text:
In how many different ways, can the letters of the word 'ASSASSINATION' be arranged, so that all S are together? So, there are 5C3 Ã 4C1 = 40 selections where both cousins are included. Copyright © 2005, 2020 - OnlineMathLearning.com.

Initially Permutation and Combination problems may seem hard but once you practice online problems and go through the solution which is provided for every Permutation and Combination problem these aptitude problems will not remain that demanding. i) Find the number of ways in which this can be done. Inter maths solutions for Permutations and Combinations Text book exercises solutions for Permutations and Combinations second inter maths IIA.

problem solver below to practice various math topics. 2). 9). There are 12 boys and 8 girls in the class. ii) Find the number of different ways the paintings can be displayed if the paintings by each of the artists are kept together. Find the number of different ways in which This simply means in how many ways 2 people can be selected out of 12. i) Find the number of different ways the paintings can be displayed if there are no restrictions. 7). selections would have at most one of the cousins. Permutation and combination Questions and answers. So the answer is 12C2, Answer: b. Solution: Solution: There are 20 stations. When all the S are taken together, then AS^AS^INATION are letters. b) Tickets for a concert are given out randomly to a class containing 20 students.

= \frac{11!

All 12 boys got tickets, so there is only 1 way to select all the boys.

Thus, the number of ways in which the child can put the marbles. 66 Permutation & Combination - Aptitude Questions and Answers Part 2. ” Most Important Permutation & Combination Question PDF with Answers“

∴ the total is 12C10 Ã 8C5 = 3,696 ways. C 25200 . The remaining 3 tickets go to 3 girls from 8, we have 8C3 = 56 ways. ∴ the total is 6C4 Ã 5C2 = 150 selections.

Monet's can be arranged in 4! 1). D 210 . = 11!, but it is not mentioned that either it is clockwise or anti-clockwise. So, required number of arrangements = $$\large\frac{1}{2}(12 - 1)! In a meeting between two countries, each country has 12 delegates, all the delegates of one country shakes hands with all delegates of the other country. Number of arrangements = \( \large\frac{n!}{p! Solved Aptitude questions on permutations and combinations with detailed explanations. Answer: b. No student is given more than one ticket. Selecting 4 seniors from 6, we have 6C4 = 15 selections. b) A committee of 4 senior students and 2 junior students is to be selected from a group of 6 senior students and 5 junior students. These solutions are very easy to understand. An alternative is to work out the number of selections where both cousins are in; then we subtract from the total (from b(i) above) and the remaining Ã 3! Solution: Tip: Since there are 9 different letters, and we pick 5 to be arranged, there are 9P5 = 15,120 permutations. Permutation MCQ Question with Answer Permutation MCQ with detailed explanation for interview, entrance and competitive exams. i) Calculate the number of different committees which can be selected. Solution (i) We consider the arrangements by taking 2 particular children together as one and hence the remaining 4 can be arranged in 4! Since A and E are fixed, there are only 3 other letters to arrange in between them, from the remaining 7 letters (9 letters minus the A and E). We welcome your feedback, comments and questions about this site or page. Here, we first have to select 10 ladies from 19. The word 'INHALE' has 6 distinct letters. PERMUTATIONS AND COMBINATIONS 117 Example 4 In how many ways can 5 children be arranged in a line such that (i) two particular children of them are always together (ii) two particular children of them are never together. If both cousins are included, then we select only 3 other seniors from the remaining 6, and 1 other junior from the remaining 4. Ticket is needed between 2 stops. Total number of handshakes = 12 x 12 = 144. Solution: A child has four pockets and three marbles. In how many different ways, the letters of the word 'ARMOUR' can be arranged? Solution: Access the answers to hundreds of Permutation questions that are explained in a way that's easy for you to understand. We can arrange 'n' things in 'n!' ways. In how many ways, the child can put the marbles in the pockets? That means, we simply need to select 2 stops from possible 20 stops. How many different signals , can be made by 5 flags from 8 flags of different colors? Solution: we can work out all the different scenarios: none of the cousins, only the senior cousin included, or only the junior cousin included and add all the selections. Complex numbers 2. Number of arrangements of beads = (12 -1)! 6). One of the 6 senior students is a cousin of one of the 5 junior students. ∴ the total is 8C3 Ã 1 = 56 ways. Chapter 7 Permutations And Combinations Download NCERT Solutions for Class 11 Mathematics (Link of Pdf file is given below at the end of the Questions List) = 1 way. Picasso's paintings can be arranged in 5! }{2}$$. = 24 ways. You can also see the solutions for 1. There are 12 celebrities. De Moivre’s theorem 3. ways and

Explanation: In how many different ways, the letters of the word 'BANKING' can be arranged? ∴ the total is 5!
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Initially Permutation and Combination problems may seem hard but once you practice online problems and go through the solution which is provided for every Permutation and Combination problem these aptitude problems will not remain that demanding. i) Find the number of ways in which this can be done. Inter maths solutions for Permutations and Combinations Text book exercises solutions for Permutations and Combinations second inter maths IIA.

problem solver below to practice various math topics. 2). 9). There are 12 boys and 8 girls in the class. ii) Find the number of different ways the paintings can be displayed if the paintings by each of the artists are kept together. Find the number of different ways in which This simply means in how many ways 2 people can be selected out of 12. i) Find the number of different ways the paintings can be displayed if there are no restrictions. 7). selections would have at most one of the cousins. Permutation and combination Questions and answers. So the answer is 12C2, Answer: b. Solution: Solution: There are 20 stations. When all the S are taken together, then AS^AS^INATION are letters. b) Tickets for a concert are given out randomly to a class containing 20 students.

= \frac{11!

All 12 boys got tickets, so there is only 1 way to select all the boys.

Thus, the number of ways in which the child can put the marbles. 66 Permutation & Combination - Aptitude Questions and Answers Part 2. ” Most Important Permutation & Combination Question PDF with Answers“

∴ the total is 12C10 Ã 8C5 = 3,696 ways. C 25200 . The remaining 3 tickets go to 3 girls from 8, we have 8C3 = 56 ways. ∴ the total is 6C4 Ã 5C2 = 150 selections.

Monet's can be arranged in 4! 1). D 210 . = 11!, but it is not mentioned that either it is clockwise or anti-clockwise. So, required number of arrangements = $$\large\frac{1}{2}(12 - 1)! In a meeting between two countries, each country has 12 delegates, all the delegates of one country shakes hands with all delegates of the other country. Number of arrangements = \( \large\frac{n!}{p! Solved Aptitude questions on permutations and combinations with detailed explanations. Answer: b. No student is given more than one ticket. Selecting 4 seniors from 6, we have 6C4 = 15 selections. b) A committee of 4 senior students and 2 junior students is to be selected from a group of 6 senior students and 5 junior students. These solutions are very easy to understand. An alternative is to work out the number of selections where both cousins are in; then we subtract from the total (from b(i) above) and the remaining Ã 3! Solution: Tip: Since there are 9 different letters, and we pick 5 to be arranged, there are 9P5 = 15,120 permutations. Permutation MCQ Question with Answer Permutation MCQ with detailed explanation for interview, entrance and competitive exams. i) Calculate the number of different committees which can be selected. Solution (i) We consider the arrangements by taking 2 particular children together as one and hence the remaining 4 can be arranged in 4! Since A and E are fixed, there are only 3 other letters to arrange in between them, from the remaining 7 letters (9 letters minus the A and E). We welcome your feedback, comments and questions about this site or page. Here, we first have to select 10 ladies from 19. The word 'INHALE' has 6 distinct letters. PERMUTATIONS AND COMBINATIONS 117 Example 4 In how many ways can 5 children be arranged in a line such that (i) two particular children of them are always together (ii) two particular children of them are never together. If both cousins are included, then we select only 3 other seniors from the remaining 6, and 1 other junior from the remaining 4. Ticket is needed between 2 stops. Total number of handshakes = 12 x 12 = 144. Solution: A child has four pockets and three marbles. In how many different ways, the letters of the word 'ARMOUR' can be arranged? Solution: Access the answers to hundreds of Permutation questions that are explained in a way that's easy for you to understand. We can arrange 'n' things in 'n!' ways. In how many ways, the child can put the marbles in the pockets? That means, we simply need to select 2 stops from possible 20 stops. How many different signals , can be made by 5 flags from 8 flags of different colors? Solution: we can work out all the different scenarios: none of the cousins, only the senior cousin included, or only the junior cousin included and add all the selections. Complex numbers 2. Number of arrangements of beads = (12 -1)! 6). One of the 6 senior students is a cousin of one of the 5 junior students. ∴ the total is 8C3 Ã 1 = 56 ways. Chapter 7 Permutations And Combinations Download NCERT Solutions for Class 11 Mathematics (Link of Pdf file is given below at the end of the Questions List) = 1 way. Picasso's paintings can be arranged in 5! }{2}$$. = 24 ways. You can also see the solutions for 1. There are 12 celebrities. De Moivre’s theorem 3. ways and

Explanation: In how many different ways, the letters of the word 'BANKING' can be arranged? ∴ the total is 5!
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# Uncategorized

## permutation and combination questions and answers pdf

Date: October 1, 2020 Author: Categories: Uncategorized

then we can arrange them in (n-1)! ways. The first marble can be put into the pockets in 4 ways, so can the second and third.

8).

Explanation: Explanation are given for understanding. 7. Turner's can be arranged in 1!

4). Of these paintings, 5 are by Picasso, 4 by Monet and 1 by Turner.

Scroll down the page for examples and solutions on how to use the formulas to solve examination word problems. Answer: c. 380

Exercises 5(a), 5(b), 5(c), 5(d) and 5(e) solutions are given. Also, the 3 artists can be arranged in 3! 0606 S12 Paper 11 Question 4. a) Arrangements containing 5 different letters from the word AMPLITUDE are to be made. r!} B 21300 . Additional Maths Paper 1 May/June 2012 (pdf). A 24000 . Explanation: This page is on "Permutation and Combination" which is a important part of Aptitude problems. But if they are to be arranged in a circle,
In how many different ways, can the letters of the word 'ASSASSINATION' be arranged, so that all S are together? So, there are 5C3 Ã 4C1 = 40 selections where both cousins are included. Copyright © 2005, 2020 - OnlineMathLearning.com.

Initially Permutation and Combination problems may seem hard but once you practice online problems and go through the solution which is provided for every Permutation and Combination problem these aptitude problems will not remain that demanding. i) Find the number of ways in which this can be done. Inter maths solutions for Permutations and Combinations Text book exercises solutions for Permutations and Combinations second inter maths IIA.

problem solver below to practice various math topics. 2). 9). There are 12 boys and 8 girls in the class. ii) Find the number of different ways the paintings can be displayed if the paintings by each of the artists are kept together. Find the number of different ways in which This simply means in how many ways 2 people can be selected out of 12. i) Find the number of different ways the paintings can be displayed if there are no restrictions. 7). selections would have at most one of the cousins. Permutation and combination Questions and answers. So the answer is 12C2, Answer: b. Solution: Solution: There are 20 stations. When all the S are taken together, then AS^AS^INATION are letters. b) Tickets for a concert are given out randomly to a class containing 20 students.

= \frac{11!

All 12 boys got tickets, so there is only 1 way to select all the boys.

Thus, the number of ways in which the child can put the marbles. 66 Permutation & Combination - Aptitude Questions and Answers Part 2. ” Most Important Permutation & Combination Question PDF with Answers“

∴ the total is 12C10 Ã 8C5 = 3,696 ways. C 25200 . The remaining 3 tickets go to 3 girls from 8, we have 8C3 = 56 ways. ∴ the total is 6C4 Ã 5C2 = 150 selections.

Monet's can be arranged in 4! 1). D 210 . = 11!, but it is not mentioned that either it is clockwise or anti-clockwise. So, required number of arrangements = $$\large\frac{1}{2}(12 - 1)! In a meeting between two countries, each country has 12 delegates, all the delegates of one country shakes hands with all delegates of the other country. Number of arrangements = \( \large\frac{n!}{p! Solved Aptitude questions on permutations and combinations with detailed explanations. Answer: b. No student is given more than one ticket. Selecting 4 seniors from 6, we have 6C4 = 15 selections. b) A committee of 4 senior students and 2 junior students is to be selected from a group of 6 senior students and 5 junior students. These solutions are very easy to understand. An alternative is to work out the number of selections where both cousins are in; then we subtract from the total (from b(i) above) and the remaining Ã 3! Solution: Tip: Since there are 9 different letters, and we pick 5 to be arranged, there are 9P5 = 15,120 permutations. Permutation MCQ Question with Answer Permutation MCQ with detailed explanation for interview, entrance and competitive exams. i) Calculate the number of different committees which can be selected. Solution (i) We consider the arrangements by taking 2 particular children together as one and hence the remaining 4 can be arranged in 4! Since A and E are fixed, there are only 3 other letters to arrange in between them, from the remaining 7 letters (9 letters minus the A and E). We welcome your feedback, comments and questions about this site or page. Here, we first have to select 10 ladies from 19. The word 'INHALE' has 6 distinct letters. PERMUTATIONS AND COMBINATIONS 117 Example 4 In how many ways can 5 children be arranged in a line such that (i) two particular children of them are always together (ii) two particular children of them are never together. If both cousins are included, then we select only 3 other seniors from the remaining 6, and 1 other junior from the remaining 4. Ticket is needed between 2 stops. Total number of handshakes = 12 x 12 = 144. Solution: A child has four pockets and three marbles. In how many different ways, the letters of the word 'ARMOUR' can be arranged? Solution: Access the answers to hundreds of Permutation questions that are explained in a way that's easy for you to understand. We can arrange 'n' things in 'n!' ways. In how many ways, the child can put the marbles in the pockets? That means, we simply need to select 2 stops from possible 20 stops. How many different signals , can be made by 5 flags from 8 flags of different colors? Solution: we can work out all the different scenarios: none of the cousins, only the senior cousin included, or only the junior cousin included and add all the selections. Complex numbers 2. Number of arrangements of beads = (12 -1)! 6). One of the 6 senior students is a cousin of one of the 5 junior students. ∴ the total is 8C3 Ã 1 = 56 ways. Chapter 7 Permutations And Combinations Download NCERT Solutions for Class 11 Mathematics (Link of Pdf file is given below at the end of the Questions List) = 1 way. Picasso's paintings can be arranged in 5! }{2}$$. = 24 ways. You can also see the solutions for 1. There are 12 celebrities. De Moivre’s theorem 3. ways and

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### 300iq's blog

By 300iq, 2 months ago,

Hello Codeforces!

I became a coordinator of CodeChef Lunchtimes, and we are in need of high-quality proposals.

We hope to get rid of the 'CodeChef has low-quality problems' label.

So we would be grateful if you can provide a problem set that will work fine for the IOI-style contest! (Note that your problems should not necessarily follow the IOI syllabus).

You can read about compensation and the required difficulty of problems here.

Proposals for Lunchtimes should be submitted to the following e-mail: contest.admin2@codechef.com

P.S. If you have hard problems for CodeChef Long Challenges, you can send them here

• +550

 » 2 months ago, # |   -162 my girlfriend broke up with me and now she's ghosting me?? what do i do?
•  » » 2 months ago, # ^ |   +155 delete your comment : )
•  » » 2 months ago, # ^ |   -42 i broke up with my ex girl, here is the number S I K E thats the wrong numba
 » 2 months ago, # |   +25 So finally you want IOI-style problems or problems for your three type of contest!??
•  » » 2 months ago, # ^ |   +6 What do you mean? IOI-style just means that problems should have subtasks.
•  » » » 2 months ago, # ^ |   +4 problems of type 9, doesnt have subtasks and they are in Long contests(ig), but you've said you want IOI-style problems, i thought maybe you only need these problems for special contest or something like that. (btw ive never participated in any codechef contests so i was confused)
 » 2 months ago, # |   +432 RIP Codeforces 2010-2020
•  » » 2 months ago, # ^ |   +35 Why? as long as you are the coordinator CF has nothing to worry about :P
•  » » » 2 months ago, # ^ |   +97 that's the thing CF need to worry about
•  » » » » 2 months ago, # ^ |   +79 True
 » 2 months ago, # |   -169 Codechef should learn one thing, money can't buy everything, there is reason why Indians use forces more than chef.
•  » » 2 months ago, # ^ |   +30 Don't you know in codeforces also, people are paid to write contests?
•  » » » 2 months ago, # ^ | ← Rev. 2 →   -22 More like they are paid for writing contestsEDIT: I don't know why people are downvoting this as 'for' is the correct expression because codeforces does not pay people to make contests, people decide to make a contest and they are paid a small compensation for the efforts.
•  » » 2 months ago, # ^ |   -14 I am not sure if Indians use codeforces more than codechef..most of my friends have accounts in codechef but not codeforces...may be the more serious ones prefer codeforces.
 » 2 months ago, # |   +105 Oh no... How dare you ruin my impression that Codechef's problems are really bad?! Damn you, Ildar. But honestly, I am really looking forward to seeing you change this platform.
•  » » 2 months ago, # ^ |   +2 Nice trick! :ursmart:
•  » » » 2 months ago, # ^ |   -13 What's the trick?
•  » » » » 2 months ago, # ^ |   +8 no one will downvote him because he said the codechef in trash and he hope to see change at the same time!!
•  » » » » » 2 months ago, # ^ |   +44 I don't think he intended to do that. You are over-analyzing, just like my English teacher.
•  » » 2 months ago, # ^ |   0 diplomacy 10000
 » 2 months ago, # |   +33 The page you linked still says that, for Lunchtime contests, "The syllabus is strictly restricted to IOI."
•  » » 2 months ago, # ^ |   +70 Yeah, it was intended to be like that when Lunchtimes were born, but nowadays this restriction is waived.
•  » » » 6 weeks ago, # ^ |   -28 which code editor do u use for coding ?
 » 2 months ago, # |   -21 All the best 300iq. BIGFAN HERE
•  » » 2 months ago, # ^ |   -15 I am a bigger fan.
•  » » » 2 months ago, # ^ |   +8 okay
•  » » » » 2 months ago, # ^ |   +6 By accepting your defeat, you're now in second place, making you the biggest 300iq fan! Noooooooo
•  » » » » » 2 months ago, # ^ | ← Rev. 2 →   -41 ...
•  » » » » » 2 months ago, # ^ |   0 My english is weak, as far i understand i am 2nd biggest fan and you are first. Right? what does that Nooooo indicate? Noooo means not ?
•  » » » » » » 2 months ago, # ^ |   +19 Just a joke because 300iq always get second place.
•  » » » » » » » 2 months ago, # ^ |   +3 okay
 » 2 months ago, # | ← Rev. 3 →   -57 Some of the areas where I think codechef should improve1)First of all the way it shows our answer is correct.On codeforces,when it comes in green color [Accepted] and when it comes on codechef [green color showing all subtasks have passed], it changes our mind and i can't express my feeling exactly in words,but i basically don't practise on codechef [or practise less] beacuse of this reason. Ya, I know it's a kind of bad thing not looking at problems,and looking on such silly things, but deep inside,I think it matters and when we ask someone why don't you code on codechef they just say "level of problems" [actually i also say this to some of my frnds], but somewhere the reason it also that green color.2)Secondly, lets say if someone is solving a problem,then codeforces show that how many testcases have passed or how many pretests have passed, but codechef doesn't shows this, it just show red color or the green one.Even if someone is failing on the sample testcases, then also codechef doesn't shows that sample answer is wrong [Although i know its coders responsibility to check and run on sample testcases],but that small thing also affects our behaiviour towards codechef,and then when it comes why don't you code on codechef,we don't actually explain this all ,we simply say "level of problems".3)Other reasons are just the way it displays problems and the testcases, and one thing why the problem is displayed on the left side of the screen and not in the centre and the right side panel is just for the submissions,why isn't the problem and the testcases given the centre alignment like codeforces.And again when it comes to why don't you code on codechef we just say .................So that's all i want to mention,and these are my reasons,what i think personally,I know that building a platform like codechef requires a lot of hardwork, but this is what i think and therefore uses codechef less. I know i should just enjoy the problems and should not bother about such things,but when it comes to work on a nicely organized platform and platform [I am just talking about the way the codechef pages appear,don't take it wrong way],I prefer to work and spend time on the first one.One thing i don't like about codeforces is that sometimes questions are not given ratings in a proper manner ,means sometimes they are underrated or overrated, but then also when it comes to practise, i normally type codeforces.com because there are a lot of things [actually everything] which i love about it.
•  » » 2 months ago, # ^ |   0 I didn't get your first point. CodeForces shows green and CodeChef shows green, what is wrong with that? Could you explain in a simpler way?
•  » » » 2 months ago, # ^ |   -23 I mean it comes it green color [Accepted] ---> it looks awesomebut in codechef it just shows in light green color subtasks 1 is passed,subtasks 2 and so on.what i mean is its not as attractive as codeforces.
•  » » » » 2 months ago, # ^ | ← Rev. 2 →   +13 [I dont think you want more green than this]()
•  » » 2 months ago, # ^ |   +55 be mature stop comparing this silly things green vs less green or whatever.
•  » » » 2 months ago, # ^ |   -18 Believe it or not but when you would make a website and someone will suggest you to apply some changes with respect to light and dark color,your maturity would go to hell and you would make that color light color --> dark color
•  » » » » 2 months ago, # ^ |   0 in codechef also it shows green color in fact it shows green color for all the subtasks which makes us really satisfied but in codeforces just accepted is shown in green.
•  » » » » » 2 months ago, # ^ |   -19 Now where's your maturity,you are also comparing"green color for all the subtasks which makes us really satisfied but in codeforces just accepted is shown in green."
•  » » » » » » 2 months ago, # ^ |   -14 first u started then i followed.
•  » » » » » » » 2 months ago, # ^ |   -14 so its not a silly thing to compare green and less green or whateverbcoz i started and then u followed it.
•  » » » » » » » » 2 months ago, # ^ |   0 see if someone is wrong then it's our responsibility to rectify him.so u were proposing wrong statement so i intervene to amend it.
 » 2 months ago, # |   +20 Hey! Thanks for taking up this role.Can we now expect more, and better quality subtasks in each problem? As far as I know, IOI problems tend to have at least ~5 or more subtasks, but most lunchtime problems have about 2.
•  » » 2 months ago, # ^ |   +46 I believe they have an "unwritten" rule that each problem should have just $1$ subtask worth $50$ points to make the scoring uniform. I doubt that people at CodeChef even care about the subtask quality since they're barely able to get the actual problems in time.
 » 2 months ago, # |   +12 Please Change the UI look as well as problem quality because codechef looks is rather distracting and very ancient, whereas Codeforces UI look is quite gorgeous.
•  » » 2 months ago, # ^ |   -14 I guess it's the opposite.
•  » » 2 months ago, # ^ |   +2 I love codeforces, but the UI is not 'gorgeous'
•  » » » 2 months ago, # ^ |   0 Just wondering. Which cp sites are then better from the ui point of view?
•  » » » » 2 months ago, # ^ |   -17 CSAcademy is the best, most other sites other than CF have better looking UIs since they're filled with less options everywhere
•  » » » » 2 months ago, # ^ |   +24 I feel that AtCoder is neat, but there isn't a discussion forum there.
•  » » » » » 2 months ago, # ^ | ← Rev. 5 →   +11 That's what I feel too. Atcoder is quite decent, but it is missing a lot of convenient features. Also overall it seems somewhat cheap, because it is just plain bootstrap. Not like it matters much. Though it is easier to get used to it than codeforces because its design is way simplierCodechef is terrible. Participated in a couple of contests, ui was not enjoyable in the slightest. Topcoder is far beyond being just terribleSo from my experience, codeforces is really the best
•  » » » 2 months ago, # ^ | ← Rev. 2 →   +60 I like CF UI. It looks professional and clean while not being overly minimalistic.IMO many websites try too hard to have a very "modern" look but it just ends up looking cheap and kinda ugly. Many websites look like iPad apps but computers are not tablets and UI decisions need not be the same. I especially heavily dislike some fancy animated websites with title "React App" that don't even work half the time. Normal HTML+CSS is much nicer, let JS be a scripting language.And IMO an indirect reason CodeChef and TopCoder UIs suck is that they try to be fancy but can not pull it off.
•  » » » » 2 months ago, # ^ |   +3 Google was clean Yahoo was not. Internet Explorer had many toolbars, then came chrome. a clean and simple look is better.
 » 2 months ago, # |   +6 Not only quality of problems but codechef has to change it's whole format to compete with codeforces. 10 days for a contest is too much of time. There are only 2 official short contests in a month.
•  » » 2 months ago, # ^ |   +43 As long as the contest offers actually interesting problems that requires something like 5 hours of thinking and 2-3 hours of implementation rather than think for 5 minutes and then code for 3 days (say something like the problems that use generating functions, but with a greater variety of algorithms), I wholeheartedly support a contest that last 10 days.
•  » » » 2 months ago, # ^ | ← Rev. 2 →   -11 I feel Codechef is slow as compared to Codeforces in many ways. There should be quality + pace of learning.
•  » » » » 2 months ago, # ^ |   +3 It's indeed slower, but if the contests are genuinely good it would worth it (see Atcoder/Topcoder for example). OC, the problem is that Codechef's problems are often of very poor or poor quality and their website not exactly user-friendly, but with Ildar being a coordinator, we can hope for some changes in the future.
 » 2 months ago, # |   +9 I've sent a problem idea a year and a half ago. No response :/
•  » » 2 months ago, # ^ |   +53 Have you tried making a blog post complaining about how you got no response?
•  » » » 2 months ago, # ^ |   +15 Didn't care that much
 » 2 months ago, # |   +82 People who are saying codechef has low quality problems are probably very out-dated (especially if they mean the problems offered in short contests too). I mean they got this impression many years ago and never gave codechef a second chance.
•  » » 2 months ago, # ^ |   -11 To be fair, I recently gave Codechef another chance in the August Cook-Off, and one of the problems was the exact same as a CSAcademy problem (both statements even used red and blue, lol).However, I think 300iq becoming coordinator will improve the quality tremendously. Great decision by Codechef, and I'll definitely continue to compete because of it.
•  » » » 2 months ago, # ^ | ← Rev. 3 →   +51 This is different from what I meant.the issue of repeated problem in general is really difficult to avoid because the only perfect way to avoid it is by having contest admin who knows all problems on the internet. I mean when a contest admin receive a proposal of interesting problem idea and he hasn't seen it before then it's natural to approve and use it in a contest. Surely the contest admin who have seen more problems on the internet will do a better job at avoiding this issue.What I meant in my first comment is that some people think that it's a habit of codechef to just offer standard/repeated problems or problems which require zero thinking and heavy coding, it's been very long time that this is no longer the case in codechef.
•  » » » » 2 months ago, # ^ |   0 I think you are right !! codechef has good problems, especially related to mathematics. Not until I read the blog , my initial impression was codeforces is borrowing mathematical problems from codechef, lol.
•  » » » » 2 months ago, # ^ |   0 Both are equally good and should learn from each other. :)
•  » » » » 2 months ago, # ^ |   +5 I also had the same mindset about codechef, but for the last 3-4 months i have only been giving short contests and i feel the quality of questions especially in Div 1 has greatly improved other than some exceptional cases. Though I strongly feel that quality of servers can be improved and frequency of short contests can be increased.
•  » » » » 2 months ago, # ^ |   -17 So ultimately you are saying that codechef admin sucks,right ?
 » 2 months ago, # | ← Rev. 2 →   0 I only give short challenges at codechef, Came in CP around 6-7 months ago and probably don't know large set of problems(as which ones are copied or not from other cp websites) but I found their short challenges pretty interesting and tough to solve(can only solve 2 in cookoff/lunchtimes) but this may vary to more experienced user who are more familiar with CC and CF.I just hope if there is at-least 1 more short challenge on CC then it would be pretty interesting. Right now they only have 2.
 » 2 months ago, # | ← Rev. 2 →   0 If 300iq will be coordinator of lunchtime. Will he leave his duties involving codeforces?
 » 2 months ago, # |   +6 I just wish CodeChef increases the frequency of short contests. It's a pain to wait a month for the next contest. But yeah, of course, quality comes first.Recent memory, screwed up in Cook-off, thought would do good at lunchtime, missed lunchtime by accident, had to painfully wait 30 days for the next contest.
 » 2 months ago, # |   0 Can you increase the frequency of contests per month?
 » 2 months ago, # |   -15 Interesting that codechef has now a Legendary GM as coordinator..hope to see changes now..
 » 2 months ago, # |   +11 To all people suggesting increasing the frequency of contests: what about Codechef first establishes the quality, then increases the quantity?
•  » » 2 months ago, # ^ |   -12 To the point CodeChef_admin, 300iq please consider this first
•  » » 2 months ago, # ^ |   -18 With all due respect, CC is having much better contests than CF these days. Have a look at some previous longs/cookoffs/lunchtimes. Problems in CC actually involve algorithms and good logic, whereas in my opinion, CF problems especially A,B,C (Div 3,2) are largely based on observational skills and maths (constructive).However, this is just my opinion, and others may of course disagree.
•  » » » 2 months ago, # ^ |   +16 The issue here is that many authors treat low-rated problems (i.e. Div 2 A-C) as perfunctory, so the problems don't have much thought put into them. Another thing is that there are only so many ways one can write problems for grey->cyan coders, as they normally can't do many things beyond the basic math, greedy and dp, so you really can't pull something very creative. ofc, you mostly do these low-rated problems so I can't really blame you for thinking this.CF has many interesting problems though, you just need to look higher up the rating scale. On the other hand, I feel like many CC problems are very implementation-based (e.g. most of the DS problems, which take no thought and 200+ lines of implementation). In my opinion though, the best place to go for interesting problems is AtCoder, which mostly has really light implementation but require a lot of thought.
 » 2 months ago, # |   0 Nice Initiative
 » 2 months ago, # |   +18 We hope to get rid of the 'CodeChef has low-quality problems' label. On codechef, it's not easy to know whether a contest is an official (high-quality) or not (no guarantee of quality). Actually, I judge it from only my experience (cook-off, lunchtime, and challenge are official). Is there another easy way?
•  » » 2 months ago, # ^ |   +8 With my experience you can identify if the contest is rated or not. Rated contest are more legit as compared to non-rated ones. Plus there are many college contests as well, I generally go by the prizes as that kind of ensures that organizing team has put some efforts in the preparation.
•  » » » 2 months ago, # ^ |   +14 So, how can people know whether a contest is rated or not?(IMO, the prize doesn't ensure that. Here is an example from a recent contest. All of 3 problem statement was super unclear, and nobody understands the 3rd problem after all.)
•  » » » » 2 months ago, # ^ |   +8 For the rated contest except the ones you mentioned, Cook off, Lunchtime and Long they mention along with the contest name. For eg {name}(Rated for all/Div2) . And yes not all contests that have prizes are legit but they have a decent probability of being good. Club with a reliable organisation and it becomes more reliable, like many organisations conduct some sort of annual coding contests and for such contests there is a codeforces blog for the same.
•  » » » » » 2 months ago, # ^ | ← Rev. 2 →   0 except the ones you mentioned, Cook-off, Lunchtime, and Long I'm talking about the official contests, and these ARE official contests :(
•  » » » » » » 7 weeks ago, # ^ |   -10 codechef official contest are:cookoff lunchtime and long
•  » » » » » » 5 weeks ago, # ^ |   +2 darklight13 means that it's easy to know whether contest is rated on CodeChef, because for all rated contests except monthly ones (Cook-off, Lunchtime and Challenge) it's explicitly stated in its name. For example, "Coders' Legacy (Rated for all)".


text:
# Two packages stacked on one another

1. Oct 5, 2014

### hamzaarfeen

1. The problem statement, all variables and given/known data
A delivery van has two packages left that are stacked one on top of another. The upper packages
has a mass of 4.0 kg and is a poorly packaged glass vase, while the lower package has a mass
6.5 kg. The coefficient of static friction between the two packages is 0.211 and the lower box is
fixed to the floor of the van. Since the delivery person is late, he has been accelerating quickly
whenever he has stopped and started (at lights, stop sign etc.), however he never exceeds the
town's speed limit of 60 km/h. What is the minimum amount of time it takes for him to reach
his top speed while still keeping the vase from breaking (sliding off the top box).

2. Relevant equations
friction= coefficient x contact force
fnet=ma

3. The attempt at a solution
friction = 0.211x 4kg x 9.81
= 8.24N
what do i do next?

Last edited: Oct 5, 2014
2. Oct 5, 2014

### _N3WTON_

a hint: for the 4kg box not to slide off of the 6.5kg box it must have the same acceleration as the 6.5kg box, this acceleration is caused by the static friction between the two boxes

3. Oct 5, 2014

### hamzaarfeen

so how can i solve it? if i make two equations, then one can be made for the upper box using f=ma, but what about the other equation?

4. Oct 5, 2014

### _N3WTON_

find the acceleration using the hint, and then using this acceleration find the time to reach 60 km/h...I hope i'm not giving away too much but to find the acceleration know that:
$F_{fr top} = (m_{top})(a) = (u_s)(F_{N top})$


text:
listen; there's a hell of a good universe next door: let's go.go theremore quotes

# information: exciting

DNA on 10th — street art, wayfinding and font

# The Ptolemaic Clock — A Proposal

## the standard clock

Consider the lowly wall clock. It's practical and generally tells the correct time. It's the same clock everywhere and after a while it gets boring pretty quickly—maybe now?

In a standard clock, the bezel is fixed and the hands rotate.

In the regular clock the face bezels stay in place and the hands move. Why am I telling you this? Well, maybe you see where I'm going.

## the Ptolemaic Clock

Who says it's the hands that have to rotate? Instead of rotating hands and a stationary bezel, consider the clock with stationary hands rotating bezels.

In the Ptolemaic clock, the hands stay in place while independent minute and hour hand bezels rotate to simulate the movement of the hands.

In the Ptolemaic clock there are two independent bezels and two independent hands. The bezels rotate counterclockwise to simulate the standard clockwise motion of the hands. The hands are not moving but in the frame of reference of the bezels, it's the hands that are rotating. The position of the bezel is always related to the current time and the position of its corresponding hand.

The bezel can move clockwise.

Thanks to Rodrigo Goya for suggesting the name for this kind of clock—Ptolemaic Clock, named so after the geocentric Ptolemaic model of the solar system.

## telling time on the Ptolemaic clock

To tell the time on the Ptolemaic clock is a process identical to using the standard clock. You look at the bezel numbers at the ends of the hour and minute hands.

On the fixed bezel layout, most people will take a short cut and tell the time by the position of the hands. This works as long as you have a standard clock. On a Ptolemaic clock the position of the hands tells you nothing.

Here is a Ptolemaic clock telling us it is 6:30. It uses the same position of hands as in the figures above.

You know this because the blue hour hand points to midway between 6 and 7 on the inner hour bezel and the grey minute hand points to 30 on the outer minute bezel.

It is 6:30 on this Ptolemaic clock.

After 15 minutes, it's 6:45 and our Ptolemaic clock bezels have moved a little bit.

It is 6:45 on this Ptolemaic clock.

Can you tell what time it is on the Ptolemaic clock below?

If you answered 8:50, you are correct. It is 8:50.

## customizing the Ptolemaic clock

Customizing your Ptolemaic clock is easy. Simply adjust the hands to desired positions and set the time by moving the bezels. The clock below shows the same time as the clock in the above figure — both show 8:50.

This clock tells us it's 8:50. Compare this to the clock in the figure above, which also tells the same time.

## ptolemaic clock — hard layout

In the clock design shown here, the hands are the same size and only differ by color. To make things less confusing, emphasize the hour hand.

To make things more confusing, remove all color and number cues, keeping only a single symbol on each of the bezels to indicate 12 o'clock and 0 minutes. This is shown in the clock below.

In the hard layout of a Ptolemaic clock, there are fewer cues. I think it's 8:50.

## news room parodies

Spice it up with multiple Ptolemaic clocks side-by-side telling the same time with different hand positions.

Suppose it is 2:30 in Vancouver—this is my location. The clocks below all show 2:30, but with hands set to 5:30, 11:30 and 7:30.

Looks like a wall of clocks in a newsroom. Except these Ptolemaic clocks tell us that it's 2:30, three times over in Vancouver.

These hand positions are those that would appear on a standard clock showing the times in New York (5:30), Paris (11:30) and Tokyo (7:30).

Let's now use the Ptolemaic clock to show times at these three locations but with the hand set to the curiously satisfying layout of 10ish minutes to 2.

A challenging panel of Ptolemaic clocks.

### TIP

Set both hand positions to 12 o'clock and then remove the hands; to tell time, read the numbers on the hour and minute bezels at the apex of the clock.

### EXTENSION

Sophisticated implementations of the Ptolemaic clock could periodically randomize hand positions to keep things interesting; by the time you've figured out the time in the morning, you're wide awake.

Every minute the clock randomly resets its hand positions. The movement is smooth and the bezels follow.

## hardware implementation

If you would like to implement the Ptolemaic clock, I would be happy to hear from you. One should be able to take a regular wall clock, reverse the direction of the hand mechanism and rig a freely moving bezel to each of the minute and hour mechanism. The hands should not move and can be fixed to the front glass plate, for example.

## conclusions

It should now be clear that the Ptolemaic clock is superior to the standard clock. The reasons are

• it's much harder to tell time on the Ptolemaic clock, which makes your brain do more work
• it tips its hat off to a simpler time when we didn't know anything and hints at the possibility of regression anytime
• it will confuse everyone
• you have a great excuse for being late
• return to geocentric values!
• you can customize your own Ptolemaic clock by moving the hands to arbitrary locations
• two Ptolemaic clocks can have their hands and bezels at different positions but still be telling the same time
• two Ptolemaic clocks can have their hands at the same position but be telling different times
VIEW ALL

# Quantile regression

Sat 01-06-2019
Quantile regression robustly estimates the typical and extreme values of a response.

Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"

Nature Methods Points of Significance column: Quantile regression. (read)

Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.

Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.

### Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.

# Analyzing outliers: Robust methods to the rescue

Sat 30-03-2019
Robust regression generates more reliable estimates by detecting and downweighting outliers.

Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.

Nature Methods Points of Significance column: Analyzing outliers: Robust methods to the rescue. (read)

We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.

Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.

### Background reading

Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.

# Two-level factorial experiments

Fri 22-03-2019
To find which experimental factors have an effect, simultaneously examine the difference between the high and low levels of each.

Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.

They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.

Nature Methods Points of Significance column: Two-level factorial experiments. (read)

Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).

Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.

### Background reading

Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.

# Happy 2019 $\pi$ Day—Digits, internationally

Tue 12-03-2019

Celebrate $\pi$ Day (March 14th) and set out on an exploration explore accents unknown (to you)!

This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.

A special kids' edition merges math with color and fat fonts.

116 digits in 64 languages. (details)
223 digits in 102 languages. (details)

Check out art from previous years: 2013 $\pi$ Day and 2014 $\pi$ Day, 2015 $\pi$ Day, 2016 $\pi$ Day, 2017 $\pi$ Day and 2018 $\pi$ Day.

# Tree of Emotional Life

Sun 17-02-2019

One moment you're $:)$ and the next you're $:-.$

Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.

A section of the Tree of Emotional Life.

# me as a keyword list

aikido | analogies | animals | astronomy | comfortable silence | cosmology | dorothy parker | drumming | espresso | fundamental forces | good kerning | graphic design | humanism | humour | jean michel jarre | kayaking | latin | little fluffy clouds | lord of the rings | mathematics | negative space | nuance | perceptual color palettes | philosophy of science | photography | physical constants | physics | poetry | pon farr | reason | rhythm | richard feynman | science | secularism | swing | symmetry and its breaking | technology | things that make me go hmmm | typography | unix | victoria arduino | wine | words


text:
# High Altitude Balloon Communication

Our team is planning to make a HAB (High Altitude Ballon) project for our university. We are planning to use XBee pro 868 RF modules (we are in Europe so we can not use 900 MHz band). We have to communicate to the base station from the payload from 20-30 km distance. My question is, what kind of antennas will we need to use? The Xbee data-sheet says that with high gain antennas the module can communicate up to 40 km with clear LOS (line of sight). If we put high gain antennas like YAGI types on the base station, do we still need to attach high gain antennas or are dipole antennas enough for the payload ?

Note : I know that at some distance the connection will be lost and we have to move our base station according to last GPS data to find payload location landing area. But we are trying to do best as we can to extend communication duration before we lose the connection.

Module specifications:

• What data rate do you have to communicate or is it voice or voice and data? What power output is the RF module? Is it two-way comms? What is the stated sensitivity for your receiver? Can you link a data sheet? – Andy aka Nov 29 '14 at 17:25
• Since you're a student I will mention this but given that English may not be your first language, I won't comment on those edits, but in general, you should treat this as you would your school assignments. Your question as posted was very sloppy with poor attention to presentation. Attending university isn't just about the course work, it's also about communicating and making yourself understood. – placeholder Nov 29 '14 at 18:08
• The specifications you list here say that 40km is attainable with dipole antennas, which are hardly directional at all. With more directional antennas, even greater distances should be attainable. – Phil Frost Nov 29 '14 at 20:23
• Instead of posting a snapshot of what the spec says why don't you state the data rate YOU need to use. If you don't understand my previous comment you may be over your head on this. – Andy aka Nov 30 '14 at 1:01
• Consider a low cost cell phone. Good range, clear communications, video, built in GPS, light weight, easily replaced, external battery options, some support Data modes, built in antenna. – Optionparty Nov 30 '14 at 2:41

What you need is a link budget. The specifications you supply say that the maximum transmit power is 25 dBm, and the receiver sensitivity is -112 dBm. This means that you can afford, at best:

$$25\:\mathrm{dBm} - (-112\:\mathrm{dBm}) = 137\:\mathrm{dB} \text{ of loss }$$

You will, of course, want to leave a healthy margin for robustness, but it gives you some bounds.

Loss calculation is greatly simplified for a balloon, since we can reasonably assume a clear line of sight. Atmospheric conditions (fog, rain, etc) can increase the loss, and you may have to compete against noise from other radios on the same frequency, but that's what the margin is for.

The most obvious loss is that due to the distance between the antennas. This is called the free space path loss, and we can calculate this loss, in decibels, as:

$$20 \log_{10}(d) + 20 \log_{10}(f) + 32.45$$

Where:

• $d$ is the distance, in kilometers
• $f$ is the frequency, in megahertz

So for your specified distance of 30 km, and a frequency of 868 MHz:

$$20 \log_{10}(30) + 20 \log_{10}(868) + 32.45 = 120.76 \:\mathrm{dB}$$

This loss (121 dB) is less than the maximum loss based on the transmit power and sensitivity above (137 dB), so in theory, the link should work, even with an isotropic antenna.

In fact, you have a margin of $137 - 121 = 16 \:\mathrm{dB}$. Any gain that your antennas have is going to increase this margin. It doesn't matter if you add antenna gain at the receiver, transmitter, or both. Because of reciprocity, any gain in the system helps the same way. Additional margin may also allow the transmitters to operate at a lower power, which will increase your battery life, if that's a concern.

There's another source of loss that may not be obvious: polarization loss. Since the balloon is spinning about, you don't know what its orientation will be. Satellite communications have the same problem, and the canonical solution is circular polarization.

Since you don't need a lot of gain (and in fact, too much gain will make it hard to aim the antennas), a turnstile antenna may be a good option. It's circularly polarized and easy to construct. Adding a set of reflectors as in the first image from that Wikipedia article might not be a bad idea for the ground antenna, just for some extra margin:

This antenna could also be described as two crossed Yagi antennas on the same boom and fed in quadrature, so to calculate the geometry of the antenna elements you can use existing Yagi designs. If you research Yagi antennas for satellite communication you should find ample information.

The issue that you will have in any high gain antenna is the loss of spatial diversity. Simply put the more gain, the better the tracking had better be. The balloon-borne side of things dictates that you probably can't have any tracking there simply because of weight, power and complexity. However, consider that you don't need to be transmitting upwards, so an antenna with only a forward (downward) component will give a nice trade off between antenna gain and spatial diversity, there really is no trade off there. If you have a good idea of the wind conditions (i.e. predicting down wind travel distance) that are typical and the height you intend to reach then you might be able to restrict your antenna directionality further and still not have to have tracking.

A nice directional antenna like a YAGI with tracking at the base station sounds like the right idea. Especially if it is mobile and you can move to keep closer.

• What about using YAGI for base and using PATCH(180 degree) antenna for payload ? – user2638084 Nov 29 '14 at 17:49

If you are going to be transmitting 20-30 km from the antenna, I would suggest using am omnidirectional antenna on the balloon. You can't have a directional antenna pointing straight down, and if you try to mount it at an angle, you won't be able to control the direction since the balloon can rotate in any direction.

Although it would seem that the longer the antenna the better, actually a 1/4 wavelength (86 mm at 868 MHz) monopole "whip" antenna is the best choice for you. For other lengths such as 1/2 or 5/8 wavelength there will be a reactive component at the feed point which requires additional loading to match to 50 ohms.

The advantage of monopole antennas is its radiation pattern is uniform in all directions, unlike for example a dipole antenna (which are typically 1/2 wavelength) which has radiation patterns concentrated into two lobes.

Whip antennas are designed to be mounted above (or below, in your case) a ground plane, such as the roof of a card, and there is no radiation below (above) this ground plane. Pretend the car below is your balloon.

So you need to provide either a ground plane, or provide a pseudo ground plane using additional elements angling down from the antenna as shown below on the right. Thee are actually four, the two perpendicular to the others are not shown. They can be any stiff material; coat hangers would do fine. These other elements are the same length, 1/4 wavelength, as the antenna. The metal ground plane below the antenna on the left is the roof of a car.

At your base station I would use a directional antenna such as a Yagi since you can precisely control the direction.

I have successfully used this arrangement to receive data at 920 MHz from a transmitter on a balloon flying at 70,000 feet and 240 miles away from my base station (a truck), using a whip antenna at both ends.

• Why can't a directional antenna point straight down? – Phil Frost Nov 29 '14 at 19:12
• Also, a 1/4 wave monopole has exactly the same radiation pattern as a 1/2 wave dipole, except for the lack of radiation below the ground plane as you mention. The dipole's radiation pattern is a doughnut, and the monopole is a sliced bagel. A horizontal dipole over ground can have its doughnut pattern distorted by the image antenna created by the ground, but this isn't going to happen in a balloon. – Phil Frost Nov 29 '14 at 19:18
• Also, coat hangers, usually being made of mild steel, aren't a great choice for antenna material. The high permeability of steel (iron in particular) increases skin effect, making the lossier than it needs to be. The lacquer coating on a typical coat hanger is also a pain to remove for a good electrical connection. Aluminum or copper are better choices. – Phil Frost Nov 29 '14 at 20:20
• "Why can't a directional antenna point straight down?" I hadn't thought of that, but I imagine it would work. I'm not sure it would have any advantages over the monopole, since you would lose half of the power in wasted the backward lobe. Re the coat hangers, that was suggested in the article accompanying that diagram, but you make some good points. – tcrosley Nov 29 '14 at 20:28
• Why the downvote? – tcrosley Nov 29 '14 at 20:34


text:
Getting Started
Using Euphoria
Protocol Mechanics
Contracts
Bonding

# Bonds Overview

Bonding is the secondary value accrual strategy of Euphoria. Bonds both incentivize and lock liquidity by offering an attractive risk/reward profile.
When users mint WAGMI tokens, they are actually selling their assets in order to buy a bond from the protocol. Buying a bond entitles users to purchase WAGMI at a discount when the rates are favorable.
Bonds are a cross between a fixed income product, a futures contract, and an option. The protocol quotes the bonder with terms for a trade at a future date. These terms include a predefined amount of WAGMI the bonder will be entitled to, and the time when vesting is complete. The bond becomes redeemable as it vests - e.g. in a 5-day term, after 2 days into the term 40% of the rewards can be claimed.
Bonding is an active, short-term strategy. The price discovery mechanism of the secondary bond market renders bond discounts more or less unpredictable. Therefore bonding is considered a more active investment strategy that has to be monitored constantly in order to be more profitable as compared to staking.
Allowing users to purchases bonds by minting WAGMI allows Euphoria to accumulate its own liquidity. We call our own liquidity POL. More POL ensures there is always locked exit liquidity in our trading pools to facilitate market operations and protect token holders. Since Euphoria becomes its own market, on top of additional certainty for WAGMI investors, the protocol accrues more and more revenue from LP rewards bolstering our treasury, and allowing more rewards for stakers.

# Bond Pricing

$Bond Price = 1 + Premium$
$Premium = BCV * Debt Ratio$
The premium is derived from a scaling variable called the Bond Control Variable (BCV) and the debt ratio. Protocol controlled adjustments to the BCV allows us to control the rate at which bond prices increase. This ties the price of bonds to the number of bonds outstanding. The fewer bonds outstanding, the lower the premium, and the higher the discount.
Profits for the protocol, and in turn stakers, is determined from the premium. New WAGMI is minted from the protocol's profit and distributed to stakers.
$DebtRatio = Bonds Outstanding / WagmiSupply$
The debt ratio is the total WAGMI still due to be paid out to bonders divided by the total supply of WAGMI.


text:
## Augmentations and Legendrians at the Institute for Advanced Study

### Thursday and Friday February 11-12, 2016

Poster

Speakers
Roger Casals (MIT)
Baptiste Chantraine (Nantes)
John Etnyre (Georgia Tech)
Emmy Murphy (MIT)
Lenny Ng (Duke)
Lisa Traynor (Bryn Mawr)

Schedule (all talks to take place in Simonyi Hall 101)

Thursday February 11, 2016

 10.4 Chantraine Restrictions on the fundamental group of some Lagrangian cobordisms. 1 Ng Toward a contact Fukaya category 2.3 Etnyre Satellite operations and Legendrian knot theory

Friday February 12
 10.4 Murphy A frontal view on Lefschetz fibrations I 1 Casals A frontal view on Lefschetz fibrations II 2.3 Traynor A Quantitative Look at Lagrangian Cobordisms

Abstracts

3/10

Chantraine Abstract: In this talk we will describe two methods which shows that, under some rigidity assumptions on the involved Legendrian submanifolds, a Lagrangian cobordism is simply connected. The first one uses the functoriality of the fundamental class in Legendrian contact homology with twisted coefficients. The second uses a L^2-completion of the Floer complex associated to the cobordism. This is joint work with G. Dimitroglou Rizell, P. Ghiggini and R. Golovko.

Ng Abstract: I will describe some work in progress (maybe more accurately, wild speculation) regarding a version of the derived Fukaya category for contact 1-jet spaces J^1(X). This category is built from Legendrian submanifolds equipped with augmentations, and the full subcategory corresponding to a fixed Legendrian submanifold \Lambda is the augmentation category Aug(\Lambda), which I will attempt to review. The derived Fukaya category is generated by unknots, with the corollary that all augmentations come from unknot fillings''. I will also describe a potential application to proving that augmentations = sheaves''. This is work in progress with Tobias Ekholm and Vivek Shende, building on joint work with Dan Rutherford, Vivek Shende, Steven Sivek, and Eric Zaslow.

Etnyre Abstract: Satellite operations are a common way to create interesting knot types in the smooth category. It starts with a knot K, called the companion knot, in some manifold M and another knot P, called the pattern, in S^1\times D^2 and then creates a third knot P(K), called the satellite knot, as the image of P when S^1\times D^2 is identified with a neighborhood of K. In this talk we will discuss the relation between Legendrian knots representing K, P, and P(K). Sometimes the classification of Legendrian representatives for K and P yields a classification for P(K), but other times it does not. We will discuss why this happens and a general framework for studying Legendrian Satellites.

3/11

Casals & Murphy Abstract: In this series of two talks we will discuss Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. The main focus is on Weinstein manifolds which admit a Weinstein Lefschetz fibration with an $A_k$--fibre; this provides a large class of Weinstein structures ranging from flexible Weinstein manifolds to rich rigid examples. In particular, we will describe the computation of their symplectic homologies and discuss its implications to Legendrian submanifolds and their Lagrangian fillings.

Traynor Abstract: Lagrangian cobordisms between Legendrian submanifolds arise in Relative Symplectic Field Theory. In recent years, there has been much progress on answering qualitative questions such as: For a fixed pair of Legendrians, does there exist a Lagrangian cobordism? I will address two quantitative questions about Lagrangian cobordisms: For a fixed pair of Legendrians, what is the minimal “length” of a Lagrangian cobordism? What is the relative Gromov width of a Lagrangian cobordism? Regarding length, I will give examples of pairs of Legendrians where Lagrangian cobordisms are flexible in that the non-cylindrical region can be arbitrarily short; I will also give examples of other pairs of Legendrians where Lagrangian cobordisms are rigid in that there is a positive lower bound to their length. For the second quantitative measure, I will give some calculations and estimates of the relative Gromov width of particular Lagrangian cobordisms. This is joint work with Joshua M. Sabloff.

Sadly we have no funding, however there will be free cookies, tea, and coffee each day from 3-4pm in Fuld Hall. Additionally, the talks will be videotaped, with links appearing on this webpage.


text:
# Elastic propagation and FWI¶

The regular scalar propagator has one model parameter (wavespeed). The scalar Born propagator has two (wavespeed and scattering potential). The elastic propagator has three. This makes it interesting to study as an inverse problem, because, in addition to the difficulties that already exist with scalar wave propagation inversion, there are problems caused by crosstalk between the model parameters. The ease of experimenting with different model parameterisations and loss functions makes Deepwave well suited to trying out new ideas to solve these problems. In this example we will just perform a simple forward propagation and inversion, though, to show you the basics.

One popular way to parameterise elastic propagation is with $$v_p$$, $$v_s$$, and $$\rho$$ (the p and s wavespeeds and the density). Another uses $$\lambda$$, $$\mu$$, and buoyancy (the two Lamé parameters and the reciprocal of density). Deepwave internally uses the latter, and provides functions to convert between the two parameterisations. To demonstrate that you can parameterise the model any way that you like and use PyTorch’s end-to-end forward and backward propagation to update your own model parameters, in this example we will use $$v_p$$, $$v_s$$, and $$\rho$$.

We begin by setting up the model (both background and true, the latter of which we will use to generate the “observed” data) and acquisition:

device = torch.device('cuda' if torch.cuda.is_available()
else 'cpu')
ny = 30
nx = 100
dx = 4.0

vp_background = torch.ones(ny, nx, device=device) * 1500
vs_background = torch.ones(ny, nx, device=device) * 1000
rho_background = torch.ones(ny, nx, device=device) * 2200

vp_true = vp_background.clone()
vp_true[10:20, 30:40] = 1600
vs_true = vs_background.clone()
vs_true[10:20, 45:55] = 1100
rho_true = rho_background.clone()
rho_true[10:20, 60:70] = 2300

n_shots = 8

n_sources_per_shot = 1
d_source = 12
first_source = 8
source_depth = 2

freq = 15
nt = 200
dt = 0.004
peak_time = 1.5 / freq

# source_locations
source_locations = torch.zeros(n_shots, n_sources_per_shot, 2,
dtype=torch.long, device=device)
source_locations[..., 0] = source_depth
source_locations[:, 0, 1] = (torch.arange(n_shots) * d_source +
first_source)

dtype=torch.long, device=device)
.repeat(n_shots, 1)
)

# source_amplitudes
source_amplitudes = (
(deepwave.wavelets.ricker(freq, nt, dt, peak_time))
.repeat(n_shots, n_sources_per_shot, 1).to(device)
)

This created a model where each of the three parameters is constant except for a box, which is in a different location for each parameter. We will use eight shots, with sources spread over the top surface, and receivers covering the top surface. We are now ready to generate data using the true model:

observed_data = elastic(
*deepwave.common.vpvsrho_to_lambmubuoyancy(vp_true, vs_true,
rho_true),
dx, dt,
source_amplitudes_y=source_amplitudes,
source_locations_y=source_locations,
pml_freq=freq,
)[-2]

This is similar to how the scalar propagator is called, but with two differences.

The first is that we pass the three elastic model parameters. We are parameterising the model with $$v_p$$, $$v_s$$, and $$\rho$$, but Deepwave wants us to provide them as $$\lambda$$, $$\mu$$, and buoyancy, so we convert them. Deepwave provides a function to do this, which we use here, but you can also create your own conversion function if you parameterise your model in some other way.

The elastic propagator can have sources and receivers oriented in each of the spatial dimensions. In this example we are only going to use sources and receivers that are oriented in the first (y) dimension. We could also provide receiver_locations_x if we wanted receivers that record particle velocity in the second dimension, for example.

Now let’s try starting from the background models (constant, without the boxes) and see if we can obtain something close to the true model when we invert with the true observed data:

vp = vp_background.clone().requires_grad_()
optimiser = torch.optim.LBFGS([vp, vs, rho])
loss_fn = torch.nn.MSELoss()

# Run optimisation/inversion
n_epochs = 20

for epoch in range(n_epochs):
def closure():
out = elastic(
*deepwave.common.vpvsrho_to_lambmubuoyancy(vp, vs, rho),
dx, dt,
source_amplitudes_y=source_amplitudes,
source_locations_y=source_locations,
pml_freq=freq,
)[-2]
loss = 1e20*loss_fn(out, observed_data)
loss.backward()
return loss

optimiser.step(closure)

This just used a standard inversion with the LBFGS optimiser, but the result looks quite good.

The gradients flowed end-to-end, back into the vp, vs, and rho parameters. You can see that there is a little bit of crosstalk between the parameters, though. Maybe you can come-up with a way of parameterising the model, or a different loss function, that does better?

Full example code


text:
# Does length contraction apply to the far galaxies moving due to expansion?

From Wikipedia:

Universe in an expanding sphere. The galaxies farthest away are moving fastest and hence experience length contraction and so become smaller to an observer in the centre.

Does length contraction really apply to the far galaxies moving due to expansion? If the galaxies near the edge of the observable universe are moving away faster than light, then how to apply the length contraction formula? And can we observe this contraction effect, considering that it's in a direction perpendicular to our observation?

• Please note: the quote you provide concerns the "Milne model", which uses just special relativity, and where there is no general relativistic expansion. In most cosmological models there is no "edge" or "centre". – Rob Jeffries Apr 23 '18 at 18:25

The material on WP is describing a cartoonish illustration, not making a claim about what is actually observed. Note that the cartoon is drawn from an imaginary point of view outside the universe, which isn't actually possible.

There are at least two reasons why this part of the article is misleading.

(1) Even in special relativity, length contraction isn't what we actually see in optical observations. The time for propagation of light from different parts of an object to the observer is different, so what we see is more complicated. Objects can appear elongated rather than contracted, and there can be a rotation as well.

(2) It's an oversimplification to say that distant galaxies are moving away from us at some speed.

In reality, I don't think it's feasible to detect relativistic distortions of the shape of a galaxy optically. For galaxies close enough that it makes sense to use special relativity, the velocities $\ll c$. For distant galaxies, the motion (to the extent that it makes sense to call it motion) is almost purely radial. And in any case we don't necessarily have an undistorted shape to compare with, since galaxies aren't simple geometrical shapes.