the geographic position encoders commonly used today. Similar to
the work from the previous section, this paper studies how to use geographic coordinates for improving image classification models.
The key idea behind their position encoder is to leverage the periodicity of sine and cosine functions to encode the way geographic coordinates wrap around the surface of the Earth. Given latitude
and longitude (λ, ϕ), both normalized to the range [-1, 1], the WRAP position encoder is defined as:
Unlike the approaches in the previous section, WRAP is continuous and easily computed for any position on Earth. The paper then shows empirically that training a fully-connected network on top of
these features and combining them with latent image features can lead to improved performance on fine-grained image classification benchmarks.
The Double Fourier Sphere Method
The WRAP encoder appears simple, but it successfully encodes a key inductive bias about geographic position while remaining expressive and flexible. In order to see why this choice of position
encoder is so powerful, we need to understand the Double Fourier Sphere (DFS) method [5].
DFS is a method of transforming any real-valued function f (x, y, z) defined on the surface of a unit sphere into a 2π-periodic function defined on a rectangle [-π, π] × [-π, π]. At a high level, DFS
consists of two steps:
Re-parametrize the function f (x, y, z) using spherical coordinates, where (λ, ϕ) ∈ [-π, π] × [0, π]
2. Define a new piece-wise function over the rectangle [-π, π] × [-π, π] based on the re-parametrized f (essentially “doubling it over”).
Notice that the DFS re-parametrization of the Earth’s surface (step 1.) preserves the properties we discussed earlier. For one, as ϕ tends to 0 or ± π (the Earth’s poles), the distance between two
points (λ, ϕ) and (λ’, ϕ) after re-parametrization decreases. Moreover, the re-parametrization is periodic and smooth.
Fourier Theorem
It is a fact that any continuous, periodic, real-valued function can be represented as a weighted sum of sines and cosines. This is called the Fourier Theorem, and this weighted sum representation is
called a Fourier series. It turns out that any DFS-transformed function can be represented with a finite set of sines and cosines. They are known as DFS basis functions, listed below:
Here, ∪ denotes union of sets, and S is a collection of scales (i.e. frequencies) for the sinusoids.
DFS-Based Position Encoders
Notice that the set of DFS basis functions includes the four terms in the WRAP position encoder. “Sphere2Vec” [6] is the earliest publication to observe this, proposing a unified view of position
encoders based on DFS. In fact, with this generalization in mind, we can construct a geographic position encoder by choosing any subset of the DFS basis functions—WRAP is just one such choice. Take
a look at [7] for a comprehensive overview of various DFS-based position encoders.
Why are DFS-based encoders so powerful?
Consider what happens when a linear layer is trained on top of a DFS-based position encoder: each output element of the network is a weighted sum of the chosen DFS basis functions. Hence, the network
can be interpreted as a learned Fourier series. Since virtually any function defined on the surface of a sphere can be transformed using the DFS method, it follows that a linear layer trained on top
of DFS basis functions is powerful enough to encode arbitrary functions on the sphere! This is akin to the universal approximation theorem for multilayer perceptrons.
In practice, only a small subset of the DFS basis functions is used for the position encoder and a fully-connected network is trained on top of these. The composition of a non-parametric position
encoder with a neural network is commonly referred to as a location encoder:
A depiction of a geographic location encoder. Image by author.
Geographic Location Encoders Today
As we have seen, a DFS-based position encoder can effectively encode inductive biases we have about the curvature of the Earth’s surface. One limitation of DFS-based encoders is that they assume a
rectangular domain [-π, π] × [-π, π]. While this is mostly fine since the DFS re-parametrization already accounts for how distances get warped closer to the poles, this assumption breaks down at the
poles themselves (ϕ = 0, ± π), which are lines in the rectangular domain that collapse to singular points on the Earth’s surface.
A different set of basis functions called spherical harmonics have recently emerged as an alternative. Spherical harmonics are basis functions that are natively defined on the surface of the sphere
as opposed to a rectangle. They have been shown to exhibit fewer artifacts around the Earth’s poles compared to DFS-based encoders [7]. Notably, spherical harmonics are the basis functions used in
the SatCLIP location encoder [8], a recent foundation model for geographic coordinates trained in the style of CLIP.
Though geographic position encoders began with discrete, hand-crafted features in the 2010s, these do not easily generalize to arbitrary locations and require domain-specific metadata such as land
cover and demographic data. Today, geographic coordinates are much more commonly used as neural network inputs because simple yet meaningful and expressive ways of encoding them have emerged. With
the rise of web-scale datasets which are often geo-tagged, the potential for using geographic coordinates as inputs for prediction tasks is now immense.
[1] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser & I. Polosukhin, Attention Is All You Need (2017), 31st Conference on Neural Information Processing Systems
[2] A Kazemnejad, Transformer Architecture: The Positional Encoding (2019), Amirhossein Kazemnejad’s Blog
[3] K. Tang, M. Paluri, L. Fei-Fei, R. Fergus, L. Bourdev, Improving Image Classification with Location Context (2015)
[4] O. Mac Aodha, E. Cole, P. Perona, Presence-Only Geographical Priors for Fine-Grained Image Classification (2019)
[5] Double Fourier Sphere Method, Wikipedia
[6] G. Mai, Y. Xuan, W. Zuo, K. Janowicz, N. Lao Sphere2Vec: Multi-Scale Representation Learning over a Spherical Surface for Geospatial Predictions (2022)
[7] M. Rußwurm, K. Klemmer, E. Rolf, R. Zbinden, D. Tuia, Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Network (2024), ICLR 2024
[8] K. Klemmer, E. Rolf, C. Robinson, L. Mackey, M. Rußwurm, SatCLIP: Global, General-Purpose Location Embeddings with Satellite Imagery (2024)
Geographic Position Encoders was originally published in Towards Data Science on Medium, where people are continuing the conversation by highlighting and responding to this story.
Leave a Comment
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Computer Engineering Algorithms - Get Neural Net
Computer Engineering Algorithms
Computer engineering algorithms play a crucial role in designing, developing, and optimizing software and hardware systems. These algorithms enable computers to solve complex problems efficiently,
resulting in improved performance and capabilities of computer systems.
Key Takeaways:
• Computer engineering algorithms are essential for efficient problem-solving in software and hardware systems.
• These algorithms improve the performance and capabilities of computer systems.
• They play a crucial role in several domains like data analysis, artificial intelligence, and networking.
In computer engineering, algorithms serve as a set of instructions or rules that guide the behavior of machines. They help in solving various computational problems and automating repetitive tasks,
making computer systems more efficient and effective.
**Implementations** of algorithms can vary, ranging from simple ones, like sorting or searching algorithms, to complex ones, such as machine learning algorithms used in artificial intelligence.
*Algorithms form the foundation of computer engineering and are necessary for developing innovative technologies.*
The Importance of Computer Engineering Algorithms
Computer engineering algorithms have far-reaching implications in various fields. They are vital in enhancing the performance and functionality of computer systems and enabling advancements in areas
like data analysis, artificial intelligence, networking, and more.
• **Data Analysis**: Algorithms play a key role in analyzing large datasets and extracting meaningful insights. They enable efficient sorting, filtering, and searching of data to identify patterns
and trends.
• **Artificial Intelligence**: Machine learning algorithms empower computer systems to learn from data and make future predictions or decisions. This technology is transforming industries such as
healthcare, finance, and autonomous vehicles.
• **Networking**: Algorithms are crucial for routing data packets efficiently through computer networks, ensuring faster and reliable communication.
Types of Algorithms Used in Computer Engineering
Computer engineering algorithms encompass a wide range of types, each with its unique purpose and characteristics. Some commonly used algorithms include:
1. Sorting Algorithms:
• Bubble Sort
• Insertion Sort
• Quick Sort
• Merge Sort
2. Searching Algorithms:
• Linear Search
• Binary Search
• Breadth-First Search
• Depth-First Search
3. Graph Algorithms:
• Dijkstra’s Algorithm
• Prim’s Algorithm
• Kruskal’s Algorithm
Advancements in Algorithmic Techniques
As technology evolves, computer engineers continuously develop and improve algorithmic techniques to solve complex problems more efficiently. Some notable advancements include:
1. **Parallel Computing**: Algorithms designed for parallel computing enable tasks to be split among multiple processors, reducing processing time by performing computations simultaneously.
2. **Approximation Algorithms**: These algorithms provide approximate solutions to optimization problems, allowing efficient computation when exact solutions are hard to achieve.
3. **Quantum Algorithms**: Quantum computing algorithms harness the power of quantum mechanics to perform complex computations at exponentially faster speeds compared to classical computers.
Algorithm Usage Advantages
Bubble Sort Sorting items in ascending or descending order Simple implementation, works well for small-sized datasets
Quick Sort Sorting large datasets efficiently Fast average case performance, widely used in practice
Algorithm Application Key Features
Linear Search Finding an element in an unordered list Simple to implement, checks every element in sequence
Binary Search Searching in a sorted list Efficient on large datasets, divides search space in half at each step
Algorithm Domain Benefits
Dijkstra’s Algorithm Network routing Finds the shortest path between nodes in a graph
Prim’s Algorithm MST (Minimum Spanning Tree) construction Constructs the minimum spanning tree of a weighted graph
In conclusion, computer engineering algorithms serve as the backbone of software and hardware systems. They enable computers to efficiently solve complex problems, paving the way for technological
advancements in various domains. By continually improving algorithmic techniques and harnessing emerging technologies, computer engineers continue to push the boundaries of what computers can
Common Misconceptions
Misconception 1: Computer Engineering Algorithms are only for programmers
One common misconception about computer engineering algorithms is that they are only relevant to programmers or individuals who work in the field of software development. While computer engineers
play a crucial role in designing and implementing algorithms, these concepts extend far beyond the realm of programming.
• Computer engineering algorithms are used in various fields such as data analysis, artificial intelligence, and network optimization.
• Understanding algorithms can be beneficial for individuals working in cybersecurity or system architecture.
• Even individuals in fields like finance or healthcare can benefit from knowledge of algorithms for tasks such as predicting stock market trends or optimizing patient care.
Misconception 2: Computer Engineering Algorithms are always complex
Some people mistakenly believe that computer engineering algorithms are always complex and difficult to understand. While it is true that certain algorithms can be intricate and require advanced
mathematical knowledge, not all algorithms fall into this category.
• There are simple algorithms used in everyday tasks such as sorting or searching.
• Some algorithms can be implemented without much mathematical complexity.
• Understanding the core principles behind algorithms can make even complex ones more approachable.
Misconception 3: Computer Engineering Algorithms are stagnant
Another misconception is that computer engineering algorithms remain unchanged over time. In reality, the field of computer engineering is constantly evolving, leading to new algorithmic techniques
and approaches.
• A new algorithm can be developed to improve the efficiency or accuracy of a task.
• The emergence of new technologies can also drive the need for novel algorithms.
• The field of computer engineering constantly seeks to address the limitations of existing algorithms.
Misconception 4: Computer Engineering Algorithms always provide the best solution
While algorithms are designed to solve problems efficiently, they do not always provide the best solution in every scenario. It is important to understand the trade-offs of different algorithms
depending on the specific problem being solved.
• Some algorithms may prioritize speed and sacrifice accuracy.
• Other algorithms may focus on minimizing memory usage rather than maximizing speed.
• The selection of an algorithm depends on the specific requirements and constraints of the problem at hand.
Misconception 5: Only experts can understand Computer Engineering Algorithms
Many people believe that only computer engineering experts can understand and apply algorithms effectively. While expertise in the field can certainly provide a deeper understanding, algorithms are
not exclusively reserved for experts.
• Basic knowledge of computer engineering algorithms can be accessible and beneficial for individuals in various fields.
• Online resources, tutorials, and courses make it easier for individuals to learn and apply algorithms in their work or personal projects.
• With practice and exposure, even non-experts can gain proficiency in algorithmic thinking and problem-solving.
Sorting Algorithms
This table illustrates the time complexity of various sorting algorithms.
| Algorithm | Best Case | Average Case | Worst Case |
| Bubble Sort | O(n) | O(n^2) | O(n^2) |
| Selection Sort| O(n^2) | O(n^2) | O(n^2) |
| Insertion Sort| O(n) | O(n^2) | O(n^2) |
| Merge Sort | O(n log n)| O(n log n) | O(n log n) |
| Quick Sort | O(n log n)| O(n log n) | O(n^2) |
| Heap Sort | O(n log n)| O(n log n) | O(n log n) |
Search Algorithms
This table compares the time complexity and use cases of different search algorithms.
| Algorithm | Time Complexity | Use Cases |
| Linear Search | O(n) | Unsorted arrays, small datasets |
| Binary Search | O(log n) | Sorted arrays, large datasets |
| Hashing | O(1) | Large datasets, frequent lookups |
| Breadth First Search| O(V + E) | Graph traversal, finding shortest paths |
| Depth First Search | O(V + E) | Graph traversal, topological sorting |
Graph Algorithms
This table provides an overview of commonly used graph algorithms and their time complexity.
| Algorithm | Time Complexity | Use Cases |
| Dijkstra’s Algorithm | O((V+E) log V) | Finding shortest paths in a weighted graph |
| Bellman-Ford | O(VE) | Finding shortest paths with negative edge weights |
| Prim’s Algorithm | O(E log V) | Finding minimum spanning trees in connected graphs |
| Kruskal’s Algorithm | O(E log E) | Finding minimum spanning trees in disconnected graphs |
String Matching
This table compares the time complexity and use cases of different string matching algorithms.
| Algorithm | Time Complexity | Use Cases |
| Naive Approach | O((n-m+1)m) | Simple pattern matching, small pattern, small text |
| Knuth-Morris-Pratt | O(n + m) | Efficient pattern matching, large pattern, large text |
| Boyer-Moore | O(nm) | Efficient pattern matching, small pattern, large text |
| Rabin-Karp | O((n-m+1)m) | Pattern matching, handling multiple patterns simultaneously |
Hashing Algorithms
This table presents different hashing algorithms and their collision resolution techniques.
| Hashing Algorithm | Collision Resolution Technique |
| Division (Modulo) | Separate Chaining |
| Multiplication | Linear Probing |
| Folding | Quadratic Probing |
| Cyclic Redundancy Check (CRC)| Double Hashing |
Compression Algorithms
This table showcases popular compression algorithms and their compression ratios.
| Compression Algorithm | Compression Ratio |
| Huffman Coding | High |
| Lempel-Ziv-Welch (LZW)| Moderate |
| Run-Length Encoding | Low |
| Burrows-Wheeler | Variable |
Machine Learning Algorithms
This table presents different machine learning algorithms and their applications.
| Algorithm | Applications |
| Linear Regression | Predicting numerical values |
| Decision Trees | Classification, regression, and feature selection |
| K-Nearest Neighbors | Pattern recognition, recommendation systems |
| Support Vector Machines | Binary classification, image recognition |
| Neural Networks | Image recognition, natural language processing |
Cryptographic Algorithms
This table illustrates various cryptographic algorithms and their purposes.
| Algorithm | Purpose |
| AES (Advanced Encryption Standard) | Symmetric encryption |
| RSA (Rivest-Shamir-Adleman) | Asymmetric encryption |
| SHA-256 (Secure Hash Algorithm) | Hashing |
| Diffie-Hellman Key Exchange | Key exchange between two parties |
| Elliptic Curve Cryptography | Public key cryptography using elliptic curves |
Network Routing Algorithms
This table compares different network routing algorithms based on their efficiency and suitability.
| Algorithm | Efficiency | Suitability |
| Distance Vector Protocol | Less efficient, prone to slow convergence | Small networks, limited resources |
| Link State Protocol | Efficient, fast convergence | Large networks, robust infrastructure |
| Border Gateway Protocol (BGP)| Scalable, supports complex routing policies | Internet backbone, autonomous systems |
| Open Shortest Path First (OSPF)| Efficient, supports multiple metrics | Enterprise networks, non-hierarchical topologies |
Computer engineering algorithms play a vital role in the design and optimization of computer systems. They are fundamental in solving complex problems efficiently, be it sorting, searching,
graph-related tasks, or data compression. Various algorithms cater to specific needs, offering different time complexities and suitable application domains. From string matching to cryptographic
algorithms, different areas of computer engineering benefit from diverse algorithmic solutions.
Frequently Asked Questions
What is the role of algorithms in computer engineering?
Algorithms play a crucial role in computer engineering by providing step-by-step instructions for solving problems or performing specific tasks. They are the building blocks for developing efficient
and reliable software and hardware solutions.
How are algorithms designed and developed?
Algorithms are designed and developed through careful analysis of the problem at hand. Computer engineers utilize various techniques, such as divide and conquer, dynamic programming, and
backtracking, to devise efficient algorithms that can solve the problem optimally and meet the desired requirements.
What are some common types of algorithms used in computer engineering?
There are various types of algorithms used in computer engineering, including sorting algorithms (such as Quicksort and Merge Sort), search algorithms (such as Binary Search), graph algorithms (such
as Dijkstra’s algorithm), and many more. Each type serves a specific purpose and has its own set of advantages and limitations.
How do algorithms impact the performance of computer systems?
The efficiency and quality of algorithms directly impact the performance of computer systems. Well-designed algorithms can significantly improve the speed, memory usage, and overall responsiveness of
a system. On the other hand, inefficient algorithms may lead to poor performance and resource wastage.
What is algorithm analysis?
Algorithm analysis is the process of evaluating the efficiency and scalability of an algorithm. It involves analyzing factors like time complexity, space complexity, and big-O notation to determine
how an algorithm performs as the input size increases. This analysis helps computer engineers select the most suitable algorithm for a given problem.
How can one optimize algorithms for better performance?
There are several techniques to optimize algorithms for better performance. These include algorithmic improvements (e.g., reducing time or space complexity), parallelization (utilizing multiple
processors or threads), caching, and utilizing specialized hardware or parallel architectures. The choice of optimization technique depends on the specific problem and available resources.
How are algorithms tested and validated?
Algorithms are tested and validated using rigorous testing methodologies. Computer engineers create test cases that cover a wide range of scenarios to ensure correct behavior and accuracy.
Furthermore, mathematical proofs and formal methods are often employed to validate the correctness and efficiency of an algorithm.
What role does data structure play in algorithms?
Data structures provide a way to organize and store data efficiently, allowing algorithms to operate on that data. Choosing the right data structure is crucial for algorithm design, as it directly
impacts the algorithm’s performance. Common data structures include arrays, linked lists, stacks, queues, trees, and hash tables.
How are algorithms used in specific areas of computer engineering?
Algorithms find applications in numerous areas of computer engineering. In artificial intelligence and machine learning, algorithms are used to train models and make predictions. In network
optimization, algorithms are employed to find the shortest paths. In cryptography, algorithms are utilized for secure communication and data protection, while in image processing, algorithms are used
for tasks like segmentation and object recognition.
What career options are available in computer engineering algorithms?
Professionals with expertise in computer engineering algorithms can pursue various career options such as software engineer, algorithm engineer, data scientist, machine learning engineer, research
scientist, and many more. These roles often involve designing, implementing, and optimizing algorithms to solve complex problems in different domains. | {"url":"https://getneuralnet.com/computer-engineering-algorithms/","timestamp":"2024-11-10T05:19:53Z","content_type":"text/html","content_length":"68055","record_id":"<urn:uuid:3b55d814-798b-47ca-af43-d415340ed5df>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00291.warc.gz"} |
Relativistic electron acceleration in focused laser fields after above-threshold ionization
Electrons produced as a result of above-threshold ionization of high-[Formula presented] atoms can be accelerated by currently producible laser pulses up to GeV energies, as shown recently by Hu and
Starace [Phys. Rev. Lett. [Formula presented] 245003 (2002)]. To describe electron acceleration by general focused laser fields, we employ an analytical model based on a Hamiltonian, fully
relativistic, ponderomotive approach. Though the above-threshold ionization represents an abrupt process compared to laser oscillations, the ponderomotive approach can still adequately predict the
resulting energy gain if the proper initial conditions are introduced for the particle drift following the ionization event. Analytical expressions for electron energy gain are derived and the
applicability conditions of the ponderomotive formulation are studied both analytically and numerically. The theoretical predictions are supported by numerical computations.
All Science Journal Classification (ASJC) codes
• Condensed Matter Physics
• Statistical and Nonlinear Physics
• Statistics and Probability
Dive into the research topics of 'Relativistic electron acceleration in focused laser fields after above-threshold ionization'. Together they form a unique fingerprint. | {"url":"https://collaborate.princeton.edu/en/publications/relativistic-electron-acceleration-in-focused-laser-fields-after--2","timestamp":"2024-11-08T22:54:36Z","content_type":"text/html","content_length":"50585","record_id":"<urn:uuid:a213d9dc-be22-4bce-9e32-3b9a853f0f24>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00483.warc.gz"} |
Numerical study of heat transfer losses by mixed convection and surface thermal radiation in an open cavity receiver for a solar tower system
The thermo solar central tower power plants are complex systems that consist of a heliostats field which provide a high solar concentrated flux to a thermal receiver located in the top of a tower.
With this type of technology, a fluid moving in the thermal receiver can be heated up to 800 to 1200 K, so a conventional thermodynamic cycle can be operated to generate electricity. In the city of
Hermosillo, in the northern state of Sonora, Mexico, the National Autonomous University of Mexico in agreement with the University of Sonora is developing this type of technology for a plant of 2 MWt
with an array of 80 heliostats (36 m2 each one) and a tower of 32 m height. Therefore, an appropriated thermal receiver has to be designed. Considering above, in this work the numerical results of
heat transfer losses by mixed convection and surface thermal radiation in an open cavity receiver considering variable fluid properties are presented. Numerical calculations were performed in a
cavity of 1 m width, 2 m height and 2 m depth, considering (a) only natural convection and (b) mixed convection, both with surface thermal radiation. The temperature difference between the hot wall
and the bulk fluid (ΔT) was 600 K. The kt-εt standard turbulence model was solved for the turbulent convection and for the surface thermal radiation the discrete ordinate method was applied. The
simulations were conducted in steady state and the fluid properties were considered as a function of temperature. The software of computational fluid dynamics FLUENT 6.3 was used. The velocity,
temperature fields and heat transfer coefficients were obtained. The total heat transfer losses increases 37.5% when the mixed convection is considered.
Nota bibliográfica
Publisher Copyright:
© 2014 The Authors Published by Elsevier Ltd.
Profundice en los temas de investigación de 'Numerical study of heat transfer losses by mixed convection and surface thermal radiation in an open cavity receiver for a solar tower system'. En
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[Solved] Two finite sets have m and n elements. The number of s... | Filo
Two finite sets have and elements. The number of subsets of the first set is 112 more than that of the second set. The values of and are, respectively.
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Since, number of subsets of a set containing m elements is 112 more than the subsets of the set containing elements.
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Question Text Two finite sets have and elements. The number of subsets of the first set is 112 more than that of the second set. The values of and are, respectively.
Updated On Oct 10, 2023
Topic Sets
Subject Mathematics
Class Class 11
Answer Type Text solution:1 Video solution: 4
Upvotes 394
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The positive semidefinite Grothendieck problem with rank constraint
Given a positive integer n and a positive semidefinite matrix A = (A_{ij}) of size m x m, the positive semidefinite Grothendieck problem with rank-n-constraint is (SDP_n) maximize \sum_{i=1}^m \sum_
{j=1}^m A_{ij} x_i \cdot x_j, where x_1, ..., x_m \in S^{n-1}. In this paper we design a polynomial time approximation algorithm for SDP_n achieving an approximation ratio of \gamma(n) = \frac{2}{n}\
left(\frac{\Gamma((n+1)/2)}{\Gamma(n/2)}\right)^2 = 1 - \Theta(1/n). We show that under the assumption of the unique games conjecture the achieved approximation ratio is optimal: There is no
polynomial time algorithm which approximates SDP_n with a ratio greater than \gamma(n). We improve the approximation ratio of the best known polynomial time algorithm for SDP_1 from 2/\pi to 2/(\pi\
gamma(m)) = 2/\pi + \Theta(1/m), and we determine the optimal constant of the positive semidefinite case of a generalized Grothendieck inequality.
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Cavitation Abrasive Surface Finishing (CASF) for the Improvement of Fatigue Strength of Titanium Alloy Ti6Al4V Manufactured by Electron Beam Melting
Science Update
in Vol. 21 - September Issue - Year 2020
Cavitation Abrasive Surface Finishing (CASF) for the Improvement of Fatigue Strength of Titanium Alloy Ti6Al4V Manufactured by Electron Beam Melting
Fig. 1: Aspect of as-built specimens
Fig. 2: Effect of compressive residual stress, roughness and hardness on S-N curve
Fig. 3: Aspect of surface treated by CASF
Fig. 4: Mechanical properties changing with processing time of CASF
Fig. 5: Improvement of fatigue properties by CASF
Fig. 6: Relationship between experimental fatigue life and estimated fatigue life
Additive manufactured AM metallic materials are attractive materials because of minimum leading time and less materials loss, as components are formed directly from CAD data. The biggest problem on
applications of AM metals is the fatigue strength, which is nearly half of the bulk metals [1-3]. One the of effective methods to improve fatigue strength is the application of mechanical surface
treatments such as shot peening, cavitation peening [4, 5] and laser peening [6]. It has been reported that shot peening, cavitation peening and submerged laser peening improved the fatigue strength
of AM metals [1-3].
In the case of as-built metals manufactured by powder bed melting AM method, surface roughness is considerably large due to un-melted particles (see Fig. 1). And also, when the depth of the surface
defect of as-built specimen was measured by the fractured surface using SEM, it was about 200 μm for a direct metal laser sintering DMLS and an electron beam melting EBM [3]. Thus, in order to remove
surface roughness and surface defects of AM metals with mechanical surface treatment, cavitation abrasive surface finishing (CASF) was proposed by the collaboration work with Tohoku University and
Boeing, and it was demonstrated that CASF improved the fatigue strength of titanium alloy manufactured by EBM [7].
At CASF, a cavitating jet with abrasive was used for the mechanical surface treatment. The impact at cavitation bubble collapse, which is generated by the cavitating jet, introduces compressive
residual stress- and work-hardening, and the abrasive, which is accelerated by the jet, is removed from the surface at the same time.
In the present paper, the enhancement of the fatigue strength of titanium alloy Ti6Al4V manufactured by EBM using CASF was demonstrated [7].
Material and Methods
The tested material was titanium alloy Ti6Al4V, and the fatigue specimens were manufactured by EBM. The thickness of the specimen was 2 ± 0.2 mm. The averaged diameter of the used particle size at
EBM was about 75 μm. The spot size of the electron beam was 0.2 mm in diameter and the stacking pitch was 90 μm. After the EBM process, the specimens were heat-treated at 1208 K under vacuum for 105
minutes then cooled in argon gas. After that, aging was carried out at 978 K under vacuum for 2 hours, then cooled in argon gas.
The fatigue specimens were treated by a cavitating jet with abrasive. The details of CASF are in the reference [7]. The injection pressure was 62 MPa and the nozzle throat diameter for the jet was
0.64 mm. The specimen was placed in the recess and treated by moving the nozzle at constant speed v = 18 mm/s with the number of scan n. After each scan, the nozzle was moved 1.2 mm sideways. In this
study, n was 1, 2, 3 and 4. As the length of the specimens was 90 mm, the processing time, tp, was 5 s, 10 s, 15 s and 20 s for n was 1, 2, 3 and 4 respectively. The specimens with and without CASF
were tested by a conventional Schenk-type displacement-controlled plane bending fatigue tester at R = ―1. In order to find out the optimum processing time, the number of cycles to failure Nf at
constant bending stress σa = 330 MPa was calculated as follows. As the displacement-controlled plane bending fatigue tester was used, the number of cycles at σa = 330 MPa was unknown. Thus, the
number of cycles at σa ≈ 330 MPa of specimen was obtained experimentally, then Nf 330 was calculated from Nf at σa ≈ 330 MPa by the following procedure. It was assumed that the S-N curve for low
cycle fatigue of non-treated specimens is described by Eq. (1), and that for treated specimens is described by Eq. (2), where, c1, c2 and c3 are constants. Thus, these S-N curves were parallel to
each other.
Nf 330 for treated specimens was given by Eq. (3).
In the present experiment, c1 and c2were obtained from the 3 experimental data of non-treated specimens by the least-squares method, and c3 was obtained from c1 and the one experimental data for each
treated specimen with σa ≈ 330 MPa respectively.
From Eq. (3), we get
From Eq. (4), we obtain Nf 330. In order to investigate the fatigue strength, the fatigue tests were carried out under the optimum processing time that maximizes the fatigue life, Nf 330. A test was
considered a runout when a specimen exceeded 107 cycles and stopped.
As the plane bending fatigue strength was affected by the surface mechanical properties such as roughness, hardness and residuals stress, the surface roughness Rz was measured by a stylus type
profilometer and the surface hardness HR15T was measured using a Rockwell superficial tester. The surface residuals stress was measured by a 2D-XRD method.
As the compressive residual stress σCR reduces applied stress, the fatigue life was improved as shown in Fig. 2. The a and b are constants. The surface hardness HR15T also improves fatigue life. On
the other hand, the surface roughness Rz reduces fatigue life as shown in Fig. 2. The fatigue life Nf3 at σa can be estimated from σCR, HR15T and Rz by Eq. (5).
Aspect of Specimen Surface Treated by CASF
Figure 3 shows the aspect of specimen surface treated by CASF. At tp = 5 s, most unmelted particles were removed from the surface, but the wavy pattern was observed. At tp = 10 s, the wavy pattern
became shallow, however, several surface defects were observed at the surface. The surface defects were removed from the surface at tp = 15 s, and the imbricate pattern became deeper at tp = 20 s.
In order to find out the optimum processing time, Fig. 4 reveals the number of cycles to failure Nf 330 at σa = 330 MPa changing with processing time. In Fig. 4, the surface hardness HR15T, the
surface compressive residual stress σCR and the surface roughness Rz are also shown. The Nf 330, HR15T, σCR and Rz were normalized by the maximum values, 230,647 cycles, 92.2, 271.2 MPa and 108.8 μm
respectively. The Nf 330 had a maximum at tp = 15 s. The HR15Tincreased with tp and was saturated, and the σCR increased with tp. The Rz decreased with tp and had a minimum at tp = 15 s, then
increased at tp = 20 s. As mentioned, HR15T and σCR improved fatigue properties, and Rz decreased the fatigue life. This is why Nf 330 had a maximum at tp = 15 s.
Improvement of Fatigue Strength by CASF
Figure 5 illustrates the result of the plane-bending fatigue test to reveal the effect of CASF on the fatigue properties of as-built Ti6Al4V manufactured by EBM. The specimens were treated by CASF at
tp = 15 s. As shown in Fig. 4, the fatigue life Nf 330 of as-built specimen was enhanced 2.46 times by CASF. When the fatigue strength at 107 was calculated by using Little’s method [8], it was 169 ±
8 MPa for as-built and 280 ± 10 MPa for CASF. Namely, CASF improved the fatigue strength at 107 about 66 % by CASF compared with the non-treated specimens.
In order to confirm the estimation method of fatigue life by Eq. (5), Fig. 6 shows the relationship between the experimental fatigue life Nf exp at σa ≈ 330 MPa and the estimated fatigue life Nf est
at σa = 330 MPa. Both values were normalized by the number of cycles to failure of the specimen treated by CASF at tp = 15 s. The constants a and b in Eq. (5) were obtained by the least squares
method using the five points of Fig. 4. When the correlation coefficient for the five data points was calculated, it was 0.958, meaning that the probability of non-correlation was less than 1.0%;
thus, it can be concluded that the fatigue strength of AM Ti6Al4V treated by CASF was estimated from HR15T, σCR and Rz.
In order to demonstrate the enhancement of fatigue strength of additive manufactured AM metallic materials by cavitation abrasive surface finishing CASF, the titanium alloy Ti6Al4V manufactured by
electron beam-melting EBM was treated by CASF and tested by a displacement-controlled plane fatigue test. It was revealed that the fatigue strength at 107 considering the surface roughness was
improved 1.66 times by CASF compared with that of the as-built specimen.
This work was partly supported by JSPS KAKENHI Grant Number 17H03138, 18KK0103 and 20H02021.
[1] P. Edwards, A. O'Conner, and M. Ramulu, "Electron Beam Additive Manufacturing of Titanium Components: Properties and Performance," Journal of Manufacturing Science and Engineering, Trans. ASME,
vol. 135, no. 6, paper no. 061016, pp. 1-7, 2013.
[2] H. Soyama, and Y. Okura, "The Use of Various Peening Methods to Improve the Fatigue Strength of Titanium Alloy Ti6Al4V Manufactured by Electron Beam Melting," AIMS Materials Science, vol. 5, no.
5, pp. 1000-1015, 2018.
[3] H. Soyama, and F. Takeo, "Effect of Various Peening Methods on the Fatigue Properties of Titanium Alloy Ti6Al4V Manufactured by Direct Metal Laser Sintering and Electron Beam Melting," Materials,
vol. 13, no. 10, paper no. 2216, pp. 1-26, 2020.
[4] H. Soyama, "Key Factors and Applications of Cavitation Peening," International Journal of Peening Science and Technology, vol. 1, no. 1, pp. 3-60, 2017.
[5] H. Soyama, "Cavitation Peening: A Review," Metals, vol. 10, no. 2, paper no. 270, pp. 1-27, 2020.
[6] H. Soyama, "Comparison between the Improvements Made to the Fatigue Strength of Stainless Steel by Cavitation Peening, Water Jet Peening, Shot Peening and Laser Peening," Journal of Materials
Processing Technology, vol. 269, pp. 65-78, 2019.
[7] H. Soyama, and D. Sanders, "Use of an Abrasive Water Cavitating Jet and Peening Process to Improve the Fatigue Strength of Titanium Alloy 6Al-4V Manufactured by the Electron Beam Powder Bed
Melting (EBPB) Additive Manufacturing Method," JOM, vol. 71, no. 12, pp. 4311-4318, 2019.
[8] R. E. Little, "Estimating the Median Fatigue Limit for Very Small Up-and-Down Quantal Response Tests and for S-N Data with Runouts," ASTM STP, vol. 511, pp. 29-42, 1972.
Hitoshi Soyama (Ph.D. in Eng.) Professor
Department of Finemechanics
Tohoku University
6-6-01 Aoba, Aramaki, Aoba-ku, Sendai
980-8579, Japan
E-mail: soyama@mm.mech.tohoku.ac.jp
Daniel G. Sanders (Dr. Eng.)
Senior Technical Fellow
The Boeing Company, Seattle, WA, USA.
Affiliate Professor
The University of Washington
Seattle, WA, USA. | {"url":"https://www.mfn.li/archive/issue_view/2052/1","timestamp":"2024-11-06T06:05:30Z","content_type":"text/html","content_length":"37161","record_id":"<urn:uuid:e98de531-81c5-4fd4-b5ce-a7d4bf504e2f>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00430.warc.gz"} |
Math Talk Sparks Success: Middle School Learning in Focus - Cognitive Cardio MathCognitive Cardio Math
Whether you are a well-versed teacher or just starting out, you know that middle schoolers love to talk—a lot. Like L O V E to talk! Talking is tricky because while you want them to listen and
participate during teaching time you also want them involved. I learned a long time ago about the power of using those things that interest my students in the classroom. And if talking is the goal
then I want to use it to make our math class better. I plan my lessons with the goal of allowing my middle schoolers to socialize and talk…about math. Math Talk to the rescue!
But math talks are about so much more than curbing the chattiness in class. Math talks are a powerful teaching tool that helps take our students deeper in their mathematical thinking. Math talk is
more than just talking about the answer to a homework problem. Let’s see just how powerful math talks can be.
Understanding Math Talk
Math talk isn’t your ordinary run-of-the-mill teaching method. Nope, it’s like a secret doorway to a new level of learning. Here’s the deal: math talk is about getting your students to share what
they’re thinking about math.
Imagine a classroom where everyone’s actively participating. Where one student shares the answer to a problem and explains how they solved it. This is followed up with “I agree, but I solved the
problem with a different strategy. This conversation includes statements like “I disagree because. . .” and “I solved by. . .”
This is a far different math class than the one where a student raises their hand and says “x=7” and then everyone moves on to the next problem.
With math talk, students are sharing and learning from one another. They are guiding each other through a deeper understanding of math. It turns learning into a group adventure where they are not
just a passenger. They’re driving the ship and taking ownership of their learning!
The Importance of Math Talk
Math talks are a brain workout for your learners. When students get into math talk mode, their brain thinks hard and in different ways. They are no longer just sharing an answer, they have to go
deeper. They share their thinking, why they chose a strategy, or what questions they had about a problem. Students get to figure things out, ask questions, and explore ideas with their classmates.
Their brains go on a ride full of twists and turns that help them see things from all angles. And that is the road of learning that leads to mastery.
But that’s not all – math talk is the secret recipe for becoming a pro communicator. We can all think of a kiddo who sometimes has this fantastic idea in their head but is unsure how to put it into
words. Math talk fixes that. Using prompts, your students learn how to explain their thoughts clearly, listen to others, and even debate (in a friendly way, of course). Those are skills that they’ll
use everywhere, not just in math class.
Now, remember how sometimes math can feel like staring at a wall of weird symbols and numbers? Well, math talk demolishes that wall. Instead of the focus being on the formula, the formula becomes a
tool – part of the math strategy or thinking. Students dive into thinking about math in a different way. One where understanding the concept at its roots is the priority. When this happens we get a
glimpse into how their math brains work.
I’ve seen students explain their thinking and strategy in a way that I never could. Students giving “aha” moments to other students. Students showing that they truly understand the math concept, not
just the ability to get a correct answer.
Benefits of Math Talk in Middle School
Using math talk in middle school classrooms packs some amazing perks. First up, it’s a training ground for listening. You know how you’ve got those students with cool ideas? Math talk teaches the
class to be all ears and respect their thoughts. It’s another form of teamwork!
Speaking of teamwork, math talk turns your class into a real squad. No more thinking of math as a one-person show. It’s all about joining forces, sharing ideas, and realizing that math is way more
fun when we tackle it together.
Math talk isn’t just about numbers – it’s a treasure chest of life skills. When your class dives into these math discussions, they’re becoming pro-problem-solvers. They’re thinking on their feet,
looking at concepts from all angles, and coming up with clever solutions.
Math talks also help students develop flexible thinking skills. As with most things in life, in math, there is often more than one way to get to the right answer. Math talk is a tool that allows
students to share their strategies and thinking. And sometimes, it is a different way of thinking that opens the mental blocks of other students.
The Role of Sentence Starters
Math talk starts with sentence starters. They are like the “secret sauce” that makes math talks so effective and accessible by all students.
Let’s place ourselves in our students’ shoes. Imagine you’re in class and itching to jump into a math discussion but don’t have much confidence in your math ability. Instead of sitting quietly and
not participating, math talk sentence starters help you. They give you a roadmap to kick off your thoughts. So, instead of going, “Uhh, I think, maybe the answer is…” you can confidently say, “I
think the answer might be… because…” or “I solved by…” It’s like having a short script for great conversations.
These sentence starters give students a framework for sharing their thoughts and reasoning. They are like a roadmap that helps students know where to go as they talk math.
And guess what? That makes your students and their ideas stand tall and strong, like a champion of math discussions.
These little prompts are courage boosters for students who are unsure about participating in discussions. They make it easier to dive in and share ideas without those jitters. It’s having a friendly
push to be more confident. So, start math talk in your classroom by teaching kids about the power of sentence starters.
Math Talk Notes Doodle Wheel
Want to know how I introduce math talk, its importance, and its benefits to my students? I use the Math Talk Doodle Wheel! Before we ever jump into using math talk in the classroom I take the time to
teach my students about math talk. And. . . I equip them with those very important sentence starters that they will need.
Picture this: You’ve got this awesome wheel full of math talk prompts for your students to use to engage in class discussions. They can stash it in their notebook and use it all year. The wheel is
split into different sections that are like magic keys to fantastic math talk:
1. If you’re nodding along with someone’s idea, you’ve got “I agree because…”
2. If you’ve got a different take, there’s “I disagree because…”
3. When you’re showing off your problem-solving skills, it’s “I solved by…”
4. Feeling like you’re missing a puzzle piece? Say, “To solve, I need to know…”
5. When explaining how you got an answer, say, “Answer is correct because…”
6. When you’ve got your own strategy, go with “I chose this strategy because…”
In each section, students can add related sentence starters to help find just what they need to explain their thoughts.
Introducing Math Talk to Students
Start with Simple Practice
I love to jump in and practice math talk as we fill in the wheel. Using some extremely easy problems like 2+2=4 or 2+2=5 students can practice finding the sentence starter and explaining their
thinking. While this may seem silly to them, it gets them using the sentence starters. Why? Because there is not risk. The students all know that 2+2=4 and that 2+2 does not equal 5. So we start by
taking the new and unknown math out of the process.
This allows my students to really focus on the sentence stems and how to take the math knowledge they already have and put it into words.
Another fun way to get students to practice thinking and explaining their thinking is with “Which One Doesn’t Belong?” pictures. I love these pictures because there really is no wrong answer!
Students get to use their analytical thinking and math knowledge to explain which picture they feel doesn’t belong. And they are right – and so is their neighbor with a different answer.
The goal of using these pictures with math talk is to get students comfortable with explaining their thinking. And. . . these pictures also lay a foundation for them understanding that there is more
than one way of thinking.
Not sure what I’m talking about? Take a look at these examples (from wodb.ca) and ask yourself “Which one doesn’t belong?”:
Begin Using Them Everyday
Once students have had some chance to practice using these math sentence starters, then we begin using them with our daily math lessons.
At first, I have students take out their math wheel. We do a quick reminder of the sentence stems and how to choose one. And occasionally, I will even help guide students to a sentence starter when
they forget. I also love having these math talk sentence stems posted in the classroom.
After introducing math talk, stick with it. At first, it might feel hard, disjointed or even a little frustrating. But don’t stop – push through. Remember that you are likely teaching a new skill to
your students. It is going to take some practice for students to learn how to stop giving an answer and start explaining their answer.
It doesn’t take long for math talk and these sentence starters to become the norm in the math classroom.
Save for Later!
Remember to save this post to your favorite math Pinterest board to return to when you need help enhancing your classroom discussions with math talk! | {"url":"https://cognitivecardiomath.com/cognitive-cardio-blog/math-talk/","timestamp":"2024-11-06T14:22:08Z","content_type":"text/html","content_length":"240857","record_id":"<urn:uuid:df66c47a-0a27-43fa-b0c9-99ae149ea1dc>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00115.warc.gz"} |
PPT - Collisions: Momentum and Impulse PowerPoint Presentation, free download - ID:5075499
1. Collisions: Momentum and Impulse SC.CE.05.01
2. The product of the mass of an object and its velocity Momentum = “p” p=mv If mass is constant, then a change of momentum equals mass times change in velocity: Δp=mΔv A vector quantity Vector
means… Momentum:
3. Impulse: • The average force multiplied by its time interval of action • Impulse = FΔt • A vector quantity • Vector means…
4. Simply stated: • Impulse = change in momentum =Δp
5. Impulse/momentum principle: • The impulse acting on an object produces a change in momentum of the object that is equal both in magnitude and direction to the impulse
6. For example: m=7kg v=2m/s p=14kg ×m/s m=0.07kg v=200m/s p=14 kg × m/s
7. Conservation of Momentum: • When the net external force acting on a system is zero, the total momentum of the system is conserved • In other words: the momentum before a collision will equal the
momentum after a collision • When internal forces are equal (but opposite), momentum is conserved
9. Example: • A 100 kg fullback moving straight downfield with a velocity of 5 m/s collides head on with a 75 kg defensive back moving in the opposite direction with a velocity of -4m/s. The
defensive back hangs on to the fullback, and the two players move together after the collision. • a. What is the initial momentum of each player? • b. What is the total momentum of the system? •
c. What is the velocity of the two players immediately after the collision?
10. Fullback: m = 100 kg v = 5 m/s p = ? p = mv p = Defensive back: m = 75 kg v = -4 m/s p = ? p = mv p = Example (cont’d) a: What is the initial momentum of each player?
11. b. What is the total momentum of the system? • p total = p fullback + p defensive back • p total = 500 kg x m/s + -300 kg x m/s • p total = 200 kg x m/s
12. v=? m= 100 kg + 75 kg =175 kg p=mv So: v=p/m v= 200 kg x m/s 175 kg c. What is the velocity of the two players immediately after the collision?
13. Types of Collisions: Perfectly Inelastic to Perfectly Elastic Extend your knowledge of momentum and energy conservation!
14. Perfectly Inelastic Collisions • A collision in which the objects stick together after colliding • No bounce • If p is known before collision for both objects, we simply add them together to get
final p • A lot of the original kinetic energy is transformed • Example: railroad car coupling, two balls of clay, a football tackle
15. Partially Inelastic • Some kinetic energy is transformed
16. Elastic • No kinetic energy is transformed • Atoms collide without “spending” energy
17. When pool balls collide: • Most collisions are elastic: both momentum and kinetic energy are conserved • Momentum is transferred from the cue ball to the target ball • We can determine the
velocity of both balls after collision • It gets tricky when multiple pool balls are involved, but I know you can do it!
18. Collisions at an Angle Oh geez, here we go…
19. An Inelastic Two-Dimensional Collision: • Remember that momentum is a vector quantity? • Now our football players from Monday are running perpendicular to one another 583 kg x m/s p2=300kg x m/s
31° p1=500kg x m/s
20. Elastic Two-Dimensional Collisions • Initial kinetic energy = 1/2mv2 must also equal the sum of the kinetic energies | {"url":"https://www.slideserve.com/mareo/collisions-momentum-and-impulse","timestamp":"2024-11-07T14:21:32Z","content_type":"text/html","content_length":"86005","record_id":"<urn:uuid:a48984f2-13e3-480a-b6b1-96bac9516e86>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00548.warc.gz"} |
What does statTarget offer statistically
The statTarget has two basic sections. The first section is Signal Correction (See the shiftCor function). It includes ‘Ensemble Learning’ for QC based signal correction. For example, QC-based random
forest correction (QC-RFSC). In addition, Combat is also provided for QC free datasets. The second section is Statistical Analysis (See the statAnalysis function). It provides comprehensively
computational and statistical methods that are commonly applied to analyze Omics data, and offers multiple results for biomarker discovery.
Section 1 - Signal Correction provide ensemble learning method for QC based signal correction. i.e. QC based random forest signal correction (QC-RFSC) that fit the QC data, and each metabolites in
the true sample will be normalized to the QC sample.
Section 2 - Statistical Analysis provide features including Data preprocessing, Data descriptions, Multivariate statistics analysis and Univariate analysis.
Data preprocessing : 80-precent rule, sum normalization (SUM) and probabilistic quotient normalization (PQN), glog transformation, KNN imputation, median imputation, and minimum imputation.
Data descriptions : Mean value, Median value, sum, Quartile, Standard derivatives, etc.
Multivariate statistics analysis : PCA, PLSDA, VIP, Random forest, Permutation-based feature selection.
Univariate analysis : Welch’s T-test, Shapiro-Wilk normality test and Mann-Whitney test.
Biomarkers analysis: ROC, Odd ratio, Adjusted P-value, Box plot and Volcano plot.
Running Signal Correction (the shiftCor function) from the GUI
Meta File
Meta information includes the Sample name, class, batch and order. Do not change the name of each column
1. Class: The QC should be labeled as NA
2. Order : Injection sequence.
3. Batch: The analysis blocks or batches
4. Sample: Sample name should be consistent in Meta file and Profile file. *The QC sample name should be tagged with “QC”.
(See the example data)
Profile File
Expression data includes the sample name and expression data.(See the example data)
Modified n precent rule function. A variable will be kept if it has a non-zero value for at least n precent of samples in any one group. (Default: 0.8)
The QC-based signal correction (i.e. QC-RFSC.) or QC-free methods (Combat)
Number of trees to grow for QC-RFSC (Default: 500) .
The parameter for imputation method.(i.e., nearest neighbor averaging, “KNN”; minimum values, “min”; Half of minimum values “minHalf” median values, “median”. (Default: KNN)
## Examples Code
datpath <- system.file('extdata',package = 'statTarget')
samPeno <- paste(datpath,'MTBLS79_sampleList.csv', sep='/')
samFile <- paste(datpath,'MTBLS79.csv', sep='/')
shiftCor(samPeno,samFile, Frule = 0.8, MLmethod = "QCRFSC", imputeM = "KNN")
# Combat for QC-free datasets
samPeno2 <- paste(datpath,'MTBLS79_dQC_sampleList.csv', sep='/')
shiftCor_dQC(samPeno2,samFile, Frule = 0.8, MLmethod = "Combat")
See ?shiftCor for off-line help
Running Statistical Analysis (the statAnalysis function) from the GUI
Stat File
Expression data includes the sample name, group, and expression data with long format.
Modified n precent rule function. A variable will be kept if it has a non-zero value for at least n precent of samples in any one group. (Default: 0.8)
The parameter for imputation method.(i.e., nearest neighbor averaging, “KNN”; minimum values, “min”; Half of minimum values “minHalf”; median values, “median”. (Default: KNN)
The parameter for normalization method (i.e probabilistic quotient normalization, “PQN”; integral normalization , “SUM”, and “none”).
Generalised logarithm (glog) transformation for Variance stabilization
(Default: TRUE)
Scaling Method
Scaling method before statistic analysis i.e. PCA or PLS(DA). Center can be used for specifying the Center scaling. Pareto can be used for specifying the Pareto scaling. Auto can be used for
specifying the Auto scaling (or unit variance scaling). Vast can be used for specifying the vast scaling. Range can be used for specifying the Range scaling. (Default: Pareto)
Permutation times
The number of permutation times for cross-validation of PLS-DA model, and variable importance of randomforest model
PCs in the Xaxis or Yaxis: Principal components in PCA-PLS model for the x or y-axis (Default: 1 and 2)
The number of variables with top permutation importance in randomforest model. (Default: 20)
To show the name of sample or groups in the Score plot. (Default: TRUE)
Multiple testing
This multiple testing correction via false discovery rate (FDR) estimation with Benjamini-Hochberg method. The false discovery rate for conceptualizing the rate of type I errors in null hypothesis
testing when conducting multiple comparisons. (Default: TRUE)
Volcano FC
The up or down -regulated metabolites using Fold Changes cut off values in the Volcano plot. (Default: > 2 or < 0.5)
Volcano Pvalue
The significance level for metabolites in the Volcano plot.(Default: 0.05)
## Examples Code
datpath <- system.file('extdata',package = 'statTarget')
file <- paste(datpath,'data_example.csv', sep='/')
statAnalysis(file,Frule = 0.8, normM = "NONE", imputeM = "KNN", glog = TRUE,scaling = "Pareto")
Generation of input file (the transX function)
The transX function is to generate statTarget input file formats from Mass Spectrometry Data softwares, such as XCMS, MZmine2, SIEVE and SKYLINE. ‘?transX’ for off-line help.
## Examples Code
datpath <- system.file('extdata',package = 'statTarget')
dataXcms <- paste(datpath,'xcmsOutput.tsv', sep='/')
dataSkyline <- paste(datpath,'skylineDemo.csv', sep='/')
See ?transX for off-line help
Random Forest classfication and variable importance measures
rForest provides the Breiman’s random forest algorithm for classification and permutation-based variable importance measures (PIMP-algorithm).
## Examples Code
datpath <- system.file('extdata',package = 'statTarget')
statFile <- paste(datpath,'data_example.csv', sep='/')
getFile <- read.csv(statFile,header=TRUE)
# Random Forest classfication
rFtest <- rForest(getFile,ntree = 10,times = 5)
# Prediction of test data using random forest in statTarget.
predictOutput <- predict_RF(rFtest, getFile[1:19,3:8])
# Multi-dimensional scaling plot of proximity matrix from randomForest.
# Create plots for Gini importance and permutation-based variable Gini importance measures.
See ?rForest for off-line help
Once data files have been analysed it is time to investigate them. Please get this info. through the GitHub page. (URL: https://stattarget.github.io)
Results of Signal Correction (ShiftCor)
statTarget -- shiftCor
-- After_shiftCor # The fold for intergrated and corrected data
-- shift_all_cor.csv # The corrected data of samples and QCs
-- shift_QC_cor.csv # The corrected data of QCs only
-- shift_sample_cor.csv # The corrected data of samples only
-- loplot # The fold for quality control images
-- *.pdf # The quality control images for each features
-- Before_shiftCor # The fold for raw data
-- shift_QC_raw.csv # The raw data of QCs
-- shift_sam_raw.csv # The raw data of samples
-- RSDresult # The fold for variation analysis and quality assessment
-- RSD_all.csv # The RSD values of each feature
-- RSDdist_QC_stat.csv # The RSD distribution of QCs in each batch and all batches
-- RSD distribution.pdf # The RSD distribution plot in samples and QCs of all batches
-- RSD variation.pdf # The RSD variation plot for pre- and post- signal correction
Luan H., Ji F., Chen Y., Cai Z. (2018) statTarget: A streamlined tool for signal drift correction and interpretations of quantitative mass spectrometry-based omics data. Analytica Chimica Acta. dio:
Luan H., Ji F., Chen Y., Cai Z. (2018) Quality control-based signal drift correction and interpretations of metabolomics/proteomics data using random forest regression. bioRxiv 253583; doi: https://
Dunn, W.B., et al.,Procedures for large-scale metabolic profiling of serum and plasma using gas chromatography and liquid chromatography coupled to mass spectrometry. Nature Protocols 2011, 6, 1060.
Luan H., LC-MS-Based Urinary Metabolite Signatures in Idiopathic Parkinson’s Disease. J Proteome Res., 2015, 14,467.
Luan H., Non-targeted metabolomics and lipidomics LC-MS data from maternal plasma of 180 healthy pregnant women. GigaScience 2015 4:16 | {"url":"http://master.bioconductor.org/packages/release/bioc/vignettes/statTarget/inst/doc/statTarget.html","timestamp":"2024-11-05T18:51:51Z","content_type":"text/html","content_length":"645631","record_id":"<urn:uuid:2bfa73f7-b31d-47f8-bac2-59bd47b031ab>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00527.warc.gz"} |
islessequal(3m) [sunos man page]
islessequal(3m) [sunos man page]
islessequal(3M) Mathematical Library Functions islessequal(3M)
islessequal - test if x is less than or equal to y
#include <math.h>
int islessequal(real-floating x, real-floating y);
The islessequal() macro determines whether its first argument is less than or equal to its second argument. The value of islessequal(x, y)
is equal to (x) <= (y); however, unlike (x) <= (y), islessequal(x, y) does not raise the invalid floating-point exception when x and y are
Upon successful completion, the islessequal() macro returns the value of (x) <= (y).
If x or y is NaN, 0 is returned.
No errors are defined.
The relational and equality operators support the usual mathematical relationships between numeric values. For any ordered pair of numeric
values, exactly one of the relationships (less, greater, and equal) is true. Relational operators can raise the invalid floating-point
exception when argument values are NaNs. For a NaN and a numeric value, or for two NaNs, just the unordered relationship is true. This
macro is a quiet (non-floating-point exception raising) version of a relational operator. It facilitates writing efficient code that
accounts for quiet NaNs without suffering the invalid floating-point exception. In the SYNOPSIS section, real-floating indicates that the
argument is an expression of real-floating type.
See attributes(5) for descriptions of the following attributes:
| ATTRIBUTE TYPE | ATTRIBUTE VALUE |
|Interface Stability |Standard |
|MT-Level |MT-Safe |
isgreater(3M), isgreaterequal(3M), isless(3M), islessgreater(3M), isunordered(3M), math.h(3HEAD), attributes(5), standards(5)
SunOS 5.10 1 Nov 2003 islessequal(3M)
Check Out this Related Man Page
islessequal(3M) Mathematical Library Functions islessequal(3M)
islessequal - test if x is less than or equal to y
c99 [ flag... ] file... -lm [ library... ]
#include <math.h>
int islessequal(real-floating x, real-floating y);
The islessequal() macro determines whether its first argument is less than or equal to its second argument. The value of islessequal(x, y)
is equal to (x) <= (y); however, unlike (x) <= (y), islessequal(x, y) does not raise the invalid floating-point exception when x and y are
Upon successful completion, the islessequal() macro returns the value of (x) <= (y).
If x or y is NaN, 0 is returned.
No errors are defined.
The relational and equality operators support the usual mathematical relationships between numeric values. For any ordered pair of numeric
values, exactly one of the relationships (less, greater, and equal) is true. Relational operators can raise the invalid floating-point
exception when argument values are NaNs. For a NaN and a numeric value, or for two NaNs, just the unordered relationship is true. This
macro is a quiet (non-floating-point exception raising) version of a relational operator. It facilitates writing efficient code that
accounts for quiet NaNs without suffering the invalid floating-point exception. In the SYNOPSIS section, real-floating indicates that the
argument is an expression of real-floating type.
See attributes(5) for descriptions of the following attributes:
| ATTRIBUTE TYPE | ATTRIBUTE VALUE |
|Interface Stability |Standard |
|MT-Level |MT-Safe |
isgreater(3M), isgreaterequal(3M), isless(3M), islessgreater(3M), isunordered(3M), math.h(3HEAD), attributes(5), standards(5)
SunOS 5.11 12 Jul 2006 islessequal(3M) | {"url":"https://www.unix.com/man-page/sunos/3m/islessequal","timestamp":"2024-11-05T23:22:42Z","content_type":"text/html","content_length":"36699","record_id":"<urn:uuid:2541a49b-e991-4f11-8c3f-862d5afbb8c2>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00599.warc.gz"} |
Assignment 2 - Pointers and Dynamically Allocated Multi-dimensional Arrays solution
Problem 2.1 Pointer arithmetic (2 points) Presence assignment, due by 18:30 h today Writeaprogramthatcountsthenumberofelementsinanarrayuntilencounteringthefirstvalue which has the fractional part 0
without the usage of any integer variables for counting. Your program should read an int for the length of the array and an array of doubles (containing at least one value with fractional part 0)
from the standard input. The number of “real” floating point values before the first value with fractional part 0 should be outputted on the standard output.
Youcanassumethattheinputwillbevalidandatleastoneelementwithfractionalpart 0 willbe entered. Testcase 2.1: input 5 1.2 -3.4 5.00 4 5.45 Testcase 2.1: output Before the first integer: 2 elements
Problem 2.2 Substring of a string (2 points) Presence assignment, due by 18:30 h today Writeaprogramthatextractsasubstring(specifyingtwopositionsforfromanduntil)ofastring putting the result into a
dynamically allocated array of chars. Your program should read from the standard input one string (may be statically allocated with at most 100 elements) and two positions. The dynamically allocated
string containing the result of the substring operation on the input string should be printed on the standard output. Please check if the positions are valid or not (you can see the concrete “error”
messages which have to be printed on the screen by submitting your solution and observing the results of the comparisons against the specified testcases). You are not allowed to use the strstr()
function from string.h. You may use pointers and the strcpy() and strncpy() functions. You can assume that the input will be syntactically valid. Testcase 2.2: input onestringtwo 3 8 Testcase 2.2:
output Result of substring(3, 8): string
Problem 2.3 Dynamically allocated matrix comparison (3 points) Write a program that compares two dynamically allocated matrices based on their elements on the main and secondary diagonals. Your
program should dynamically allocate the memory for the two input matrices. You should write functions for reading a matrix from the standard input, printing a matrix to the standard output and finally
a function for comparing the main and secondary diagonals of the two matrices. Do not forget about the allocation and deallocation of the memory. The main diagonal of a square matrix is the diagonal
from the left to the right and the secondary diagonal is the one from the right to the left. Your program should read one integer value (the dimension n) and the elements of two integer
matricesfromthestandardinput(firstiteratingthroughtherowsandthenthroughthecolumns). The result of the matrix comparison should be printed on the standard output. In case the result of the comparison
is that they are not identical then the message “The comparison result: NOT identical” should be printed on the screen. You can assume that the input will be valid. Testcase 2.3: input 3 1 2 3 4 5 6
7 8 9 1 0 3 0 5 0 7 0 9 Testcase 2.3: output Matrix A: 1 2 3 4 5 6 7 8 9 Matrix B: 1 0 3 0 5 0 7 0 9 The comparison result: identical
Problem 2.4 Printing dynamically allocated 3D array sections (4 points) Write a program that dynamically allocates memory for a 3D array of integers and prints the 2D sections parallel to the “y0z
axis” (considering the array dimensions column-dimension, rowdimension and depth-dimension similar to the geometrical x, y and z dimensions) of a 3D array. Your program should read three integer
values corresponding to the dimensions of a 3D array and should dynamically allocate the memory for this 3D array. You should write functions for reading the elements of the 3D array from standard
input (first iterating through rows, then columns and then the depth) and finally a function for printing the 2D sections of the 3D array which are parallel to the “y0z axis”. Do not forget about the
allocation and deallocation of the memory. You can assume that the input will be valid.
Testcase 2.4: input 2 2 3 1 2 3 4 4 4 1 2 3 4 4 4
Testcase 2.4: output Section 1: 1 2 3 1 2 3 Section 2: 4 4 4 4 4 4
How to submit your solutions • Your source code should be properly indented and compile with gcc without any warnings (You canuse gcc -Wall -o program program.c). Insertsuitablecomments
(notoneveryline…) to explain what your program does. • Please name the programs according to the suggested filenames (they should match the description of the problem) in Grader. Otherwise you might
have problems with the inclusion of header files. Each program must include a comment on the top like the following: /* JTSK-320112 a2 p1.c Firstname Lastname myemail@jacobs-university.de */
• You have to submit your solutions via Grader at https://cantaloupe.eecs.jacobs-university.de. If there are problems (but only then) you can submit the programs by sending mail to
k.lipskoch@jacobs-university.de with a subject line that begins with JTSK-320112. It is important that you do begin your subject with the coursenumber, otherwise I might have problems to identify
your submission. • Pleasenote,thatafterthedeadlineitwillnotbepossibletosubmitanysolutions. Itisuselesstosend late solutions by mail, because they will not be accepted. This assignment is due by
Wednesday, February 14th, 10:00 h. | {"url":"https://jarviscodinghub.com/product/assignment-2-pointers-and-dynamically-allocated-multi-dimensional-arrays-solution/","timestamp":"2024-11-03T10:13:27Z","content_type":"text/html","content_length":"111104","record_id":"<urn:uuid:9bd30913-bd60-4263-8e8f-113de0019d2a>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00515.warc.gz"} |
Brief communication: A momentum-conserving superposition method applied to the super-Gaussian wind turbine wake model
Articles | Volume 8, issue 2
© Author(s) 2023. This work is distributed under the Creative Commons Attribution 4.0 License.
Brief communication: A momentum-conserving superposition method applied to the super-Gaussian wind turbine wake model
Accurate wind farm flow predictions based on analytical wake models are crucial for wind farm design and layout optimization. In this regard, wake superposition methods play a key role and remain a
substantial source of uncertainty. Recently, new models based on mass and momentum conservation have been proposed in the literature. In the present work, such methods are extended to the
superposition of super-Gaussian-type velocity deficit models, allowing the full wake velocity deficit estimation and design of closely packed wind farms.
Received: 13 May 2022 – Discussion started: 27 Jun 2022 – Revised: 29 Aug 2022 – Accepted: 17 Jan 2023 – Published: 08 Feb 2023
Wind farm design and layout optimization rely on analytical flow models due to a large number of configurations to be evaluated and the computational efficiency of such numerical methods. A typical
wind farm flow solver consists of a combination of several sub-models, including a minima a velocity deficit model; a wake-added-turbulence (WAT) model; and possibly a wake deflection model, a
blockage model, and a coupled wake–atmospheric-boundary-layer model. The velocity deficit and WAT models usually apply to a single wind turbine: wake superposition methods accumulate the wakes and
estimate a wind farm power production for given environmental conditions. Concerning the superposition of velocity deficits, the available methods lacked theoretical justification, until the recent
work of Zong and Porté-Agel (2020) and Bastankhah et al. (2021). In these studies, analytical solutions for the velocity deficit superposition are proposed based on the mass and momentum conservation
principle. These superposition methods assume Gaussian-shaped velocity deficit profiles. In the present article, the approach of Bastankhah et al. (2021) is extended to super-Gaussian wake velocity
deficit profiles. Such models, proposed in Shapiro et al. (2019) and later refined in Blondel and Cathelain (2020), allow for the evaluation of the velocity deficit over the full wake. On the
contrary, the Gaussian-based approaches are limited to the far wake. Apart from preventing the appearance of unrepresentable numbers, this allows the study of closely packed wind farm layouts.
Indeed, some offshore wind farms such as Lillgrund exhibit small wind turbine inter-distances, down to 3.3 wind turbine diameters. Considering such super-Gaussian velocity profiles together with the
Bastankhah et al. (2021) superposition method, an integral has no analytical solution, and an approximation is proposed and compared with the numerical solution. It is also shown in Sect. 3 that the
method proposed in Bay et al. (2022) leads to similar results in terms of centerline velocity deficit and is suited for wind farm power predictions. The new superposition method has more robust
theoretical foundations than the traditionally used local-linear-sum (LLS) superposition technique (method C in Zong and Porté-Agel, 2020), and its applicability is demonstrated based on the large
Horns Rev wind farm.
2Extension of the Bastankhah et al. (2021) model
2.1Model derivation
In Bastankhah et al. (2021), the conservation of momentum deficit for multiple wakes takes the form
$\begin{array}{}\text{(1)}& \underset{\stackrel{\mathrm{̃}}{\mathcal{A}}}{\int }\left({u}_{\mathrm{0}}{c}_{n}{f}_{n}-{\left({c}_{n}{f}_{n}\right)}^{\mathrm{2}}-\mathrm{2}{c}_{n}{f}_{n}\sum _{i=\mathrm
{1}}^{n-\mathrm{1}}{c}_{i}{f}_{i}\right)d\stackrel{\mathrm{̃}}{A}\approx \frac{{\stackrel{\mathrm{̃}}{T}}_{n}}{\mathit{\rho }},\end{array}$
with c[n] the maximum velocity deficit of turbine n, i the index of the turbines upwind of turbine n, f[n] the self-similar function, $\stackrel{\mathrm{̃}}{A}=\mathit{\pi }{\stackrel{\mathrm{̃}}{r}}^
{\mathrm{2}}$ the rotor surface with $\stackrel{\mathrm{̃}}{r}=r/{d}_{\mathrm{0}}$ and d[0] the wind turbine diameter, ${\stackrel{\mathrm{̃}}{T}}_{n}$ the thrust force of the unit diameter rotor, u[0]
the undisturbed wind velocity, and ρ the fluid density. Based on comparisons to numerical results from a large-eddy-simulation (LES) solver, a modified form was proposed in Bastankhah et al. (2021):
the factor “2” in the left-hand side of Eq. (1) is dropped.
Let us consider the original form, Eq. (1). Given a super-Gaussian shape function f[n], a solution for c[n] is sought. Following Blondel and Cathelain (2020), the shape function reads ${f}_{i}=\
mathrm{exp}\left(-{\stackrel{\mathrm{̃}}{{r}_{i}}}^{k}/\mathrm{2}{\stackrel{\mathrm{̃}}{{\mathit{\sigma }}_{i}}}^{\mathrm{2}}\right)$, with $k=k\left(\stackrel{\mathrm{̃}}{x}\right)$ the super-Gaussian
order and i or n the index of a wind turbine. In the following, we assume that the turbines are sorted from the most upwind to the most downwind, and for two turbines i and n, we have i<n.
Here, as indicated by the tilde, the radius and the super-Gaussian characteristic width are both normalized by the wind turbine diameter d[0], such as $\stackrel{\mathrm{̃}}{{r}_{i}}=\sqrt{\left(y-{y}
_{i}{\right)}^{\mathrm{2}}+\left(z-{z}_{i}{\right)}^{\mathrm{2}}}/{d}_{\mathrm{0}}$ and $\stackrel{\mathrm{̃}}{{\mathit{\sigma }}_{i}}={\mathit{\sigma }}_{i}/{d}_{\mathrm{0}}$. The following integrals
are defined in terms of the gamma function Γ:
$\begin{array}{}\text{(2)}& \begin{array}{rl}& \underset{\stackrel{\mathrm{̃}}{\mathcal{A}}}{\int }{f}_{n}d\stackrel{\mathrm{̃}}{A}=\frac{\mathit{\pi }}{k}\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\
right){\mathrm{2}}^{\mathrm{2}/k+\mathrm{1}}{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{4}/k},\\ & \underset{\stackrel{\mathrm{̃}}{\mathcal{A}}}{\int }{f}_{n}^{\mathrm{2}}d\stackrel{\mathrm
{̃}}{A}=\frac{\mathrm{2}\mathit{\pi }}{k}\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\right){\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{4}/k},\phantom{\rule{0.25em}{0ex}}\mathrm{and}\phantom{\
rule{0.25em}{0ex}}\underset{\stackrel{\mathrm{̃}}{\mathcal{A}}}{\int }{f}_{n}{f}_{i}d\stackrel{\mathrm{̃}}{A}=\mathcal{I}.\end{array}\end{array}$
No analytical solution could be found for the last integral, denoted ℐ. Inserting Eq. (2) into Eq. (1) leads to
$\begin{array}{}\text{(3)}& \begin{array}{rl}{u}_{\mathrm{0}}{c}_{n}\frac{\mathit{\pi }}{k}\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\right){\mathrm{2}}^{\mathrm{2}/k+\mathrm{1}}{\stackrel{\mathrm{̃}}
{\mathit{\sigma }}}_{n}^{\mathrm{4}/k}& -{c}_{n}^{\mathrm{2}}\frac{\mathrm{2}\mathit{\pi }}{k}\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\right){\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{4}
/k}\\ & -\mathrm{2}{c}_{n}\sum _{i}^{n-\mathrm{1}}{c}_{i}\mathcal{I}\approx \frac{{\stackrel{\mathrm{̃}}{T}}_{n}}{\mathit{\rho }}.\end{array}\end{array}$
Using the thrust coefficient ${C}_{{\mathrm{T}}_{n}}=\mathrm{8}{\stackrel{\mathrm{̃}}{T}}_{n}/\left(\mathit{\pi }\mathit{\rho }{\stackrel{\mathrm{̃}}{{d}_{\mathrm{0}}}}^{\mathrm{2}}<{u}_{n-\mathrm{1}}
{>}_{\left(n,{x}_{n}\right)}^{\mathrm{2}}\right)$, the operator $〈\phantom{\rule{0.125em}{0ex}}{〉}_{\left(n,{x}_{n}\right)}$ denoting the spatial averaging over the frontal projected area of rotor
n at x=x[n], and u the streamwise velocity component as in Bastankhah et al. (2021), one obtains
$\begin{array}{}\text{(4)}& \begin{array}{rl}{c}_{n}^{\mathrm{2}}& -{c}_{n}{\mathrm{2}}^{\mathrm{2}/k}\left({u}_{\mathrm{0}}-\mathrm{2}\sum _{i}^{n-\mathrm{1}}\frac{{c}_{i}}{{\mathrm{2}}^{\mathrm{2}/
k}}\frac{k\mathcal{I}}{\mathrm{2}\mathit{\pi }\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\right){\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{4}/k}}\right)\\ & +\frac{k{C}_{{\mathrm{T}}_{n}}}
{\mathrm{16}}\frac{{〈{u}_{n-\mathrm{1}}〉}_{\left(n,{x}_{n}\right)}^{\mathrm{2}}}{\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\right){\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{4}/k}}\approx
Let us introduce a modified integral $\mathcal{J}=k\mathcal{I}/\left({\mathrm{2}}^{\mathrm{2}/k}\mathit{\pi }\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\right){\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_
{n}^{\mathrm{4}/k}\right)$. After straightforward manipulations, and assuming u[0]=u[h], i.e., a constant, shear-free inflow, the solution for c[n] reads
The modified form is obtained by using a modified 𝒥 together with Eq. (5) and ${\mathcal{I}}^{\mathrm{mod}}=\mathcal{I}/\mathrm{2}$:
$\begin{array}{}\text{(6)}& {\mathcal{J}}^{\mathrm{mod}}=\frac{k{\mathcal{I}}^{\mathrm{mod}}}{{\mathrm{2}}^{\mathrm{2}/k}\mathit{\pi }\mathrm{\Gamma }\left(\frac{\mathrm{2}}{k}\right){\stackrel{\
mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{4}/k}}.\end{array}$
2.2Approximate solutions of the integral ℐ
In a first approach, hereafter referred to as the Gauss approach, one may assume a Gaussian behavior of the model to evaluate 𝒥, as done in Bay et al. (2022). One obtains (see Bastankhah et al., 2021
$\begin{array}{}\text{(7)}& \begin{array}{rl}{\mathcal{J}}_{\mathrm{Gauss}}^{\mathrm{mod}}=& \frac{\mathit{\pi }{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}^{\mathrm{2}}{\stackrel{\mathrm{̃}}{\mathit
{\sigma }}}_{n}^{\mathrm{2}}}{{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}^{\mathrm{2}}+{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{2}}}\mathrm{exp}\left(-\frac{{\left({\stackrel{\mathrm{̃}}
{y}}_{n}-{\stackrel{\mathrm{̃}}{y}}_{i}\right)}^{\mathrm{2}}}{\mathrm{2}\left({\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{2}}+{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}^{\mathrm{2}}\
right)}\right)\\ & \mathrm{exp}\left(-\frac{{\left({\stackrel{\mathrm{̃}}{z}}_{n}-{\stackrel{\mathrm{̃}}{z}}_{i}\right)}^{\mathrm{2}}}{\mathrm{2}\left({\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\
mathrm{2}}+{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}^{\mathrm{2}}\right)}\right).\end{array}\end{array}$
Alternatively, in a second approach hereafter referred to as the kEquiv approach, one may first consider aligned turbines (${\stackrel{\mathrm{̃}}{y}}_{i}-{\stackrel{\mathrm{̃}}{y}}_{n}=\mathrm{0}$, $
{\stackrel{\mathrm{̃}}{z}}_{i}-{\stackrel{\mathrm{̃}}{z}}_{n}=\mathrm{0}$) and later correct the integral for the lateral distance between the rotors using a function $\mathit{\delta }\left(\stackrel{\
mathrm{̃}}{y},\stackrel{\mathrm{̃}}{z}\right)$. This function is identified from the Gaussian solution. A second approximation consists in considering an equivalent super-Gaussian order, ${k}_{\mathrm
{eq}}=\mathrm{1}/\mathrm{2}\left({k}_{i}+{k}_{n}\right)$. Under these hypotheses, the integral ℐ takes the form
$\begin{array}{}\text{(8)}& \begin{array}{rl}{\mathcal{I}}_{\mathrm{kEquiv}}^{\mathrm{mod}}=& \frac{\mathit{\pi }\mathrm{\Gamma }\left(\mathrm{2}/{k}_{\mathrm{eq}}\right){\mathrm{2}}^{\mathrm{2}/{k}_
{\mathrm{eq}}+\mathrm{1}}{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}^{\mathrm{4}/{k}_{\mathrm{eq}}}{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{4}/{k}_{\mathrm{eq}}}}{{k}_{\mathrm{eq}}{\
left({\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}^{\mathrm{2}}+{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{2}}\right)}^{\mathrm{2}/{k}_{\mathrm{eq}}}}\mathit{\delta }\left(\stackrel{\mathrm
{̃}}{y},\stackrel{\mathrm{̃}}{z}\right),\\ & \mathrm{with}\phantom{\rule{0.25em}{0ex}}\mathit{\delta }\left(\stackrel{\mathrm{̃}}{y},\stackrel{\mathrm{̃}}{z}\right)=\mathrm{exp}\left(-\frac{{\left({\
stackrel{\mathrm{̃}}{y}}_{n}-{\stackrel{\mathrm{̃}}{y}}_{i}\right)}^{{k}_{\mathrm{eq}}}}{\mathrm{2}\left({\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{n}^{\mathrm{2}}+{\stackrel{\mathrm{̃}}{\mathit{\sigma
}}}_{i}^{\mathrm{2}}\right)}\right)\\ & \mathrm{exp}\left(-\frac{{\left({\stackrel{\mathrm{̃}}{z}}_{n}-{\stackrel{\mathrm{̃}}{z}}_{i}\right)}^{{k}_{\mathrm{eq}}}}{\mathrm{2}\left({\stackrel{\mathrm{̃}}
{\mathit{\sigma }}}_{n}^{\mathrm{2}}+{\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}^{\mathrm{2}}\right)}\right),\end{array}\end{array}$
and Eq. (6) is used to calculate ${\mathcal{J}}_{\mathrm{kEquiv}}^{\mathrm{mod}}$. Another straightforward approach consists in tabulating the integral values (excluding the $\mathit{\delta }\left(\
stackrel{\mathrm{̃}}{y},\stackrel{\mathrm{̃}}{z}\right)$ function) and linearly interpolating between the data, which is the one retained in practice. For a quantitative comparison, the proposed
analytical approximations of the integral 𝒥 are compared to the numerical integration. An interval of $\mathrm{0.2}\le {\stackrel{\mathrm{̃}}{\mathit{\sigma }}}_{i}$, ${\stackrel{\mathrm{̃}}{\mathit{\
sigma }}}_{n}\le \mathrm{2.5}$ is considered for the characteristic width, and several intervals 2≤k[i], k[n]<maxk are considered for the super-Gaussian order, with $\mathrm{2}<{\mathrm{max}}_{k}\le
\mathrm{8}$. The bounding values are representative of the very near wake of a wind turbine under laminar flow conditions and the very far wake ($\stackrel{\mathrm{̃}}{x}>\mathrm{15}{d}_{\mathrm{0}}$)
under highly turbulent conditions: the typical operating range of a turbine in a wind farm is covered. Among the characteristic width and super-Gaussian order intervals, 15 values are sampled.
Regarding the maximum super-Gaussian order, six equally spaced values are sampled. For each set of four inputs, and for a given maximum super-Gaussian order, the analytical approximations are
evaluated, and the error is computed ($\mathrm{error}=\left(\left|{\mathcal{J}}_{\mathrm{Analytical}}\right|-\left|{\mathcal{J}}_{\mathrm{Numerical}}\right|\right)/\left|{\mathcal{J}}_{\mathrm
{Numerical}}\right|$). The numerical evaluation is based on the SciPy (Virtanen et al., 2020) “integrate.quad” integration routine and extends from 0 to $\mathrm{6}\cdot \mathrm{max}\left({\mathit{\
sigma }}_{i},{\mathit{\sigma }}_{n}\right)$. Then, for each max[k], the average and maximal error are computed and reported in Fig. 1. From these results, the so-called kEquiv method seemingly
outperforms the Gauss method and should be preferred. However, it will be shown in Sect. 3 that the impact on the velocity deficit is limited.
In a recent study, Lanzilao and Meyers (2022) showed that the super-Gaussian model performed poorly compared with other models: for both Horns Rev and the London Array wind farms, the predicted power
production is far below the measured power from supervisory control and data acquisition (SCADA) data. Due to these observations, the model is re-calibrated for the present study. The calibration
procedure and the notations used hereafter follow the work of Cathelain et al. (2020). The main difference here lies in the use of a Gaussian profile in the far wake, i.e., ${lim}_{\stackrel{\mathrm
{̃}}{x}\to \mathrm{\infty }}k\left(\stackrel{\mathrm{̃}}{x}\right)=\mathrm{2}$. The wake characteristic width is assumed to evolve linearly with axial distance:
$\begin{array}{}\text{(9)}& \stackrel{\mathrm{̃}}{\mathit{\sigma }}=\left({a}_{\mathrm{s}}\mathrm{TI}+{b}_{\mathrm{s}}\right)\stackrel{\mathrm{̃}}{x}+{c}_{\mathrm{s}}\sqrt{\left(\frac{\mathrm{1}}{\
The three parameters, a[s], b[s], and c[s], are used for both the super-Gaussian and the Gaussian model. The super-Gaussian order follows an exponential decay function:
$\begin{array}{}\text{(10)}& k={a}_{\mathrm{f}}{e}^{{b}_{\mathrm{f}}\stackrel{\mathrm{̃}}{x}}+{c}_{\mathrm{f}}.\end{array}$
A Gaussian profile is assumed in the far wake; thus, c[f]=2. The parameter b[f] controls the decay of the super-Gaussian order and is taken as a function of the turbulence intensity. a[f] is chosen
in such a way that the model fulfills the actuator-disk theory (see Cathelain et al., 2020). This can be enforced numerically using a Newton fixed-point algorithm. To facilitate the implementation,
this inversion is performed in a pre-processing stage, and a third-order polynomial fit is proposed:
$\begin{array}{}\text{(11)}& {a}_{\mathrm{f}}=-\mathrm{8.2635}{C}_{\mathrm{T}}^{\mathrm{3}}+\mathrm{8.5939}{C}_{\mathrm{T}}^{\mathrm{2}}-\mathrm{8.9691}{C}_{\mathrm{T}}+\mathrm{10.7286}.\end{array}$
The proposed calibration is not meant to be universal but dedicated to the present study. Future work will be dedicated to a calibration that is reliable in both near- and far-wake regions. Table 1
provides the list of the model coefficients used in this study, obtained using a differential evolution algorithm and a set of nine LES simulations.
3.1Comparison against large-eddy simulations from Bastankhah et al. (2021)
For the model comparison, the numerical setup based on the aligned wind farm introduced in Bastankhah et al. (2021) is reproduced. A schematic view of the wind farm is given in Fig. 2. It consist of
five columns of three wind turbines, which are all included in the simulation. The velocity deficit studied later is extracted over a line passing through the hub of the wind turbines of the central
line, as shown in the schema. The first column in our simulations is located at $\stackrel{\mathrm{̃}}{x}=\mathrm{0}$.
The wind farm flow model builds upon the super-Gaussian model as described in Blondel and Cathelain (2020), using the calibration introduced in Sect. 3. The WAT model proposed in Ishihara and Qian (
2018) is employed, together with a so-called maximum-value WAT superposition; see Niayifar and Porté-Agel (2016). A correction factor of 1.25 is applied on the maximum of added turbulence to match
the results presented in Bastankhah et al. (2021). Following a convergence study, the rotor disks are discretized based on 12×12 polar grids. Velocity deficit and WAT due to upwind rotor wakes are
evaluated at every point on the disk. Then, mean velocity and turbulence intensity are computed and used as an input for the wake models and rotor performance evaluation; i.e., the power and thrust
coefficients are given as a function of wind speed. Using a polar discretization, the mesh cells are not uniform in size: the ones located near the edge of the disk are significantly larger than the
ones near the hub. Thus, when computing the mean quantities, we use a weighted average whose weighting factors are based on the mesh cell surface. In practice, in the case of aligned rotors, this
tends to lower the wake effect since the higher velocity deficit is located at the rotor center where the mesh cell's relative areas are the smallest. A blockage correction based on the vortex
cylinder flow model is used; see Branlard and Meyer Forsting (2020). The LLS method is compared to the present method, denoted MC (momentum conserving), with the two approximations for 𝒥^mod, as well
as a direct numerical evaluation of the integral, denoted ${\mathcal{J}}_{\mathrm{Num}}^{\mathrm{mod}}$.
Figure 3a shows that, compared with the LLS superposition method, the MC model predicts a lower velocity deficit in both near- and far-wake regions, which is more consistent with LES data. Moreover,
the proposed analytical approximations of the integral 𝒥^mod are very close to the numerical approximation in the presented test case. At the rotor planes, discontinuities are observed. This can be
partially attributed to the use of the modified momentum-conservation method which improves the results in the far wake as shown in Fig. 3b but does not fully respect the conservation laws, as
detailed in Bastankhah et al. (2021). Using the unmodified formulation leads to very high near-wake velocity deficits or even unrepresentable numbers in the presented test case. More than three
diameters behind the wind turbine, the results based on the ${\mathcal{J}}_{\mathrm{kEquiv}}^{\mathrm{mod}}$ and ${\mathcal{J}}_{\mathrm{Gauss}}^{\mathrm{mod}}$ approximations are superimposed since
the super-Gaussian order is close to 2. These observations validate the approach employed in Bay et al. (2022), despite the higher errors noticed in Fig. 1. In practice, using a tabulated version of
the integral is a fast and convenient approach. However, it does not circumvent the approximation based on the rotor distance function, $\mathit{\delta }\left(\stackrel{\mathrm{̃}}{y},\stackrel{\
mathrm{̃}}{z}\right)$, since tabulating the complete integral results in large data files that are time-consuming to load. The global agreement against the LES dataset is satisfying. In the first
turbine wake, the hub effect prevents a proper analysis of the results. For the second turbine, a good agreement is obtained with the LLS method, while the MC method underpredicts the velocity
deficit. This behavior, as noted in Bastankhah et al. (2021), is a consequence of the application of the modified momentum conservation law. For the following three turbines, a good agreement is
For a more quantitative analysis, the root-mean-square error (RMSE) between the different analytical models from $\stackrel{\mathrm{̃}}{x}=\mathrm{0}$ to $\stackrel{\mathrm{̃}}{x}=\mathrm{30}$ and the
LES results are given in Table 2. First, the use of Gaussian wake models leads to a rather high error, due to the inaccuracy in the near wake. This behavior is expected, and we are here using the
model outside of its definition domain, i.e., the Gaussian model is a far-wake model. Using the super-Gaussian model, the RMSEs fall below 8%. Whatever the approximation performed on the 𝒥 integral,
the momentum-conserving approach outperforms the LLS method: the RMSEs fall again from approximately 8% to less than 6%. Using the ${\mathcal{J}}_{\mathrm{Gauss}}^{\mathrm{mod}}$ approximation, the
error is slightly higher compared with ${\mathcal{J}}_{\mathrm{kEquiv}}^{\mathrm{mod}}$ and ${\mathcal{J}}_{\mathrm{Num}}^{\mathrm{mod}}$. One should thus prefer one of these two formulations over
the so-called ${\mathcal{J}}_{\mathrm{Gauss}}^{\mathrm{mod}}$ approximation.
3.2Comparison against large-eddy simulations of the Horns Rev wind farm from Portéé-Agel et al. (2013)
The model predictions are also compared with large-eddy simulations of the Horns Rev wind farm, as presented in Porté-Agel et al. (2013). With a minimal inter-turbine distance of seven diameters,
this wind farm can not be considered as closely packed. However, the availability of a large set of large-eddy-simulation results makes it a good candidate for validation purposes. The inflow
conditions are based on inflow velocity and turbulence intensity profiles scanned from Porté-Agel et al. (2013). Figure 4 compares the wind farm efficiency η (predicted power divided by theoretical
power without wake effect) over a wide range of wind directions θ. We use the LES as a reference to avoid the uncertainties of SCADA measurements, mainly due to the wind direction changes during the
10min averaging in the available data.
The agreement between the analytical model and the LES dataset is overall good. Differences between the momentum-conserving superposition method and the LLS approach are noticed for wind directions
where the wake effects are strong, typically at θ≈{222, 270, 312^∘}. Around such directions, the lower velocity deficits predicted by the MC approach lead to lower wake losses and better efficiency
of the wind farm, which is more consistent with the LES data. Both the Gaussian and the super-Gaussian models predict the same wind farm efficiency whatever the wind direction: this is due to the
large inter-turbine distances in the Horns Rev wind farm. It confirms that the poor results obtained in Lanzilao and Meyers (2022) for the same wind farm are mostly due to inaccuracies in the model
calibration introduced in Cathelain et al. (2020).
For a more quantitative comparison, the RMSEs of the different analytical models against the LES results are provided in Table 3. The LLS method together with the super-Gaussian model has the highest
level of error, around 3.7%, while using the momentum-conserving approach, both with a Gaussian or a super-Gaussian model, causes the RMSEs to fall below 2.5%. Differences between the two
aforementioned models appear in the RMSEs only at the fourth decimal. Considering the large inter-turbine spacing in the Horns Rev wind farm, this was expected, since both models use the same
characteristic width, and the inter-turbine distances are large enough to have super-Gaussian orders very close to k=2 at the rotor planes.
In this work, the momentum-conserving wake superposition method proposed in Bastankhah et al. (2021) was extended to super-Gaussian-type velocity deficit models. An integral could not be resolved
analytically, and an approximation has been proposed. This approximation is closer to numerical evaluations of the integral that the Gaussian assumption used in Bay et al. (2022). Comparisons against
large-eddy simulations of wind farms show a satisfactory agreement, allowing the simulation of large wind farms using the super-Gaussian wake model. Further studies will include an extensive
validation of the resulting wind farm flow model, including closely packed wind farms.
Code and data availability
The numerical results based on the analytical models can be made available on demand.
The author has declared that there are no competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The author is grateful to Majid Bastankhah for the helpful discussions.
This paper was edited by Joachim Peinke and reviewed by two anonymous referees.
Bastankhah, M., Welch, B. L., Martínez-Tossas, L. A., King, J., and Fleming, P.: Analytical solution for the cumulative wake of wind turbines in wind farms, J. Fluid Mech., 911, A53, https://doi.org/
10.1017/jfm.2020.1037, 2021.a, b, c, d, e, f, g, h, i, j, k, l, m, n
Bay, C. J., Fleming, P., Doekemeijer, B., King, J., Churchfield, M., and Mudafort, R.: Addressing deep array effects and impacts to wake steering with the cumulative-curl wake model, Wind Energ. Sci.
Discuss. [preprint], https://doi.org/10.5194/wes-2022-17, in review, 2022.a, b, c, d
Blondel, F. and Cathelain, M.: An alternative form of the super-Gaussian wind turbine wake model, Wind Energ. Sci., 5, 1225–1236, https://doi.org/10.5194/wes-5-1225-2020, 2020.a, b, c
Branlard, E. and Meyer Forsting, A. R.: Assessing the blockage effect of wind turbines and wind farms using an analytical vortex model, Wind Energy, 23, 2068–2086, https://doi.org/10.1002/we.2546,
Cathelain, M., Blondel, F., Joulin, P., and Bozonnet, P.: Calibration of a super-Gaussian wake model with a focus on near-wake characteristics, J. Phys.: Conf. Ser., 1618, 062008, https://doi.org/
10.1088/1742-6596/1618/6/062008, 2020.a, b, c
Ishihara, T. and Qian, G.-W.: A new Gaussian-based analytical wake model for wind turbines considering ambient turbulence intensities and thrust coefficient effects, J. Wind Eng. Indust. Aerodynam.,
177, 275–292, https://doi.org/10.1016/j.jweia.2018.04.010, 2018.a
Lanzilao, L. and Meyers, J.: A new wake-merging method for wind-farm power prediction in the presence of heterogeneous background velocity fields, Wind Energy, 25, 237–259, https://doi.org/10.1002/
we.2669, 2022.a, b
Niayifar, A. and Porté-Agel, F.: Analytical Modeling of Wind Farms: A New Approach for Power Prediction, Energies, 9, 41, https://doi.org/10.3390/en9090741, 2016.a
Porté-Agel, F., Wu, Y.-T., and Chen, C.-H.: A Numerical Study of the Effects of Wind Direction on Turbine Wakes and Power Losses in a Large Wind Farm, Energies, 6, 5297–5313, https://doi.org/10.3390/
en6105297, 2013.a, b, c, d
Shapiro, C. R., Starke, G. M., Meneveau, C., and Gayme, D. F.: A Wake Modeling Paradigm for Wind Farm Design and Control, Energies, 12, 2956, https://doi.org/10.3390/en12152956, 2019.a
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K.
J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, İ., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero,
E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nat. Meth.,
17, 261–272, https://doi.org/10.1038/s41592-019-0686-2, 2020. a
Zong, H. and Porté-Agel, F.: A momentum-conserving wake superposition method for wind farm power prediction, J. Fluid Mech., 889, A8, https://doi.org/10.1017/jfm.2020.77, 2020.a, b | {"url":"https://wes.copernicus.org/articles/8/141/2023/","timestamp":"2024-11-08T06:00:36Z","content_type":"text/html","content_length":"269958","record_id":"<urn:uuid:b35038f2-ef04-43ab-87ce-1ce3c6a9d627>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00637.warc.gz"} |
Casio fx-CG50 - Hyperbolic functions of complex numbers
02-29-2020, 02:28 AM
(This post was last modified: 02-29-2020 02:35 AM by Dands.)
Post: #1
Dands Posts: 68
Member Joined: Jul 2015
Casio fx-CG50 - Hyperbolic functions of complex numbers
I recently discovered that my CG50 can't evaluate hyperbolic functions of complex numbers such as
Giving me a "Non-real ERROR".
It's important to point out that other calculators such as the HP Prime and TI Nspire can do this with no problem. If you're asking yourself why I need this: calculating impedance parameters of power
distribution lines.
I tried both rad and deg modes and my calculator is in Complex mode. Latest OS installed.
Any ideas on how why this isn't working? It's a shame because I really expected this calculator to do this.
02-29-2020, 05:58 AM
(This post was last modified: 02-29-2020 06:03 AM by Steve Simpkin.)
Post: #2
Steve Simpkin Posts: 1,290
Senior Member Joined: Dec 2013
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 02:28 AM)Dands Wrote: Hello,
I recently discovered that my CG50 can't evaluate hyperbolic functions of complex numbers such as
Giving me a "Non-real ERROR".
It's important to point out that other calculators such as the HP Prime and TI Nspire can do this with no problem. If you're asking yourself why I need this: calculating impedance parameters of
power distribution lines.
I tried both rad and deg modes and my calculator is in Complex mode. Latest OS installed.
Any ideas on how why this isn't working? It's a shame because I really expected this calculator to do this.
In looking at Appendix 2 (Input ranges) of the fx-CG50 Software User's Guide, it appears that the CG50 will accept complex numbers for a number of functions (log, powers, roots, etc) but not for any
trig functions.
One way around this limitation is to install Bernard Parisse's excellent port of Xcas for the fx-CG50 named KhiCAS. More information and documentation is available at:
Once you install KhiCAS, you can evaluate cosh(2*i) for an answer of -.41614837 or sinh(2+2*i) for an answer of -1.50930649+3.42095489*i in that environment (rad).
Tip: press the "S<->D" key first to enter "approx(" before typing in "cosh(2*i))" to get a decimal answer.
Of course this is also a full featured CAS much like the one available on the Prime [ I wonder why
02-29-2020, 08:37 AM
(This post was last modified: 02-29-2020 08:38 AM by Dands.)
Post: #3
Dands Posts: 68
Member Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 05:58 AM)Steve Simpkin Wrote: In looking at Appendix 2 (Input ranges) of the fx-CG50 Software User's Guide, it appears that the CG50 will accept complex numbers for a number of
functions (log, powers, roots, etc) but not for any trig functions.
One way around this limitation is to install Bernard Parisse's excellent port of Xcas for the fx-CG50 named KhiCAS. More information and documentation is available at: https://www.cemetech.net/
Once you install KhiCAS, you can evaluate cosh(2*i) for an answer of -.41614837 or sinh(2+2*i) for an answer of -1.50930649+3.42095489*i in that environment (rad).
Tip: press the "S<->D" key first to enter "approx(" before typing in "cosh(2*i))" to get a decimal answer.
Of course this is also a full featured CAS much like the one available on the Prime [ I wonder why
WOW! This is really amazing! Thank you so much for the quick answer. It's definitely a great solution for what I need.
It would be amazing if it integrated with the run-matrix mode. Do you know if there's a way to save the most used functions, say cosh, so that it's easier to access? It seems that I always have to
find it in the list or type it.
Also, is there a way to show the decimal approximation by default instead of always using approx() before the functions?
Thanks again!
02-29-2020, 05:00 PM
Post: #4
ijabbott Posts: 1,307
Senior Member Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
I suppose you could use the identities \(\sinh(z) = \frac{e^z - e^{-z}}{2}\), \(\cosh(z) = \frac{e^z + e^{-z}}{2}\), \(\tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}\), etc. - but it would be nicer if
they were built in!
— Ian Abbott
02-29-2020, 05:02 PM
Post: #5
Dands Posts: 68
Member Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 05:00 PM)ijabbott Wrote: I suppose you could use the identities \(\sinh(z) = \frac{e^z - e^{-z}}{2}\), \(\cosh(z) = \frac{e^z + e^{-z}}{2}\), \(\tanh(z) = \frac{e^z - e^{-z}}{e^z + e
^{-z}}\), etc. - but it would be nicer if they were built in!
Yeah these work but are one extra step in my lengthy calculations. I agree those should be built in. I wish Casio had a channel for users to request future OS updates. Thanks
02-29-2020, 08:03 PM
Post: #6
Steve Simpkin Posts: 1,290
Senior Member Joined: Dec 2013
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 08:37 AM)Dands Wrote:
(02-29-2020 05:58 AM)Steve Simpkin Wrote: In looking at Appendix 2 (Input ranges) of the fx-CG50 Software User's Guide, it appears that the CG50 will accept complex numbers for a number of
functions (log, powers, roots, etc) but not for any trig functions.
One way around this limitation is to install Bernard Parisse's excellent port of Xcas for the fx-CG50 named KhiCAS. More information and documentation is available at: https://
Once you install KhiCAS, you can evaluate cosh(2*i) for an answer of -.41614837 or sinh(2+2*i) for an answer of -1.50930649+3.42095489*i in that environment (rad).
Tip: press the "S<->D" key first to enter "approx(" before typing in "cosh(2*i))" to get a decimal answer.
Of course this is also a full featured CAS much like the one available on the Prime [ I wonder why
WOW! This is really amazing! Thank you so much for the quick answer. It's definitely a great solution for what I need.
It would be amazing if it integrated with the run-matrix mode. Do you know if there's a way to save the most used functions, say cosh, so that it's easier to access? It seems that I always have
to find it in the list or type it.
Also, is there a way to show the decimal approximation by default instead of always using approx() before the functions?
Thanks again!
Unfortunately I don't see a quick shortcut for entering the hyperbolic functions. I have been pressing the normal trig key (sin, cos, tan, etc) then left cursor, F5 (A<->a), h, Alpha (to turn off
Alpha lock), right cursor. Not very elegant.
I also don't see a way to force approximate answers without entering the "approx(" first. At least there is a shortcut key for that (S<->D). I suspect since Xcas is typically used to find exact
answers, a persistent approximate mode was not seen as important. You could *normally* use the Run-Matrix mode for that. There is also the fact that, due to memory size limitations for Casio apps
(2MB), Bernard had to cut back on the features included in KhiCAS. This may also explain why you can't share results outside of the KhiCAS environment. By design, it is like a separate calculator.
KhiCAS has a lot of features! Read the 20 posts in the cenetech.net link I provided and look at the documentation link in Bernard's first post for more information.
02-29-2020, 09:30 PM
(This post was last modified: 02-29-2020 09:31 PM by Dands.)
Post: #7
Dands Posts: 68
Member Joined: Jul 2015
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 08:03 PM)Steve Simpkin Wrote: Unfortunately I don't see a quick shortcut for entering the hyperbolic functions. I have been pressing the normal trig key (sin, cos, tan, etc) then
left cursor, F5 (A<->a), h, Alpha (to turn off Alpha lock), right cursor. Not very elegant.
I also don't see a way to force approximate answers without entering the "approx(" first. At least there is a shortcut key for that (S<->D). I suspect since Xcas is typically used to find exact
answers, a persistent approximate mode was not seen as important. You could *normally* use the Run-Matrix mode for that. There is also the fact that, due to memory size limitations for Casio apps
(2MB), Bernard had to cut back on the features included in KhiCAS. This may also explain why you can't share results outside of the KhiCAS environment. By design, it is like a separate
KhiCAS has a lot of features! Read the 20 posts in the cenetech.net link I provided and look at the documentation link in Bernard's first post for more information.
That's a great way to do it indeed, just use the shortcut for sin and cos and add an 'h'. I like it.
I also believe that it was not meant to show approximations right away. Parisse stated that "There is no auto-simplification in KhiCAS, except for fractions of integers.".
A feature I'd love to see would be to be able to paste results to the run matrix mode. It seems to be not possible right now.
Thanks again for all your help Steve.
03-01-2020, 04:54 AM
Post: #8
Eddie W. Shore Posts: 1,614
Senior Member Joined: Dec 2013
RE: Casio fx-CG50 - Hyperbolic functions of complex numbers
(02-29-2020 05:00 PM)ijabbott Wrote: I suppose you could use the identities \(\sinh(z) = \frac{e^z - e^{-z}}{2}\), \(\cosh(z) = \frac{e^z + e^{-z}}{2}\), \(\tanh(z) = \frac{e^z - e^{-z}}{e^z + e
^{-z}}\), etc. - but it would be nicer if they were built in!
Agree to both of your points
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ADC Signal-to-Noise Ratio (SNR)
Last modified by Microchip on 2023/11/10 11:07
If an Alternate Current (AC) signal is applied to an ideal Analog-to-Digital Converter (ADC), noise present in the digitized output will be due to quantization error. For the ideal converter, the
maximum error for any given input will be +/- ½ Least Significant Bit (LSB). If a linear ramp signal is applied to the converter input and the output error is plotted for all analog inputs, the
result will be a sawtooth waveform with a peak-to-peak value of 1 LSB as shown in the accompanying image:
The Root-Mean-Square (RMS) amplitude of the error output can be approximated by the equation below.
(1) ERRORRMS=1/(12−−√)∙1LSB
The maximum theoretical Signal-to-Noise Ratio (SNR) for an ADC can be determined based on the RMS quantization error determined above. If a Full-Scale (FS) sine wave is applied to the input of the
ADC, the maximum theoretical SNR is determined by the equation below, where N is the resolution of the ADC in bits. The above formula assumes that the signal noise is measured over the entire usable
bandwidth of the ADC (0 - fs/2), where fs = sampling frequency. For the case of oversampling, where the signal bandwidth is less than the Nyquist bandwidth, the theoretical SNR of the ADC is
increased by 3 dB each time the fs is doubled.
(2) SNR=6.02∙N+1.76dB
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math symbol for all real numbers Archives - PickupBrain: Be Smart
For all (∀) symbol, also known as universal quantification, is used in mathematics to denote “given any” or “for all”. Three different ways viz. insert symbol, alt code, and the fastest math
autocorrect are available in Ms Word to type for all symbol. Three ways to type “for all” symbol in Word Method 1: Insert > Symbol 1: Navigate Insert Tab > Symbol in symbols group. 2: Select More
Symbols. 3: Select “normal text” from Font &“Mathematical Operators” from the Subset dropdown.… Read More »How to type for all (∀) symbol in Word | {"url":"https://www.pickupbrain.com/tag/math-symbol-for-all-real-numbers/","timestamp":"2024-11-11T21:30:52Z","content_type":"text/html","content_length":"127092","record_id":"<urn:uuid:1283a817-ff8c-4330-840e-dc6b068fae77>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00278.warc.gz"} |
Probability Distribution - Learns About Random Number Generators - Do My GRE Exam
A probability distribution is a mathematical description of the distributions of probability within a sample. A distribution refers to the probability of an outcome and can be either continuous or
discrete. A continuous probability distribution is one in which the value of an outcome is a constant. A discrete probability distribution is one in which the value of an outcome varies over time and
in different samples. The following are some examples of probability distributions:
The following are examples of questions for the test to do my GRE Examination:
How would a person who has never studied calculus, probability, or probability distribution arrive at a distribution? Would they take a random number generator and draw from it a bunch of random
numbers, with the probability that all the numbers are the same. This can be done by just looking up the random number generator’s Wikipedia page, and clicking on the random number generator link.
What are the properties of the random number generator that would make it good enough for use as a distribution? Some random number generators (RNGs) tend to be better than others, and the properties
of the generator itself can determine the quality of the random number generator. Random number generators also tend to have different distributions when used for other purposes.
There are many different types of random number generators. Most of the RNGs can generate random numbers in either binary (either two’s complement or a sequence) or in a finite field. Binary random
number generators produce the most random outcomes but are the least reliable and accurate, so they are not usually recommended.
On a finite field, a finite-frequency generator produces a much higher probability of a random number than a continuous-frequency generator, because a finite frequency is not affected by external
sources like gravity or noise. Finite frequency RNGs are typically used in scientific simulations where the random number generator is used for more complicated algorithms, but they are also useful
for determining the likelihood of a number occurring.
How do you choose a distribution of the probability of the results you got from the Greeks? What are the properties of the Greek probability distribution that help your chosen distribution give you
good results?
The properties of the Greek distribution can be described by looking at the distributions of its denominators and their probabilities. The denominator of a distribution is the chance of the answer
being the correct answer when the question is asked; the probability is the probability that the question is asked and the answer is given. The properties of a distribution include the shape of the
curve, the uniformity of the curve, and the direction in which the curve moves.
The distribution of the curves is quite simple, since each of the distributions has a uniform probability of being the correct answer. There is only one curve in the distribution, which is a straight
The uniform distribution is called the Gaussian curve, and it is usually a smooth curve. A normal curve has steep turns, with the top side of the curve moving in the same direction as the bottom side
of the curve. The distribution curve does not have any steep turns and moves in a more linear fashion. The uniform distribution has a smooth curve and is called a power curve.
The normal distribution is called the bell curve, because the curves are generally very bell-shaped. There are some exceptions, such as when the distribution has steep turns on the high side of the
curve and then slopes slightly to the low side. The bell-shaped distribution has a very steep curve, with a small peak and a high minimum, and a very steep minimum and no maximum.
The probability distribution can be obtained from a random number generator by taking the difference between the expected values and the actual values and applying a normal distribution to the data.
It’s important that the difference between the expected and actual values is statistically significant, otherwise the resulting distribution will not be very useful. | {"url":"https://domygreexam.com/probability-distribution-learns-about-random-number-generators/","timestamp":"2024-11-07T15:59:22Z","content_type":"text/html","content_length":"107253","record_id":"<urn:uuid:c466bd0a-963b-4c06-a93b-6c6b573f25ed>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00278.warc.gz"} |
What is the difference between centrifugal and centripetal forceWhat is the difference between centrifugal and centripetal force 🚩 Science.
The distinction between centrifugal and centripetal force
On any object that rotates on a circular path, a force. It is directed to the center point of the circle described by the trajectory. This force is called centripetal.
Centrifugal force is often referred to as the inertial force or fictitious force. It is mainly used to refer to the forces associated with motion in non-inertial reference frame.
According to Newton's third law, every action has the opposite in direction and equal and opposite reaction. In this concept, the centrifugal force is a reaction to the action of the centripetal
Both forces are inertial, as arise only when the object moves. Also, they always appear in pairs and cancel each other. Therefore, in practice, they often can be neglected.
Examples of centrifugal and centripetal forces
If you take a rock and tie him to a rope and then start to spin the rope over your head, there is a centripetal force. It will act through the rope on the stone and not allow him to retire to a
distance greater than the length of the rope as would happen with normal roll. The centrifugal force will act in the opposite way. It will be quantitatively equal and opposite in direction to the
centripetal force. This force is greater the more massive a body moving along a closed path.
It is well known that the Moon rotates around the Earth in a circular orbit. The force of attraction that exists between Earth and the Moon is the result of the action of the centripetal force. The
centrifugal force in this case is virtual and not really there. This follows from Newton's third law. However, despite the abstractness, the centrifugal force plays a very important role in the
interaction of two celestial bodies. Thanks to the Earth and its moon is not moving away and not closer to each other, and move in stationary orbits. Without the centrifugal force they have long
1. While the centripetal force is directed toward the center of the circle, the centrifugal opposite to it.
2. Centrifugal force is often called the inertial or fictitious.
3. The centrifugal force is always equal to the quantitative value and opposite in direction to the centripetal force.
5. The word "centripetal" was derived from Latin words. Centrum means center, and "petere" means "to search". The concept of "centrifugal" is derived from the Latin words "centrum" and "fugere" which
means "to run". | {"url":"https://eng.kakprosto.ru/how-905148-what-is-the-difference-between-centrifugal-and-centripetal-force","timestamp":"2024-11-04T23:43:03Z","content_type":"text/html","content_length":"31754","record_id":"<urn:uuid:ab052c4e-97ec-4d7d-9eea-058ef1053257>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00508.warc.gz"} |
Minimum Spanning Tree | Algorithm Notes | B.Tech
Mobiprep has created last-minute notes for all topics of Algorithm to help you with the revision of concepts for your university examinations. So let’s get started with the lecture notes on
Our team has curated a list of the most important questions asked in universities such as DU, DTU, VIT, SRM, IP, Pune University, Manipal University, and many more. The questions are created from the
previous year's question papers of colleges and universities.
Minimum Spanning Tree
Question- 1) What is Minimum Spanning Tree
Answer: The cost of the spanning tree is the sum of the weights of all the edges in the tree. There can be many spanning trees. Minimum spanning tree is the spanning tree where the cost is minimum
among all the spanning trees. There also can be many minimum spanning trees.
Question- 2) How to find a minimum spanning tree?
• Designing Local Area Networks.
• Laying pipelines connecting offshore drilling sites, refineries and consumer markets.
• Used to find approximate solutions for complex mathematical problems, NP-hard solutions like the Traveling Salesman Problem.
• Cluster analysis.
• Real-time face tracking and verification (i.e. locating human faces in a video stream).
• Protocols in computer science to avoid network cycles.
Question- 3) Discuss Application of Minimum Spanning Tree
Answer: Minimum Spanning Tree (MST) problem: Given connected graph G with positive edge weights, find a min weight set of edges that connects all of the vertices.
MST is fundamental problem with diverse applications.
• telephone, electrical, hydraulic, TV cable, computer, road
Approximation algorithms for NP-hard problems.
• traveling salesperson problem, Steiner tree
• max bottleneck paths
• LDPC codes for error correction
• image registration with Renyi entropy
• learning salient features for real-time face verification
• reducing data storage in sequencing amino acids in a protein
• model locality of particle interactions in turbulent fluid flows
• auto-config protocol for Ethernet bridging to avoid cycles in a network
Question- 4) Discuss Kruskal's Algorithm
Answer: Kruskal's Algorithm builds the spanning tree by adding edges one by one into a growing spanning tree. Kruskal's algorithm follows a greedy approach as in each iteration it finds an edge which
has least weight and adds it to the growing spanning tree.
• Sort the graph edges with respect to their weights.
• Start adding edges to the MST from the edge with the smallest weight until the edge of the largest weight.
• Only add edges which don't form a cycle, edges which connect only disconnected components.
Floyd's algorithm is a dynamic approach to find the shortest path between all the pairs of vertices in a weighted graph. The graph can be directed or undirected graph.
n = no of vertices
A = matrix of dimension n*n
for k = 1 to n
for i = 1 to n
for j = 1 to n
Ak[i, j] = min (Ak-1[i, j], Ak-1[i, k] + Ak-1[k, j])
return A
C program:
#include <stdio.h>
// defining the number of vertices
#define nV 4
#define INF 999
void printMatrix(int matrix[][nV]);
// Implementing floyd warshall algorithm
void floydWarshall(int graph[][nV]) {
int matrix[nV][nV], i, j, k;
for (i = 0; i < nV; i++)
for (j = 0; j < nV; j++)
matrix[i][j] = graph[i][j];
// Adding vertices individually
for (k = 0; k < nV; k++) {
for (i = 0; i < nV; i++) {
for (j = 0; j < nV; j++) {
if (matrix[i][k] + matrix[k][j] < matrix[i][j])
matrix[i][j] = matrix[i][k] + matrix[k][j];
void printMatrix(int matrix[][nV]) {
for (int i = 0; i < nV; i++) {
for (int j = 0; j < nV; j++) {
if (matrix[i][j] == INF)
printf("%4s", "INF");
printf("%4d", matrix[i][j]);
int main() {
int graph[nV][nV] = {{0, 3, INF, 5},
{2, 0, INF, 4},
{INF, 1, 0, INF},
{INF, INF, 2, 0}};
Question- 5) Discuss Prim's Algorithm.
Answer: Prim's Algorithm also uses the Greedy approach to find the minimum spanning tree. In Prim's Algorithm we grow the spanning tree from a starting position. Unlike an edge in Kruskal's, we add
vertex to the growing spanning tree in Prim's.
1. Remove all the loops and parallel edges.(keep the edges with least cost).
2. Choose any node as a root node and add it to the spanning tree
3. Add another vertex which is not in spanning tree and has least weight edge connected with the spanning tree.
4. Repeat previous step until all the vertices of the graph added to the spanning tree
5. Print the cost.
C code to implement Prims Algorithm:
int a,b,u,v,n,i,j,ne=1;
int visited[10]= {
void main() {
printf("\n Enter the number of nodes:");
printf("\n Enter the adjacency matrix:\n");
for (i=1;i<=n;i++)
for (j=1;j<=n;j++) {
while(ne<n) {
for (i=1,min=999;i<=n;i++)
for (j=1;j<=n;j++)
if(visited[i]!=0) {
if(visited[u]==0 || visited[v]==0) {
printf("\n Edge %d:(%d %d) cost:%d",ne++,a,b,min);
printf("\n Minimun cost=%d",mincost);
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What is the relation between the number of Support Vectors and training data and classifiers performance?
I am using LibSVM to classify some documents. The documents seem to be a bit difficult to classify as the final results show. However, I have noticed something while training my models. and that is:
If my training set is for example 1000 around 800 of them are selected as support vectors. I have looked everywhere to find if this is a good thing or bad. I mean is there a relation between the
number of support vectors and the performance of the classifier? I have read this post previous post. However, I am performing a parameter selection and also I am sure that the attributes in the
feature vectors are all ordered. I just need to know the relation. Thanks. p.s: I use a linear kernel.
Support Vector Machines: SVM is a commonly used machine learning algorithm. It works on the principle to find a hyperplane that divides the two classes with the largest margin.most of the data points
which fall within this margin.
It performs classification in the following ways:
Hard Margin Linear SVM
If data is linearly separable, then you can use a hard margin SVM classifier, the support vectors in this technique are the points which lie along the supporting hyperplanes.
Almost every support vectors lie exactly on the margin. Support vectors are independent of the number of dimensions or size of the data set, the number of support vectors can be at least two.
Soft-Margin Linear SVM
This technique is used when data is non- linearly separable. It is not required that our data points lie outside the margin. There is a slack parameter C used to control this. This gives us a larger
margin and greater error on the training dataset, but improves generalization and/or allows us to find a linear separation of data that is not linearly separable.
Non-Linear SVM
We use different kernel functions in SVM. They have their own set of parameters. When we translate this back to the original feature space, the result is non-linear:
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