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# Quark Matter 2018 May 13 – 19, 2018 Venice, Italy Europe/Zurich timezone The organisers warmly thank all participants for such a lively QM2018! See you in China in 2019! ## Quarkonium production in p-A collisions with ALICE May 16, 2018, 4:50 PM 20m Sala Mosaici-2, 3rd Floor (Palazzo del Casinò) ### Sala Mosaici-2, 3rd Floor #### Palazzo del Casinò Parallel Talk Quarkonia ### Speaker Dr Biswarup Paul (Universita e INFN Torino (IT)) ### Description The study of quarkonium production in proton-nucleus collisions is an important tool to investigate cold nuclear matter (CNM) effects. Mechanisms such as the modification of the parton distribution functions in nuclei, the presence of a color glass condensate or coherent energy loss of the $c\overline{c}$ pair in the medium have been employed to describe J/$\psi$ production in proton-nucleus collisions at LHC energies. In addition, final state mechanisms, possibly related to the presence of a dense medium, are required to explain the stronger suppression observed for the loosely bound $\psi$(2S) state. ALICE has measured quarkonium production in p-Pb collisions at backward ($-$4.46 $<$ $y_{\rm cms}$ $<$ $-$2.96), mid ($-$1.37 $<$ $y_{\rm cms}$ $<$ 0.43) and forward (2.03 $<$ $y_{\rm cms}$ $<$ 3.53) rapidity down to zero transverse momentum ($p_{\rm T}$). Results on J/$\psi$ nuclear modification factor ($R_{\rm pPb}$) measured at mid-$y$ at $\sqrt{s_{\rm NN}}$ = 5.02 TeV and at forward and backward $y$ at $\sqrt{s_{\rm NN}}$ = 8.16 TeV will be presented. J/$\psi$ production as a function of multiplicity and results on the J/$\psi$ $v_{2}$, obtained using J/$\psi$-hadron correlations, will also be discussed. Finally, we will present the results on $\psi$(2S) and $\Upsilon$ $R_{\rm pPb}$ in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 8.16 TeV at forward and backward $y$. All the results will be compared to those obtained at lower energies and with available theoretical calculations. Content type Experiment Presenter name already specified ALICE	{}
# Problem: Ethyl chloride (C2H5Cl) boils at 12 oC. When liquid C2H5Cl under pressure is sprayed on a room-temperature (25 oC) surface in air, the surface is cooled considerably.Assume that the heat lost by the surface is gained by ethyl chloride. What enthalpies must you consider if you were to calculate the final temperature of the surface? ⚠️Our tutors found the solution shown to be helpful for the problem you're searching for. We don't have the exact solution yet. ###### Problem Details Ethyl chloride (C2H5Cl) boils at 12 oC. When liquid C2H5Cl under pressure is sprayed on a room-temperature (25 oC) surface in air, the surface is cooled considerably. Assume that the heat lost by the surface is gained by ethyl chloride. What enthalpies must you consider if you were to calculate the final temperature of the surface?	{}
# Required information The following information applies to the questions displayed below) On October 29, Lobo Co.... Required information The following information applies to the questions displayed below) On October 29, Lobo Co. began operations by purchasing razors for resale. The razors have a 90-day warranty. When a razor is returned, the company discards it and mails a new one from Merchandise Inventory to the customer. The company's cost per new razor is $20 and its retail selling price is$75. The company expects warranty costs to equal 8% of dollar sales. The following transactions occurred. Nov. 11 Sold 105 razors for $7,875 cash. 30 Recognized warranty expense related to November sales with an adjusting entry. Dec. 9 Replaced 15 razors that were returned under the warranty. 16 Sold 220 razors for$16,500 cash. 29 Replaced 30 razors that were returned under the warranty. 31 Recognized warranty expense related to December sales with an adjusting entry. Jan. 5 Sold 150 razors for $11,250 cash. 17 Replaced 50 razors that were returned under the warranty. 31 Recognized warranty expense related to January sales with an adjusting entry. 2. How much warranty expense is reported for November and odcember? Warranty expense for November Prey 8 9 10 11 of 11 H Next > ## Answers #### Similar Solved Questions 1 answer ##### Your storage firm has been offered$96,900 in one year to store some goods for one... Your storage firm has been offered $96,900 in one year to store some goods for one year. Assume your costs are$97,000, payable immediately, and the cost of capital is 8.4%. Should you take the contract? The NPV will be s. (Round to the nearest cent.) Should you take the contract? (Select from the d... ##### The scores on a certain test are normally distributed with a mean score of 53 and... The scores on a certain test are normally distributed with a mean score of 53 and a standard deviation of 2. What is the probability that a sample of 90 students will have a mean score of at least 53.2108? 0.8413 0.3174 0.3413 0.1587... ##### The charter of a corporation provides for the issuance of 134,000 shares of common stock. Assume... The charter of a corporation provides for the issuance of 134,000 shares of common stock. Assume that 62,000 shares were originally issued and 13,100 were subsequently reacquired. What is the number of shares outstanding? a. 134,000 b. 48,900 c. 62,000 d. 13,100 The Sneed Corporation issues 14,100 s... ##### Text Question 1.7 Question Help To discourage people from breaking laws against speeding. Society can increase... Text Question 1.7 Question Help To discourage people from breaking laws against speeding. Society can increase the probability that someone exceeding the speed limit will be caught and punished or it can increase the size of the line for speeding. Explain why either method can be used to discourage ... Your answer is partially correct. The pretax financial income (or loss) figures for Jenny Spangler Company are as follows. 2015 2016 2017 2018 2019 2020 2021 $160,000 250,000 80,000 (160,000) (380,000) 120,000 100,000 Pretax financial income (or loss) and taxable income (loss) were the same for all ... 1 answer ##### One unit of A is made of one unit of B and one unit of C. B is made of four units of C and one unit each of E and F. C is made of two units of D and one unit of E. E is made of three units of F. Item... One unit of A is made of one unit of B and one unit of C. B is made of four units of C and one unit each of E and F. C is made of two units of D and one unit of E. E is made of three units of F. Item C has a lead time of one week; Items A, B, E, and F have two-week lead times; and Item D has a lead ... 1 answer ##### Homowon oraptero-Assignment Score: 0.33 of 1 pt 2 of 142 complete Exercise 3.1 Lebendom na polony... Homowon oraptero-Assignment Score: 0.33 of 1 pt 2 of 142 complete Exercise 3.1 Lebendom na polony 50 and 49. Use the contraint there tower the following questions. Not any intermediate results should be rounded to four decimal places) In a random sample of 15 find (<51) Pr(Ý<51) - Round... 1 answer ##### MNS Company produces helmets which it normally sells to retailers for$6 each. The cost of... MNS Company produces helmets which it normally sells to retailers for $6 each. The cost of manufacturing 25,000 helmets is: Materials$ 10,000 &... ##### Hi, can you help me add these requirements in my Turtle python program. The program is... Hi, can you help me add these requirements in my Turtle python program. The program is supposed to run an Olympics skating game. The program is below the requirements. Thanks Requirements -Your race will be random generated so each time there is a possibility that a different winner. -Have a countdo... ##### 2 and 3 2 -6 4 -4 0 -4 6 1. Define A =... 2 and 3 2 -6 4 -4 0 -4 6 1. Define A = 8 01 . Determine, by hand, the LU factorization, of A. You may of course check your answer using appropriate technology tools. Then use your result to solve the system of equations Ax b, where b--4 2 0 5 2 2. Suppose A-6 -3 133Even though A is not square... ##### Consider the following reaction: 2Ca(s)+O2(g) → 2CaO(s) ΔH∘rxn= -1269.8 kJ; ΔS∘rxn= -364.6 J/K Assume that all... Consider the following reaction: 2Ca(s)+O2(g) → 2CaO(s) ΔH∘rxn= -1269.8 kJ; ΔS∘rxn= -364.6 J/K Assume that all reactants and products are in their standard states. Calculate the free energy change for the reaction at 34 ∘C. Express your answer using four significan... ##### How do you solve these? this is all the information available. it says to calculate for... how do you solve these? this is all the information available. it says to calculate for each 14.26 The questions that follow make use of this тар: + 10 15 20 10 ki 20 + 151 Calculate a. the frequency of jb gametes from a J B/j b genotype, 0. the frequency of AM gametes from an... ##### I would like to do grocery stores Initial Response: Choose a product or service that you... i would like to do grocery stores Initial Response: Choose a product or service that you are familiar with something you use or have used, something related to a job you or someone close to you has held, etc.). Are there a lot or few firms in the industry? Are the products similar or identical or... ##### Here is a sample data set. 346.6 346.8 370.6 378.6 401.3 402.4 403.9 416.8 417.6 431.9... Here is a sample data set. 346.6 346.8 370.6 378.6 401.3 402.4 403.9 416.8 417.6 431.9 433.7 454.3 460.9 460.9 460.9 481.8 481.9 483.4 484.4 485.3 485.7 486.3 488.3 490.2 490.7 493.3 496.3 496.3 496.6 501.8 506 518.5 548.1 548.4 548.8 552.6 565.8 570.9 572.5 575.2 575.2 575.2 609.6 ... ##### Assign oxidation numbers to all of the atoms of each element in the following reaction a) Cu(s) + NO3-1(aq) => &... Assign oxidation numbers to all of the atoms of each element in the following reaction a) Cu(s) + NO3-1(aq) => Cu+2(aq) + NO(g) The oxidizing agent in this reaction is_________________ The reducing agent is this reaction is_________________...	{}
Browse Questions # The number of ways four boys can be seated around a round-table in four chairs of different colours is $\begin{array}{1 1}(A)\;24\\(B)\;12\\(C)\;23\\(D)\;64\end{array}$ Toolbox: • $n!=n(n-1)(n-2)(n-3).....(3)(2)(1)$ Total no of boys =4 Total no of chairs =4 Required number of ways =4! $\Rightarrow 4\times 3\times 2\times 1$ $\Rightarrow 24$ Hence (A) is the correct answer.	{}
Diffie-Hellman explicit key confirmation Suppose I wanted to add explicit key confirmation to Diffie-Hellman key exchange, would the following scheme be secure? 1. Alice selects a random $a$ and sends $g^a \mod p$ to Bob 2. Bob selects a random $b$, computes the shared secret $S = (g^a \mod p)^b$ 3. Bob computes two keys using HKDF ($H(k, m)$ denotes the HMAC of message $m$ using key $k$): • Compute $k = H(salt, S)$ • Compute $k_1 = H(k, CTX \|\| 0)$ and $k_2 = H(k, CTX \|\| 1)$ 4. Bob sends $g^b \mod p$, $H(k_1, k_2)$, the salt, and the string CTX to Alice 5. Alice computes the shared secret $S = (g^b \mod p)^a$, computes $k_1$ and $k_2$ using HKDF given the salt and the string CTX 6. Alice computes $H(k_1, k_2)$ and verifies whether it's the same as the value that she received from Bob. - The major thing missing from Diffie-Hellman is that it provides no protection from someone running a man-in-the-middle attack. Your changes don't actually do anything to prevent that. That is, suppose Eve was between Alice and Bob; when Alice sends the first message to Bob, Eve intercepts the message, and performs the exchange with Alice. At the same time, Eve forwards her own exchange to Bob. If Alice and Bob were attempting to perform this exchange to create secret keys, well, they will really share keys with Eve; when Alice sends a message, Eve will receive that encrypted message, decrypt it with the key she shares with Alice, examine it, and then encrypt it with the key she shares with Bob, and forwards it. That way, Eve sees all the traffic between Alice and Bob without being aware of it. There is nothing that this key confirmation does that makes this any more difficult for Eve; she can compute $H(k_1, k_2)$ just as well as Alice and Bob, and so she will be able to impersonate Bob to Alice (and impersonating Alice to Bob). Now, if the question was "is it secure if we don't have to worry about man-in-the-middle", the answer is "well, straight Diffie-Hellman is secure in that scenario; your additions don't appear to have made anything worse". - Thanks for looking at it, @poncho. Yes, I was assuming that man-in-the-middle was not an issue in the question. – herrfz Feb 7 '14 at 16:20 @herrfz: The sole additional information you're providing an evesdropper is $H(k_1, k_2)$; given that the only way to attack that is either to brute force it, or to have a Rainbow table, and the shared secret $S$ is too large for either; this doesn't give an evesdropper any additional edge. – poncho Feb 7 '14 at 16:47 @herrfz man-in-the-middle is always issue. – catpnosis Feb 7 '14 at 20:52 @catpnosis I'm totally aware of that. In my application we've achieved authentication through some other means, which I intentionally excluded from the question. I really just want to focus on the "explicit key confirmation" issue. – herrfz Feb 7 '14 at 21:26	{}
# - Name two elements that have the SAME (rounded) atomic mass: ###### Question: - Name two elements that have the SAME (rounded) atomic mass: ### In 3-4 sentences describe the geologic history of North America. In what order did events occur? What is the cause of the mountains lining the western and eastern continental margins? In 3-4 sentences describe the geologic history of North America. In what order did events occur? What is the cause of the mountains lining the western and eastern continental margins?... ### On monday morning, there were 30 tickets available for a concert. if 1/3 tickets were sold on monday and 1/5 of those left were sold on tuesday, how many tickets were still available after tuesday's tickets sales? on monday morning, there were 30 tickets available for a concert. if 1/3 tickets were sold on monday and 1/5 of those left were sold on tuesday, how many tickets were still available after tuesday's tickets sales?... ### Interactive Practice: Solve Problems involving Scale >>> The figure shows the floor plan for a rectangular room. Every 2 cm in the floor plan represents 8 ft in the actual room. - What is the scale factor from the floor plan to the actual room? 5 cm 4 3 cm ) What is the length of the actual room? ? ft Interactive Practice: Solve Problems involving Scale >>> The figure shows the floor plan for a rectangular room. Every 2 cm in the floor plan represents 8 ft in the actual room. - What is the scale factor from the floor plan to the actual room? 5 cm 4 3 cm ) What is the length of the actual... ### Kale works in a packaging factory that has 900 employees. By the end of each day, they manage to package 3.2 × 105 products. What is the average amount of products packaged per employee represented in scientific notation? Round so the first factor goes to the tenths place. Kale works in a packaging factory that has 900 employees. By the end of each day, they manage to package 3.2 × 105 products. What is the average amount of products packaged per employee represented in scientific notation? Round so the first factor goes to the tenths place.... ### 23. What is Jan Hus known for? (lesson 4.04) becoming the first man to drcle the globe in a boat O leading armles on crusades to oust Muslims and Jews from Southern Europe O defending the pope against Protestant criticisms O starting a revolt against the Catholic Church in what is now the Czech Republic based on his criticisms of church practices 23. What is Jan Hus known for? (lesson 4.04) becoming the first man to drcle the globe in a boat O leading armles on crusades to oust Muslims and Jews from Southern Europe O defending the pope against Protestant criticisms O starting a revolt against the Catholic Church in what is now the Czech Repu... ### Scientists can measure the depths of craters on the moon by looking at photos of shadows. The length of the shadow cast by the edge of a crater is 500 meters. The angle of elevation of the rays of the Sun is 55∘. Estimate the depth d of the crater to the nearest tenth. Scientists can measure the depths of craters on the moon by looking at photos of shadows. The length of the shadow cast by the edge of a crater is 500 meters. The angle of elevation of the rays of the Sun is 55∘. Estimate the depth d of the crater to the nearest tenth.... ### For every 16 games the baseball team w on, they lost three. Represent the ratio that compares the number of games lost to the number of games played? For every 16 games the baseball team w on, they lost three. Represent the ratio that compares the number of games lost to the number of games played?... ### Factor polynomial x^ + 9x + 20 factor polynomial x^ + 9x + 20... ### When your performing CPR and giving breaths how do you know that the air actually went into the victims lungs? When your performing CPR and giving breaths how do you know that the air actually went into the victims lungs?... ### How is lava formed during an volcano How is lava formed during an volcano... ### Which of these composers did not write during the Romantic period? A. Berlioz B. Schubert C. Bach D. Tchaikovsky Which of these composers did not write during the Romantic period? A. Berlioz B. Schubert C. Bach D. Tchaikovsky... ### Solve the formula V=h for r. Solve the formula V=h for r.... ### Four students are to solve 5(x-3)=2x+6 which solution and explanation is right? Four students are to solve 5(x-3)=2x+6 which solution and explanation is right?... ### The minimum and maximum temperature for a day in Cupcake Town can be modeled by the equation below: 3\|x − 8\| + 15 = 18 What are the minimum and maximum temperatures for this day? The minimum and maximum temperature for a day in Cupcake Town can be modeled by the equation below: 3\|x − 8\| + 15 = 18 What are the minimum and maximum temperatures for this day?... ### What is one watt power?? what is one watt power??... ### The distance between two cities on a map is 4 - inches. The actual distance between the two cities is 24 miles.TONa. What is the scale used on the map?b. If the scale on a different map of the same area is - inch = 1 mile, how many inches separate the same two cities?ro The distance between two cities on a map is 4 - inches. The actual distance between the two cities is 24 miles.TONa. What is the scale used on the map?b. If the scale on a different map of the same area is - inch = 1 mile, how many inches separate the same two cities?ro... ### A fundraising event offered people a chance to pay $3 to go through a corn maze (shown below) in a field in the fall. The maze either led to nothing or a prize of$4 (ie their $3 back and an extra$1). The participants can only move forward and when they come to a fork in the maze they are equally likely to take any one of the paths. What is the expected monetary value for each participant that goes through the maze? -0.33 -0.67 -0.75 -1.00 A fundraising event offered people a chance to pay $3 to go through a corn maze (shown below) in a field in the fall. The maze either led to nothing or a prize of$4 (ie their $3 back and an extra$1). The participants can only move forward and when they come to a fork in the maze they are equally l...	{}
# xcopy deletes destination folder and copies 0 files I am trying to write a batch file to back up my locally stored files to a network drive. Some folders are being successfully copied, but others are not; instead the destination folder is being deleted when the command is executed. Working as expected (copies all files into destination folder): XCOPY /Y "C:\APPS\lse_jboss-4.2.3.GA-1.1\server\default\deploy\lse_datasources-esl_sourcesdedonnees" "H:\My Documents\RESTORE\Data sources" XCOPY /Y "%AllUsersProfile%\Desktop" "H:\My Documents\RESTORE\Desktop - Global" XCOPY /Y "%UserProfile%\Desktop" "H:\My Documents\RESTORE\Desktop - mwa700" XCOPY /Y "%UserProfile%\Favorites" "H:\My Documents\RESTORE\Favorites" XCOPY /Y "%UserProfile%\Application Data\Microsoft\Templates" "H:\My Documents\RESTORE\Office templates" Not working as expected (copies 0 files, and deletes destination folder): XCOPY /Y "%UserProfile%\java_libraries" "H:\My Documents\RESTORE\java_libraries" XCOPY /Y "%UserProfile%\workspaces" "H:\My Documents\RESTORE\workspace" Are there contents or properties of either folder that could explain this behaviour? • Xcopy is sooo 20th century. Have you considered using Robocopy? Dec 14, 2011 at 15:08 • @kinokijuf: Work computer, so installing non-standard software isn't an option. – Matt Dec 14, 2011 at 15:41 • Robocopy is a microsoft app that is included in the server admin pack. Your IT shop shouldn't have a problem with it: google.com/search?q=robocopy+download Dec 14, 2011 at 15:50 Yes. By default xcopy copies files only, not directories. So if your source directories only contains other subdirectories it will not copy anything. To make sure you also copy directores use the /E flag to copy directores and subdirectores (including empty ones) or /S to skip the empty directories. xcopy /Y /E "src" "dest" Also use /I to assume destination is a directory if more than one file is copied. xcopy /Y /E /I "src" "dest" For more help use xcopy /? I don't know if this is an answer that works for you, but I used an xcopy command to copy all of a C: folder to a backup location on another disk device (call it folder E:\A). After the copy completed successfully, folder E:\A disappeared from Explorer! By moving the device at E: to another computer, I could see that xcopy had set the S and H (System and Hidden) attributes of E:\A, causing it to vanish. These attributes had, perhaps correctly, been copied from the C:\ folder to the E:\A folder itself. I used the attrib command to restore those two attributes, and all is now well. E:\A contains the folders and files that were copied from C: . Try using the dos formatted filename for the Documents and Settings, or use the %userprofile% path command variable. The only difference between your two statements above is there are not spaces in the source in the working script, and there are spaces in the path of the non-working script. Use the %userprofile% path command first, it's easier and supported by all MS OSes. • Behaviour is unchanged using this instead (commands that worked before continue to work, commands that deleted the destination folder continue to delete the destination folder). I will update my question to use this format instead, since it does eliminate a variable. – Matt Dec 14, 2011 at 15:36 • Downvote? Why? I provided a possible answer and it turned out to be incorrect. Save the downvotes for unhelpful, not merely inaccurate answers and posts. Dec 14, 2011 at 16:29	{}
Suggested languages for you: Americas Europe Q22E Expert-verified Found in: Page 127 ### Essential Calculus: Early Transcendentals Book edition 2nd Author(s) James Stewart Pages 830 pages ISBN 9781133112280 # Use implicit differentiation to find an equation of the tangent line to the curve at the given point.22. $${{\rm{x}}^{{\raise0.7ex\hbox{{\rm{2}}} \!\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ + }}{{\rm{y}}^{{\raise0.7ex\hbox{{\rm{2}}}\!\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ = 4, }}\left( {{\rm{ - 3}}\sqrt {\rm{3}}{\rm{,1}}} \right)$$ (astroid) The equation of the tangent line at $$\left( {{\rm{ - 3}}\sqrt {\rm{3}} {\rm{,1}}} \right)$$is $${\rm{y = }}\frac{{\rm{1}}}{{\sqrt {\rm{3}} }}{\rm{x + 4}}$$ See the step by step solution ## Step$${\rm{1}}$$: Given information The given equation is $${{\rm{x}}^{{\raise0.7ex\hbox{{\rm{2}}} \!\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ + }}{{\rm{y}}^{{\raise0.7ex\hbox{{\rm{2}}}\!\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ = 4}}$$ with the point $$\left( {{\rm{ -3}}\sqrt {\rm{3}} {\rm{,1}}} \right)$$ ## Step$${\rm{2}}$$: Definition of implicit differentiation Implicit differentiation: This method consists of differentiating both sides of the equation with respect to $${\rm{x}}$$ and then solving the resulting equation for $${\rm{y'}}$$ ## Step$${\rm{3}}$$: Differentiate the given equation with respect to $${\rm{x}}$$ The equation is $${{\rm{x}}^{{\raise0.7ex\hbox{{\rm{2}}} \!\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ + }} {{\rm{y}}^{{\raise0.7ex\hbox{{\rm{2}}}\!\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ = 4,}}$$ Differentiate both sides with respect to $${\rm{x}}$$ $$\frac{{\rm{d}}}{{{\rm{dx}}}}\left( {{{\rm{x}}^{{\raise0.7ex\hbox{{\rm{2}}} \!\mathord{\left/ {\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ + }}{{\rm{y}}^{{\raise0.7ex\hbox{{\rm{2}}} \!\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}} \right){\rm{ = }}\frac{{\rm{d}}}{{{\rm{dx}}}}\left( {\rm{4}} \right)$$ The Sum rule for differentiation $$\frac{{\rm{d}}}{{{\rm{dx}}}}\left( {{\rm{f}}\left( {\rm{x}} \right){\rm{ + g}}\left( {\rm{x}} \right)} \right){\rm{ = }}\frac{{{\rm{d}}\left( {{\rm{f}}\left( {\rm{x}} \right)} \right)}}{{{\rm{dx}}}}{\rm{ + }}\frac{{{\rm{d}}\left( {{\rm{g}}\left( {\rm{x}} \right)} \right)}}{{{\rm{dx}}}}$$ $$\frac{{\rm{d}}}{{{\rm{dx}}}}\left( {{{\rm{x}}^{{\raise0.7ex\hbox{{\rm{2}}} !\mathord{\left/{\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}} \right){\rm{ + }}\frac{{\rm{d}}}{{{\rm{dx}}}}\left({{{\rm{y}}^{{\raise0.7ex\hbox{{\rm{2}}} \!\mathord{\left/ {\vphantom {{\rm{2}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}} \right){\rm{ = 0}}$$ Chain rule: The chain rule states that the derivative of $${\rm{f}}\left( {{\rm{g}}\left( {\rm{x}} \right)} \right)$$ is equal to $${\rm{f'}}\left({{\rm{g}}\left( {\rm{x}} \right)} \right){\rm{ \times g'}}\left( {\rm{x}} \right)$$ \begin{aligned}\frac{2}{3}{{\rm{x}}^{{\raise0.7ex\hbox{{ - 1}} \!\mathord{\left/{\vphantom {{ 1}{\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ + }}\frac{2}{3}{{\rm{y}}^{{\raise0.7ex\hbox{{ - 1}} \!\mathord{\left/{\vphantom {{ - 1}{\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{y' = 0}}\\{{\rm{x}}^{{\raise0.7ex\hbox{{ -1}} \!\mathord{\left/{\vphantom {{ - 1} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ +}}{{\rm{y}}^{{\raise0.7ex\hbox{{ - 1}} \!\mathord{\left/{\vphantom {{ - 1}{\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{y' = 0}}\end{aligned} Take $${\rm{y'}}$$ common from the two terms in left hand side \begin{aligned}{{\rm{y}}^{{\raise0.7ex\hbox{{{\rm{ - 1}}}} \!\mathord{\left/ {\vphantom {{{\rm{ -1}}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}y' &= - {{\rm{x}}^{{\raise0.7ex\hbox{{{\rm{ - 1}}}}\!\mathord{\left/ {\vphantom {{{\rm{ - 1}}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}\\y' &= \frac{{{\rm{ - }}{{\rm{x}}^{{\raise0.7ex\hbox{{{\rm{ - 1}}}} \!\mathord{\left/ {\vphantom {{{\rm{ - 1}}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}}}{{{{\rm{y}}^{{\raise0.7ex\hbox{{{\rm{ - 1}}}} \!\mathord{\left/ {\vphantom {{{\rm{ - 1}}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}}}& = -{\left( {\frac{{\rm{x}}}{{\rm{y}}}} \right)^{{\raise0.7ex\hbox{{{\rm{ - 1}}}} \!\mathord{\left/{\vphantom {{{\rm{ - 1}}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}&= - {\left( {\frac{{\rm{y}}}{{\rm{x}}}} \right)^{{\raise0.7ex\hbox{{\rm{1}}} \!\mathord{\left/ {\vphantom {{\rm{1}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}\end{aligned} ## Step$${\rm{4}}$$: Find the slope of the tangent line at $$\left( {{\rm{ - 3}}\sqrt {\rm{3}} {\rm{,1}}} \right)$$ The tangent line of a curve at a given point is a line that just touches the curve at that point and the slope of the tangent line of $${\rm{y = f}}\left( {\rm{x}} \right)$$ at a point $$\left( {{{\rm{x}}_{\rm{0}}}{\rm{,}}{{\rm{y}}_{\rm{0}}}} \right)$$ is $${\left. {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right\|_{\left( {{{\rm{x}}_{\rm{0}}}{\rm{,}}{{\rm{y}}_{\rm{0}}}} \right)}}$$ So the slope of the tangent line at $$\left( {{\rm{ - 3}}\sqrt {\rm{3}} {\rm{,1}}} \right)$$ is $${\left. {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right\|_{\left( {{\rm{ - 3}}\sqrt {\rm{3}} {\rm{,1}}} \right)}}{\rm{ = - }}{\left( {\frac{{\rm{1}}}{{{\rm{ - 3}}\sqrt {\rm{3}} }}} \right)^{{\raise0.7ex\hbox{{\rm{1}}} \!\mathord{\left/{\vphantom {{\rm{1}} {\rm{3}}}}\right.}\!\lower0.7ex\hbox{{\rm{3}}}}}}{\rm{ = }}\frac{{\rm{1}}}{{\sqrt {\rm{3}} }}$$ ## Step$${\rm{5}}$$: Find an equation of the tangent line at $$\left( {{\rm{ - 3}}\sqrt {\rm{3}} {\rm{,1}}} \right)$$ The tangent line formula is, $${\rm{y - }}{{\rm{y}}_{\rm{0}}}{\rm{ = }}{\left. {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right\|_{\left( {{{\rm{x}}_{\rm{0}}}{\rm{,}}{{\rm{y}}_{\rm{0}}}} \right)}}\left( {{\rm{x - }}{{\rm{x}}_{\rm{0}}}} \right)$$ An equation of the tangent line at $$\left( {{\rm{ - 3}}\sqrt {\rm{3}} {\rm{,1}}} \right)$$ is \begin{aligned}y - 1 &= \frac{{\rm{1}}}{{\sqrt {\rm{3}} }}\left( {{\rm{x - }}\left( {{\rm{ - 3}}\sqrt {\rm{3}} } \right)} \right)\\y - 1 &=\frac{{\rm{1}}}{{\sqrt {\rm{3}} }}{\rm{x + 3}}\\y &= \frac{{\rm{1}}}{{\sqrt {\rm{3}} }}{\rm{x + 4}}\end{aligned} ## Step$${\rm{6}}$$: Plot the graph Therefore, the equation of the tangent line at $$\left( {{\rm{ - 3}}\sqrt {\rm{3}} {\rm{,1}}} \right)$$is $${\rm{y = }}\frac{{\rm{1}}}{{\sqrt {\rm{3}} }}{\rm{x + 4}}$$	{}
Solar-like oscillations from the depths of the red-giant star KIC 4351319 # Solar-like oscillations from the depths of the red-giant star KIC 4351319 observed with Kepler M. P. Di Mauro, D. Cardini, G. Catanzaro, R. Ventura, C. Barban, T. R. Bedding, J. Christensen-Dalsgaard, J. De Ridder, S. Hekker, D. Huber, T. Kallinger, A. Miglio, J. Montalban, B. Mosser, D. Stello, K. Uytterhoeven, K. Kinemuchi, H. Kjeldsen, F. Mullally, M. Still INAF - IASF, Istituto di Astrofisica Spaziale e Fisica Cosmica, Via del Fosso del Cavaliere 100, 00133 Roma, Italy INAF - Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy LESIA, CNRS, Université Pierre et Marie Curie, Université Denis, Diderot, Observatoire de Paris, 92195 Meudon Cedex, France Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney , NSW 2006, Australia Institut for Fysik og Astronomi, Bygn. 1520, Aarhus Universitet, Ny Munkegade, DK-8000 Aarhus C, Denmark Institut voor Sterrenkunde, K. U. Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium School of Physics and Astronomy, University of Birmingham, Birmingham B 15 2TT, UK Astronomical Institute ’Anton Pannekoek’, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Institut d’Astrophysique et de Géofisique de l’Universitè de Liège, Allè du 6 Aout 17-B 4000 Liège, Belgium Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot; CEA, IRFU, SAp, Centre de Saclay, 91191, Gif-sur-Yvette, France Kiepenheuer-Institut für Sonnenphysik, Schöneckstraße 6, 79104 Freiburg im Breisgau, Germany Bay Area Environmental Research Inst./NASA Ames Research Center, Moffett Field, CA 94035 SETI Institute/NASA Ames Research Center, Moffett Field, CA 94035 Released 2011Accepted 2011 May 2. Received 2011 May 2; in original form 2011 January 10 Released 2011Accepted 2011 May 2. Received 2011 May 2; in original form 2011 January 10 ###### Abstract We present the results of the asteroseismic analysis of the red-giant star KIC 4351319 (TYC 3124-914-1), observed for 30 days in short-cadence mode with the Kepler satellite. The analysis has allowed us to determine the large and small frequency separations, Hz and Hz respectively, and the frequency of maximum oscillation power, Hz. The high signal-to-noise ratio of the observations allowed us to identify independent pulsation modes whose frequencies range approximately from to Hz. The observed oscillation frequencies together with the accurate determination of the atmospheric parameters (effective temperature, gravity and metallicity), provided by additional ground-based spectroscopic observations, enabled us to theoretically interpret the observed oscillation spectrum. KIC 4351319 appears to oscillate with a well defined solar-type p-modes pattern due to radial acoustic modes and non-radial nearly pure p modes. In addition, several non-radial mixed modes have been identified. Theoretical models well reproduce the observed oscillation frequencies and indicate that this star, located at the base of the ascending red-giant branch, is in the hydrogen-shell burning phase, with a mass of , a radius of and an age of Gyr. The main parameters of this star have been determined with an unprecedent level of precision for a red-giant star, with uncertainties of for mass, for age, for radius, and for luminosity. ###### keywords: stars: individual: KIC 4351319 - stars: variables: solar-type - stars: oscillations - stars: red giants ## 1 Introduction Oscillations excited by turbulent convection - solar-like oscillations - have been successfully identified in cool main-sequence and post-main-sequence stars with convective envelopes. In the red giants, solar-like oscillations have been first detected by ground-based observations (Merline, 1999; Frandsen et al., 2002; Stello et al., 2004) and by the WIRE satellite (Buzasi, 2000; Retter et al., 2003, 2004). Difficulties in the identification of the observed modes, led several authors (Guenther et al., 2000; Dziembowski et al., 2001; Teixeira et al., 2003; Christensen-Dalsgaard, 2004a) to speculate on the pulsational properties of the red-giant stars. Red giants are characterized by a deep convective envelope and a small degenerate helium core. Since the density in the core of these stars is quite large, the buoyancy frequency can reach very large values in the central part. In these conditions, g modes of high frequencies can propagate and might eventually interact with p modes giving rise to modes of mixed character. As a consequence, the spectrum of the red giants is predicted to have a quite complicated appearance, with a sequence of peaks uniformly spaced in frequency due to acoustic modes, and other peaks with less clear pattern due to mixed modes. The detection of solar-like oscillations in red giants has been well established by the space mission MOST (Barban et al., 2007; Kallinger et al., 2008a, b), while the CoRoT satellite was able to detect for the first time non-radial modes in red-giant stars (De Ridder et al., 2009) and to find solar-like oscillations in a very large sample of G and K giant stars (Hekker et al., 2009; Kallinger et al., 2010b; Mosser et al., 2010) mainly lying in the core-helium-burning evolutionary phase (Miglio et al., 2009). The high-quality observations of the Kepler mission (Borucki, 2010; Koch et al., 2010) enabled to extend the detection of solar-like oscillations from the red clump to the lower luminosity region of the red-giant branch (Bedding et al., 2010; Hekker et al., 2010; Huber et al., 2010; Kallinger et al., 2010a), where stars are still burning H in the shell. This finding enables us to study the structure and the evolution of the stars from the main-sequence phase up to advanced evolutionary stages by means of asteroseismology (Gilliland et al., 2010). In this article we present the results of the analysis of the oscillation spectrum of the red giant KIC 4351319 (TYC 3124-914-1) – nicknamed ‘Pooh’ (Milne, 1926) within the authorship team – observed by the Kepler satellite for 30 days in short-cadence mode (integration time 1 min, Gilliland et al. 2010). Here, we also consider the theoretical interpretation of the observations and derive the asteroseismic estimates of age, mass and radius and of other structural characteristics, making use of the accurate atmospheric parameters obtained by ground-based spectroscopy performed at McDonald Observatory. The star selected for this study is of particular interest because its oscillation spectrum shows an excess of power centered at frequency Hz, higher than is typical for Kepler red giants (Bedding et al., 2010; Hekker et al., 2010; Huber et al., 2010; Kallinger et al., 2010a). This indicates that the star is well below the red clump in luminosity and is still ascending the red-giant branch (Miglio et al., 2009). Its relatively high frequencies require Kepler’s short-cadence mode (see Section 4), which means that only relatively few stars with these characteristics are being observed by Kepler. KIC 4351319 therefore provides a very important opportunity to study this evolutionary phase and hence it has been selected for long-term observations by Kepler. ## 2 Atmospheric parameters from spectroscopy Spectroscopic observations of KIC 4351319 in the visible spectral range have been carried out on 2010 July 26 (HJD = 2 455 404.7756) with the Cross-Dispersed Echelle Spectrograph at the 2.7-m “Harlan J. Smith” telescope at the McDonald Observatory, Texas, USA, in the framework of the ground-based observational support of the Kepler space mission (Uytterhoeven et al., 2010a, b). A stellar spectrum, wavelength-calibrated and normalized to the continuum, was obtained using standard data-reduction procedures for spectroscopic observations within the NOAO /IRAF package. The resulting signal-to-noise ratio was . The spectral resolution as measured from the Th-Ar emission lines is about R = 65 000. In order to derive the effective temperature and surface gravity for our target, we minimized the difference between observed and synthetic profiles. As a goodness-of-fit test we used the parameter: χ2=1N∑(Iobs−IthδIobs)2, where is the total number of independent points in the spectrum, and are the intensities of the observed and computed profiles, respectively, and is the photon noise. The synthetic spectra were generated in three steps: first we computed the stellar atmosphere model by using the ATLAS9 code (Kurucz, 1993), then the stellar spectrum was synthesized using SYNTHE (Kurucz & Avrett, 1981) and finally the instrumental and rotational convolutions were applied. The ATLAS9 code includes the metal opacity by means of distribution functions (ODF) that are tabulated for multiples of the solar metallicity and for various microturbulence velocities. We selected a set of vanadium and iron lines in the range between 6180 Å and 6280 Å, which are free of blending and whose atomic parameters are well known and already explored for temperature calibrations (see Biazzo et al., 2007, and reference therein). For surface gravity we used the non-saturated line Cai at 6162.173 Å, whose wings are very sensitive to gravity changes (see Grey, 1992). First of all, we computed the of the star by using the parameters from the KIC catalogue (Latham et al., 2005) reported in Table 1. We used SYNTHE to reproduce the observed metal lines, and our best match was achieved convolving the computed lines with a stellar rotational profile having = 6 1 km s, while the microturbulent velocity was obtained by using the relation published by Allende Prieto et al. (2004). Then, with an iterative procedure starting with the values of the KIC catalogue of and and the solar abundances given by Asplund et al. (2009), we obtained the best fit values reported in Table 1. Uncertainties in and have been estimated within a 1 level of confidence, as the variation in the parameters which increases the by one (Lampton et al., 1976). The uncertainty in the iron abundance is the standard deviation of the weighted average of the abundances derived from each single line. After having fixed , and , we used SYNTHE to derive the abundance pattern of our target by the method of spectral synthesis. The results are summarized in Table 2 and plotted in Fig. 1. We then conclude that, according to estimated errors, the metallicity is slightly over the solar ones. In particular, iron abundance is equal to dex. ## 3 Solar-like properties in red-giants stars ### 3.1 Large and small separations It is well known that the properties of solar-like oscillations in main-sequence stars can be described by adopting the asymptotic development (Tassoul, 1980), which predicts that the oscillations frequencies of acoustic modes, characterized by radial order , and harmonic degree , for should satisfy the following approximation: νn,l∼Δν(n+l2+ϵ), (1) where is a function of frequency and depends on the properties of the surface layers and , known as the large frequency separation, is the inverse of the sound travel time across the stellar diameter and is proportional to the square root of the mean density. Thus, the solar-like oscillations spectra should show a series of equally spaced peaks separated by between p modes of same degree and adjacent : Δν∼Δνl=νn+1,l−νn,l. (2) In addition, the solar-like power spectra are characterized by another series of peaks, whose separation is , known as the small separation: δνl,l+2=νn,l−νn−1,l+2, (3) which is sensitive to the chemical composition gradient in the central regions of the star and hence to its evolutionary state. The determination of the large and small frequency separations can provide asteroseismic inferences on the mass and the age of main-sequence and post-main-sequence solar-type stars, using the so-called seismic diagnostic C-D diagram (Christensen-Dalsgaard, 1988). However, these two seismic indicators alone do not represent an unambiguous diagnostic tool for more evolved stars, for which the relation between the small and large separation is almost linear (Bedding et al., 2010; Montalbán et al., 2010; Mosser et al., 2010). On the other hand, it has been demonstrated that the stellar mass and radius of a solar-like star can successfully be derived, within and respectively (e.g. Kallinger et al., 2010b), from measurements of the large separation and , the frequency at which the oscillation signal reaches a maximum, by using the scaling laws given by Kjeldsen & Bedding (1995) and Bedding & Kjeldsen (2003). Hence, in order to characterize in details the structure of a red-giant star, it is necessary to consider individual frequencies of oscillation and other oscillation properties, as we will discuss in the following. ### 3.2 The potential of the mixed modes The properties of solar-like oscillations are expected to change as the stellar structure evolves. According to Eq. (1) and considering that , oscillation frequencies of a given harmonic degree should decrease as the star evolves and the radius increases and should be almost uniformly spaced by at each stage of evolution. However, in subgiants and red giants the radial modes seem to follow Eq. (1) closely, but the frequencies of some non-radial modes appear to be shifted from the regular spacing due to the occurrence of the so-called ‘avoided crossing’ (Christensen-Dalsgaard, 2004a). As the star evolves away from the main sequence, the core contracts and the radius expands, causing an increase of the local gravitational acceleration and of the gradients in the hydrogen abundance, and hence of the buoyancy frequency in the deep interior of the star. As a consequence g modes with high frequencies are allowed to propagate and can interact with p modes of similar frequency and same harmonic degree, giving rise to modes with mixed character, which behave as g modes in the interior and p modes in the outer envelope (Aizenman et al., 1977). The interaction can be explained as the coupling of two oscillators of similar frequencies. The effect of the coupling becomes much weaker for modes with higher harmonic degree, since in these cases the gravity waves are better trapped in the stellar interior and hence better separated from the region of propagation of the acoustic waves (Dziembowski et al., 2001; Christensen-Dalsgaard, 2004a; Dupret et al., 2009). It has been found by Montalbán et al. (2010) and observationally demonstrated by Huber et al. (2010), that the scatter of modes caused by ‘avoided crossing’ decreases as the star goes up to the red-giant branch: as the luminosity increases and the core become denser, the acoustic modes are better trapped and the oscillation spectra become more regular. Once the star ignites He in the core, the core expands and the external convective zone becomes shallower which has the effect of increasing the probability of coupling between g and p modes again. Very recently, Beck et al. (2011) have demonstrated that the quality of the Kepler observations gives the possibility to measure the period spacings of mixed-modes with gravity-dominated character which, like pure gravity modes, penetrate deeply in the core allowing to study the density contrast between the core region and the convective envelope and, like p modes, have amplitude at the surface high enough to be observed. In particular, Bedding et al. (2011) found that measurements of the the period spacings of the gravity-dominated mixed modes, permit to distinguish between hydrogen- and helium-burning stages of evolution of the red giants. The occurrence of mixed modes is then a strong indicator of the evolutionary state of a red-giant star and the fitting of the observed modes with those calculated by theoretical models can provide not only mass and radius but, with a good approximation, an estimate of the age of the star. ### 3.3 Sharp features inside the star Sharp variations localized at a certain acoustic depth in the structure of pulsating stars produce a distinctive quasi-periodic signal in the frequencies of oscillations. The characteristics of such signal are related to the location and thermodynamic properties of the layer where the sharp variation occurs. Sources of sharp variations are for example the borders of convection zones and regions of rapid variation in the first adiabatic exponent , where the derivative corresponds to an adiabatic change, such as the one that occurs in the region of the second ionization of helium. In the main-sequence stars the signals coming from different sharp features in the interior, overlap generating a complex behaviour (Mazumdar & Antia, 2001). In red giants, a recent study by Miglio et al. (2010) demonstrated that the oscillatory signal of the frequencies observed is directly related only to the second helium ionization zone. Several attempts have been made in order to isolate the generated oscillatory components from the frequencies of oscillations or from linear combinations of them such as large separations and second differences. In principle, this approach can be applied to determine the properties of the base of the convective envelope (Monteiro, Christensen-Dalsgaard, Thompson, 2000; Ballot, Turck-Chièze and García, 2004) and in particular to infer the helium abundance in the stellar envelope (Lopes et al., 1997; Monteiro & Thompson, 1998; Pérez Hernández and Christensen-Dalsgaard, 1998; Miglio et al., 2003; Basu et al., 2004; Houdek & Gough, 2007). ## 4 Kepler observations and analysis of the oscillation spectrum KIC 4351319 has been observed by the Kepler satellite (Koch et al., 2010) during the Q0, Q1 and Q2 runs in long cadence mode (integration time of 30 min) and during the Q3 run in short cadence mode (integration time of 1 min). The data that we describe here were obtained during 30 consecutive days, starting on 2009, September 18, which corresponds to the first month of observing quarter 3 (Q3.1). The Kepler short-cadence observation mode corresponds to a Nyquist frequency of 8497 Hz. In the present analysis, we used the SOC corrected data obtained by the Kepler team after reducing and correcting the raw photometric data for slopes and discontinuities as described in Jenkins et al. (2010) and García et al. (2011). The effective duty cycle resulted to be and the spectral window does not show aliasing artifacts that could interfere with the identification of real frequencies. The top panel of Fig. 2 shows the cleaned light curve normalized to the mean value. The Fourier analysis of the data set has been performed by using the PERIOD04 package (Lenz & Breger, 2005), which allows to extract the individual frequencies from large multiperiodic time series - also containing gaps - and can perform multiple-frequency least-squares fit up to several hundred simultaneous sinusoidal components. The resulting power spectrum of KIC 4351319 shows a clear power excess in the frequency range Hz with regularly spaced peaks (bottom panel of Fig. 2), while no relevant features appear between Hz and the Nyquist limit. We have considered only peaks in the spectrum with a signal-to-noise ratio (SNR) in amplitude greater than 3. In order to confirm the results obtained, the analysis of the spectrum was also independently performed by five additional teams which adopted the following methods: 1. the power spectrum was smoothed with a Gaussian with a FWHM of 0.5 Hz and the frequencies of the peaks with (in amplitude) were measured. 2. peak-bagging methods, substantially based on the fit of Lorentzian profiles to the power density spectrum, using: • Maximum Likelihood Estimators (MLE), (see Appendix A for details) • Bayesian MCMC (Gruberbauer et al., 2009), (see Appendix B for details) • Envelope autocorrelation function analysis (Mosser & Appourchaux, 2009) Table 3 reports the set of frequencies confirmed, within the errors, by at least two of the peak-bagging solutions. Frequencies labeled with () have been detected by all the teams. The values of the radial order for are as obtained by adopting the scaling law proposed by Mosser et al. (2011a) (see also Huber et al., 2010). Three possible excited modes with , namely Hz, Hz and Hz have been also found, but their validity must be carefully checked by additional future observations. In order to estimate the large frequency separation, we first computed the autocorrelation function of the power spectrum in the region of p-mode power excess. With such an initial guess value of the large separation, we built an échelle diagram and identified the ridge. Afterwards, we computed the comb-response function, as defined by Kjeldsen et al. (1995), for each frequency reported in Table 3 and for the three additional frequencies with , searching for the maximum value of the comb response in the range Hz. The result, reported in Fig. 3, shows that many modes lie around the mean value of Hz computed for the radial modes, while the other frequencies shows a quite large scatter indicative of their mixed mode character. Fig. 4 shows the region from 250 to 650 Hz of the power spectrum folded with a spacing equal to the mean value of the large frequency separation. Two sharp peaks, corresponding to modes with and , as well as a broader peak, corresponding to modes with , can be clearly seen. The final mode identification in terms of the degree , based on both the alignment in the échelle diagram (see Fig. 13) and the result of the peak bagging is reported in Table 3. A value of the mean small frequency separation Hz has been also derived from each pairs of and reported in Table 3. ### 4.1 Background and p-mode power excess modelling After converting the power spectrum (ppm) to power spectral density (ppm), by multiplying the power by the effective length of the observing run – estimated as the reciprocal of the area under the spectral window (Bedding et al., 2005) – a model fitting of the stellar background due to stellar activity and granulation has been performed. In order to simultaneously model the stellar background as well as the p-mode power excess, we fitted the observed power density spectrum by a superposition of white noise, two semi-Lorentzian functions (Harvey, 1985) and a Gaussian function representing the power excess hump (see Kallinger et al., 2010b, for details): P(ν)=2∑i=1Ai(1+νBi)ci+De−(νmax−ν)22σ2+E (4) where is the frequency, , and are the amplitudes, the characteristic timescales and the slopes of the power laws; is the white noise contribution; , and are the height, the central frequency and the width of the power excess hump, respectively. We adopted as initial guess for the white noise the average of the power spectrum in the frequency range Hz, where the photon noise is expected to dominate over the other components. The guess values for the remaining parameters have been evaluated by scaling from typical solar values (Aigrain et al., 2004; Pallè et al., 1999; Huber et al., 2009) for active region and granulation timescales. We smoothed the raw power spectrum density by applying a Hz boxcar using the independent averages only, as suggested by García et al. (2009), in order to perform properly the fit by means of a weighted least-squares procedure. The weights we adopted, as in García et al. (2009), have been determined by the uncertainties on each independent Hz average. As in Mathur et al. (2010) we adopted the IDL least-squares MPFIT package (provided by Craig B. Markwardt, NASA/GSFC111craigm/idl/idl.html), implementation of the Levenberg-Marquardt fitting algorithm. The results are shown in Fig. 5. The fit returned, among other parameters, the maximum amplitude of the smoothed excess power PHz. The corresponding frequency is Hz, where the uncertainty is given by the resolution of the smoothed spectrum. This value and its uncertainty are in a very good agreement with what found by fitting the raw spectrum by the envelope autocorrelation function analysis (Mosser & Appourchaux, 2009). Following Kjeldsen et al. (2008a), we evaluated the maximum amplitude per radial mode by adopting the calibration factor c = 3.16, whose value depends on the spatial response of the observations to modes with different degree relative to radial modes, and obtained ppm. ### 4.2 Global asteroseismic parameters In order to extract a rough estimate of the global parameters of the star, to be adopted as guess values for the model computation, we adopted the scaling laws provided by Kjeldsen & Bedding (1995) and Bedding & Kjeldsen (2003), relating the observed mean large frequency separation Hz and Hz to the fundamental parameters of the star. We obtained: and . We also derived the expected radial order of the mode with maximum amplitude in the spectrum, . This latter value is in agreement with the radial order identification of the radial mode with higher SNR reported in Sect. 4. ## 5 On the characterization of the structure of KIC 4351319 ### 5.1 Evolutionary models Given the identified pulsation frequencies and the basic photospheric parameters, we faced the theoretical challenge to interpret the observed oscillation modes by constructing stellar models which satisfy the observational constraints. We assumed the effective temperature and gravity as calculated in Section 2 respectively, K, dex (Table 1). We calculated several grids of theoretical structure models for the star by using the ASTEC evolution code (Christensen-Dalsgaard, 2008a) by varying the mass and the composition in order to match the atmospheric parameters available. All the models have been calculated with the OPAL 2005 equation of state (Rogers & Nayvonov, 2002), OPAL opacities (Iglesias & Rogers, 1996), and the NACRE nuclear reaction rates (Angulo et al., 1999). Convection was treated according to the mixing-length formalism (MLT) (Böhm-Vitense, 1958) and defined through the parameter , where is the pressure scale height and is assumed to vary from to . Inclusion of overshooting or diffusion outside the convective core during the main-sequence phase did not produce any appreciable effect on the oscillation frequencies of models in such evolved phases of the evolution. A crucial input quantity is the iron abundance, whose logarithmic value relative to the solar one has been taken as [Fe/H] dex, as determined in Sect. 2. The initial heavy element mass fraction can be calculated from the relation [Fe/H], where is the ratio at the stellar surface and the solar value is (Grevesse & Noels, 1993). Thus, it has been assumed . In the present modelling we neglect the difference in the relative abundances of the heavy elements between the star and the Sun (cf. Fig. 1); although this should be taken into account in future, more detailed investigations, the effects on the opacity and hence the model structure are likely to be contained within the assumed range of uncertainty in . The uncertainty in the observed value of introduces an uncertainty in the determination of the mass whose value, considering only the observed spectroscopic parameters, seems to be limited to the range . Extra mixing outside the convective region was obtained by adding turbulent diffusion from the convective envelope, as described in Proffitt & Michaud (1991), by using the parameterized formulation: D=Dmax(ρ/ρbcz)−3 (5) where is the density at the base of the convective envelope and is a parameter which sets the maximum diffusion. Additional evolutionary models were calculated by including overshoot beneath the convective envelope by a distance , where is the pressure scale height at the base of the convective envelope and is a nondimensional parameter. The resulting evolutionary tracks are characterized by the mass , the initial chemical composition and a mixing-length parameter. Fig. 6 shows a series of evolutionary tracks obtained for different masses and fixed initial composition and plotted in two H-R diagrams, representing respectively the effective temperature-gravity plane and the effective temperature-luminosity plane. The location of the star in the Hertzsprung-Russell diagram identifies KIC 4351319 as being in the post-main-sequence phase of evolution at the beginning of the ascending red-giant branch. It has a small, degenerate helium core, having exhausted its central hydrogen, and it is in the shell-hydrogen-burning phase, with a very deep convective zone, extending from the base located at about to the photosphere. Figure 7 shows the internal content of hydrogen in three models of this star, which include respectively extra mixing by turbulent diffusion from the convective envelope, overshooting from the convective envelope with and without any extra mixing effect. The internal hydrogen profiles show that the core, where the hydrogen is exhausted, is very small and a sharp variation, as a step-like function, occurs at the base of the convective envelope located at and for the model with no extra effects considered. Models with inclusion of turbulent diffusion show a smooth profile of the abundance of the hydrogen with no sharp variation at the base of the envelope. We expect to be able to distinguish among the different internal characteristics of the structure by studying the oscillation properties of this star. Furthermore, we wish to verify whether, as demonstrated by Christensen-Dalsgaard et al. (1993) for the case of the Sun, the inclusion of diffusion in the models results in a better agreement between theory and observations. ### 5.2 The seismic properties of the models In order to investigate the observed solar-like oscillations, we used the ADIPLS package (Christensen-Dalsgaard, 2008b) to compute adiabatic oscillation frequencies with degree for all the models satisfying the spectroscopic constraints. Figure 8 shows the evolution of frequencies computed for an evolutionary model of KIC 4351319 calculated with , , without additional extra mixing effects. The ranges in frequency and effective temperature have been chosen to correspond approximately to the observed ranges. The location of the acoustical cut-off frequency, decreasing with increasing age, at the top of the atmosphere in the model has been indicated by grey dots. As it has been already explained in Sect. 3, according to Eq. (1), the plot should be characterized by frequencies which decrease as the star evolves and almost uniformly spaced by at each stage of evolution. In the case of more evolved stars, as it has been shown by Di Mauro et al. (2003) and Metcalfe et al. (2010), while the radial modes seem to follow closely Eq. (1), the frequencies of the modes with show the typical oscillating behaviour due to the presence of the mixed modes. In addition, Fig. 8 shows that at each stage of the evolution the distance between two frequencies of adjacent orders become smaller and smaller as the frequency decreases: while the upper part of the panel hosts mixed modes with prevalent p-mode character, below Hz the panel appears more crowded by mixed modes with predominant g-mode character and the general trend of frequencies decreasing as the star evolves does no longer hold. In particular, pure g modes of high radial order are located at very low frequencies and high radial orders, below Hz. Fig. 9 shows the evolution of the frequencies for modes as function of the age and the effective temperature. It shows that modes, similarly to what happen for modes, undergo avoided crossings during the evolution and the theoretical oscillation spectrum is as a result very crowded. The presence of mixed modes with prevalent g mode character is also evident for : below Hz frequencies do not appear to decrease with the decrease of the effective temperature. The behaviour of the mixed modes inside the star can be understood by considering the propagation diagram in Fig. 10 obtained for three models of KIC 4351319, calculated respectively without extra mixing effect and with the inclusion of a weak and an efficient turbulent diffusion below the convective envelope. The characteristics of the non-radial modes depend on the separation between gravity and acoustic domains, defined respectively by the Brunt-Väisälä () and Lamb frequencies (). The Lamb frequencies appear close to the g-modes region. Thus, the gravity waves, trapped in a region not so well separated from the region of propagation of the acoustic waves, can interact with the p modes of similar frequencies. In addition, it is possible to notice that at nearly the same value of effective temperature and luminosity, the model without extra-mixing effect shows a second maximum in its buoyancy frequency located at the base of the convective envelope (). This maximum becomes smaller and totally disappears as the effect of the helium diffusion beneath the base of the convective envelope becomes stronger. The characteristics of this second maximum in reflects the behaviour of the hydrogen abundance inside the star as seen in Fig. 7 and it will be discussed in Sect. 5.4. It is important to notice that, according to the theory, the spectra of g modes are denser than that of p modes: many g modes can interact with the same p mode of close frequency. In order to have an idea about the modes expected to be visible, amplitudes of all the calculated modes were roughly estimated by making the following considerations. The total energy of a mode of radial order and harmonic degree can be expressed as , where is the surface amplitude, and is the inertia of the mode. For stochastically excited modes it is generally expected that the mode energy is independent of the harmonic degree at fixed frequency. It follows that the amplitude of a mode can be estimated relative to a radial mode of the same frequency, such that the modes would have the same total energy (e.g. Christensen-Dalsgaard et al., 1995; Dupret et al., 2009): AnlA0=[E0Enl]1/2, (6) where and have been obtained by interpolating to the frequencies of radial modes. Figure 11 shows the normalized inertia for the frequencies of Model 1 of Table 4 of KIC 4351319. It shows that radial modes have a very low inertia relative to most of the nonradial modes and are the modes which will show highest amplitude at the surface. Some modes with , and have an inertia similar to that of the radial modes , and appear quite regularly spaced in frequency. These modes which preserve strong p-mode character are solar-like oscillations and are predicted to be visible at the surface with a quite high amplitude. The effect of coupling, typically expected only for , strongly appear also for modes with . As the inertia grows, during the coupling the gravity character of the modes predominates on the acoustic character. Modes with the highest inertia are evanescent towards the surface and hence have the lowest probability to be observed. Thus, due to the low amplitude, the probability to detect any mixed modes for appears quite low, but it is quite likely that we can observe many of the mixed modes for and probably a few of the mixed modes for (Beck et al., 2011). In order to clearly distinguish the nature of the mixed modes, it is useful to study the behaviour of the displacement eigenfunctions of the modes. Figure 12 shows the radial variation of the eigenfunctions of three mixed modes calculated for Model 1 of KIC 4351319 described in Table 4. The upper panels of Fig. 12 show the eigenfunction for a mixed mode with high inertia and hence with a predominant gravity nature, characterized by a quite large amplitude in the core. The middle panels of Fig. 12 show the eigenfunction for a mixed mode with both gravity and pressure character. The lower panels of Fig. 12 show the eigenfunction for a nearly pure acoustic mode, with an inertia comparable to that of the radial modes: the amplitude in the core is negligible. ### 5.3 Interpretation of the observed oscillation spectrum Among all the possible models, we selected a few models able to reproduce the set of all the observed frequencies of Table 3 and the observed values of the large and small separations. The characteristics of some models that satisfy the observed constraints are given in Table 4. According to the stellar evolution constraints, given the match with the observed oscillation properties, and with the use of all the possible values of mass and metallicity, our computations show that the age of KIC 4351319 is Gyr, with a mass , a radius and a luminosity . The values of mass and radius which have been obtained by direct modelling of the individual frequencies are better constrained and well compatible with those obtained by the scaling laws as described in Sect. 4.2. A detailed comparison between the theoretical oscillation spectra for Model 1 and Model 5 of KIC 4351319 reported in Table 4 and the observed data is provided in the échelle diagrams of Fig. 13. The size of the symbols is proportional to the theoretical oscillation amplitudes of p modes, relative to the amplitudes of radial modes with the same frequency (see Eq. 6). The results show, as explained in previous sections, that the observed modes are pure acoustic modes, and and nearly pure p modes and some and g-p mixed modes. Some non-radial modes with mixed gravity-pressure character have an inertia so low as to propagate up to the surface and appear to behave like solar-like oscillations. Very few mixed modes, with a quite high inertia, keep their gravity character, although the combination with a p mode enhance their amplitude so that they can be observed at the surface and in the échelle diagram appear to depart strongly from the regular solar-like pattern. Pure g modes at lower frequencies, have not been detected with the present observations. Solar-like oscillations with , although theoretically predicted, have not been detected, probably due to geometrical reasons which produce the cancellation of the observed signal. We found that there is a very good agreement between observed and theoretical frequencies. In particular we are able to reproduce all the mixed modes. The presence of mixed-modes with needs to be better investigated: unfortunately none of our best models, shown in Fig. 13, is able to reproduce the mode with frequency Hz. In addition, the results show that it is quite difficult to determine which of Model 1 and Model 5 best reproduces the observations. Perhaps the ambiguity will be solved by the identification of modes at lower frequencies and in particular if the reality of the mode of Hz (see Sect. 4) will be confirmed or not. Another important issue is related to the possibility of observing rotational splittings in this star. We estimate that the observed rotational velocity , quite high for this kind of objects, might produce a rotational splitting of Hz for the modes of , in case of rigid rotation. Such a rotational splitting is about twice the value of the frequency resolution of the data set. To check for the signature of rotation we have re-run the frequency determination now adding rotational split components for and modes. The rotation frequency and the inclination angle were allowed to vary in the range between Hz and respectively, following the approach of Gizon & Solanki (2003). A comparison of the global likelihoods of the two models (with and without rotation) indicates that the rotation-free model is about 70 times more likely than the model including rotation. Indeed, the presence of two modes closely spaced in frequency does not prove that we deal with rotational splitting although this possibility cannot be excluded. Moreover, the two pairs of close frequencies of suspected for evidence of rotational splittings (Hz with Hz and Hz with Hz), appear to be not separated by a same amount in frequency, indicating that they cannot be both appearance of rotational splittings. We finally notice that in order to reproduce the observed modes, we did not need to correct the frequencies for the surface effects, as suggested by Kjeldsen et al. (2008b), but the small departure of the modes at high frequency might be indicative of the need of such a correction. In fact, the structure of the near-surface regions of the stars is quite uncertain: there are still substantial ambiguity in modelling the convective flux, defining an appropriate equation of state to describe the thermodynamic properties of the stellar structure, as well as in the treatment of non-adiabatic effects. The conditions and limits of the applicability of the surface effect are still unknown and will be the subject of future studies. Since there is no evidence for fast rotation, we exclude any possible effect on the frequencies due to magnetic activity. It was possible to determine the evolutionary state of this star through direct modelling, which places it in the hydrogen-shell-burning phase at the base of the ascending red-giant branch. This star is substantially less evolved than the red giants, whose gravity-mode period spacings were measured by Bedding et al. (2011) and Mosser et al. (2011b). This is reflected in Fig. 8 where we see that the spacing of the g-dominated modes (the upward sloping features) is comparable to the p-mode spacing. This fact, together with the very strong mode bumping, makes it is quite hard to see a regular spacing in the l=1 modes of any single model. This makes it difficult to measure a clear g-mode period spacing. However, we see from the list of observed modes in Table 3 that the consecutive modes have period spacings in the range 35–50 s, which is consistent with a hydrogen-shell-burning star Bedding et al. (2011). Applying the method described by Mosser et al. (2011b) confirms a period spacing of about 404 s. ### 5.4 Sharp features inside KIC 4351319 Figure 14 shows that a weak oscillatory motion is present in the calculated frequencies for the acoustic modes which follow closely the asymptotic law, namely the radial modes and the non-radial modes with very low inertia. This oscillatory signal, as explained in Sect. 3.3, is produced only by the region of the second ionization of helium, which induces a local minimum in the first adiabatic coefficient and hence a sharp variation in the sound speed. Figure 15, which shows the behaviour of the first adiabatic coefficient as function of the acoustic radius , indicates that in the models of KIC 4351319 the second helium ionization zone occurs at about , while the base of the convective envelope is located at , too deeply to produce an effective signal into the solar-like frequencies (Miglio et al., 2010). The properties of the helium ionization zone, once determined from the oscillation frequencies, may be used to constrain the structure of the star, in particular the envelope helium abundance. Further studies and developments are required in order to determine how a different content of He and a different equation of state for the computation of the models will result in a different oscillatory behaviour in the theoretical frequencies. Secondly, we have also considered the possibility to isolate the signal coming from the base of the convective envelope, by looking at the observed modes which penetrate deeply inside the star, namely the mixed modes with a high inertia. This can be studied following Miglio et al. (2008), by comparing models modified by adding turbulent diffusion or overshooting at the base of the convective envelope. The results have shown that the inclusion of turbulent diffusion, or overshooting, below the convective envelope produces a displacements only in the mixed modes for and modes, while all the other frequencies are not modified as shown in Fig. 16. Thus, although we have not observed high-order g modes, we can still use the mixed modes to probe qualitatively the interior of this star. However, it is impossible to distinguish the effect on the frequencies due to the inclusion of diffusion from that of overshooting. ## 6 Conclusion KIC 4351319 has been observed for 30 days by the Kepler satellite. These observations have yielded a clear detection of 25 modes identified with harmonic degrees between and Hz with a large separation Hz and a small separation Hz respectively. The oscillation spectrum of this star is characterized by the presence of a well defined solar-like oscillations pattern due to radial acoustic modes and non-radial nearly pure p modes equally spaced in frequencies. The nearly pure p modes have mixed gravity-pressure character with an inertia so low as to propagate up to the surface and appear to behave like solar-like oscillations, although they penetrate deeply to the core. The oscillation spectrum also showed evidence for the presence of mixed modes with strong gravity-mode character. Those modes sound the internal region of this star and, besides constraining the stellar age, carry tight information about the location of the convective envelope and the condition in the core. This enabled to define characteristics of this star with an accuracy which cannot be reached by the use of only the global asteroseismic parameters, and . Thus, in this paper we have addressed the problem of identifying the structural properties and the evolutionary state of KIC 4351319 by using the results of the analysis of the oscillation spectrum and the atmospheric parameters provided by supplementary ground-based spectroscopic observations. Detailed modelling of this star, in the attempt to match both the asteroseismic and spectroscopic constraints, allowed us to determine the main parameters with an unprecedent level of precision for a red-giant star, with uncertainties of for mass, for age, for radius, and for luminosity. In the end, we are able to conclude that this star is in the red-giant phase of the evolution, with a mass , an age of Gyr, a radius and a luminosity . The uncertainties obtained for the stellar parameters come from the degeneracy of the models describing the stars in the red-giant phase of the evolution. Only the detection of g modes, which better sound the condition of the core, could improve the results obtained by the present analyses, while strong theoretical efforts need to be done in order to achieve a better description of the stellar structure. It is clear that KIC 4351319 represents an excellent candidate for long-term observations, which have been already scheduled for Kepler future runs. This will allow us to open a window on the understanding of this phase of the evolution and to unveil all the raised questions including those relative to the identification of the mixed modes, to the signature of the ionization of the He and to the presence of diffusion or overshooting below the convective envelope. In particular, the possibility to detect rotational splittings in KIC 4351319 appears very fascinating and represents an unique opportunity for sounding the internal dynamics of a red-giant star. ## Acknowledgments Funding for this mission is provided by NASA’s Science Mission Directorate. We thank the entire Kepler team for the development and operations of this outstanding mission. The work presented here is also based on observations obtained with the Harlan J. Smith Telescope at McDonald Observatory, Texas. SH acknowledges financial support from the UK Science and Technology Facilities Council (STFC). SH acknowledges financial support from the Netherlands Organization for Scientific Research (NWO). KU acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG) in the framework of project UY 52/1-1. TK is supported by the Canadian Space Agency and the Austrian Science Fund (FWF P22691-N16) ## References • Aigrain et al. (2004) Aigrain, S., Favata, F., Gilmore, G., 2004, A&A 414, 1139 • Aizenman et al. (1977) Aizenman, M., Smeyers, P., Weigert, A., 1977, A&A, 58, 41 • Allende Prieto et al. (2004) Allende Prieto C., Barkelm P. S., Lambert D. L., Cunha K., 2004, A&A, 420, 183 • Anderson et al. (1990) Anderson, E. R., Duvall, T. L., Jr., Jefferies, S. M., 1990, ApJ, 364, 699 • Angulo et al. (1999) Angulo, C., Arnould, M. Rayet M. et al. 1999, Nucl. Phys. A, 656, 3 • Appourchaux et al. (1998) Appourchaux, T., Gizon, L., Rabello-Soares, M.C., 1998, A&AS 132, 107 • Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., Scott, P., 2009, Annu. Rev. Astron. Astrophys., 47, 481 • Ballot, Turck-Chièze and García (2004) Ballot, J., Turck-Chièze, S., and García, R. A., 2004, A&A, 423, 1051 • Barban et al. (2007) Barban, C., Matthews, J. M., De Ridder, J., Baudin, F., Kuschnig, R., Mazumdar, A., Samadi, R., Guenther, D. B., Moffat, A. F. J., Rucinski, S. M., et al. A&A, 468, 1033 • Basu et al. (2004) Basu S., Mazumdar, A., Antia, H. M., & Demarque, P. 2004, MNRAS, 350, 277 • Beck et al. (2011) Beck, P., Bedding, T. R., Mosser, B., et al., 2011, Sci, 332, 205 • Bedding et al. (2011) Bedding, T. R., Mosser, B., Huber, D., et al., 2011, Nat, 471, 608 • Bedding et al. (2010) Bedding, T. R., Huber, D., Stello, D., et al., 2010, ApJ, 713, L176 • Bedding et al. (2005) Bedding, T. R., Kjeldsen, H., Bouchy, F., et al., 2005, A&A, 432, L43 • Bedding & Kjeldsen (2003) Bedding, T. R., Kjeldsen, H., 2003, Publ. Astron. Soc. Austr., 20, 203 • Biazzo et al. (2007) Biazzo, K., Frasca, A., Catalano, S., Marilli, E., 2007, AN, 328, 938 • Böhm-Vitense (1958) Böhm-Vitense, E., 1958, Zeitschrift für Astrophysik, 46, 1115 • Borucki (2010) Borucki, W. J., Koch, D., Basri, Gibor; et al. 2010, Sci, 327, 977 • Buzasi (2000) Buzasi, D., Catanzarite, J., Laher, R., et al., 2000, ApJ, 532, L133 • Chaplin et al. (2002) Chaplin, W,J., Elsworth, Y., Isaak, G. R., et al., 2002, MNRAS, 336, 979 • Chaplin et al. (2008) Chaplin, W,J., Appourchaux, T., Arentoft, T., et al., 2008, AN, 329, 549 • Christensen-Dalsgaard (1988) Christensen-Dalsgaard J. 1988, in Proc. IAU Symp. 123, Advances in Helio-and Asteroseismology, ed. J. Christensen-Dalsgaard & S. Frandsen, Dordrecht: Kluwer, 295 • Christensen-Dalsgaard (2004a) Christensen-Dalsgaard J. 2004, Sol. Phys., 220, 137 • Christensen-Dalsgaard (2008a) Christensen-Dalsgaard J. 2008a, ApSS, 316, 13 • Christensen-Dalsgaard (2008b) Christensen-Dalsgaard J. 2008b, ApSS, 316, 113 • Christensen-Dalsgaard et al. (1993) Christensen-Dalsgaard, J., Proffitt, C. R., Thompson, M. J. 1993, ApJ, 403, 75 • Christensen-Dalsgaard et al. (1995) Christensen-Dalsgaard J., Bedding T. R. & Kjeldsen H., 1995, ApJ, 443, L29 • De Ridder et al. (2009) De Ridder, J., Barban, C., Baudin, F., Carrier, F., Hatzes, A. P., Hekker, S., Kallinger, T., Weiss, W. W., Baglin, A., Auvergne, M., et al. 2009, Nature, 459, 398 • Di Mauro et al. (2003) Di Mauro, M. P., Christensen-Dalsgaard, J., Kjeldsen, H., Bedding, T. R., Paternò, L. 2003, A&A 404, 341 • Dupret et al. (2009) Dupret, M.A., Belkacem, K., Samadi, R., et al., 2009, A&A, 506, 57 • Dziembowski et al. (2001) Dziembowski, W. A., Gough, D. O., Houdek, G., Sienkiewicz, R., 2001, MNRAS, 328, 601 • Frandsen et al. (2002) Frandsen, S., Carrier, F., Aerts, C., et al., 2002, A&A, 394, L5 • García et al. (2009) García, R. A., Régulo, C., Samadi, R., et al., 2009, A&A, 506, 41 • García et al. (2011) García, R. A., Hekker, S., Stello, D., et al. 2011, arXiv:1103.0382 • Gilliland et al. (2010) Gilliland, R. L., Brown, T. M., Christensen-Dalsgaard, J., Kjeldsen, H., Aerts, C., Appourchaux, T., Basu, S., Bedding, T. R., Chaplin, W. J., Cunha, M. S., et al. 2010, PASP, 122, 131 • Gizon & Solanki (2003) Gizon, L. & Solanki, S. K. 2003 ApJ 589, 1009 • Grevesse & Noels (1993) Grevesse, N. & Noels, A. 1993 in Origin and Evolution of the Elements, ed. S. Kubono & T. Kajino, 14 • Grey (1992) Grey R., “The observation and analysis of stellar photospheres”, Cambridge University Press, 1992 • Gruberbauer et al. (2009) Grubebauer, M., Kallinger T.,Weiss, W.W.,Guenther, D.B., 2009, A&A, 506, 1043 • Guenther et al. (2000) Guenther, D. B., Demarque, P., Buzasi, D., 2000, ApJ, 530, L45 • Harvey (1985) Harvey, J., ESA SP-235, 199 • Hekker et al. (2009) Hekker, S., Kallinger, T., Baudin, F., De Ridder, J., Barban, C., Carrier, F., Hatzes, A. P., Weiss, W. W., Baglin, A., 2009, A&A, 506, 465 • Hekker et al. (2010) Hekker, S., Barban, C., Baudin, F., De Ridder, J., Kallinger, T., Morel, T., Chaplin, W. J., Elsworth, Y. 2010, A&A, 520,60 • Hekker et al. (2010) Hekker, S., Debosscher, J., Huber, D., et al., 2010, ApJ, 713, L187 • Houdek & Gough (2007) Houdek, G. & Gough, D. O., 2007, MNRAS, 375, 861 • Huber et al. (2010) Huber, D., Bedding, T. R., Stello, D., et al., 2010, ApJ, 723, 1607 • Huber et al. (2009) Huber, D., Stello, D., Bedding, T. R., et al. 2009, CoAst, 160, 74 • Iglesias & Rogers (1996) Iglesias, C. A., & Rogers F. J. 1996, ApJ, 464, 943 • Kallinger et al. (2008a) Kallinger, T., Guenther, D. B., Weiss, W. W., Hareter, M., Matthews, J. M., Kuschnig, R., Reegen, P., Walker, G. A. H., Rucinski, S. M., Moffat, A. F. J., Sasselov, D., 2008a, CoAst, 153, 84 • Kallinger et al. (2008b) Kallinger, T., Guenther, D. B., Matthews, J. M., Weiss, W. W., Huber, D., Kuschnig, R., Moffat, A. F. J., Rucinski, S. M., Sasselov, D., 2008b, A&A 478, 497 • Kallinger et al. (2010a) Kallinger, T., Mosser, B., Hekker, S., et al.,2010, A&A, 522, 1 • Kallinger et al. (2010b) Kallinger, T., Weiss, W. W., Barban, C., et al.,2010, A&A, 509, 77 • Kjeldsen & Bedding (1995) Kjeldsen, H., Bedding, T., 1995, A&A, 293, 87 • Kjeldsen et al. (1995) Kjeldsen, H., Bedding, T. R., Viskum, M., Frandsen, S., 1995 AJ 109, 1313 • Kjeldsen et al. (2008a) Kjeldsen, H., Bedding, T. R., Arentoft, T., et al., 2008a, ApJ, 682, 1370 • Kjeldsen et al. (2008b) Kjeldsen, H., Bedding, T. R., Christensen-Dalsgaaard, J. et al., 2008b, ApJ, 683, L175 • Koch et al. (2010) Koch, D. G., Borucki, W. J., Basri, G., et al. 2010, ApJ, 713, 79 • Kurucz & Bell (1995) Kurucz R. L., Bell B., 1995, Kurucz CD-ROM No. 23. Cambridge, Mass.: Smithsonian Astrophysical Observatory. • Kurucz (1993) Kurucz R.L., 1993, A new opacity-sampling model atmosphere program for arbitrary abundances. In: Peculiar versus normal phenomena in A-type and related stars, IAU Colloquium 138, M.M. Dworetsky, F. Castelli, R. Faraggiana (eds.), A.S.P Conferences Series Vol. 44, p.87 • Kurucz & Avrett (1981) Kurucz R.L., Avrett E.H., 1981, SAO Special Rep. 391 • Jenkins et al. (2010) Jenkins, J. M., Caldwell, D. A., Chandrasekaran, H., et al. 2010, ApJ, 713, L87 • Lampton et al. (1976) Lampton M., Margon B., Bowyer S., 1976, ApJ, 208, 177 • Latham et al. (2005) Latham D. W., Brown T. M., Monet, D. G., Everett, M., Esquerdo, G. A., Hergenrother, C. W., 2005, BAAS, 37, 1340 • Lenz & Breger (2005) Lenz and Breger, M. 2005, CoAst 146, 53 • Lopes et al. (1997) Lopes I., Turck-Chieze, S. Michel, E., Goupil, M.-J. , 1997, ApJ, 480, 794 • Mathur et al. (2010) Mathur, S., García, R.A., Catala, C. et al., 2010, A&A, 518, 53 • Mazumdar & Antia (2001) Mazumdar A. and Antia H. M., 2001, A&A, 377, 192 • Merline (1999) Merline, W. J., 1999, ASP Conference Series 185 • Metcalfe et al. (2010) Metcalfe, T. S., Monteiro, M. J. P. F. G., Thompson, M. J., Molenda-Zakowicz, J., Appourchaux, T., Chaplin, W. J., Dogan, G., Eggenberger, P., Bedding, T. R., Bruntt, H. et al. 2010, ApJ, 723, 1583 • Miglio et al. (2003) Miglio, A., Christensen-Dalsgaard, J., Di Mauro, M. P., Monteiro, M. J. P. F. G., Thompson, M. J., 2003, in Asteroseismology Across the HR diagram, ed. M. J. Thompson, M. S., Cunha & M. J. P. F. G. Monteiro, 537 • Miglio et al. (2008) Miglio, A., Montalbán, J., Noels, A., Eggenberger, A. 2008, MNRAS 386, 1487 • Miglio et al. (2009) Miglio, A., Montalbán, J., Baudin, F. , Eggenberger, A., Noels, A., Hekker, S., De Ridder, J., Weiss, W., Baglin, A., 2009, A&A 503L, 21 • Miglio et al. (2010) Miglio, A., Montalbán, J., Carrier, F., De Ridder, J., Mosser, B., Eggenberger, P., Scuflaire, R., Ventura, P., D’Antona, F., Noels, A., Baglin, A., 2010, A&A 520L, 6 • Milne (1926) Milne, A. A., 1926, Winnie-the-Pooh, Methuen & Co. Ltd, London • Montalbán et al. (2010) Montalbán, J., Miglio, A., Noels, A., Scuflaire, R., Ventura, P. 2010, ApJ, 721, L182 • Monteiro & Thompson (1998) Monteiro, M. J. P. F. G., Thompson, M. J., 1998, in New Eyes to See Inside the Sun and Stars, Proc. IAU Symp. 185, eds. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Kluwer, Dordrecht, 317 • Monteiro, Christensen-Dalsgaard, Thompson (2000) Monteiro, M. J. P. F. G., Christensen-Dalsgaard J. and Thompson, M. J., 2000, MNRAS, 316, 165 • Mosser & Appourchaux (2009) Mosser, B., Appourchaux, T., 2009, A&A, 508, 877 • Mosser et al. (2010) Mosser, B., Belkacem, K., Goupil, M.-J., Miglio, A., Morel, T., Barban, C., Baudin, F., Hekker, S., Samadi, R., De Ridder, J., Weiss, W., Auvergne, M., Baglin, A., 2010, A&A 517, 22 • Mosser et al. (2011a) Mosser, B., Belkacem, K., Goupil, M.-J., et al. 2011a, A&A, 525, 9 • Mosser et al. (2011b) Mosser, B., Barban, C., Montalban, J., et al. 2011b, submitted to A&A • Pallè et al. (1999) Pallè, P. L., Roca Cortés, T., Jimenez, A. et al., 1999, ASP Conf. Series, 173, 297 • Pérez Hernández and Christensen-Dalsgaard (1998) Pérez Hernández F. and Christensen-Dalsgaard J., 1998, MNRAS, 295, 344 • Proffitt & Michaud (1991) Proffitt, C. R. & Michaud, G. J. 1991, ApJ, 380, 238 • Retter et al. (2003) Retter, A., Bedding, T.R., Buzasi, D. L., et al., 2003, ApJ, 591, L151 • Retter et al. (2004) Retter, A., Bedding, T. R., Buzasi, D. L., et al., 2004, ApJ, 601, L95 • Rogers & Nayvonov (2002) Rogers, F. J., Nayvonov, A. 2002, ApJ, 576, 1064 • Stello et al. (2004) Stello, D., Kjeldsen, H., Bedding, T. R., De Ridder, J., Aerts, C., Carrier, F., Frandsen, S. 2004 Sol. Phys 220, 207 • Stello et al. (2009) Stello, D. Chaplin, W. J., Basu, S. Elsworth, Y., Bedding, T. R., 2009 MNRAS 400, L80 • Tassoul (1980) Tassoul, M., 1980, ApJS, 43, 469 • Teixeira et al. (2003) Teixeira T., Christensen-Dalsgaard J., Carrier F., Aerts C., Frandsen, S. et al., 2003, Ap&SS 284, 233 • Uytterhoeven et al. (2010a) Uytterhoeven, K., Briquet, M., Bruntt, H., De Cat, P., Frandsen, S., Gutiérrez-Soto, J., Kiss, L., Kurtz, D., Marconi, M., Molenda-Zakowicz, J., Østensen, R., Randall, S., Ripepi, V., Southworth, J., & Szabó, R., 2010a, Astronomische Nachrichten, 331, 993 • Uytterhoeven et al. (2010b) Uytterhoeven, K., Szabo, R., Southworth, J., Randall, S., Ostensen, R., Molenda-Zakowicz, J., Marconi, M., Kurtz, D.W., Kiss, L., Gutierrez-Soto, J., Frandsen, S., De Cat, P., Bruntt, H., Briquet, M., Zhang, X.B., Telting, J.H., Steslicki, M., Ripepi, V., Pigulski, A., Paparo, M., Oreiro,R., Ngeow C., Niemczura, E., Nemec, J., Narwid, A., Mathias, P., Martin-Ruiz, S., Lehmann, H., Kopacki, G., Karoff, C., Jackiewicz, J., Ireland, M., Huber, D., Henden, A.A., Handler, G., Grigahcène, A., Green, E.M., Garrido, R., Fox Machado, L., Debosscher, J., Creevey, O.L., Catanzaro, G., Bognar, Z., Biazzo, K., & Bernabei, S., 2010b, Astronomische Nachrichten, in press ## Appendix A Maximum Likelihood Estimators (MLE) According to this method, the p-mode parameters are estimated by finding the best fit between a modelled and the observational power density spectrum by using a maximum-likelihood technique (Anderson et al., 1990). Two different models have been assumed: ### a.1 Lorentzian with convolution of the window function The fitting of the non-oversampled power spectrum has been done in two steps. First the background, for which we use a power law fit to account for long term effects, such as granulation, rotation or activity related to spots, is fitted. Then, we computed a global maximum likelihood fit (Anderson et al., 1990) to all oscillation modes, where the final model is a convolution of the model with the power spectrum of the observed window function of the data set, normalised to unit total area (see Eq. 7). This takes the redistribution of power caused by gaps in the data into account. M=(∑jHj1+((νcen,j−ν)/Bj)2)∗window (7) In this model the previously determined background is kept fixed, while each of the th oscillation peak is fitted with the height (), the central frequency () and HWHM () and the noise level as free parameters. The selection of the oscillation modes is based on a statistical test of the binned power spectrum. For this test we bin the power spectrum over intervals of three frequency bins. Then we compute the probability of the power in the binned power spectrum to be due to noise. This probability is computed using a distribution in which we take the width and number of the bins into account in the degrees of freedom. Frequencies at which the probability of the power not being due to white noise is larger than 95% are selected as candidate oscillation frequencies. After performing the fit, we also verify that in the ratio of the observed to the fitted spectra no prominent peaks are left. Therefore we compute the relative height for the investigated frequency range for which the probability of observing at least one spike with this height due to noise is 10%, following the formulation by Chaplin et al. (2002) and references therein. This is also described in Hekker et al. (2010). ### a.2 Sum of Lorentzians or sinc If the modes are resolved (i.e. the mode width is larger than the frequency resolution) we chose to model the oscillation spectrum by a sum of Lorentzians plus a background model that counts for the signal which is not due to the p modes such as the instrumental noise or stellar background. In the frequency range considered here, the background has been modelled by a straight line (i.e. ). When the mode width is of the order of the frequency resolution we change the sum of Lorentzians by a sum of sinc. The modelled power spectrum used to match the data is: P(νk)=Q∑n=1M(n,νk)+B(νk), (8) where is the number of oscillation modes, the radial order, the Fourier frequencies, and the background noise in the power spectrum, modelled as a straight line, i.e. with and , two constants and free parameters of the fit. is a Lorentzian when the mode width is larger than the frequency resolution: M(n,νk)=Hn11+(2(νk−νn)Γn)2 (9) where is the height of the Lorentzian profile, is the oscillation mode frequency and is the mode line width (FWHM) with , being the mode lifetime. When the modes are not resolved, is a sinc function: M(n,νk)=Hnsinc2(ΠT(νk−νn)) (10) where is the total length of the observing run. The power spectrum is fitted “globally” over a frequency range corresponding to the detected excess power. The free parameters of the fitting process are: • the height of the Lorentzian profile, , being the radial order. A single height parameter is fitted per mode. • the frequency for each mode, . • the line width for each mode (FWHM) with , being the mode lifetime. A single width has been considered. • the parameters describing the background model as mentioned above. The mode-parameter 1 error bars are derived from the Hessian matrix. No oversampling has been used in the computation of the power spectrum for the fitting procedure in order to minimize the correlation of the points. The degree of each mode is identified using échelle diagrams. ## Appendix B Bayesian MCMC method The p-mode parameters are estimated by fitting a sequence of Lorentzian profiles to the power density spectrum, where we use the previously determined stellar activity and granulation signal (Eq. 4 without the Gaussian) as a fixed background. The visually identified mode profiles are parameterized by their central frequencies, mode heights, and lifetimes. As it can be seen in Fig. 2, the mode profiles are quite narrow. To prevent the algorithm from over-fitting the data and to keep the number of free parameters to a reasonable amount we use two lifetime parameters, one for l=0 and 2 modes and one for l=1 modes. Furthermore, we assume the individual mode heights to follow a Gaussian envelope parameterized by a single central frequency and width but with individual heights for each mode degree. For the 25 modes in Tab. 3, this results in a total of 32 free parameters. For the fit we use a Bayesian MCMC algorithm (Gruberbauer et al., 2009) that delivers probability density functions for all fitted parameters and their marginal distributions, from which we compute the most probable values and their 1 uncertainties. During the fit the mode frequency parameters are allowed to vary independently within 2Hz around the value inferred from a visual inspection of the spectrum. The lifetimes are kept between 1 and 50 days. Whereas the centre and width of the Gaussian envelope are kept within 0.9 and 1.1 times and (Eq.4), respectively, the height for each mode degree is allowed to vary independently between 0 and 2 times the highest peak in power density spectrum. You are adding the first comment! How to quickly get a good reply: • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made. • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements. • Your comment should inspire ideas to flow and help the author improves the paper. The better we are at sharing our knowledge with each other, the faster we move forward. The feedback must be of minimum 40 characters and the title a minimum of 5 characters	{}
# Determine the Grams of Sodium Chloride Produced When 10.0g EstateName.com – Determine the Grams of Sodium Chloride Produced When 10.0g ## 7.5: Solution Stoichiometry As we learned in Chapter 5, double replacement reactions involve the reaction between ionic compounds in solution and, in the course of the reaction, the ions in the two reacting compounds are “switched” (they replace each other). As an example, silver nitrate and sodium chloride react to form sodium nitrate and the insoluble compound, silver chloride. $\ce{AgNO3 (aq) + NaCl (aq) → AgCl (s) + NaNO3 (aq)} \nonumber$ Because these reactions occur in aqueous solution, we can use the concept of molarity to directly calculate the number of moles of products that will be formed, and hence the mass of precipitates. In the reaction shown above, if we mixed 123 mL of a 1.00 M solution of NaCl with 72.5 mL of a 2.71 M solution of AgNO 3 , we could calculate the moles (and hence, the mass) of AgCl that will be formed as follows: First, we must examine the reaction stoichiometry. In this reaction, one mole of AgNO 3 reacts with one mole of NaCl to give one mole of AgCl. Because our ratios are one, we don’t need to include them in the equation. Next, we need to calculate the number of moles of each reactant: $0.123L\times \left ( \frac{1.00\: mole}{1.00\: L} \right )=0.123\: moles\: NaCl \nonumber$ $0.0725L\times \left ( \frac{2.71\: mole}{1.00\: L} \right )=0.196\: moles\: AgNO_{3} \nonumber$ Because this is a limiting reactant problem, we need to recall that the moles of product that can be formed will equal the smaller of the number of moles of the two reactants. In this case, NaCl is limiting and AgNO 3 is in excess. Because our stoichiometry is one-to-one, we will therefore form 0.123 moles of AgCl. Finally, we can convert this to mass using the molar mass of AgCl: $0.0725L\times \left ( \frac{2.71\: mole}{1.00\: L} \right )=0.196\: moles\: AgNO_{3} \nonumber$ In a reaction where the stoichiometry is not one-to-one, you simply need to include the stoichiometric ratio in you equations. Thus, for the reaction between lead (II) nitrate and potassium iodide, two moles of potassium iodide are required for every mole of lead (II) iodide that is formed. $\ce{Pb(NO3)2 (aq) + 2 KI (aq) → PbI2 (s) + 2 KNO3 (aq)} \nonumber$ For example: 1.78 grams of lead (II) nitrate are dissolved in 17.0 mL of water and then mixed with 25.0 mL of 2.5 M potassium iodide solution. What mass of lead (II) iodide will be formed and what will be the final concentration of potassium nitrate in the solution? Again, we need to look at this as a limiting reactant problem and first calculate the number of moles of each reactant: $1.78\: g\times \left ( \frac{1.00\: mole}{331.2\: g} \right )=5.37\times 10^{-3}\: moles\: Pb(NO_{3})_{2} \nonumber$ $0.0025\: L\times \left ( \frac{2.50\: mole}{1.00\: L} \right )=6.25\times 10^{-3}\: moles\: KI \nonumber$ The stoichiometry of this reaction is given by the ratios: $\left ( \frac{1\: mole\: PbI_{2}}{2\: mole\: KI} \right )\; and\; \left ( \frac{1\: mole\: PbI_{2}}{1\: mole\: Pb(NO_{3})_{2}} \right ) \nonumber$ so the number of moles of product that would be formed from each reactant is calculated as: $\left ( \frac{1\: mole\: PbI_{2}}{1\: mole\: Pb(NO_{3})_{2}} \right ) \nonumber$ $6.25\times 10^{-3}\: moles\: KI\times \left ( \frac{1\: mole\: PbI_{2}}{2\: moles\: KI} \right )=3.12\times 10^{-3}\: moles\: PbI_{2} \nonumber$ Potassium iodide produces the smaller amount of PbI 2 and hence, is limiting and lead (II) nitrate is in excess. The mass of lead (II) iodide that will be produced is then calculated from the number of moles and the molar mass: Read: Which Graph Represents the Function Y 2x 4 $3.12\times 10^{-3}\: moles\: \times \left ( \frac{461\: grams}{1\: mole} \right )=1.44\: grams\: PbI_{2} \nonumber$ To determine the concentration of potassium nitrate in the final solution, we need to note that two moles of potassium nitrate are formed for every mole of PbI 2 , or a stoichiometric ratio of $\left ( \frac{2\: moles\: KNO_{3}}{1\: mole\: PbI_{2}} \right ) \nonumber$ Our final volume is (17.0 + 25.0) = 42.0 mL, and the concentration of potassium nitrate is calculated as: $\frac{3.12\times 10^{-3}\: moles\:PbI_{2}\times \left ( \frac{2\: moles\: KNO_{3}}{1\: mole\: PbI_{2}} \right )}{0.0420\: L}=0.148\; moles\; KNO_{3}/L\; or\; 0.148\; M \nonumber$ ## Exercise $$\PageIndex{1}$$ 1. A sample of 12.7 grams of sodium sulfate (Na 2 SO 4 ) is dissolved in 672 mL of distilled water. 1. What is the molar concentration of sodium sulfate in the solution? 2. What is the concentration of sodium ion in the solution? 2. How many moles of sodium sulfate must be added to an aqueous solution that contains 2.0 moles of barium chloride in order to precipitate 0.50 moles of barium sulfate? 3. If 1.0 g of NaN 3 reacts with 25 mL of 0.20 M NaNO 3 according to the reaction shown below, how many moles of N 2 (g) are produced? $5 NaN3(s) + NaNO3(aq) → 3 Na2O(s) + 8 N2(g) \nonumber$ • Paul R. Young, Professor of Chemistry, University of Illinois at Chicago, Wiki: AskTheNerd; PRYaskthenerd.com – pyounguic.edu; ChemistryOnline.com ### Determine the Grams of Sodium Chloride Produced When 10.0g Sumber: https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Book:_Introductory_Chemistry_Online_%28Young%29/07:_Aqueous_Solutions/7.5:_Solution_Stoichiometry ## 0.9 0.72 EstateName.com – 0.9 0.72 simmental 1st Enter an EPD Value 2nd Enter an EPD Value …	{}
# BITLAST - Editorial Contest Author: Rahul Sharma Tester: Sumukh Bhardwaj Editorialist: Rahul Sharma Easy # PREREQUISITES: Bits, Observation, Math # PROBLEM: Given two integers N and K. For the binary representation of N following transformation is applied The most significant set bit is moved to the last and new N is computed. This transformation is done K times. Can you predict value of N after K transformations ? # EXPLANATION: Let number of set bits in number N be \alpha and most significan set bit be \beta. At each transformation we are move most significant bit to last This is equivalent to resetting the most significant bit, shifting all bits to left by 1 and setting the last bit. Thus a new N can be computed as N = ((N - 2^\beta) << 1) + 1 If we compute N for K times using above equation we will eventually get the answer. But it will only pass subtask #1. If you observe carefully the minimum N will be reached after apply transformation \alpha times because after than all set bits will be on extreme right and applying the transformation will not generate any new number. Thus if K > \alpha we can directly give answer as 2^\alpha-1. # COMPLEXITIES: Time Complexity: O(logN) for each test case Space Complexity: O(1) for each test case # SOLUTIONS: Setter's Solution #include<bits/stdc++.h> using namespace std; long long int countSetBits(long long int n) { long long int i = 0, count = 0; while(n >= (1ULL<<i)) { if ((n & (1ULL<<i))) count++; i++; } return count; } long long int setBitNumber(long long int n) { long long int k = (long long int)(log2(n)); return 1ULL << k; } int main() { long long int n, setBits, setBitNum, minVal = 0, ans = 0, k; cin >> n >> k; setBits = countSetBits(n); minVal = pow(2ULL,setBits) - 1; while (k && n > minVal) { setBitNum = setBitNumber(n); n = ((n - setBitNum) << 1ULL) + 1; k--; } cout << n; return 0; }	{}
# Proper time in General Relativity and change of coordinates Let $$M$$ be the spacetime manifold and let us consider a local coordinate system \begin{align} \varphi_i:\,U_i&\subset M\to \varphi_i(U_i)\subset \mathbb R^n, \end{align} which associates $$p\in U_i\to \varphi_i(p)\equiv x_i^\mu.$$ This is a way of describing the spacetime event $$p$$ with a set of numbers: a different local coordinate system $$\varphi_j$$ defined on $$U_j$$ describes the same event with different numbers $$x'^\mu$$, which must be related to $$x_i^\mu$$ on the intersection $$U_i\cap U_j$$ by $$x'^\mu=\varphi_j\circ\varphi^{-1}_i(x^\mu)$$. As far as I understand, local coordinate systems are just observers, who see the same event from different points of view and describe them with different numbers. Given a pseudo Riemannian metric $$g$$, one can express it wrt two different coordinate system as \begin{align}g&=g_{\mu\nu}(x)dx^\mu dx^\nu\\ &=g'_{\mu\nu}(x')dx'^\mu dx'^\nu,\end{align} from which is it possible to derive the transformation rule of the coefficients $$g_{\mu\nu}.$$ It is often said that the proper time of a moving particle is given by an OBSERVER that sits on the particle, which sees the particle itself at rest. Thus $$d\tau^2=g=g_{\mu\nu}(x)dx^\mu dx^\nu.$$ Is proper time a coordinate system, since it is an observer? 1. If so, LHS should be related to the RHS through some change of coordinates which however seems quite singular, since it does not look invertible. Am I wrong? 2. Furthermore, I struggle making sense of an observer (ie a coordinate systems) that changes point by point as we follow the trajectory of the particle (because point by point the spatial coordinates describing the particle are zero), in the context of differential geometry. In other words, is the reference frame sitting on the moving particle a single coordinate system? I would like to understand the above points from a mathematical point of view. The relation between observers and coordinates isn't quite so simple, unfortunately. This is true in special relativity for inertial observers (to some degree), but in a more general case, the relationship between the two is more subtle. An observer is, generally speaking, a future-oriented timelike curve $$\gamma$$. Sometimes we also give them additional attributes to reflect how an actual physical apparatus might work : an onboard clock $$h$$ (this is because the time an observer measures may not necessarily be the proper time), which is some monotone increasing function from points of the curve to $$\mathbb{R}$$ : $$h : \mathrm{Im}(\gamma) \to \mathbb{R}$$ This is used mostly if we're thinking about actual experiments, usually $$h$$ will simply reflect the proper time. An observer may also have a local frame $$e_a$$, which is three linearly independant spacelike directions, so that we can do measurements of directions such as incident angles and such. Now as an observer is a simple curve, it cannot be equivalent to a coordinate system, because an observer cannot really measure anything beyond its immediate surroundings. A simple reason why not is the following : consider a coordinate system adapted to an observer, and then perform a diffeomorphism on it that is the identity around the observer but not outside of its region. From the point of view of the observer, there will be no difference. So in what way can we associate an observer to a coordinate system? The simplest way in which this is usually done is that your observer can be a line of constant spatial coordinates, and its coordinate in the timelike direction can be equivalent to the proper time (or its onboard clock, if you so choose). In addition, if our local frame isn't too crazy, we can also make it so that the local frame is oriented along the same direction as the coordinate basis. If the observer is a geodesic, those are the Fermi coordinates. There are more general processes you can use for more arbitrary observers, but those are the most common ones. Fermi coordinates and other coordinates of their types (such as radar coordinates) are always local in nature, and somewhat arbitrary. They will usually somewhat agree near the observer, but may start diverging the further away you go, and there is usually a point beyond which they stop being valid altogether (such as in the presence of a cut locus). It is possible to have a better method to construct coordinates "physically" if you have an observer going through every point of space, but that is a more complex process. On the flipside, can you get an observer the other way around, starting with some coordinates? The answer at first is going to be obviously no. A classic example is the null coordinates $$ds^2 = -dtdx$$ The constant lines of those coordinates are all null curves, and therefore not observers, even though this is just Minkowski space. If one of your coordinate is a timelike curve, though, then yes, you can simply trace a line along that coordinate (at spatial coordinates zero, for extra fun), put the tetrads as the local frame, and this will indeed be the observer of that coordinate system at that point. But beware that this curve is neither guaranteed to be a geodesic, nor even of proper time. It's a common trick in general relativity that if your metric is stationary, you can always just perform a rather simple coordinate transformation $$t' = f(t)$$ which will not change anything but the timelike component of the metric, in which case, if your curve was originally going along as proper time, it will no longer do so.	{}
# Math Help - series problem 1. ## series problem if $f(x)= \sum_{k=0}^{\infty} (cos^2x)^k$, then $f(\frac{\pi}{4})$ is 2. $\cos^2(\frac\pi4) = \frac12$. 3. So this is simply the geometric sum $\sum_{k=0}^\infty \left(\frac{1}{2}\right)^2$	{}
2.9k views Consider the following expression grammar. The semantic rules for expression evaluation are stated next to each grammar production.$$\begin{array}{l\|l} E\rightarrow number & E.val = {number.val} \\\qquad \mid \ E \ \ ‘+\text{'} \ E & E^{(1)}.val = E^{(2)}.val + E^{(3)}.val \\\qquad \mid \ E \ \ ‘\times\text{'} \ E & E^{(1)}.val = E^{(2)}.val \times E^{(3)}.val \end{array}$$ Assume the conflicts of this question are resolved using yacc tool and an LALR(1) parser is generated for parsing arithmetic expressions as per the given grammar. Consider an expression $3 \times 2 + 1$. What precedence and associativity properties does the generated parser realize? 1. Equal precedence and left associativity; expression is evaluated to $7$ 2. Equal precedence and right associativity; expression is evaluated to $9$ 3. Precedence of ‘$\times$’ is higher than that of ‘$+$’, and both operators are left associative; expression is evaluated to $7$ 4. Precedence of ‘$+$’ is higher than that of ‘$\times$’, and both operators are left associative; expression is evaluated to $9$ edited \| 2.9k views +1 the question asks- What precedence and associativity properties does the generated parser realize? according to me + is having higher precedence than . Since yaac prefers shift over reduce and it performs 2+1 first and then multiplied so how + and have same precedence? 0 @sushmita LALR parser is SR parser here we use right most derivation...that's why we use right associativity...because we reduced from right .. All the productions are in same level therefore all have same precedence. 0 If a grammar has same precedence for 2 different operator (+,) then it is ambiguous Grammar. LALR Parser is type of Bottom up Parser which uses Right most Derivation For $3×2+1$ $E \rightarrow E E$ (Both shift and reduce possible but yacc prefers shift) $\rightarrow E * E + E$ $\rightarrow E * E + 1$ $\rightarrow E * 2 + 1$ $\rightarrow E * 3$ $\rightarrow 3 * 3$ $\rightarrow 9$ All the productions are in same level therefore all have same precedence Therefore Ans is B. Equal precedence and right associativity; expression is evaluated to 9. by Boss (11.2k points) edited by +2 simple & good explanation.. 0 0 the link which you gave is part-a and this particular question is part-b both are linked. +1 @Prajwal, LALR Parser is type of Bottom up Parser which uses Right most Derivation By this info. I think we may get result as 7 also. (We know grammar is ambiguous here so same precedency ) But due to YACC tool(prefer shift over reduce) given as part of linked question here even if 3∗2 (E∗E) handle found on top of the stack at some point of time, it will shift on reading + instead of reducing with E→E∗E. But as per ur given quotation it may compute 32 also. Plz see Debashis's ans in given link there he have put the o/p with black screen. +1 Actually after writing this ans, Shobith had informed me about ambiguity in this grammar so i had hidden this answer but it was Arjun Sir who has reshown this answer which you can see in the status He had removed all other ans in this particular question and just retained my answer. It would be better if he only tell the reason for that!! +1 @Rajesh, question here assumes "yacc". I just corrected it. 0 @Arjun sir So the question says conflicts will be resolved by "yacc" does that mean ambiguity will be resolved? +1 yes. +3 Ok. @Arjun Sir. @Prajwal Shift-Reduce Conflict (NOT AMBIGUITY)will solve by yacc by preferring Shift operation over reduce operation. So, here though it will find 3∗2 (E∗E) handle on top of the stack initially, it will shift on reading + instead of reducing with E→E∗E. so it work like right associativity(and we know priority is same due to ambiguous grammar.) so 3(2+1) =9 0 What makes it right associative? 0 (Both shift and reduce possible but yacc prefers shift) why do we say this 0 How is it right associative? +2 Why can't precedence change? As SR conflict resolved in favour of shift, '+' is done before ''. Why can't we say that '+' has higher precedence over ''? +2 I think precedence depends upon the grammar we use. Also, YACC just resolves the SR to choose Shift over Reduce if expression will be "1+23" then is chosen over adding 1+2, it doesn't mean that precedence changes. Precedence will be same of both + and * as they are on same level in tree. +1 Got it thanx!! 0 @Arjun sir, idid+id Whenever we are at first id.We push to stack. Now in stack we have id which is handle.And next input is .Now on + also i can either result E->id or shift .So Shift is not preferred over reduce here at first step in the answer i think First of all everything will goto stack and then reduce in reverse order.Please clear 0 draw corresponding LALR(1) DFA, you will get exactly how is it working. 0 yes i checked with that.Because on reading "num" ,we will go to the state that will reduce E->num. and there are no conflicts,is this correct ? 0 it is going like this 32+1 3 E->3 E->3* E->32 E->3E->2 E->3E->2+ // see here it is not reducing E->EE, instead shifting +, because S will be favoured over R E->3E->2+1 E->3E->2+E->1 E->3E E 0 ok.I have one doubt here :- 32+1 3 E->3 E->3* Doubt:- 3 is look ahead,then you applied E->3 and reduce it to E,after that why is it E->3?Here stack contains only E as E->3 is reduced? Also this E->3 is reduced because there is no SR conflict on reading num? 0 these are not productions, instead these are steps of formation of parse tree, E->3* means E / 3 * and yes E->3, this reduction took place because there was no SR conflict in that state where this reduction is done, otherwise, shift move would be taken over reduce by YACC. 0 Can someone please explain how the preference of S over R is leading to right associativity? +3 I have made the parsing table from DFA, using which input can be parsed and checked what happens when shift is favoured over reduce. Consider production as $1:E \Rightarrow num$ $2:E \Rightarrow E+E$ $3:E \Rightarrow E \times E$ + X $num E 0 S1 2 1 R1 R1 R1 2 S4 S3 Accept 3 S1 5 4 S1 6 5 S4/R3 S3/R3 R3 6 S4/R2 S5/R2 R2 Now, when you'll parse input$3 \times 2+1$, it is resolved like$3 \times 3\Rightarrow 9$Equal precedence and Right associativity observed. 0 @Ayush Upadhyaya I am at state 0 and looking at 3... what shall I do according to your table? There is no reduce move from E-> num. 0 @Ayush Upadhyaya state 0 on num should be S1 not 0 on$ 0 @tusharp-is it correct now? 0 0 All the productions are at the same level, therefore, all have the same precedence, still + is evaluated first before * so this grammar is Right Associative we can also say this because bottom-up parsers follow rightmost derivation so right most operators will be evaluated first. +1 vote None of the Options is correct here ... The answer has to be "precedence of + is higher than * " and "both * and + are right associative" Here we will never come across an RR conflict because we dont have 2 productions with the same RHS but different LHS ... EX : In the grammar, S->A/a, A->a we have 2 productions with the same RHS (which is a) but different LHS (S and A) ... Now while parsing a string I might come across a single state with productions as A->a. and S->a. Now this state will create a conflict on whether should I reduce string "a" to S or A ... So clearly there is an RR conflict here .... But in the given grammar it is not the case ... While parsing a string say "num+numnum" from the above grammar,I will come across an SR conflict ... When ?? after scanning num+num , I have a choice on whether should I shift on (as good as giving higher precedence to * over +) or reduce "num+num" to E (as good as giving higher precedence to + over ) ... So here there is an SR conflict ... YACC tool always goes in-favour of SHIFT incase of SR conflict (and first reduce incase of RR conflict) ... So,since we are using YACC to resolve conflicts, here + will be given higher precedence over but incase if we come across a string like 2+3+5 , it will be right associative ... None of the Options is correct here ... by Loyal (7.8k points) edited 0 although your answer explains that in certain cases when the grammar poses an RR conflict, the grammar rule which comes before will get a priority, it still is misleading as far as this grammar and question is concerned. Since the case that you are mentioning here (RR conflict priority decision) doesn't concern the grammar given in question, I think the correct option, according to you, that " precedence of + is higher than * " is simply wrong. Also after reading your answer, I feel that you don't clearly understand the precedence and associativity concepts. Always, remember, precedence is established first. Once the precedence rules are established, and there comes a case where two operators come one after another and have equal precedence (the operators may be same or different), only then, we apply the associativity rule. In the last part of your answer, you are using the associativity rule to derive the precedence of + and x which I find to be a reason in concluding the possibility of confusion that you might have regarding associativity and precedence. Nice catch though regarding RR conflict.	{}
# Robust Sensor Fault Detection for Linear Parameter-Varying Systems using Interval Observer 1 CEDRIC - LAETITIA - CEDRIC. Traitement du signal et architectures électroniques CEDRIC - Centre d'études et de recherche en informatique et communications Abstract : This paper proposes a new interval observer for continuous-time linear parameter-varying systems with an unmeasurable parameter vector subject to unknown but bounded disturbances. The parameter-varying matrices are assumed to be elementwise bounded. This observer is used to compute a so-called residual interval used for sensor fault detection by checking if zero is contained in the interval. To attenuate the effect of the system's uncertainties on the detectability of faults, additional weighting matrices and different upper and lower observer gains are introduced, providing more degrees of freedom than the classical interval observer strategies. In addition, a $L_{\infty}$ procedure is proposed to tune the value of the observer gains, this procedure being easy to modify to introduce additional constraints on the estimation algorithm. Simulations are run to show the efficiency of the proposed fault detection strategy. Keywords : Document type : Conference papers Domain : https://hal-cnam.archives-ouvertes.fr/hal-03239385 Contributor : Thach Ngoc Dinh Connect in order to contact the contributor Submitted on : Tuesday, February 15, 2022 - 10:21:57 AM Last modification on : Friday, August 5, 2022 - 2:54:00 PM Long-term archiving on: : Monday, May 16, 2022 - 7:21:16 PM ### File Chevet_et_al-ESREL2021 (1).pdf Files produced by the author(s) ### Citation Thomas Chevet, Thach Ngoc Dinh, Julien Marzat, Tarek Raïssi. Robust Sensor Fault Detection for Linear Parameter-Varying Systems using Interval Observer. 31st European Safety and Reliability Conference, Sep 2021, Angers, France. pp.1486-1493, ⟨10.3850/978-981-18-2016-8_380-cd⟩. ⟨hal-03239385⟩ Record views	{}
## Whole Numbers and also Its Properties WHOLE NUMBERSNow if we add zero (0) in the set of natural numbers, we obtain a brand-new set that numbers dubbed the whole numbers. Therefore the set of entirety numbers consists of zero and the collection of organic numbers. The is denoted by W. I.e., W = 0, 1, 2, 3, . . .. Smallest whole number is zero. You are watching: Division of whole numbers is associative ### Properties of entirety numbers All the nature of number satisfied by natural numbers are also satisfied by entirety numbers. Currently we shall find out some an essential properties of number satisfied by whole numbers. (a) Closure Property: The amount of two whole numbers is constantly a entirety number. Permit a and b be two entirety numbers, climate a + b = c is additionally a totality number.This property is referred to as the closure property of addition Example: 1 + 5 = 6 is a whole number. (b) Commutative Property: The sum of two whole numbers stays the exact same if the order of number is changed. Permit a and also b it is in two whole numbers, thena + b = b + aThis property is called the commutative property of addition. (c) Associative Property: The sum of three whole numbers stays the same even if the grouping is changed. Let a, b, and c be three whole numbers, then(a + b) + c = a + (b + c)This residential property is called the associative property of addition. (d) identification Element: If zero is added to any type of whole number, the sum stays the number itself. As we can see the 0+a=a=a+0 wherein a is a totality number.Therefore, the number zero is called the additive identity, as it does not change the value of the number when addition is perform on the number. ### Properties the Subtraction (a) Closure Property: The difference of two whole numbers will certainly not always be a totality number. Allow a and also b be two totality numbers, then a – b will be a entirety number if a > b or a = b. If a Examples17 – 5 = 12 is a totality number.5 – 17 = – 12 is no a whole number. (b) Commutative Property: If a and b space two whole numbers, then a – b ≠ b – a. It mirrors that subtraction of two whole numbers is no commutative. Hence, commutative building does not hold great for individually of entirety numbers, i.e.,a – b ≠ b – a.Example: 3 – 4 = – 1 and 4 – 3 = 1∴ 3 – 4 ≠ 4 – 3 (c) Associative Property: If a, b, and c are whole numbers, then (a – b) – c ≠ a – (b – c). It shows that subtraction of entirety numbers is no associative. Hence, associative property does not hold great for individually of entirety numbers.Example: (40 – 25) – 10 = 15 – 10 = 540 – (25 – 10) =40- 15 = 25∴ (40 – 25) – 10 ≠ 40 – (25 – 10) (d) residential or commercial property of Zero: If we subtract zero from any whole number, the result remains the number itself.Example: 7 – 0 = 75 – 0 = 5 ### Properties of Multiplication (a) Closure Property: If a and also b room two entirety numbers, climate a × b = c will constantly be a totality number. Hence, closure residential property holds an excellent for multiplication of totality numbers.Example: 5 × 7 = 35 (a whole number)6 × 1 = 6 (a whole number) (b) Commutative Property: If a and b space two whole numbers, climate the product that two whole numbers remains unchanged if the order the the numbers is interchanged, i.e.,a × b = b × a.Example: 6 × 5 = 5 × 630 = 30i. E., 6 rows of 5 or 5 rows of 6 offer the very same results.so, 6 × 5 = 30 = 5 × 6 (c) Associative Property: If a, b, and c space whole numbers, climate the product the three entirety numbers remains unchanged also if they are multiplied in any type of order. Hence, associative home does hold an excellent for multiplication of totality numbers, i.e.,(a × b) × c = a × (b × c)Example:(4 × 5) × 8 = 4 × (5 × 8)20 × 8 = 4 × 40160 = 160 (d) Multiplicative Identity: If any kind of whole number is multiplied by 1, the product continues to be the number itself. Allow a whole number it is in a, thena × 1 = a = 1 × a.3 × 1 = 3 = 1 × 3Examples75 × 1 = 75 = 1 × 753 × 1 = 3 = 1 × 3Hence, 1 is dubbed the multiplicative identity. (e) Multiplicative residential property of Zero: any whole number multiply by zero gives the product together zero.If a is any kind of whole number, then 0 × a = a × 0 = 0.Example: 3 × 0 = 0 × 3 = 0 ### Properties the Division (a) Closure Property: If a and b are whole numbers, climate a ÷ b is not constantly a whole number. Hence, closure home does not hold good for department of entirety numbers.Example: 7 ÷ 5 = $$\frac 7 5$$ is no a totality number.7 ÷ 7 = 1 is a entirety number. (b) Commutative Property: If a and b are whole numbers, climate a ÷ b ≠ b ÷ a. Hence, commutative residential property does not hold good for division of entirety numbers.Example: 18 ÷ 3 = 6 is a whole number.3 ÷ 18 = $$\frac 3 18$$ = $$\frac 1 6$$ is not a entirety number.∴ 3 ÷ 18 ≠ 18 ÷ 3 (c) Associative Property: If a, b, and c space whole numbers climate (a ÷ b) ÷ c ≠ a ÷ (b ÷ c). Hence, associative building does no hold an excellent for division of whole numbers. Example: (15 ÷ 3) ÷ 5 = 5 ÷ 5 = 115 ÷ (3 ÷ 5) = 15 ÷ 3/5 = 15 × 5/3= 25∴ (15 ÷ 3) ÷ 5 ≠ 15 ÷ (3 ÷ 5) (d) building of Zero: If a is a entirety number climate 0 ÷ a = 0 however a ÷ 0 is undefined.Example: 6 ÷ 0 is undefined. Note: Product of zero and a whole number provides zero.a × 0 = 0Zero separated by any whole number provides zero.0 ÷ a = 0a ÷ 0 = undefinedAny number split by 1 is the number itself.a ÷ 1 = a DISTRIBUTIVE PROPERTY You space distributing something together you separate or rest it into parts.Example: Raj distributes 4 crate of sweets. Each box comprises 6 chocolates and also 10 candies. How plenty of sweets space there in these 4 boxes?∴ Chocolates in 1 box = 6Chocolates in 4 boxes = 4 × 6 = 24Candies in 1 box =10Candies in 4 boxes = 4 × 10 = 40Total variety of sweets in 4 boxes= 4 × 6 + 4 × 10 = 4 × (6 + 10)= 4 × 16 = 64 Hence, us conclude the following:(a) Multiplication distributes end addition, i.e., a(b + c) = abdominal muscle + ac, wherein a, b, c are entirety numbers.Example: 10 × (6 + 5) = 10 × 6 + 10 × 510 × 11 = 60 + 50110 = 110This residential property is referred to as the distributive building of multiplication end addition.(b) Similarly, multiplication distributes end subtraction, i.e., a × (b – c) = abdominal muscle – ac where a, b, c are totality numbers and also b > c.Example: 10 × (6 – 5) = 10 × 6 – 10 × 510 × 1 = 60 – 5010 = 10This building is dubbed the distributive residential property of multiplication end subtraction. Example 1: determine the following by an ideal arrangement.2 × 17 × 5Solution: 2 × 17 × 5 = (2 × 5) × 17= 10 × 17 = 170 Example 2: fix the following using distributive property.97 × 101Solution: 97 × 101 = 97 × (100 + 1)= 9700 + 97 = 9797 Example 3: Tina gets 78 clues in math in the half-yearly Examination and 92 marks in the final Examination. Reena gets 92 point out in the half- yearly Examination and 78 point out in the last Examination in Mathematics. Who has obtained the higher total marks?Solution: Tina gets the following marks = 78 + 92 = 170 complete marksReena gets the following marks = 92 + 78 = 170 complete marksSo, both that them obtained equal marks. Example 4: A fruit seller placed 12 bananas, 10 oranges, and also 6 apologize in a fruit basket. Tarun buys 3 fruit baskets for a function. What is the total number of fruits in these 3 baskets?Solution: number of bananas in 3 baskets = 12 × 3 = 36 bananasNumber that oranges in 3 baskets = 10 × 3 = 30 orangesNumber of to apologize in 3 baskets = 6×3 = 18 applesTotal variety of fruits = 36 + 30+ 18 = 84Alternative MethodTotal number of fruits in 3 baskets= 3 × < 12 +(10 + 6)>= 3 × < 12 + 16>= 3 × 28 = 84 ### Representation Of entirety Numbers on A Number Line We can represent whole numbers-on a straight line. To stand for a set of entirety numbers on a number line, let’s an initial draw a straight line and also mark a point O on it. After that, note points A, B, C, D, E, F ~ above the line at equal distance, top top the best side of allude O. See more: What Bible Do Christian Churches Use ? Get The Facts 5 Tips For Picking The Best Bible Translation Now, OA = ab = BC = CD and also so onLet OA = 1 unitOB = OA + ab = 1 + 1 = 2 unitsOC = OB + BC = 2 + 1 = 3 unitsOD = OC + CD = 3 + 1 = 4 units and also so on.Let the point O correspond to the totality number 0, climate points A, B, C, D, E, ….. Exchange mail to the entirety numbers 1, 2, 3, 4, 5,…. In this means every totality number have the right to be stood for on the number line.	{}
Chapter 1 The Nature of Science and Physics # Accuracy and Precision of a Measurement Science is based on observation and experiment—that is, on measurements. is how close a measurement is to the correct value for that measurement. For example, let us say that you are measuring the length of standard computer paper. The packaging in which you purchased the paper states that it is 11.0 inches long. You measure the length of the paper three times and obtain the following measurements: 11.1 in., 11.2 in., and 10.9 in. These measurements are quite accurate because they are very close to the correct value of 11.0 inches. In contrast, if you had obtained a measurement of 12 inches, your measurement would not be very accurate. The of a measurement system is refers to how close the agreement is between repeated measurements (which are repeated under the same conditions). Consider the example of the paper measurements. The precision of the measurements refers to the spread of the measured values. One way to analyze the precision of the measurements would be to determine the range, or difference, between the lowest and the highest measured values. In that case, the lowest value was 10.9 in. and the highest value was 11.2 in. Thus, the measured values deviated from each other by at most 0.3 in. These measurements were relatively precise because they did not vary too much in value. However, if the measured values had been 10.9, 11.1, and 11.9, then the measurements would not be very precise because there would be significant variation from one measurement to another. The measurements in the paper example are both accurate and precise, but in some cases, measurements are accurate but not precise, or they are precise but not accurate. Let us consider an example of a GPS system that is attempting to locate the position of a restaurant in a city. Think of the restaurant location as existing at the center of a bull’s-eye target, and think of each GPS attempt to locate the restaurant as a black dot. In Figure 3, you can see that the GPS measurements are spread out far apart from each other, but they are all relatively close to the actual location of the restaurant at the center of the target. This indicates a low precision, high accuracy measuring system. However, in Figure 4, the GPS measurements are concentrated quite closely to one another, but they are far away from the target location. This indicates a high precision, low accuracy measuring system. # Accuracy, Precision, and Uncertainty The degree of accuracy and precision of a measuring system are related to the in the measurements. Uncertainty is a quantitative measure of how much your measured values deviate from a standard or expected value. If your measurements are not very accurate or precise, then the uncertainty of your values will be very high. In more general terms, uncertainty can be thought of as a disclaimer for your measured values. For example, if someone asked you to provide the mileage on your car, you might say that it is 45,000 miles, plus or minus 500 miles. The plus or minus amount is the uncertainty in your value. That is, you are indicating that the actual mileage of your car might be as low as 44,500 miles or as high as 45,500 miles, or anywhere in between. All measurements contain some amount of uncertainty. In our example of measuring the length of the paper, we might say that the length of the paper is 11 in., plus or minus 0.2 in. The uncertainty in a measurement, ${A}$, is often denoted as ${\delta}{A}$ (“delta ${A}$ ”), so the measurement result would be recorded as ${A}{\pm\delta}{A}$. In our paper example, the length of the paper could be expressed as ${11\text{ in.}\pm 0.2}$. The factors contributing to uncertainty in a measurement include: 1. Limitations of the measuring device, 2. The skill of the person making the measurement, 3. Irregularities in the object being measured, 4. Any other factors that affect the outcome (highly dependent on the situation). In our example, such factors contributing to the uncertainty could be the following: the smallest division on the ruler is 0.1 in., the person using the ruler has bad eyesight, or one side of the paper is slightly longer than the other. At any rate, the uncertainty in a measurement must be based on a careful consideration of all the factors that might contribute and their possible effects. ### MAKING CONNECTIONS: REAL-WORLD CONNECTIONS – FEVER OR CHILLS? Uncertainty is a critical piece of information, both in physics and in many other real-world applications. Imagine you are caring for a sick child. You suspect the child has a fever, so you check his or her temperature with a thermometer. What if the uncertainty of the thermometer were ${3.0^{\text{o}}\text{C}}$ ? If the child’s temperature reading was ${37.0^{\text{o}}\text{C}}$ (which is normal body temperature), the “true” temperature could be anywhere from a hypothermic ${34.0^{\text{o}}\text{C}}$ to a dangerously high ${40.0^{\text{o}}\text{C}}$. A thermometer with an uncertainty of ${3.0^{\text{o}}\text{C}}$ would be useless. ## Percent Uncertainty One method of expressing uncertainty is as a percent of the measured value. If a measurement ${A}$ is expressed with uncertainty, ${\delta{A,}}$ the (%unc) is defined to be: ${\%\text{ unc} =}$ $\frac{{\delta}{A}}{{A}}$ ${\times 100\%}$ ### Example 1: Calculating Percent Uncertainty: A Bag of Apples A grocery store sells ${5\text{-lb}}$ bags of apples. You purchase four bags over the course of a month and weigh the apples each time. You obtain the following measurements: • Week 1 weight: ${4.8\text{ lb}}$ • Week 2 weight: ${5.3\text{ lb}}$ • Week 3 weight: ${4.9\text{ lb}}$ • Week 4 weight: ${5.4\text{ lb}}$ You determine that the weight of the ${5\text{-lb}}$ bag has an uncertainty of ${\pm0.4\text{ lb.}}$ What is the percent uncertainty of the bag’s weight? Strategy First, observe that the expected value of the bag’s weight, ${A}$, is 5 lb. The uncertainty in this value, ${\delta}{A}$, is 0.4 lb. We can use the following equation to determine the percent uncertainty of the weight: ${\%\text{ unc} =}$ $\frac{{\delta}{A}}{\text{A}}$ ${\times 100\%}$ Solution Plug the known values into the equation: ${\%\text{ unc} =}$ ${ \frac{0.4\text{ lb}}{5\text{ lb}}}$ ${ \times 100\% = 8\%}$ Discussion We can conclude that the weight of the apple bag is ${5\text{ lb}\pm8\%}$. Consider how this percent uncertainty would change if the bag of apples were half as heavy, but the uncertainty in the weight remained the same. Hint for future calculations: when calculating percent uncertainty, always remember that you must multiply the fraction by 100%. If you do not do this, you will have a decimal quantity, not a percent value. ## Uncertainties in Calculations There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its length and width has an uncertainty because the length and width have uncertainties. How big is the uncertainty in something you calculate by multiplication or division? If the measurements going into the calculation have small uncertainties (a few percent or less), then the can be used for multiplication or division. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation. For example, if a floor has a length of ${4.00\text{ m}}$ and a width of ${3.00}\text{ m,}$ with uncertainties of ${2}{\%}$ and ${1}{\%}$, respectively, then the area of the floor is ${12.0\text{ m}^2}$ and has an uncertainty of ${3}{\%}$. (Expressed as an area this is ${0.36\text{ m}^2}$, which we round to ${0.4\text{ m}^2}$ since the area of the floor is given to a tenth of a square meter.) # Precision of Measuring Tools and Significant Figures An important factor in the accuracy and precision of measurements involves the precision of the measuring tool. In general, a precise measuring tool is one that can measure values in very small increments. For example, a standard ruler can measure length to the nearest millimeter, while a caliper can measure length to the nearest 0.01 millimeter. The caliper is a more precise measuring tool because it can measure extremely small differences in length. The more precise the measuring tool, the more precise and accurate the measurements can be. When we express measured values, we can only list as many digits as we initially measured with our measuring tool. For example, if you use a standard ruler to measure the length of a stick, you may measure it to be ${36.7}\text{ cm}$. You could not express this value as ${36.71}\text{ cm}$ because your measuring tool was not precise enough to measure a hundredth of a centimeter. It should be noted that the last digit in a measured value has been estimated in some way by the person performing the measurement. For example, the person measuring the length of a stick with a ruler notices that the stick length seems to be somewhere in between ${36.6}\text{ cm}$ and ${36.7}\text{ cm}$, and he or she must estimate the value of the last digit. Using the method of , the rule is that the last digit written down in a measurement is the first digit with some uncertainty. In order to determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right. For example, the measured value ${36.7}\text{ cm}$ has three digits, or significant figures. Significant figures indicate the precision of a measuring tool that was used to measure a value. ## Zeros Special consideration is given to zeros when counting significant figures. The zeros in 0.053 are not significant, because they are only placekeepers that locate the decimal point. There are two significant figures in 0.053. The zeros in 10.053 are not placekeepers but are significant—this number has five significant figures. The zeros in 1300 may or may not be significant depending on the style of writing numbers. They could mean the number is known to the last digit, or they could be placekeepers. So 1300 could have two, three, or four significant figures. (To avoid this ambiguity, write 1300 in scientific notation.) Zeros are significant except when they serve only as placekeepers. ## Significant Figures in Calculations When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be no greater than the number of significant digits in the least precise measured value. There are two different rules, one for multiplication and division and the other for addition and subtraction, as discussed below. 1. For multiplication and division: The result should have the same number of significant figures as the quantity having the least significant figures entering into the calculation. For example, the area of a circle can be calculated from its radius using ${A}{=\pi{r}^2}$. Let us see how many significant figures the area has if the radius has only two—say, ${r=1.2}\text{ m.}$ Then, ${A}{=\pi{r}^2=(3.1415927\ldots)\times(1.2\text{ m})^2=4.5238934\text{ m}^2}$ is what you would get using a calculator that has an eight-digit output. But because the radius has only two significant figures, it limits the calculated quantity to two significant figures or ${A} {= 4.5\text{ m}^2}$ , even though ${\pi}$ is good to at least eight digits. 2. For addition and subtraction: The answer can contain no more decimal places than the least precise measurement. Suppose that you buy 7.56-kg of potatoes in a grocery store as measured with a scale with precision 0.01 kg. Then you drop off 6.052-kg of potatoes at your laboratory as measured by a scale with precision 0.001 kg. Finally, you go home and add 13.7 kg of potatoes as measured by a bathroom scale with precision 0.1 kg. How many kilograms of potatoes do you now have, and how many significant figures are appropriate in the answer? The mass is found by simple addition and subtraction: $\begin{array}{r @{{}{}} l} {7.56 \;\text{kg}} \\[0em] {-6.052 \;\text{kg}} \\[0em] \rule[-0.65ex]{5.35em}{0.1ex}\hspace{-5.35em} {+ \;\;\; 13.7 \;\text{kg}} \\[0.2em] {15.208 \;\text{kg}} & \; {= 15.2 \;\text{kg}} \end{array}$ Next, we identify the least precise measurement: 13.7 kg. This measurement is expressed to the 0.1 decimal place, so our final answer must also be expressed to the 0.1 decimal place. Thus, the answer is rounded to the tenths place, giving us 15.2 kg. ## Significant Figures in this Text In this text, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all worked examples. You will note that an answer given to three digits is based on input good to at least three digits, for example. If the input has fewer significant figures, the answer will also have fewer significant figures. Care is also taken that the number of significant figures is reasonable for the situation posed. In some topics, particularly in optics, more accurate numbers are needed and more than three significant figures will be used. Finally, if a number is exact, such as the two in the formula for the circumference of a circle, ${c}{=2\pi{r}}$, it does not affect the number of significant figures in a calculation. ### PHET EXPLORATION: ESTIMATION Explore size estimation in one, two, and three dimensions! Multiple levels of difficulty allow for progressive skill improvement. # Summary • Accuracy of a measured value refers to how close a measurement is to the correct value. The uncertainty in a measurement is an estimate of the amount by which the measurement result may differ from this value. • Precision of measured values refers to how close the agreement is between repeated measurements. • The precision of a measuring tool is related to the size of its measurement increments. The smaller the measurement increment, the more precise the tool. • Significant figures express the precision of a measuring tool. • When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value. • When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value. ### Conceptual Questions 1: What is the relationship between the accuracy and uncertainty of a measurement? 2: Prescriptions for vision correction are given in units called diopters (D). Determine the meaning of that unit. Obtain information (perhaps by calling an optometrist or performing an internet search) on the minimum uncertainty with which corrections in diopters are determined and the accuracy with which corrective lenses can be produced. Discuss the sources of uncertainties in both the prescription and accuracy in the manufacture of lenses. ### Problems & Exercises Express your answer to problems in this section to the correct number of significant figures and proper units. 1: Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)? 3: (a) A car speedometer has a ${5.0\%}$ uncertainty. What is the range of possible speeds when it reads ${90\text{ km/h}}$ ? (b) Convert this range to miles per hour. ${(1\text{ km} = 0.6214\text{ mi})}$ 5: (a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y? 7: State how many significant figures are proper in the results of the following calculations: (a) ${(106.7)(98.2)\backslash(46.210)(1.01)}$ (b) ${(18.7)^2}$ (c) ${(1.60\times 10^{-19}) (3712)}$. 9: (a) If your speedometer has an uncertainty of ${2.0\text{ km/h}}$ at a speed of ${90\text{ km/h}}$, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads ${60\text{ km/h}}$, what is the range of speeds you could be going? 11: A person measures his or her heart rate by counting the number of beats in ${30}\text{ s}$. If ${40 \pm 1}$ beats are counted in ${30.0 \pm 0.5\text{ s}}$, what is the heart rate and its uncertainty in beats per minute? 13: If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon? 15: The sides of a small rectangular box are measured to be ${1.80 \pm 0.01\text{ cm}}$, ${2.05 \pm 0.0\text{ 2cm}}$, and ${3.1 \pm 0.1\text{ cm}}$ long. Calculate its volume and uncertainty in cubic centimeters. 17: The length and width of a rectangular room are measured to be ${3.955 \pm 0.005\text{ m}}$ and ${3.050 \pm 0.005\text{ m}}$. Calculate the area of the room and its uncertainty in square meters. ## Glossary accuracy the degree to which a measure value agrees with the correct value for that measurement method of adding percents the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation percent uncertainty the ratio of the uncertainty of a measurement to the measure value, express as a percentage precision the degree to which repeated measurements agree with each other significant figures express the precision of a measuring tool used to measure a value uncertainty a quantitative measure of how much your measured values deviate from a standard or expected value ### Solutions Problems & Exercises 1: 2 kg 3: (a) ${85.5\text{ to }94.5\text{ km/h}}$, (b) ${53.1\text{ to }58.7\text{ mi/h}}$ 5: (a) ${7.6\times10^6\text{ beats}}$, (b) ${7.57\times10^7\text{ beats}}$, (c) ${7.57\times10^7\text{ beats}}$ 7: (a) 3, (b) 3, (c) 3 9: (a) ${2.2\%}$, (b) ${59\text{ to }61\text{ km/h}}$ 11: ${80\pm3\text{ beats/min}}$ 13: ${2.8\text{ h}}$ 15: ${11.1 \pm 1\text{ m}^3}$ 17: ${12.06\pm0.04\text{ m}^2}$	{}
# Is there a clear definition of "computable" for models of computation which are not turing complete? This is a follow-up of another question here, and I hope it is not too philosophical. As Raphael pointed out in a comment on my previous question, I don't really get the definition of "computable", but according to some papers I read, the definition is also not really clear when it comes to models of computation weaker than turing machines because of the encoding of the input and output. The typical definition of turing computable is as follows: Definition 1: A function $f : \mathbb{N}^k \to \mathbb{N}$ is called turing computable iff there is a turing machine $M$ which computes $f$ using a suitable encoding of the natural numbers as strings. The definitions differ in what exactly is a suitable encoding is, but most refer to binary encoding, unary encoding or decimal encoding as the one fixed and suitable encoding. It is also possible to show that fixing one encoding is required for the definition of turing computability. But what makes, say, binary encoding of natural numbers special so that we can axiomatize it as the one suitable encoding? Probably because it fits the intuitive notion of what computability means coincidentally. Now what if we look at weaker models of computation than turing machines? For example, let's consider the set $M_c$ of "crippled" turing machines with the alphabet $\{0,1\}$ which may only move to the right, and a definition of crippled turing computable which is consistent with that of turing computability: Definition 2: A function $f : \mathbb{N}^k \to \mathbb{N}$ is called crippled turing computable or computable in $M_c$ iff there is a crippled turing machine $M$ which computes $f$ using a suitable encoding of the natural numbers as a string. If we define "suitable encoding" as "binary encoding", then the function $f : \mathbb{N} \to \mathbb{N}, n \mapsto n+1$ is not computable in $M_c$. If we axiomatize "suitable encoding" as "unary encoding", then $f$ is computable in $M_c$. This seems awkward given the fact that everyone may fix one of the infinitely many intuitive encodings at will. It should be clear if a computation model can compute $f$ or not without referring to some specific encoding - at least I have never seen anyone mention what encoding is used when stating "loop programs are weaker than turing machines". After this introduction I can finally phrase my question: How would one define "suitable encodings" and "computability" for arbitrary models of computation which do not coincide with the intuitive notion of computability? Is this possible within the framework of turing computability? Edit: I shortened the introduction, it didn't add to the question. Some basic fact that you are missing here is that all the encodings that you mention are equivalent from the perspective of computability: there is a computable function mapping the binary encoding of a number to its unary encoding, or vice versa. Therefore for the sake of defining computability, it does not matter which of these encodings you choose for numbers. Just fix your favorite encoding. Computability is at its core a property of string functions $f\colon \Sigma^* \to \Sigma^$. When you define computability in any other domain, you have to fix an encoding. In practice, all "reasonable" encodings are equivalent in the sense of the preceding paragraph, so the exact encoding doesn't matter. The encoding does, however, matter in restricted models of computation. To take an extreme example, suppose that you consider time-restricted Turing machines: say you want your machine to terminate in time $O(n^c)$ for some $c$, where $n$ is the length of the input (as a string). We can no longer switch between binary encoding and unary encoding, because binary encoding is much more compact. When we talk about a polynomial time computable function of integers, we specify that integers are encoded in binary. Even this is a somewhat arbitrary choice, since decimal encoding would lead to the same notion of polynomial time computability. So to answer your question – the encoding is specified as part of the definition of the restricted model. • "Some basic fact that you are missing here is that all the encodings that you mention are equivalent from the perspective of computability: there is a computable function mapping the binary encoding of a number to its unary encoding, or vice versa" - yeah, I had that in the original version of my question, but I cannot see how it is relevant for the question about weaker models. It is also clear that the encoding has to be specified as part of the model definition, but the question is how one can arrive at such a reasonable definition. Mar 4 '15 at 23:01 • One pulls this definition out of the hat. Since different definitions tend to be equivalent, the exact definition doesn't matter. When it does, there will be several different notions of complexity. For example, for some graph algorithms it makes a difference if you're given an adjacency matrix or a list of edges. Mar 4 '15 at 23:03 • So to summarize: a) The definition of each single computation model must include it syntax, semantics AND a suitable encoding. b) The definition of "suitable encoding" is completely independent of syntax and semantics of the model. c) There is no way to give a definition of "suitable encoding" which is valid for all models of computation. Is that correct? Mar 4 '15 at 23:44 • I agree with a) and b), but with c) only partially. You can define a suitable encoding which serves as the "standard encoding", used unless explicit mention of the fact is made. In the case of numbers, such a standard encoding exists – binary encoding. Mar 4 '15 at 23:49 • Alright, but that does not really constitute as a general definition, it just saves people's time because they don't have to explicity write down "In this model $M$, we use binary encoding" because it is implied if they don't write it down. They still might choose another encoding for their model. What I meant with "general definition" is a set of properties which each encoding must fulfil to be allowed as an encoding. Mar 4 '15 at 23:57 First of all, you cannot fix "suitable encoding" to be binary strings, or any other encoding. This is because you would loose too many models of computation, because different models of computation may have very different models of input and output. In other words, they may not "speak" strings. For example, terms of the untyped lambda calculus are either variables, or the application of one term to another, or an abstraction of a lambda term. Input and output are terms, arbitrary strings. Still, the untyped lambda calculus is Turing-complete because there exists a "suitable encoding" which encodes natural numbers as lambda terms of a certain form, and under this encoding for each computable function there exists a lambda term which computes it. You can formalize "suitable encoding" if you fix Turing machines as your reference model of computation, and then require that the encoding and decoding from and to binary strings must be carried out by a Turing machine which always halts. For example, a Turing machine would be able to translate a natural number as a binary string to a Lambda term which expresses this number, simulate the reduction in the lambda calculus, and translate the result back to a binary string. For simpler models of computation I would expect the same approach: take a reference model of computation and fix an encoding of the natural numbers, and then make sure that the encoding and decoding is done by instances of that simple model. As you noted, for crippled Turing machines, using unary and binary encoded numbers would not yield an equivalent model of computation. • Is it possible that you have things turned around in the last paragraph? You write that the encoding is done by the simple model, not the reference model - in the previous paragraph you want to have the encoding done by the reference model, not the other model (lambda calculus). Mar 4 '15 at 23:29 • If you are studying weaker models of computation you don't want to use Turing machines anywhere, not even in the encoding/decoding phase. Then you could just perform all computations in the encoding phase and about any model of computation would be Turing complete. So you need to use the simpler reference model for encoding/decoding. Mar 5 '15 at 6:31 • Then I do not see how we can prove the turing-completeness of lambda calculus with church numerals if we fix turing machines. We have to assume that LC is weaker than TM, so some instance of the "weaker" model lambda calc is given a number $n \in \mathbb{N}$ using its encoding $church : \mathbb{N} \to lambdaterm$ as $church(n)$, then computes its function $toBinary : lambdaterm \to lambdaterm$ which output a binary string $w \in \Sigma^$? The codomains don't match. Even if I allow lambdaterms to be interpreted as strings, there are other models which do not "speak" strings, as you stated. Mar 5 '15 at 14:07	{}
# Mozgostroje ## New Statistics needs causal inference 27 Aug 2014 [] In psychology, when it comes to methodology and data analysis, you can't miss a vocal movement that advocates adoption effect sizes as an replacement for p-values. This movement has been labeled new statistics by Geoff Cumming (2013). Cumming acknowledges, that their ideas are not new. There is nothing new about the concepts such as effect size, power or meta-analysis. Jacob Cohen, one of the most emblematic proponents of new statistics has been preaching power calculation already in the sixties. Rather, what would be revolutionary, is the adoption of these practices by researchers. I have been doing my best to like these guys - after-all they are in favor of parameter estimation. I love parameter estimation. But I have been constantly annoyed by their resistance to shackle off hypothesis testing in favor of causal analysis. As a consequence new statistics emerges more and more as an desperate attempt to hide the real problem with psychology research which is, of course, its love affair with HT. The spectacular aspect of this episode, is that parameter estimation is by definition the counter part of hypothesis testing. It takes serious contortionist effort to downplay and hide this conflict. I very much liked how recently Morey et al. (2014) pointed out to Cumming his implicit conflict with HT. Fidler & Cumming (2014) were of course quick to deny that he has misspoken against the goddess. And so, to Matus' complete annoyance the state of unity with HT was restored. The basic idea of NS - focus on effect size estimation, is sound. NS fails to draw the proper consequences. First, it fails to acknowledge the conflict with HT. Second, it fails to acknowledge the importance of causal inference. The latter is also a remarkable feat, since the cause is in the name "effect size" itself. If we try to apply NS seriously causal inference pops up at every corner. Let me give you few examples of this. First, here is the definition by Cumming (2014) of what effect size is: An ES is simply an amount of anything of interest (Cumming & Fidler, 2009). Means, differences between means, frequencies, correlations, and many other familiar quantities are ESs. A p value, however, is not an ES. The definition begs the question - can we somehow rank the various quantities with respect to the "amount of interest". Are there some quantities that are of more interest than others? This question is important, because it would provide researchers with rules how to determine the quantity that is most informative with respect to their research question. If this question remains unresolved there is a danger that researchers choose quantities that are irrelevant to the question at hand and that lead to false conclusions. Furthermore, the choice of the effect size provides additional degrees of freedom and as we learned from Simmons et al. (2011) degrees of freedom are bad. To find the rules for ranking ESs let's consider some positive examples of ES approved by NS people. Maybe, by looking at the context in which these informative ES occur, we will find some regularities. Then maybe we can determine a rule that will allow us to go the other way round - to infer the proper ES given the research context. As a first examples consider this one provided by Cumming in Chapter 12 of his book. Cumming describes invented data from a clinical study that compared Treatment and Control group at pretest, post-test and two follow up time points. I re-plot the data here. In [2]: %pylab inline y=[[88,80,72,85],[76,44,46,38]] yci=[[16,14,18,17],[12,15,14,22]] for k in range(2): plt.errorbar(np.arange(4)+(k-0.5)*0.1, y[k],yerr=yci[k],fmt='-o') plt.xlim([-0.5,3.5]) plt.grid(False,axis='x') ax=plt.gca() ax.set_xticks(range(4)) plt.legend(['treatment','control'],loc=3) plt.ylabel('anxiety score'); Populating the interactive namespace from numpy and matplotlib Cumming doesn't like omnibus Anova (4x2 with time-point as repeated-measures factor). He also feels uncomfortable with the variance-derived effect sizes such as $\omega^2$. Good, we don't like these ES either. Instead Cumming recommends to compare the pretest-posttest differences and to report CIs. Why are these differences so appealing? The differences allow us to infer the direct causal effect of the treatment. This is given by $E=s_{t,post}-s_{t,pre}-(s_{c,post}-s_{c,pre})$. It gives the decrease in anxiety score due to treatment while holding all other factors constant. This assumes that the effect of treatment is additive. (In fact, the multiplicative model is much more plausible and we should look at quotients instead of differences. However, to recover the full functional shape we would require many more measurement time points.) This also assumes that the control and treatment are representative samples. Conclusion from the first example? Cumming likes the ES that has causal interpretation. He doesn't like ESs that do not have causal interpretation such as the variance-derived ES in the Anova. Second example, p. 81: Sfikas, Greenhalgh, and Lewis (2007) reported a study of vaccination policies that could eliminate rubella from England and Wales. An important parameter is R0, which is the average number of further infections produced by a single case of the disease. Sfikas et al. applied a somewhat complicated epidemiological model to a large database of blood samples to estimate R0 = 3.66, [3.21, 4.36]. For any given value of R0 they could apply their model and calculate the minimum proportion of children that must be vaccinated for the disease to be eliminated. The higher the value of R0, the more infectious the disease, and so the nearer the vaccination rate must be to 100%. Assuming a single vaccination at birth, they calculated that the proportion of babies who must be vaccinated is .74, [.67, .76]. Again, we have clear causal structure that motivates the inference. Whether the disease is eliminated depends on two variables R0 and the proportion of vaccinated babies. We then recover from knowledge of R0 the proportion of vaccinated babies needed to eliminate the disease. I could provide an epic list of examples, but I think you can just read the examples in chapter 3 of Cumming's bible and figure out the causal structure that underlies each of them on your own. But we are not finished yet. The problem is that Cumming himself explicitly avoids the causal interpretation. If you measure the attitudes of a group of people before and after you present them with an advertising message, it’s natural to think of the change in attitude as an effect and the amount of change as the size of that effect. However, the term “effect size” is used much more broadly. It can refer to an amount, rather than a change, and there need not be any easily identifiable “cause” for the “effect.” The mean systolic blood pressure of a group of children, the number of companies that failed to submit tax returns by the due date, and the ratio of good to bad cholesterol in a diet are all perfectly good ESs. Now if some event of interest does not have easily identifiable cause this only tells us that we need to look harder. In the above cases it is difficult to determine the cause because we lack the details of the study. Still, presumably no study would just report a mean systolic blood pressure of a group of children. Even if it would, it would do so with a potential diagnostic or intervention context in mind - such as to predict the prevalence of coronary diseases among children. Now, it looks like my claim is tautological, because I can always provide a post-hoc causal mechanism. Actually, we can imagine ES that do only poorly support causal interpretation. How about this effect size - estimate of the average number of cells in the body of a 11 years old human. According to Cumming's all-embracing definition this is a "perfectly good ES". Why don't we see it reported anywhere? Because, number of cells does not feature anywhere in the (causal) theories of anatomy, medicine, human behavior etc. Number of cells is partly irrelevant because we have better proxies such as body height and weight. But these are more easily measurable than the average number of cells. Ok, let's take a different example. How about the relative alignment between Mars and Venus at the birth of a person. Some of the best minds of Renaissance worked with this ES. This ES is not in such a great favor today - even though it can be readily computed from the date and time of birth. What happened, such that this ES fell into disfavor? Well, research found that the character of a person are independent of the relative alignment of Venus and Mars - there is no causal relation. We could continue our list of frivolous and redundant effect sizes, but I think this suffices to demonstrate my point. NS needs causal inference.	{}
# Tag Info 2 $D$ verifies $\langle M \rangle$ is a (deterministic) TM and then builds the configurations graph and checks if the initial configuration of $\epsilon$ is connected to an accept state (there are only finitely many) and returns true if there is and false if there isn't. The problem here is that, even if you define the TM so that there are only finitely many ... 2 I think you are really asking a question about the definition of the notion of well-foundedness. I think the notion of loop variants is a bit of a red herring here: I would argue that any reasonable definition of well-foundedness should enable proving that a loop is terminating iff there is a well-founded relation which acts as a variant for it, almost as a ... 2 Yes. See the notion of an approximation-preserving reduction. 2 The answer is $\bf 0''$ (and so in particular computation in the limit - which corresponds to $\le_T\bf 0'$ - is not enough). And this stronger result is also folklore (I was assigned it as an exercise way back when). As an upper bound we just check quantifier complexity: $\Phi_e$ runs in polynomial time iff there exists some polynomial $p$ such that for ... 2 There is no generally accepted definition of Turing machine. Various authors use various models. One author's definition might specify the output tape, another's might leave the choice to the Turing machine designer. The reason that we don't care about this "calling convention" is that it doesn't matter from the point of view of computability (and, to a ... 2 Your question is very philosophical in nature because you are asking about what is considered by computation and it’s physical implementations. In short, there is a ongoing discussion on different accounts of concrete computation e.g. the simple mapping account, the semantic account, the syntactic account, the mechanistic account, the causal, the ... 1 any location except i/p part means (total unbounded tape area - tape area that includes i/p string) = (infinity length - finite length) as we know i/p string length is always finite = infinity length in the definition of linear bounded automata it is stated that the tape can be used as a function of the input string length.but here the portion that can ... 1 Humans can solve some instances of undecidable problems and so can computers. Computers cannot solve all instances of undecidable problems, and not can humans. Only top voted, non community-wiki answers of a minimum length are eligible	{}
EPS-HEP2021 conference 26-30 July 2021 Zoom Europe/Berlin timezone Model-independent test of T violation in neutrino oscillations Not scheduled 20m Zoom Zoom Poster Neutrino Physics Speaker Alejandro Segarra (KIT) Description As a function of the baseline L, neutrino oscillation probabilities are linear combinations of $\sin^2(\omega L)$ and $\sin(2\omega L)$, with oscillation frequencies $\omega$ that depend on the neutrino energy. Even though the frequencies depend on the oscillation model, in general the presence of L-odd terms in the probability requires the existence of Time Reversal Violation. We propose a $\chi^2$ test of T violation based on fitting oscillation data at a given energy to the functional form of the oscillation probability P(L) with and without the L-odd terms. A large $\Delta \chi^2$ between these two cases would show that L-odd terms are necessary to describe the data, and thus signal the presence of T violation. We use expected number of events at compatible energies in future accelerator neutrino experiments to illustrate that such a test can be applied at planned next-generation experiments. This allows to search for T violation in a largely model independent way, since the argument applies to a wide class of beyond-standard model scenarios. Email Alejandro.Segarra@kit.edu - Alejandro Segarra	{}
TheInfoList In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ... , equivariance is a form of symmetry Symmetry (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ... for function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ... s from one space with symmetry to another (such as symmetric space In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, l ... s). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group In group theory In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their chang ... , and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the same result as computing the function and then applying the transformation. Equivariant maps generalize the concept of invariants, functions whose value is unchanged by a symmetry transformation of their argument. The value of an equivariant map is often (imprecisely) called an invariant. In statistical inference Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution, distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical ... , equivariance under statistical transformations of data is an important property of various estimation methods; see invariant estimator In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a mor ... for details. In pure mathematics, equivariance is a central object of study in equivariant topology In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. In studying topological spaces, one often considers continuous function (topology), continuous maps f: X \to Y, and while equivariant topology ... and its subtopics equivariant cohomology In mathematics, equivariant cohomology (or ''Borel cohomology'') is a cohomology theory from algebraic topology which applies to topological spaces with a ''Group action (mathematics), group action''. It can be viewed as a common generalization of ... and equivariant stable homotopy theory In mathematics, equivariance is a form of symmetry for function (mathematics), functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are Group action ( ... . # Examples ## Elementary geometry In the geometry of triangle A triangle is a polygon In geometry, a polygon () is a plane (mathematics), plane Shape, figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The ... s, the area and perimeter of a triangle are invariants: translating or rotating a triangle does not change its area or perimeter. However, triangle centers such as the centroid, circumcenter, incenter and orthocenter are not invariant, because moving a triangle will also cause its centers to move. Instead, these centers are equivariant: applying any Euclidean Congruence (geometry), congruence (a combination of a translation and rotation) to a triangle, and then constructing its center, produces the same point as constructing the center first, and then applying the same congruence to the center. More generally, all triangle centers are also equivariant under Similarity (geometry), similarity transformations (combinations of translation, rotation, and scaling), and the centroid is equivariant under affine transformations. The same function may be an invariant for one group of symmetries and equivariant for a different group of symmetries. For instance, under similarity transformations instead of congruences the area and perimeter are no longer invariant: scaling a triangle also changes its area and perimeter. However, these changes happen in a predictable way: if a triangle is scaled by a factor of , the perimeter also scales by and the area scales by . In this way, the function mapping each triangle to its area or perimeter can be seen as equivariant for a multiplicative group action of the scaling transformations on the positive real numbers. ## Statistics Another class of simple examples comes from statistical estimation. The mean of a sample (a set of real numbers) is commonly used as a central tendency of the sample. It is equivariant under Linear function (calculus), linear transformations of the real numbers, so for instance it is unaffected by the choice of units used to represent the numbers. By contrast, the mean is not equivariant with respect to nonlinear transformations such as exponentials. The median of a sample is equivariant for a much larger group of transformations, the (strictly) monotonic functions of the real numbers. This analysis indicates that the median is more robust statistics, robust against certain kinds of changes to a data set, and that (unlike the mean) it is meaningful for ordinal data. The concepts of an invariant estimator In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a mor ... and equivariant estimator have been used to formalize this style of analysis. ## Representation theory In the representation theory of finite groups, a vector space equipped with a group that acts by linear transformations of the space is called a linear representation of the group. A linear map that commutes with the action is called an intertwiner. That is, an intertwiner is just an equivariant linear map between two representations. Alternatively, an intertwiner for representations of a group over a field (mathematics), field is the same thing as a module (mathematics), module homomorphism of -module (mathematics), modules, where is the group ring of ''G''. Under some conditions, if ''X'' and ''Y'' are both irreducible representations, then an intertwiner (other than the zero map) only exists if the two representations are equivalent (that is, are isomorphic as module (mathematics), modules). That intertwiner is then unique up to a multiplicative factor (a non-zero scalar (mathematics), scalar from ). These properties hold when the image of is a simple algebra, with centre (by what is called Schur's Lemma: see simple module). As a consequence, in important cases the construction of an intertwiner is enough to show the representations are effectively the same. # Formalization Equivariance can be formalized using the concept of a Group action (mathematics), -set for a group (mathematics), group . This is a mathematical object consisting of a set (mathematics), mathematical set and a Group action (mathematics), group action (on the left) of on . If and are both -sets for the same group , then a function is said to be equivariant if : for all and all . If one or both of the actions are right actions the equivariance condition may be suitably modified: :; (right-right) :; (right-left) :; (left-right) Equivariant maps are homomorphisms in the Category (mathematics), category of ''G''-sets (for a fixed ''G'').. Hence they are also known as ''G''-morphisms, ''G''-maps, or ''G''-homomorphisms.. Isomorphisms of ''G''-sets are simply bijective equivariant maps. The equivariance condition can also be understood as the following commutative diagram. Note that $g\cdot$ denotes the map that takes an element $z$ and returns $g\cdot z$. # Generalization Equivariant maps can be generalized to arbitrary category (mathematics), categories in a straightforward manner. Every group ''G'' can be viewed as a category with a single object (morphisms in this category are just the elements of ''G''). Given an arbitrary category ''C'', a ''representation'' of ''G'' in the category ''C'' is a functor from ''G'' to ''C''. Such a functor selects an object of ''C'' and a subgroup of automorphisms of that object. For example, a ''G''-set is equivalent to a functor from ''G'' to the category of sets, Set, and a linear representation is equivalent to a functor to the category of vector spaces over a field, Vect''K''. Given two representations, ρ and σ, of ''G'' in ''C'', an equivariant map between those representations is simply a natural transformation from ρ to σ. Using natural transformations as morphisms, one can form the category of all representations of ''G'' in ''C''. This is just the functor category ''C''''G''. For another example, take ''C'' = Top, the category of topological spaces. A representation of ''G'' in Top is a topological space on which ''G'' acts continuous function, continuously. An equivariant map is then a continuous map ''f'' : ''X'' → ''Y'' between representations which commutes with the action of ''G''.	{}
# The covering relation Warning: Tentative. ## Idea The covering relation on a structure (generally already equipped with other relations) is a binary relation such that $x$ is related to $y$ if and only if $y$ is (in an appropriate sense) an immediate (and only immediate) successor of $x$. ## In a poset A pair $\left(x,y\right)$ in a poset satsfies the covering relation if $x but there is no $z$ such that $x and $z. In other words, there are exactly two elements $z$ such that $x\le z\le y$: $z=x$ and $z=y$. In this case, you would say that ”$y$ covers $x$”. ## In a directed graph A pair $\left(x,y\right)$ of vertices in a directed graph or quiver satisfies the covering relation if there is an edge $x\to y$ but there is no other path from $x$ to $y$. ## Common generalisation Given any binary relation $\sim$ on a set $S$, a pair $\left(x,y\right)$ of elements of $S$ satisfies the covering relation if the only sequence $x={z}_{0},\dots ,{z}_{n}=y$ such that ${x}_{i}\sim {x}_{i+1}$ satisfies $n=1$ (so $x\sim y$). Then the covering relation on a poset is the covering relation of $\le$, and the covering relation in a directed graph is the covering relation of the adjacency relation of the graph. ## References Revised on February 13, 2011 20:35:37 by Toby Bartels (75.88.68.70)	{}
# Zener voltage regulator circuit simulate this circuit – Schematic created using CircuitLab I have here a voltage regulator circuit using a Zener diode. We were tasked to find the maximum allowable $$\i_L\$$ given the varying voltage input so the the load voltage will remain at 8 V. The way I understood the problem, we are asked to looked for $$\I_{z(max)}\$$ since past that, the Zener diode would no longer be able to maintain the voltage at 8 V. But then, I thought $$\I_{z(max)}\$$ is supposed to be given in a Zener diode's data sheet and also depends on the power rating of the diode (which was not given,) so I am unsure how to proceed with this problem. • So, the zener is 8V but what is the power rating ??? Oct 9 '20 at 8:03 • @GrahamStevenson It wasn't given. The quantities I mentioned in the post are the only ones given. – user263783 Oct 9 '20 at 8:09 • Lord Above ! Is there no end to daft question asked by lecturers. Would a classic 1.3W zener be OK ? Oct 9 '20 at 8:11 • @GrahamStevenson I don't think so lol. They don't like us making assumptions with that stuff. – user263783 Oct 9 '20 at 8:15 • @Batt max zener power dissipation is at max input voltage 33V and zero load I.e. all current is flowing through zener Oct 9 '20 at 9:45 ## 1 Answer The maximum load current is when then zener no longer has sufficient current to regulate. Since we don't have any information about the Zener diode itself, we can assume it to be perfect so it stops regulating when the zener current drops to zero. That's actually a reasonable assumption for an 8V zener. The worst-case conditions on the low side are minimum input voltage, maximum resistor value within tolerance (we're not given tolerance so assume it to be perfect) and maximum load current. You should be able to calculate this, as this is a homework problem we don't give complete answers, but this should be enough of a hint. • I got the answer right based on what you said. So then the maximum power dissipated by the zener would be when the input voltage is at maximum? – user263783 Oct 9 '20 at 8:53 • When the input voltage is at maximum and the load is at minimum. Oct 9 '20 at 9:42	{}
# JC 1 has started. What’s next? (H2 Math) Congratulations on clearing the O levels and successfully posted to a JC / MI. Credits to CJC. In this post I will share what a new JC 1 student should expect in the next 2 or 3 years for for H2 Mathematics. From 2016 onwards, most JC will offer the new H2 Math syllabus and also a new subject (actually it is just a revival of the old syllabus): H2 Further Mathematics. In a gist, there will be a reduction in the content for 2016 H2 Math but probably an increase in the difficulty, especially in the area of applying concepts to real life problems. You may refer to the new syllabus at the SEAB website. New H2 Math syllabus Many parents/ students do not have a clear idea the importance of O level Mathematics / Additional Mathematics and how are they serve as the pre-requisite to H2 Mathematics. credits to http://www.openschoolbag.com.sg* ## 1. Graphing Techniques O level: Students should recognise graphs such as $\displaystyle y={{x}^{2}}-5$$\displaystyle y=\frac{1}{x}$$\displaystyle y={{5}^{x}}$, etc. They are allowed to plot several points and sketch a graph by connecting the points. A level: Students now have the graphic calculator to sketch the graph. Hence they will be tasked to sketch more complicated graphs (without plotting of points). Examples are: $\displaystyle y=\frac{{{{x}^{2}}-3x+1}}{{x+5}}$,$\displaystyle {{x}^{2}}-3{{y}^{2}}+2x-4y=1$. Even though students have the graphic calculator, relying on it too much for basic graphs learnt at O level will probably lead to wastage of time in exam. If a student is familiar with basic graphs, he can probably sketch it within seconds, rather than spending 1 min pressing the graphic calculator with adjustment of various settings. Also students will need to be very familiar with completing the square technique too. Further more students at A level will learn graphing transformations which relies alot more on theory rather than graphic calculator. ## 2. Differentiation (tangent / normal) Students are required to find equations of tangent and normal using (explicit) differentiation. The procedure is usually straightforward and “algebra – lite” Eaxmple: Find the equation of the tangent $\displaystyle y=x\ln x$ at the point $\displaystyle x=2$. A Level: Students are often required to find equations of tangents and normal using parametric equation (new). The procedure is usually quite algebra intensive. Example: Find the equation of the normal of the curve C with equations $\displaystyle x=t+\frac{1}{t};\mathop{{}}_{{}}^{{}}y=t-\frac{1}{t}$ at the point with parameter p, simplifying your answer as much as possible. ## 3. Probability O Level: Students are required to solve probability problems using Venn diagram, tree diagram with basic rules. A level: Students will go deepeer in this topic, using the union, intersection and conditional probability formula. Further more they will do special probability distributions such as Binomial and Normal distributions. ## Conclusion: I hope this post allows you to have a clearer idea that A level is not a separate subject from O level but it is an advancement. Therefore having a strong O level background (including Additional Math) is a requirement for students taking H2 Mathematics. What if you or your child did not score A1 or A2 for both O level mathematics? My suggestion is that you may want to get professional help as soon as possible to start the year well. Imagine having to cope with the ultra fast pace of A level math yet at the same time you need to re-learn O level mathematics? Honestly I think it is super difficult. ## Where to find help? You may want to consider getting help from teachers who are familiar with the A level system and is experienced. I offer coaching services to students taking A level. 1 to 1 tuition or small group. Contact me at 81502027 for more details.	{}
2014 03-13 For a string of n bits x1, x2, x3, …, xn, the adjacent bit count of the string (AdjBC(x)) is given by x1x2 + x2x3 + x3x4 + … + xn-1xn which counts the number of times a 1 bit is adjacent to another 1 bit. For example: Write a program which takes as input integers n and k and returns the number of bit strings x of n bits (out of 2n) that satisfy AdjBC(x) = k. For example, for 5 bit strings, there are 6 ways of getting 11100, 01110, 00111, 10111, 11101, 11011 The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number (n) of bits in the bit strings, followed by a single space, followed by a decimal integer (k) giving the desired adjacent bit count. The number of bits (n) will not be greater than 100 and the parameters n and k will be chosen so that the result will fit in a signed 32-bit integer. The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number (n) of bits in the bit strings, followed by a single space, followed by a decimal integer (k) giving the desired adjacent bit count. The number of bits (n) will not be greater than 100 and the parameters n and k will be chosen so that the result will fit in a signed 32-bit integer. 10 1 5 2 2 20 8 3 30 17 4 40 24 5 50 37 6 60 52 7 70 59 8 80 73 9 90 84 10 100 90 1 6 2 63426 3 1861225 4 168212501 5 44874764 6 160916 7 22937308 8 99167 9 15476 10 23076518 #include <stdio.h> int dp[102][102][2]; int main() { int z,ca,n,k; scanf("%d",&z); dp[1][0][0] = dp[1][0][1] = 1; for(int i=2;i<=100;i++) { dp[i][0][0] = dp[i-1][0][0] + dp[i-1][0][1]; dp[i][0][1] = dp[i-1][0][0]; for(int j=1;j<i;j++) { dp[i][j][0] = dp[i-1][j][0] + dp[i-1][j][1]; dp[i][j][1] = dp[i-1][j][0] + dp[i-1][j-1][1]; } } while(z--) { scanf("%d%d%d",&ca,&n,&k); printf("%d %d\n",ca,dp[n][k][0]+dp[n][k][1]); } return 0; } 1. #include <cstdio> int main() {	{}
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE Vol. 66, 2 (1997) pp. 313-320 THE FULL PERIODICITY KERNEL FOR A CLASS OF GRAPH MAPS LL. ALSED\`A, J. PARA NOS and J. A. RODRIGUEZ Abstract. Let $X$ be a graph and let $\CC$ be a class of $X$-maps (that is, of continuous maps from $X$ into itself). A map $f\in \CC$ is said to have full periodicity if $\Per(f)=\N$ (here, $\Per(f)$ denotes the set of periods of all periodic points of $f$ and $\N$ the set of positive integers). The set $K\subseteq \N$ is a full periodicity kernel of $\CC$ if it satisfies the following two conditions: (i) If $f\in \CC$ and $K\subseteq \Per(f)$ then $f$ has full periodicity and (ii) if $S\subset \N$ is a set such that, for every $f\in \CC$, $S\subseteq \Per(f)$ implies $\Per(f)=\N$, then $K\subseteq S$. In this paper we show the existence and characterize the full periodicity kernel of the class of continuous maps from a graph with zero Euler characteristic to itself having all branching points fixed. AMS subject classification. 34C35, 54H20 Keywords	{}
CUORE, an array of 988 TeO2 bolometers, is about to be one of the most sensitive experiments searching for neutrinoless double-beta decay. Its sensitivity could be further improved by removing the background from α radioactivity. A few years ago it was pointed out that the signal from $$\beta$$βs can be tagged by detecting the emitted Cherenkov light, which is not produced by αs. In this paper we confirm this possibility. For the first time we measured the Cherenkov light emitted by a CUORE crystal, and found it to be 100 eV at the Q-value of the decay. To completely reject the α background, we compute that one needs light detectors with baseline noise below 20 eV RMS, a value which is 3–4 times smaller than the average noise of the bolometric light detectors we are using. We point out that an improved light detector technology must be developed to obtain TeO2 bolometric experiments able to probe the inverted hierarchy of neutrino masses. Casali, N., Vignati, M., Beeman, J., Bellini, F., Cardani, L., Dafinei, I., et al. (2015). TeO2 bolometers with Cherenkov signal tagging: Towards next-generation neutrinoless double-beta decay experiments. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS, 75(1), 1-5 [10.1140/epjc/s10052-014-3225-4]. TeO2 bolometers with Cherenkov signal tagging: Towards next-generation neutrinoless double-beta decay experiments Abstract CUORE, an array of 988 TeO2 bolometers, is about to be one of the most sensitive experiments searching for neutrinoless double-beta decay. Its sensitivity could be further improved by removing the background from α radioactivity. A few years ago it was pointed out that the signal from $$\beta$$βs can be tagged by detecting the emitted Cherenkov light, which is not produced by αs. In this paper we confirm this possibility. For the first time we measured the Cherenkov light emitted by a CUORE crystal, and found it to be 100 eV at the Q-value of the decay. To completely reject the α background, we compute that one needs light detectors with baseline noise below 20 eV RMS, a value which is 3–4 times smaller than the average noise of the bolometric light detectors we are using. We point out that an improved light detector technology must be developed to obtain TeO2 bolometric experiments able to probe the inverted hierarchy of neutrino masses. Scheda breve Scheda completa Scheda completa (DC) Articolo in rivista - Articolo scientifico Bolometers, Neutrinoless double beta decay English 1 5 5 Casali, N., Vignati, M., Beeman, J., Bellini, F., Cardani, L., Dafinei, I., et al. (2015). TeO2 bolometers with Cherenkov signal tagging: Towards next-generation neutrinoless double-beta decay experiments. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS, 75(1), 1-5 [10.1140/epjc/s10052-014-3225-4]. Casali, N; Vignati, M; Beeman, J; Bellini, F; Cardani, L; Dafinei, I; Di Domizio, S; Ferroni, F; Gironi, L; Nagorny, S; Orio, F; Pattavina, L; Pessina, G; Piperno, G; Pirro, S; Rusconi, C; Schäffner, K; Tomei, C File in questo prodotto: File 10281-133637.pdf accesso aperto Tipologia di allegato: Publisher’s Version (Version of Record, VoR) Dimensione 1.09 MB Formato Adobe PDF 2015_Article_.pdf Solo gestori archivio Tipologia di allegato: Publisher’s Version (Version of Record, VoR) Dimensione 1.09 MB Formato Adobe PDF I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione. Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/133637 • 45 • 37	{}
# Question 0365a Feb 27, 2016 $\text{50 mL}$ #### Explanation: Calculate the $p {K}_{a}$ of the acid and compare it with the pH of the target solution $\textcolor{b l u e}{p {K}_{a} = - \log \left({K}_{a}\right)}$ $p {K}_{a} = - \log \left(1.75 \cdot {10}^{- 5}\right) = 4.76$ Since the pH of the target solution is approximately equal to the $p {K}_{a}$ of the acid, you can assume that the resulting solution will contain equal concentrations of the weak acid and of its conjugate base, the acetate anion $\to$ think Henderson - Hasselbalch equation. Since you know that • acetic acid reacts in a $1 : 1$ mole ratio with sodium hydroxide to produce hydronium cations and acetate anions in $1 : 1$ mole ratios • the acetic acid and sodium hydroxide solutions have the same molarity • the volume of the acetic acid solution is equal to $\text{0.1 L}$ you can say that adding a volume of sodium hydroxide that is half that of acetic acid will neutralize half of the number of moles of acid present in solution and produce equal concentration of weak acid and conjugate base. Therefore, you must add $\text{0.050 L " = " 50 mL}$ of sodium hydroxide solution to get a pH that is approximately equal to $4.74$. $\textcolor{w h i t e}{a}$ !! A LITTLE MORE EXPLANATION !! The thing to remember about reacting weak acids with strong bases is that the reaction produces the conjugate base of the acid. In this case, you have ${\text{CH"_3"COOH"_text((aq]) + "OH"_text((aq])^(-) -> "CH"_3"COO"_text((aq])^(-) + "H"_2"O}}_{\textrm{\left(l\right]}}$ Here one mole of acetic acid reacts with one mole of hydroxide anions provided by the strong base to produce one mole of acetate anions, ${\text{CH"_3"COO}}^{-}$, the conjugate base of the acid. Now, if the neutralization is incomplete, i.e. if you don't add enough strong base to neutralize all the weak acid, you will produce a buffer solution. The pH of a buffer solution can be calculated using the Henderson - Hasselbalch equation color(blue)("pH" = pK_a + log( (["conjugate base"])/(["weak acid"]))) When you have equal concentrations of weak acid and conjugate base, the log term will be equal to zero, since $\log \left(1\right) = 0$. This will give you $\text{pH} = p {K}_{a}$ The problem tells you that the pH of the target solution is equal to $4.74$. The $p {K}_{a}$ of the acid is equal to $p {K}_{a} = - \log \left(1.75 \cdot {10}^{- 5}\right) = 4.76$ For all intended purposes, and considering the fact that you have one sig fig for the molarities of the two solutions, you can say that $\text{pH} \approx p {K}_{a}$ This means that you must have $\left[\text{CH"_3"COO"^(-)] = ["CH"_3"COOH}\right]$ The initial solution contained $\textcolor{b l u e}{c = \frac{n}{V} \implies n = c \cdot V}$ ${n}_{C {H}_{3} C O O H} = \text{0.1 M" * "0.1 L" = "0.01 moles CH"_3"COOH}$ Now, since adding one mole of strong base will consume one mole of weak acid and produce one mole of conjugate base, you can say that every mole of strong base added to the solution will convert one mole of weak acid to one mole of conjugate base. In order to have equal concentrations of weak acid and conjugate base, you need to have equal numbers of moles of the two chemical species. To get equal number of moles, you need to add enough strong base to consume half of the number of moles of weak acid. In this case, you will have ${n}_{C {H}_{3} C O O H} = \text{0.01 moles" - "0.005 moles" = "0.005 moles}$ ${n}_{H {O}^{-}} = \text{0.005 moles" - "0.005 moles" = "0 moles}$ ${n}_{C {H}_{3} C O {O}^{-}} = 0 + \text{0.005 moles" = "0.005 moles}$ The volume of sodium hydroxide solution that contains $0.005$ moles of hydroxide anions will be color(blue)(c = n?V implies V = n/c) V_(OH^(-)) = (0.005 color(red)(cancel(color(black)("moles"))))/(0.1color(red)(cancel(color(black)("moles")))"L"^(-)) = "0.05 L" = color(green)("50 mL") SIDE NOTE As practice, you can try using the H-H equation to find the volume of base that would correspond to a pH of 4.74. You will end up with $4.74 = 4.76 + \log \left(\left(\left[\text{CH"_3"COO"^(-)])/(["CH"_3"COOH}\right]\right)\right)$ $\log \left(\left(\left[\text{CH"_3"COO"^(-)])/(["CH"_3"COOH}\right]\right)\right) = - 0.02$ ${10}^{\log} \left(\left(\left[\text{CH"_3"COO"^(-)])/(["CH"_3"COOH}\right]\right)\right) = {10}^{- 0.02}$ $\left(\left[\text{CH"_3"COO"^(-)])/(["CH"_3"COOH}\right]\right) = 0.955$ This means that you need to have slightly more conjugate acid than weak base, since $\text{pH} < p {K}_{A}$. If you take $x$ the number of moles of strong base added, you can say that your solution will end up with ${n}_{C {H}_{3} C O {O}^{-}} = 0 + x = x \textcolor{w h i t e}{a} \text{moles}$ ${n}_{O {H}^{-}} = x - x = \text{0 moles}$ ${n}_{C {H}_{3} C O O H} = 0.01 - x \textcolor{w h i t e}{a} \text{moles}$ The volume of the solution is the same for both species, so you have $\left(\left[\text{CH"_3"COO"^(-)])/(["CH"_3"COOH}\right]\right) = \frac{x}{0.01 - x}$ This will give you $x = 0.00488$ moles of strong base needed. The corresponding volume would be V = (0.00488color(red)(cancel(color(black)("moles"))))/(0.1color(red)(cancel(color(black)("moles")))"L"^(-1)) = "0.0488 L" = "48.8 mL"# But since you have one sig fig for your values, the result will once again be ${V}_{O {H}^{-}} = \text{50 mL}$	{}
# Posts from the ‘Software’ Category ## Reproducible reports & research with knitr in R Studio Arguably, knitr (CRAN link) is the most outstanding R package of this year and its creator, Yihui Xie is the star of the useR! conference 2012. This is because the ease of use comparing to Sweave for making reproducible report. Integration of knitR and R Studio has made reproducible research much more convenience, intuitive and easier to use. R Studio: A user friendly and cross platform IDE for R Screenshot of R Studio (Windows PC) This post is an example, based on the demo by Yihui Xie himself, I will show how to create a reproducible report consisting the R code in a LaTeX style in the Cardiff R User Group session at the Cardiff Business School (CARBS) Research Fair tomorrow (19 June 2012). knitr option for sweave document in R Studio ## In the code • Lines 001-043 are just normal preamble syntax of the LaTeX code I took from the Template of useR! conference abstract. • Lines 044-96 are the R codes and descriptions. A chuck of R code is wrapped in the following code: <<chunk1, echo=TRUE, results='hide'>>= @ chunk1 is the name of the chuck echo = TRUE to show your R code in the chuck, = FALSE if you do not want to show the code. result = ‘markup’ to show the result unless = ‘hide’ ## The code of the whole document is as follow: \documentclass[11pt, a4paper]{article} \usepackage{amsfonts, amsmath, hanging, hyperref, natbib, parskip, times} \hypersetup{ urlcolor=blue } \setlength{\topmargin}{-15mm} \setlength{\oddsidemargin}{-2mm} \setlength{\textwidth}{165mm} \setlength{\textheight}{250mm} \let\section=\subsubsection \newcommand{\pkg}[1]{{\normalfont\fontseries{b}\selectfont #1}} \let\proglang=\textit \let\code=\texttt \renewcommand{\title}[1]{\begin{center}{\bf \LARGE #1}\end{center}} \newcommand{\affiliations}{\footnotesize} \newcommand{\keywords}{\paragraph{Keywords:}} \begin{document} \pagestyle{empty} \title{Using knitR (R + \LaTeX) in R Studio: A Demo} \begin{center} {\bf Pairach Piboonrungroj$^{1,2,^\star}$} \end{center} \begin{affiliations} 1. Logistics Systems Dynamics Group, Cardiff Business School, Cardiff University, United Kingdom \\[-2pt] 2. Chiang Mai School of Economics, Chiang Mai University, Thailand \\[-2pt] %3. Second affiliation of author B \\[-2pt] $^\star$Email: \href{mailto:me@pairach.com}{me@pairach.com} \end{affiliations} \vskip -0.5cm %%%%%%%%%%%%%%%%%% \begin{center} \linethickness{1mm} \line(1,0){480} \end{center} %%%%%%%%%%%%%%%%%% 1. Show only R source code <<chunk1, echo=TRUE, results='hide'>>= 1 + 1 @ 2. Show only output <<chunk2, ref.label='chunk1', echo=FALSE, results='markup'>>= @ 3. Show both source code and output <<chunk3, echo=TRUE, results='markup'>>= 1 + 1 @ 4. Show source code in grey shade but the output <<chunk4, echo=TRUE, results='asis'>>= 1 + 1 @ 5. Now, testing a linear model <<chunk5, echo=TRUE, results='markup'>>= # generating value for x variable from 1 to 100 x <- c(1:100) # creat error term e <- rnorm(100, mean = 5, sd = 10000) # computing y equal to 3 plus five times x plus random number y = 10 + 100*x + e @ Set the format of all object called pdf() <<custom-dev2>>= my_pdf = function(file, width, height) {pdf(file, width = 5, height = 5, pointsize = 10)} @ 6. See the scatter plot <<chunk6, echo=TRUE, results='markup', dev='my_pdf', fig.ext='pdf'>>= plot(x, y) @ 7. Let's build a linear model by regressing y on x <<chunk7, echo=TRUE, results='markup'>>= # creating a linear model by regressing y on x as 'lm1' object lm1 <- lm(y ~ x) # calling a summary of linear model result summary(lm1) @ 8. Now we can create a post-hoc plots to check assumptions of regression <<chunk8, echo=TRUE, results='markup', dev='my_pdf', fig.ext='pdf'>>= # Creating post-hoc plot for lm1 par(mfrow=c(2,2)) plot(lm1) @ \end{document} ## And this is the Output View this document on Scribd ## List of Free Online R Tutorials According to the post on FREE online R tutorials from universities, I have received many email suggesting more and more tutorials. However some tutorials are not hosted in an academic institutes, so I decided to create this post to list such tutorials. If you know other tutorials, please kindly suggest me by email to me@pairach.com or post the link in the comment section. ## A list of R tutorials, which are hosted in the webpages of academic institutes can be foundhere. The tutorials are listed in no particular order but categorised by subjects and/or topics. ## General guides 1. R Wiki Documentation about R contributed by the R community 2. by Rob Kabacoff 3. R Programming by Wikibooks 4. How to use R by Wikiuniversity 5. R4stats – R for SAS and SPSS Users – R for Stata Users by Bob Muenchen 6. by Vincent Zoonekynd 7. R programming for those coming from other languages by John D. Cook 8. Cookbook for R by Winston Chang (Not related to Paul Teetor’s R Cookbook!) 9. A short introduction to the R programming language by Leibniz-Rechenzentrum 10. The Guerilla Guide to R by Nikhil Gopal ## Online Tutorial 1. Introduction to R by Data Camp 2. Introduction to statistical programming in R by Leada 3. R Coder by José Carlos ## VDO/Audio tutorials 1. More than 90 Two minute tutorials on several topics by Anthony Damico 2. The R-Podcast by Eric Nantz 3. R language for Statistical Computing by Sentiment Mining Research Center 4. A list of Videos on Data Analysis with R: Introductory, Intermediate, and Advanced Resources by Jeromy Anglim ## Economics & Econometrics 1. Forecasting: principles and practice (Online Book) by Rob J Hyndman and George Athanasopoulos 2. Econometrics in R (CRAN) by Grant V. Farnsworth ## Ecology 1. R in Ecology and Evolution 2. Ecology and Epidemiology in R by Various authors ## Psychology 1. Using R for Personality Research – Introduction to R [slide] – R: Statistics for all of us [slide] by William Revelle 2. Learning R for Researchers in Psychology by Jeromy Anglim ## Using R in/for Governments Recently British government (by Office of National Statistics: ONS) just published their version of R manual for analysis of the government survey. The links to PDF and MS word versions of the manual including the R syntax are as below. Note: The R syntax link is not working now. I am contacting the ONS, hope they will fix it soon. The R Guide to ESDS Large-Scale Government Surveys PDF, Word For the US governemnt, there is an emerging awareness and recognition of the power of R in their Big Data Initiative. David Smith (Revolution Analytics) has summarised the application of R in the US governemnt in his post here. ## How to post R code on WordPress blogs Most WordPress BloggeRs are using this text highlight syntax, some are not. I hope that this post would be a reference source for new WordPress BloggeRs for posting their R code on their blog posts. According to an official guide by WordPress.com on “Posting Source Code“, To post R code in the WordPress.com, just wrap R code as follows (without “#” in both wrappers): ###################################################### [#sourcecode language="r"] x <- rnorm(100) y <- x + 10 [#/sourcecode] ###################################################### • From above, before your R code put the command in line 1, or [#sourcecode language=”r”]but without # • Then, place your R code (line 2-4). • End the code box by put the command line as in line 5, but without # or “[/sourcecode] Then the code will appear as following. Your R code and comments x <- rnorm(100) y <- x + 10 Moreover, more options can be configured to better describe the code efficiently. • autolinks (true/false) TRUE: Makes all URLs in your posted code clickable. Defaults: TRUE • collapse (true/false) TRUE: The code box will be collapsed when the page loads, requiring the visitor to click to expand it. Comment: Good for large code posts. Defaults: False. • firstline (number) Comments: Use this to change what number the line numbering starts at Defaults = 1 • gutter (true/false) TRUE: Show the line numbering on the left hand side. FALSE: The line numbering on the left side will be hidden. Defaults = TRUE • highlight (comma-seperated list of numbers) You can list the line numbers you want to be highlighted. Example = “4,7,19″. • htmlscript (true/false) TRUE: Any HTML/XML in your code will be highlighted. Comment: This is useful when you are mixing code into HTML, such as PHP inside of HTML. Defaults = FALSE (only work with certain code languages) • light (true/false) TRUE: The gutter (line numbering) and toolbar (see below) will be hidden. Comment: This is helpful when posting only one or two lines of code. Defaults = FALSE • padlinenumbers (true/false/integer) FALSE: No padding, and entering a number will force a specific amount of padding. Comment: Allows you to control the line number padding. • toolbar (true/false) FALSE: The toolbar containing the helpful buttons that appears when you hover over the code will not be shown. Defaults = TRUE • wraplines (true/false) FALSE: Line wrapping will be disabled. This will cause a horizontal scrollbar to appear for long lines of code. If you are using WordPress.org, here is a plugin. Update: I just found a nice post by William K. Morris on How to update your WordPress.com blog from R ## EURO 2012 Forecast: Spain will beat Germany in the Final again!? predicted Economists (Featureก Image from The New York Times) As EURO 2012 (European Football Championship) will kick starts today (in seconds)! Recently, there is a working paper from Faculty of Economics and Statistics, University of Innsbruck predicting the winner of the tournament to be Spain (again). Achim Zeileis (achim.zeileis@r-project.org), Christoph Leitner (christoph.leitner@wu.ac.at) and Kurt Hornik(kurt.hornik@wu.ac.at) used data from odds provided by 23 online book makers (as the experts’ opinion) in their simulation for each match from the the group round to the final, which is predicted to be Spain vs Germany. I think that they used in their study as well. EURO 2012 winning probabilities from the bookmaker consensus rating. The figure below show the probability that Team i will beat Team j, calculated by this formula; Pr (Team i beat Team j) = (Ability of Team i) / (Ability of Team i / Ability of Team j) Winning probabilities, that Team i will beat Team j, in pairwise comparisons of all EURO 2012 teams As an Econometrician and a football fan, I really like this paper and wish I can replicate their work for the tournament related to my home country team, Thailand. Probability for each team to survive in the EURO 2012 ,i.e., proceed from the group-phase to the quarter finals, semi-finals, the final and to win the tournament. The paper details are as follows. Achim Zeileis, Christoph Leitner, Kurt Hornik (2012). History Repeating: Spain Beats Germany in the EURO 2012 Final. Working Paper 2012-09, Working Papers in Economics and Statistics, Research Platform Empirical and Experimental Economics, Universität Innsbruck. ## Abstract Four years after the last European football championship (EURO) in Austria and Switzerland, the two finalists of the EURO 2008 – Spain and Germany – are again the clear favorites for the EURO 2012 in Poland and the Ukraine. Using a bookmaker consensus rating – obtained by aggregating winning odds from 23 online bookmakers – the forecast winning probability for Spain is 25.8% followed by Germany with 22.2%, while all other competitors have much lower winning probabilities (The Netherlands are in third place with a predicted 11.3%). Furthermore, by complementing the bookmaker consensus results with simulations of the whole tournament, we can infer that the probability for a rematch between Spain and Germany in the final is 8.9% with the odds just slightly in favor of Spain for prevailing again in such a final (with a winning probability of 52.9%). Thus, one can conclude that – based on bookmakers’ expectations – it seems most likely that history repeats itself and Spain defends its European championship title against Germany. However, this outcome is by no means certain and many other courses of the tournament are not unlikely as will be presented here. All forecasts are the result of an aggregation of quoted winning odds for each team in the EURO 2012: These are first adjusted for profit margins (“overrounds”), averaged on the log-odds scale, and then transformed back to winning probabilities. Moreover, team abilities (or strengths) are approximated by an “inverse” procedure of tournament simulations, yielding estimates of all pairwise probabilities (for matches between each pair of teams) as well as probabilities to proceed to the various stages of the tournament. This technique correctly predicted the EURO 2008 final (Leitner, Zeileis, Hornik 2008), with better results than other rating/forecast methods (Leitner, Zeileis, Hornik 2010a), and correctly predicted Spain as the 2010 FIFA World Champion (Leitner, Zeileis, Hornik 2010b). Compared to the EURO 2008 forecasts, there are many parallels but two notable differences: First, the gap between Spain/Germany and all remaining teams is much larger. Second, the odds for the predicted final were slightly in favor of Germany in 2008 whereas this year the situation is reversed.	{}
#### Archived This topic is now archived and is closed to further replies. # Scripting This topic is 6826 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Cool, thanks for the reply, but one more question. So would you recommend a wrapper class that would hold the Lua instance, and its functions would be mapped into Lua. Sort of like the LuaWrapper acts like a V-table? class LuaWrapper{ Lua* pL (or however it is done ) ICurrentThing* pT (An object being ''ran'') LuaWrapper() { // Set up Lua and map LuaWrapper''s functions, // isDrunk and Jump, into it. } void RunScript( ICurrentThing* pO ) { pT = PO; // RUn the script found in pO into Lua } void isDrunk( ... ) { ... pT->IsDrunk(); } void Jump( ... ) { ,,, pT->Jump() }} ##### Share on other sites Taulin: I think with the registered functions Philomath means stuff like EnemyNear() and EnemyStrength(enemy). Those are the hooks back into your engine. Philomath: I''ve looked at Lua before for scripting in a programming game (people write AI scripts and they can compete against each other). The project never got beyond the planning stage, but that''s another issue. Nevertheless, I found the Lua documentation to be a bit lacking in terms of ''example code''. I''ve also been looking at stuff like SeeR, Small, EiC and even Python (which was quite amazing in some ways). None of the scripting languages I mentioned above have been able to provide a rather seamless integration of Script-C/C++ and C/C++-Script. Take Lua for example, you still have to write wrappers which push/pop stuff from the stack. Although this in itself is fairly trivial, it''s still a pain in the ass. OK, I might be a bit lazy here , but I''ve been researching cooler ways for almost seamless integration. For a native DLL, which were to be used by the script, you wouldn''t have to register a thing (just use the exports and unmangle the names). Of course, calling scripted-functions from C/C++ is another issue. But, how about letting the script-compiler generate a C/C++ file which does all the wrapping for you ... that would be a great help and save development time! I know, that some of these features are used in current scripting languages, but I''m still waiting for the scripting language ... if I have some spare time, I might have to do my own (I''ve done a C-Parser before). Please don''t get me wrong about Lua ... it''s really fast and cool, but sometimes I''m just wondering why it''s so hard working with these things... MK42 ##### Share on other sites Thats the way I''ve used it. I''m sure that there are other ways of setting it up. In fact as you can have multiple lua "environments" you could have a seperate lua environment for each object with only object specific data and functions available. I have never tried that but it would work as well (unless you hade too many objects or create them on the fly -vs- existing in a pool from level loadup). It really is up to personal preference and the task at hand. I use a seperate lua environment for user interface elements (buttons, pulldown boxes etc...)with its own unique set of C bound functions and data. I also setup and control my particle emmiters with lua scripts (usually precompiled, and no the script does not get called every frame). I figure the more I can accomplish with scripts the more generic and reuasable I can make the engines and tools. Philo. ##### Share on other sites Thanks for the replies. The scripting part was never a problem. I just never read or saw any examples of actual code ( pref. some class ) using a scripting engine or VM. Have you all looked into the JScript vm? I read on Gamasutra that I think it was the Vampire:Masq used it. Thanks! ##### Share on other sites MK42: EnemyNear() and EnemyStrength(enemy) are hooks to the engine, anything that takes extensive calculation (like pathfinding and line of sight stuff) is not suitable for any scriping language(Yea, I know EnemyStrength is just a lookup but hey its an example). I agree with you about the lua documentation, it does not have many examples. However the language itself is simple enough not to need to many (16 odd reserved words for lua3.2). Unfortuantly the implementation side of it could use many more examples and there explanation of tables is horrible (and they are so easy to use.. go figure). I don't pretend lua is the best language by any strech of the imigination, every language has its pros and cons. Any of the languages you listed could be used effectively. I use lua because of its ease of implementation (one call to lua_open(), register your 'C' functions, and remember to call lua_close() when you are done, 20 min, depending on how many functions you need to register), its speed, I have yet to see a scripting language beat it in a comparison, and its extensability. As far as registering you functions it can be a bit of work if you are adding it to an existing project. However Tolua is supposed to do this for you from header files (I've never used it though). VBA with its com interfacing is close to what I think you are asking for, but I won't go there Philo Edited by - Philomath on October 17, 2000 5:24:35 PM ##### Share on other sites Philomath: I didn''t mean to bash lua ... it''s just that these ''limitations'' don''t make the scripting solution easier to work with. I guess tolua just looks at the PE Image of the LIB file and undecorates the mangled names ... You are right, though, that lua is still one of the simplest scripting languages to use ... but, wouldn''t it be cool to have a scripting solution, which you could just drop into your project (no matter how complex it is) and it would work ... VBA is not an option ... I refuse to use it MK42 • 11 • 9 • 9 • 10 • 24	{}
My watch list my.chemeurope.com # Stokesian dynamics Stokesian Dynamics[1] is a solution technique for the Langevin equation, which is the relevant form of Newton's 2nd law for a Brownian particle $m\frac{du}{dt} = F^{H} + F^{B} + F^{P}$ In the above equation FH is the hydrodynamic force, i.e., force exerted by the fluid on the particle due to relative motion between them. FB is the stochastic Brownian force due to thermal motion of fluid particles. FP is the inter particle force,e.g. electrostatic repulsion between like charged particles. Brownian dynamics is one of the popular techniques of solving the Langevin equation. But the hydrodynamic interaction considered in the Brownian dynamics is very naive, normally including only the single body result (isolated particle). On the other hand Stokesian dynamics includes the many body hydrodynamic interaction. Hydrodynamic interaction is very important for non-equilibrium suspensions, like a sheared suspension, where it plays a vital role in its microstructure and hence its properties. So Stokesian dynamics is used primarily for non-equilibrium suspensions and gives excellent agreement with experiments. ### Hydrodynamic Interaction One of the key features of Stokesian Dynamics is its handing of the hydrodynamic interaction, which is fairly accurate without being computationally inhibitive (like Boundary Integral Methods) for a large number of particles. Classical Stokesian dynamics requires O(N3) operation where N is the number of particles in the system (usually a periodic box). Recent advances has brought down the computational cost to O(NlnN)[2] ## References 1. ^ Brady, John; Bossis G. (1988). "Stokesian Dynamics". Ann. Rev. Fluid Mech. 20: 111-157. doi:10.1146/annurev.fl.20.010188.000551. 2. ^ Brady, John; Sierou A. (2001). "Accelerated Stokesian Dynamics simulations". Journal of Fluid Mechanics 448: 115-146.	{}
Words Per Minute Test Pages (2): « Previous 1 2 Thread Rating: 0 Votes - 0 Average 1 2 3 4 5 02-06-2013, 07:09 PM socialworkersally Newbie Likes Given: 2 Likes Received: 5 in 3 posts Posts: 4 Joined: Jun 2013 Reputation: 0 RE: Words Per Minute Test I got 90.2, but didn't take notice of how many errors. I'm assuming there were a good many. I think I could have topped that had I not been using my laptop. Will have to try with my good keyboard at work! 03-06-2013, 09:06 AM Peanut Where do I go from here? Likes Given: 1,910 Likes Received: 1,058 in 622 posts Posts: 1,639 Joined: Feb 2013 Reputation: 43 RE: Words Per Minute Test I forgot (and I was a bit preoccupied) to try this last night while drunk. Based on my drunken ramblings last night, and the complete lack of proper English, I assume I would have made the computer explode "It was life, often unsatisfying, frequently cruel, usually boring, sometimes beautiful, once in awhile exhilarating." -Stephen King 06-06-2013, 04:47 PM TheGulegon Pit Fiend Likes Given: 8,782 Likes Received: 8,777 in 4,226 posts Posts: 7,858 Joined: Apr 2013 Reputation: 90 RE: Words Per Minute Test 28.6 Apparently index fingers only aint the way to do it 10-06-2013, 03:35 PM Hobbitgirl But I'd never say boo to a goose. Likes Given: 2,612 Likes Received: 6,682 in 2,952 posts Posts: 6,160 Joined: Jan 2013 Reputation: 103 RE: Words Per Minute Test 97 wpm with 1 error. I used to be able to type around 112 back in my youth when I typed all the time. 10-06-2013, 07:22 PM cjlr товарищ 大ἄρχων Likes Given: 6,865 Likes Received: 9,665 in 4,067 posts Posts: 8,070 Joined: Jan 2013 Reputation: 133 RE: Words Per Minute Test 110, but it really messed with me not to be able to correct the words I messed up on (7 of 104, the scorecard handily informs me). So I lost a couple seconds on each typo. Of course, I almost never actually type that much plain English, at work... 11-06-2013, 07:21 AM Hafnof Frequent Poster Likes Given: 6,830 Likes Received: 3,703 in 1,607 posts Posts: 3,369 Joined: Apr 2012 Reputation: 68 RE: Words Per Minute Test I got 70 on my second try, but I can do a little better than that when my brain and hands are working together. Give me your argument in the form of a published paper, and then we can start to talk. 11-06-2013, 09:37 AM cjlr товарищ 大ἄρχων Likes Given: 6,865 Likes Received: 9,665 in 4,067 posts Posts: 8,070 Joined: Jan 2013 Reputation: 133 RE: Words Per Minute Test It'd be neat if there was such a test where you could use your own input text - anyone know of such a thing? 'Cause the crap I usually have to type looks more like cjlr Wrote:In order to diagonalize this Hamiltonian, we attempt the following substitution. \begin{aligned} \hat{c}_k^A &= v d_k + u f_k \\ \hat{c}_k^B &= -u^* d_k + v^* f_k \ \text{,} \end{aligned} where $d_k$ and $f_k$ are Fermions which, as linear combinations of $\hat{c}_k^A$ and $\hat{c}_k^B$, diagonalize $\mathbf{H}$. That is, \begin{pmatrix}\hat{c}_k^{A \dagger} & \hat{c}_k^{B \dagger} \end{pmatrix} \mathbf{H} \begin{pmatrix}\hat{c}_k^A \\ \hat{c}_k^B \end{pmatrix} \equiv \begin{pmatrix}d_k^\dagger & f_k^\dagger \end{pmatrix} \begin{pmatrix}\lambda_1 & 0 \\ 0 & \lambda_2 \end{pmatrix} \begin{pmatrix}d_k \\ f_k \end{pmatrix} \ \text{.} which is just tedious. Pages (2): « Previous 1 2 « Next Oldest \| Next Newest » User(s) browsing this thread: 1 Guest(s) Forum Jump:	{}
The choice of priors is a fundamental step of the Bayesian inference process. Vasishth et al. (2018) recommend plotting the chosen priors to see if they are reasonable. In this post I will show how to easily plot prior distributions in ggplot2 (which is part of the tidyverse). Let’s load the tidyverse first. library(tidyverse) ## ── Attaching packages ─────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.1 ── ## ✔ ggplot2 3.3.5 ✔ purrr 0.3.4 ## ✔ tibble 3.1.6 ✔ dplyr 1.0.8 ## ✔ tidyr 1.2.0 ✔ stringr 1.4.0 ## ✔ readr 2.1.2 ✔ forcats 0.5.1 ## ── Conflicts ────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ── ## ✖ dplyr::filter() masks stats::filter() ## ✖ dplyr::lag() masks stats::lag() theme_set(theme_minimal()) # I just like this theme :) ## Plotting your priors Let’s start with a simple normal prior with $$\mu$$ = 0 and sd = 1. The plot is initialised with an empty call to ggplot(). As aesthetics, you only need to specify the range of x values in aes(). Here, we use c(-4, 4), meaning that the x-axis of this plot will have these limits. For a normal distribution, it is useful to set the limits as the mean ± 4 times the standard deviation (this ensures all the distribution is shown). The function ggplot2::stat_function() allows us to specify a distribution family with the fun argument. This arguments takes the density function (the R functions of the form dxxx) of the chosen distribution family, so for the normal (Gaussian) distribution we use dnorm(). The argument n specifies the number of points along which to calculate the distribution (here 101), while args takes a list with the parameters of the distribution (here the mean 0 and standard deviation 1). ggplot(data = tibble(x = -4:4), aes(x)) + stat_function(fun = dnorm, n = 101, args = list(1)) + labs(title = "Normal (Gaussian) distribution") A beta prior will be bounded between 0 and 1, so we can specify that in aes(). The beta distribution has two arguments, shape1 and shape2 (here 2 and 5). ggplot(data = tibble(x = 0:1), aes(x)) + stat_function(fun = dbeta, n = 101, args = list(2, 5)) + labs(title = "Beta distribution") Another common distribution is the Cauchy. ggplot(data = tibble(x = -10:10), aes(x)) + stat_function(fun = dcauchy, n = 201, args = list(-2, 1)) + labs(title = "Cauchy distribution") The Poisson distribution can be plotted by changing the type of geom and using an n that creates only integers. # the range 0:20 includes 21 integers, so n = 21 ggplot(data = tibble(x = 0:20), aes(x)) + stat_function(fun = dpois, n = 21, args = list(4), geom = "point") + labs(title = "Poisson distribution") Of course any family with a corresponding dxxx function can be plotted (see ?Distributions and package-provided families). ## References Vasishth, Shravan, M. Beckman, B. Nicenboim, Fangfang Li, and Eun Jong Kong. 2018. Bayesian Data Analysis in the Phonetic Sciences: A Tutorial Introduction.” Journal of Phonetics 71: 147–61. https://doi.org/10.1016/j.wocn.2018.07.008.	{}
## badreferences Group Title Bored?$f:\mathbb R\to\mathbb R\mid e^{x-\int f\left(x\right)}=\int f\left(x\right)$Find:$\lim_{x\to\infty}\left(f\left(x\right)\right)^x$ 2 years ago 2 years ago The answer is 0. And I'm still bored -_- Haha! I'm right aren't I? No, lol, I hope that isn't a real question. XD -_- You are clearly misunderstanding me <-- (see what I did there?) The answer is F. 5. satellite73 Group Title i don't even understand the question Also, I should've specified a $$dx$$ in the integrals, so it's clear they aren't an operation of $$f$$. But I think you all knew that already. I didn't. So you misunderstood me again :D 8. FoolForMath Group Title what is $$dx$$? :P We're given conditions $$f:\mathbb R\to\mathbb R$$ which means the function maps reals into reals. We know that $$\int f\left(x\right)\,dx=e^{x-\int f\left(x\right)\,dx}$$. We want to find the limit asked knowing this much. Could you repeat that? @LifeIsADangerousGame You are a snarky one, aren't you? It's my job. It's what I do. 13. Ishaan94 Group Title Solution? ಠ_ಠ 14. Ishaan94 Group Title @Mr.Math SAVVEE MEE! 15. Mr.Math Group Title @Ishaan94 I will come back to it later and see if I can do it. I feel tired now. 16. Ishaan94 Group Title $\mathsf{ \color{yellowgreen}{\text{Okay}}}$ 17. Mr.Math Group Title By taking ln of both sides we have $x-\int f(x)dx=\ln(\int f(x)dx)) \implies 1-f(x)=\frac{f(x)}{\int f(x)dx}$ $\large \implies f(x)=\frac{\int f(x)dx}{\int f(x)dx+1}.$ Because $$\int f(x)dx>0$$, we have $$0<f(x)<1$$. Hence $\large \lim_{x\to \infty} (f(x))^x=0.$ 18. Ishaan94 Group Title 19. karatechopper Group Title ISHAAN GET IN CHAT IF U R NOT HELPIN... 20. karatechopper Group Title :D intrestin lookin R u got there 21. Mr.Math Group Title Well, he/she should post the answer then. 22. Ishaan94 Group Title Lol, I actually mistyped the question. I think the answer for this is actually $$0$$, my bad.	{}
Unit: Gauss's Law Gauss's Law (120 minutes) • Gauss' Law (SGA) 90 min - students solve for the electric field due to a charged sphere or an infinite cylinder. Emphasis is made on students making symmetry arguments (proof by contradiction) for using Gauss' Law. Divergence (40 min) • Definition of divergence (Lecture) 20 min • Visualizing Divergence (Maple Visualization) 20 min Students practice estimating divergence from graphs of various vector fields. Divergence Theorem (20 min) • Reading: GVC § Divergence Theorem • Derivation of the Divergence Theorem (lecture). We follow “div, grad, curl and all that”, by Schey. The Divergence theorem is almost a lemma based on the definition of divergence. Draw a diagram of an arbitrary volume divided into lots of little cubes. Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary. Differential Form of Gauss's Law (10 min) • Differential Form of Gauss's Law: Maxwell's Eq 1 & 3: $\Vec{\nabla} \cdot \Vec{E} = {\rho \over \epsilon_0}$, $\Vec{\nabla } \cdot \Vec{B} = 0$ (lecture) • (optional) Divergence of a Coulomb field (requires delta functions) (lecture) • (optional) Electric field lines (lecture) Unit: Current, Magnetic Vector Potential, and Magnetic Field Vector Potentials (Optional) • Reading: GVC § Magnetic Vector PotentialCurl • Vector Potential A (lecture) 10 min max This can be just an analogy with electrostatic potential. • Curl (at least the component definition in rectangular coordinates) Magnetic Fields • Derivation of the Biot-Savart Law from Magnetic Vector Potential (lecture) 15 min • (optional) Comparing B and A for spinning ring (class discussion/lecture) Unit: Ampère's Law Stokes' Theorem • Reading: GVC § Stokes' Theorem • Derivation of Stokes' Theorem (lecture). We follow “div, grad, curl and all that”, by Schey Differential Form of Ampère's Law • Stokes' Theorem (lecture) (Math 3.12: Stokes' Theorem) • Differential Form of Ampère's Law: Maxwell Eq. 2 & 4 $\Vec{\nabla } \times \Vec{E} = 0$, $\Vec{\nabla } \times \Vec{B} = \mu_0 \Vec{J}$(lecture) (Physics 41: Differential Form of Ampère's Law) Unit: Conductors Conductors (1 hr) • Conductors (lecture) Unit: Conservative Fields Conservative Fields • Conservative Fields (lecture) (Math 3.5: Independence of Path, Math 3.6: Conservative Vector Fields, Math 3.7: Finding Potential Functions) • Equivalent Statements (lecture) Unit: Energy Energy for Continuous Distributions • Energy for Continuous Distributions (lecture) Views New Users Curriculum Pedagogy Institutional Change Publications	{}
## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition) Consider the system of the block and the cable. We can find the acceleration of the system. $a = \frac{v^2-v_0^2}{2x}$ $a = \frac{(4.0~m/s)^2-0}{(2)(2.0~m)}$ $a = 4.0~m/s^2$ Let $m_b$ be the mass of the block. Let $m_c$ be the mass of the cable. We can find the mass of the cable. $F = (m_b+m_c)~a$ $m_c = \frac{F - m_b~a}{a}$ $m_c = \frac{(100~N) - (20~kg)(4.0~m/s^2)}{4.0~m/s^2}$ $m_c = 5.0~kg$ The mass of the cable is 5.0 kg	{}
In this paper, the heat transfer characteristics of a circular air jet vertically impinging on a flat plate near to the nozzle ($H/d=1–6$, where $H$ is the nozzle-to-target spacing and $d$ is the diameter of the jet) are numerically analyzed. The relative performance of seven turbulent models for predicting this type of flow and heat transfer is investigated by comparing the numerical results with available benchmark experimental data. It is found that the shear-stress transport (SST) $k−ω$ model and the large Eddy simulation (LES) time-variant model can give better predictions for the performance of fluid flow and heat transfer; especially, the SST $k−ω$ model should be the best compromise between computational cost and accuracy. In addition, using the SST $k−ω$ model, the effects of jet Reynolds number (Re), jet plate length-to-jet diameter ratio $(L/d)$, target spacing-to-jet diameter ratio $(H/d)$, and jet plate width-to-jet diameter ratio $(W/d)$ on the local Nusselt number (Nu) of the target plate are examined; a correlation for the stagnation Nu is presented. 1. San , J. Y. , Huang , C. H. , and Shu , M. H. , 1997, “ Impingement Cooling of a Confined Circular Air Jet ,” Int. J. Heat Mass Transfer 0017-9310, 40 ( 6 ), pp. 1355 1364 . 2. Dano , B. P. E. , Liburdy , J. A. , and Kanokjaruvijit , K. , 2005, “ Flow Characteristics and Heat Transfer Performances of a Semiconfined Impinging Array of Jets: Effect of Nozzle Geometry ,” Int. J. Heat Mass Transfer 0017-9310, 48 ( 3–4 ), pp. 691 701 . 3. Wang , S. J. , and Mujumdar , A. S. , 2005, “ A Comparative Study of Five Low Reynolds Number k-ε Models for Impingement Heat Transfer ,” Appl. Therm. Eng. 1359-4311, 25 ( 1 ), pp. 31 44 . 4. San , J. Y. , and Shiao , W. Z. , 2006, “ Effects of Jet Plate Size and Plate Spacing on the Stagnation Nusselt Number for a Confined Circular Air Jet Impinging on a Flat Surface ,” Int. J. Heat Mass Transfer 0017-9310, 49 ( 19–20 ), pp. 3477 3486 . 5. Zuckerman , N. , and Lior , N. , 2005, “ Impingement Heat Transfer: Correlations and Numerical Modeling ,” ASME J. Heat Transfer 0022-1481, 127 ( 5 ), pp. 544 552 . 6. Thakre , S. S. , and Joshi , J. B. , 2000, “ CFD Modeling of Heat Transfer in Turbulent Pipe Flows ,” AIChE J. 0001-1541, 46 ( 9 ), pp. 1798 1812 . 7. Launder , B. E. , and Spalding , D. B. , 1972, Lectures in Mathematical Models of Turbulence , , London . 8. Yakhot , V. , and Orszag , S. A. , 1986, “ Renormalization Group Analysis of Turbulence. I. Basic Theory ,” J. Sci. Comput. 0885-7474, 1 ( 1 ), pp. 3 51 . 9. Shih , T. H. , Liou , W. W. , Shabbir , A. , Yang , Z. G. , and Zhu , J. , 1995, “ A New k-ε Eddy Viscosity Model for High Reynolds-Number Turbulent Flows ,” Comput. Fluids 0045-7930, 24 ( 3 ), pp. 227 238 . 10. Wilcox , D. C. , 1998, Turbulence Modeling for CFD , DCW Industries, Inc. , . 11. Menter , F. R. , 1994, “ 2-Equation Eddy-Viscosity Turbulence Models for Engineering Applications ,” AIAA J. 0001-1452, 32 ( 8 ), pp. 1598 1605 . 12. Launder , B. E. , Reece , G. J. , and Rodi , W. , 1975, “ Progress in Development of a Reynolds-Stress Turbulence Closure ,” J. Fluid Mech. 0022-1120, 68 , pp. 537 566 . 13. Galperin , B. A. , and Orszag , S. A. , 1993, Large Eddy Simulation of Complex Engineering and Geophysical Flows , Cambridge University Press , Cambridge, England .	{}
# Energy conservation, and conservative forces? 1. May 23, 2014 ### Dash-IQ What is the relationship of conservative & non-conservative forces to the conservation of energy? What differs with the two? Energy in each case...? 2. May 23, 2014 ### BiGyElLoWhAt I'm not really sure that there is a connection. One is a concept, and the other is a "thing". Conservation of energy states one of two things, depending on the situation. $E_{initial} = E_{final}$ If there are external forces: $E_{initial} \pm \Delta W = E_{final}$ A conservative force is another thing entirely. A force is conservative if $\vec{∇} \times \vec{F} = 0$ Which basically states that the work done on an object moving through the vector field F is independent of path; meaning if an object moves through the field from point a to point b, the work done on the object by the field is the same no matter what path it chooses to take. $\vec{∇}$ is defined as: $<\frac{\partial}{\partial x}\hat{i},\frac{\partial}{\partial y}\hat{j},\frac{\partial}{\partial z}\hat{k}>$ 3. May 23, 2014 ### UltrafastPED Conversely, for non-conservative forces the amount of work done varies with the path taken. 4. May 23, 2014 ### abitslow Conservative force? Hmmm. Oh yeah, in certain problems it is useful to invoke a force (or a set of forces) which are constant (in the context of the problem). Are you familiar with Kilroy's 1st law? "Force is always conserved." No? Well, there is a reason for that. (there is no such law). A real (general) conservation principle will have an associated Law. 5. May 23, 2014 ### AlephZero For a conservative force, the work done moving between two points depends only on the points, not on the path between them. So you can define a potential function that describes the work done by the force when moving between any two points in space. That potential function can be interpreted as "potential energy". A simple example is gravitation, in classical mechanics. 6. May 23, 2014 ### Matterwave A conservative force will have with it an associated potential energy. The total energy, kinetic plus potential, will then be conserved. A non-conservative force, like friction, will not have an associated potential energy function, and thus you cannot say kinetic plus potential energy is constant. There may be sources of energy loss such as heat. But not all sources of non-conservative forces will lead to energy loss. The magnetic force, for example, will lead instead to no kinetic energy change since it always acts perpendicular to the direction of motion. EDIT: Whelp, looks like Aleph beat me to it. 7. May 26, 2014 ### Dash-IQ Energy is certainly conserved in BOTH kinds of forces correct? 8. May 26, 2014 ### UltrafastPED Yes, energy is always conserved; for example, friction is non-conservative - the lost work goes to heat & sound. For a conservative force like gravity the work done against gravity becomes potential energy; and the potential energy lost by a falling body goes into kinetic energy. So all of the energy is converted to other forms of energy in all cases. 9. Jul 1, 2015 ### anastasia15 Are hysteretic forces by definition non conservative? Thanks :)	{}
## Permanence and global attractivity in nonlinear difference equations.(English)Zbl 0843.39010 Lakshmikantham, V. (ed.), World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 1161-1172 (1996). Summary: We obtain sufficient conditions under which the difference equation $x_{n + 1} = x_n f(x_n, x_{n - k_1}, \dots, x_{n - k_r}), \quad n = 0,1, \dots$ is permanent. We also obtain sufficient conditions under which all positive solutions are attracted to the positive equilibrium of the equation. For the entire collection see [Zbl 0836.00032]. ### MSC: 39A12 Discrete version of topics in analysis 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 39A10 Additive difference equations	{}
# Proof that derivative of Hurwitz Zeta by the first argument is not expressable in terms of Hurwitz Zeta The set of elementary functions is defined so that it to be closed against operation of differentiation. It is also evidently close against discrete differentiation. In the discrete calculus there is a similar set of functions, but with one sufficient difference. It appears not to be closed against normal (non-discrete) differentiation. But I need a proof. So I am asking for a proof for the following statement regarding Hurwitz Zeta: $$\frac{d}{dq}\zeta(q,p)$$ cannot be expressed in terms of elementary functions and Hurwitz Zeta. UPDATE I found the following formula which connects the two functions, but still a question remains whether one of them can be expressed explicitly. $\zeta '\left(z,\frac{q}{2}\right)-2^z \zeta '(z,q)+\zeta '\left(z,\frac{q+1}{2}\right)=\zeta(z,q)2^{z}\ln 2$ • What is the "similar set of functions" in discrete calculus that plays the role of elementary functions but is not closed under differentiation? – Henry Cohn Apr 7 '12 at 12:55 • @Henry Cohn, Hurwitz Zeta, generalized Bernoulli polynomials, polylogarithm, polygamma. All expressable through each other. – Anixx Jul 7 '15 at 13:27 • Definition... $$\zeta(s,q) := \sum_{n=0}^\infty\frac{1}{(q+n)^s}$$ with analytic continuation. en.wikipedia.org/wiki/Hurwitz_zeta_function – Gerald Edgar Jul 7 '15 at 15:03	{}
# Using percentiles as predictors - good idea? I am thinking about a problem which is to predict log(spend) of a customer using linear regression. I am considering what features to use as input and wondering if it would be OK to use the percentile of a variable as inputs. For example I could use the companies revenue as a input. What I'm wondering is whether I could use the company revenue percentile instead. Another example would be a categorical industry classifier (NAICS) - if I were to look at median spend per NAICS code and then assign each NAICS code to a 'NAICS Percentile', would that be a valid explanatory variable I could use? Just wondering if there are any issues to be aware of when using percentiles? Is it in some ways equivalent to a type of feature scaling? • If you have the original data, why would you like to use percentiles? Maybe it's not a good idea, because percentiles are only ordinal, not metric measures. But I'm unsure about bias / efficiency. – hplieninger Jul 25 '13 at 9:20 • Percentiling of $X$s is inconsistent with they way the $X$s have their effect. A common error is to percentile weight or BMI when predicting a health outcome. The physics of weight dictate that it is the physical dimensions of a person that relate to their body functions, not how many persons in the sample who are below the one subject's weight or BMI. – Frank Harrell Jul 25 '13 at 11:02 • if you can reasonably cluster your industry variable in groups, e.g. 4, use dummy coding (or any other appropriate coding scheme) and you're done. That's the way I would do it. – hplieninger Jul 25 '13 at 11:18 • I can't think of a reason why the percentile would be linearly related to the dependent variable. If you can think of one, then it might be OK (and please update your question with your reason) – Peter Flom Jul 25 '13 at 11:57 • If you want to use NAICS code as a proxy for a company's spend, then you can do so using the average spend in its NAICS code - no need to use percentiles. – Scortchi - Reinstate Monica Jul 26 '13 at 10:56	{}
## Tuesday, September 30, 2014 ### Recapitulation [1.] See Alex T. Kalinka et al., "Gene expression divergence recapitulates the developmental hourglass model," Nature, Vol. 468: 811-814 (December 9, 2010); Brian K. Hall, "Phylotypic stage or phantom: is there a highly conserved embryonic stage in vertebrates?," Trends in Ecology and Evolution, Vol. 12: 461-463 (December, 1997); Andres Collazo, "Developmental Variation, Homology, and the Pharyngula Stage,"Systematic Biology, Vol. 49:3 (2000). ## Sunday, September 28, 2014 Accompanying the funny cartoon below was an explanation by a blogger about why chimps are super-smart and we humans shouldn't think too highly of ourselves. The cartoon itself seems aimed at reducing all human exceptionalism to a primate urge. (I think the urge for academics to outpublish each other is more easily traced to that urge.) It makes better humor than philosophy. Basically chimps are pretty good problem-solvers (and so are octopi for that matter) and they more or less form a sort of strategy or cognitive map of a situation to deal with or navigate a particular problem. What the psychologists are calling metacognition in this case is recognition of underdetermination or sense of (a lack of) certainty. In fact, any ability to revise that map of the problem space is in some sense metacognition. Of course, many animals have brains that recognize all sorts of things: faces, predators, disorder, direction of motion, spatial relationships. An animal that finds a better vantage point when the view is unclear is doing something analogous; investigating when the cognitive map is hazy is a similar instinct for any problem-solver like a raven or an ape. Can there be much effective problem-solving there without some recognition of underdetermination, without some sense of uncertainty bordering on confusion? It seems like lumping that in with the way humans think about their thinking is extrapolation-turned-polysemy. It stretches credulity. But the fact that a chimp can recognize when the cognitive map is shaky-- it seriously raises the question of whether a chimp has what it takes to do evolutionary science. ;-) ## Saturday, September 27, 2014 ### Jerry Was A Man I didn't plan the title of my post... It leapt from my fingers as I started typing and the title of the famous science fiction short story somehow seemed appropriate. I came across a post from Jerry Coyne, anticreationist extraordinaire, which exemplifies for me and reminds me just how bankrupt the materialist, secularist view of humanity really is. When a male lion invades another group and kills the cubs, when a chimp tears another chimp to bits, those are just bits of nature, and aren’t seen as wrong. And the amorality of nature is touted even by those who realize that our primate relatives show rudiments of morality, . . . . is it really true that all of nature, including primate societies, must be seen as amoral, while human actions must be judged by this thing called “morality”? ### Stephen Asma and the Cuvier-Geoffroy Debate The reviews of Following Form and Function are intriguing to say the least. http://embryo.asu.edu/pages/essay-cuvier-geoffroy-debate The Cuvier-Geoffroy Debate? Never heard of it. Sounds interesting. Yet, it surprises me to find that recapitulation precedes both Darwin and Haeckel, and that structuralism seems to have had a rich pre-Darwin history. Serres had been influenced by the theoretical developments in German biology, most notably by early versions of the recapitulation theory proposed by Carl Friedrich Kielmeyer in 1793 and Johann Friedrich Meckel’s theory of arrests of development in 1811. Like Meckel, Serres believed that it was necessary to study the transitional forms of embryos to understand the permanent adult forms of vertebrates. Doing so, he assumed, would reveal that the developed forms of the lower classes of animals – invertebrates, for example –mimicked the intermediate embryonic forms of higher vertebrates. This idea of development was expressed in the Meckel-Serres Law, and distinguished from the later evolutionary accounts of the recapitulation theory proposed by Ernst Haeckel. Serres’ idea of arrests of development, and Geoffroy’s understanding of it, was transcendental rather than evolutionary. For transcendental anatomists like Serres and Geoffroy, the semblances discovered in embryonic stages reflected a particular metaphysical view of life and a philosophy of anatomy exemplified by Geoffroy’s principle of the unity of composition. The similarities inferred by these kinds of embryological studies did not necessarily represent the similarities of structure between vertebrates and invertebrates as an actual empirical fact of transformation from one species to another (i.e. an evolutionary account), but rather they represented the abstraction of an ideal type required by anatomists to form general laws of development and morphology in biology (i.e. a transcendental account). In other words, the principle of unity, the theory of analogies, the theory of arrests of development and the search for homologies were all regulative principles that served as conditions for the possibility of scientific discoveries in the field of anatomy. - See more at: http://embryo.asu.edu/pages/essay-cuvier-geoffroy-debate#sthash.RsjBneyG.dpuf ## Tuesday, September 23, 2014 ### Secular creationism on the rise in molecular biology! From Jerry Coyne [emphasis mine]: Virtually all of the non-creationist opposition to the modern theory of evolution, and all of the minimal approbation of [Coyne's University of Chicago colleague James] Shapiro's views, come from molecular biologists. I'm not sure whether there's something about that discipline (the complexity of molecular mechanisms?) that makes people doubt the efficacy of natural selection, or whether it's simply that many molecular biologists don't get a good grounding in evolutionary biology. LOL (I thought I heard for the last 15 years that evolutionary theory was molecular biology...) I guess these molecular biologists are ... SECULAR CREATIONISTS! ## Monday, September 22, 2014 ### Protostome vs. Deuterostome Larval Transfer in Evolution in Horizontal Gene Transfer. . . . ## Sunday, September 21, 2014 ### Pulled Punches: Haeckel's Embryos in Peer Reviewed Literature First I'll talk about the peer-reviewed literature that Randy Olson brings up, and then I'll bring up some peer-reviewed literature that contradicts him. In Randy Olson's "Pulled Punches" extra for his Flock of Dodos, Olson references an article in The Quarterly Review of Biology ... and mentions the "peer-reviewed" status of said journal to bolster his claims about Haeckel's embryos. As I've expressed elsewhere, I find Olson's choice of this particular example (which he says he picked for personal reasons--presumably because he thought himself particularly knowledgeable on the subject) of that particular book (Icons of Evolution) to represent Intelligent Design to be a loaded choice. The authors of Olson's touted article have been key figures in the neo-Darwinian public policy think tank NCSE (National Center for Science Education) which is dedicated to having neo-Darwinian theories and hypotheses taught uncritically, and to discrediting Intelligent Design by conflating it with creationism and by promoting ad hominem arguments, and which played a key role in the mistreatment of Richard Sternberg at the Smithsonian. Kevin Padian in particular dislikes Wells' criticism of his dino-bird theories, even though Wells' criticism is probably tame compared to that of paleornithologist Dr. Alan Feduccia. At any rate, Padian and Gishlik's article seems to claim that Wells did not publish research-based papers after getting his PhD nor did engage in any research, a claim contradicted by Carolyn Larabell. The appearance of this spewing of "pro-science" blatherskite in Quarterly Review says more about the journal than it does about the article. No amount of peer review can make a journal avoid libel, it seems. Nor apologize for it. The fact that Quarterly Review has become a haven for this level of attack on Jonathan Wells, an attack all the more cheapened by associating Dr. Wells with a fictional murderous con artist (in the title no less), demeans its status as a scholarly journal. Why haven't we heard about the Talented Mr. Richards and the Talented Mr. Gould? It was not long after that creationists and advocates of intelligent design ignited thousands of websites in an electronic auto-de-fé wherein Haeckel's reputation and that of Darwinian theory were generally sacrificed to appease an angry God... (Robert J. Richards, "Haeckel's embryos: fraud not proven," Biology & Philosophy, Vol. 24:147-154 (2009).) http://www.evolutionnews.org/2012/10/darwin_lobbyist_1065151.html Contrary to the evolutionary hourglass model, variations in the adult body plan are often foreshadowed by modifications of early development. ... These modifications of embryonic development are difficult to reconcile with the idea that most or all vertebrate clades pass through an embryonic stage that is highly resistant to evolutionary change. This idea is implicit in Haeckel's drawings... ## Saturday, September 20, 2014 ### Going Nuclear: Saving Vertebrate Phylogeny From the abstract for "Going nuclear: gene family evolution and vertebrate phylogeny reconciled": Gene duplications have been common throughout vertebrate evolution, introducing paralogy and so complicating phylogenetic inference from nuclear genes. Reconciled trees are one method capable of dealing with paralogy, using the relationship between a gene phylogeny and the phylogeny of the organisms containing those genes to identify gene duplication events. This allows us to infer phylogenies from gene families containing both orthologous and paralogous copies. Vertebrate phylogeny is well understood from morphological and palaeontological data, but studies using mitochondrial sequence data have failed to reproduce this classical view. [emphases mine] The abstract continues to save the day: "Reconciled tree analysis of a database of 118 vertebrate gene families supports a largely classical vertebrate phylogeny." In other words, reconciled tree analysis picks the tree that contains the fewest departures/epicycles from the phylogenetic picture from morphology and paleontology. ## Friday, September 19, 2014 ### Punches Pulled: Michael Behe Doesn't Care In his "Punches Pulled" extra for his film Flock of Dodos, Randy Olson goes through a list of things that he left out of the film supposedly to be nice (i.e. to appear less hostile) rather than to keep his film from becoming a schlockumentary. I direct your attention to his coup-de-gras. He admits that he talked so long to Dr. Michael Behe that he felt tired afterward. Tired? Was there a debate that didn't make it into the film? (He stresses in the film that two other interviewees he didn't debate about evolution because they didn't have the background. Maybe he engaged Michael Behe about his then-forthcoming book Edge of Evolution, a book that discussed the powers of mutation and selection in detail; Flock implies that Behe wasn't doing anything in 2006 other than glorying in the publishing success of Darwin's Black Box.) In fact, there is almost nothing from his very long talk with Dr. Behe other than the Mt. Rushmore analogy. Briefly the film dwells on the mousetrap analogy--something more central, but is completely weak on it; if the film had got some of Behe's responses to Ken Miller's criticisms, there might have been some substance to the segment. But it's "Mt. Rushmore" that you hear from the lips of Behe. There's a lot more to ID concepts than a Mt. Rushmore analogy, but it seems to be on the basis of that analogy that Olson anticlimactically dismisses ID at the end of the film. Did they talk about Mt. Rushmore and mousetraps for hours, or did they get into mutation frequencies and malaria? What tired out poor Randy? But I digress. This coup-de-gras that Olson so graciously left out of his film is that Michael Behe doesn't care. That's right, folks, he doesn't give a scat, and Olson has the goods. More specifically, at the end of what was for Olson a long, grueling interview (Behe appears as relaxed as he did at the beginning of the interview), Olson baits Behe on the politics with which Flock is so deeply concerned. On how the politics affects him, Behe responds that he doesn't have a personal stake in what gets taught to kids in public school because, like so many teachers (here and here), he doesn't send his kids to public school. Perhaps, as a devout Catholic, he would never consider that option anyway. We don't know what followed that sound bite--perhaps a fuller explanation of his "yes and no" answer--nor do we have any idea what was so darn tiring about sitting around outdoors having a relaxed conversation. ## Thursday, September 18, 2014 ### p-values The concept of p-value might just be the most central idea to the notion of counterflow, design, etc. This is the Fisherian idea that I was taught in biology class at university, and the idea that Dembski has argued is more fundamental to theory choice than the likelihood inference that Elliot Sober promotes. ### Lobe-finned Fish, Amphibians, and Devolutionary Processes So earlier this week I was thinking about von Baerian development and considering a specifically non-recapitulatory view of The Vertebrate Embryo and was thinking, "Could the majority of fish be considered more specialized in terms of the general vertebrate pattern, with the more amphibian-like fish being the archetype rather than the specialization. Lo and behold, I came across something in Stuart Kauffman's work that evidence seems to have been mounting that the swim bladder came from the lung, not the other way around! It would be even more intriguing if the archetype for fish were something even more like an amphibian, say a sarcopterygian like Tiktaalik, rather than the more numerous actinopterygians. The actinopterygians depict for us how (bony) fish are different from other vertebrates. Now, is it possible that we could learn things about vertebrate development thinking this way much more efficiently than we could with this quasi-Haeckelian recapitulatory progressivism? The story as I knew it was that fish somehow developed a swim bladder around the time they replaced cartilage with bone. Since utility is the mother and father of invention in the Darwinian world, the usefulness of swim bladders for pelagic swimming was sufficient to explain their existence. If it turns out that lungs were adaptation preceding tetrapods by ages, well then that too is just what one expects in Darwinland. It's important to remember that evolutionary logic means never having to say you're sorry. . . . in 2009, just three years ago . . . the purported fact that 95 percent of the human genome "might as well not be there" was an embarrassment "for creationists," whom in typical Darwinian fashion Dawkins conveniently conflates with intelligent-design advocates. Junk DNA is just what a Darwinist would expect, in other words. Cut to 2012, and now the evident fact that "junk DNA" isn't junk at all but is instead vital for life has become "exactly what a Darwinist would hope for," namely, "to find usefulness in the living world." That is, heads you lose, tails I win. . . . suspiciously convenient self-contradiction. Ah well, as we knew already, being a Darwinist means never having to say "I was wrong." But it's not a self-contradiction. With Evolution-Did-It , whatever direction the evidence points is just what Dr. Pangloss would expect, because evolution as a theoretical framework can accommodate almost anything. Even if the upward trends of progressive (teleological) evolution makes more sense for the historical framework that the evolutionary research program has pursued, what value might there be in more devolutionary hypotheses being assumed. (Devolution is not nearly as satisfying and validating to Darwinism as complexity-building evolution.) The alligator is a reptile that is considered the pinnacle of reptilian evolution nor a transition animal but a sort of devolved representative of warm-blooded archosaurs. Ceolocanths are believed to be derived from sarcopterygians. The TTSS1 pump might be better thought of as having devolved from the flagellum. The mimivirus might best thought of as having devolved from a cellular creature. Maybe Tiktaalik, like the alligator is a throwback, an amphibian that thinks its a fish. Cynodonts might be better understood as a devolution from monotremes. The evolutionary relationships of the fossil [for the eutriconodont mammal Yanoconodon] suggest that either the "modern" middle ear evolved twice, independently or that it evolved and was then lost [i.e devolution] in at least one ancient lineage. Or maybe some are mosaics because phylic boundaries, as we know them, are a trend, not a rule (otherwise, how would either mosaics or missing links be possible?). Now, Archaeopteryx is no longer the missing link it pretended to be in our textbooks. It is, for now, more like the coelocanth or alligator. It is a mosaic that represents the diversity of archosaurs (though not as radically as ceratopsids which had apparently "recapitulated" and rediscovered their four-footed roots. And if quadruped representatives of the archosaurs were there all along, like the elusive coelocanths, they simply flew under the paleontological radar and avoided the fossil record as many group likely have. All this puts me in mind of this structuralist (and narrative-agnostic) formulation by Dr. Richard Sternberg: The approach I am taking to this problem is a variant of structural realism, by which I mean that biological phenomena are manifestations of logico-mathematical structures. This perspective is orthogonal to the origins debate, if you will, because all historical actualities are understood to be space-time instances of pre-existing non-temporal possibilities. Within this context one can accept all that is empirically valid in evolutionary biology, while not axiomatically dismissing the position that structures as well as their “real” instantiations have an intelligent cause. ## Wednesday, September 17, 2014 ### Baez on Information Geometry I think I've struck some gold here concerning information geometry in a series by John Carlos Baez. Start with part 8 where Baez gets into the relationship to evolution. Some reminder about thermodynamic models: Physicists love to think about systems that take only a little information to describe. So when they get a system that takes a lot of information to describe, they use a trick called 'statistical mechanics', where you try to ignore most of this information and focus on a few especially important variables. For example, if you hand a physicist a box of gas, they'll try to avoid thinking about the state of each atom, and instead focus on a few macroscopic quantities like the volume and total energy. Ironically, the mathematical concept of information arose first here—although they didn't call it information back then; they called it 'entropy'. The entropy of a box of gas is precisely the amount of information you've decided to forget when you play this trick of focusing on the macroscopic variables. Amazingly, remembering just this—the sheer amount of information you've forgotten—can be extremely useful... at least for the systems physicists like best. He goes on to say that in biology, there is a lot less information in the system that can be forgotten... This goes back somewhat to the use of "entropy" to correlate to different kinds of information. The (average) loss of uncertainty/entropy in Shannon information, for example. He goes on to talk about alleles as rival hypotheses. The analogy is mathematically precise, and fascinating. In rough terms, it says that the process of natural selection resembles the process of Bayesian inference. A population of organisms can be thought of as having various 'hypotheses' about how to survive—each hypothesis corresponding to a different allele. (Roughly, an allele is one of several alternative versions of a gene.) In each successive generation, the process of natural selection modifies the proportion of organisms having each hypothesis, according to Bayes' rule! It appears that this approach looks at information in terms of a distance from a destination state of stability. So in that sense, it is more about relative information. But what does all this have to do with information? . . . first discovered by Ethan Atkin. Suppose evolution as described by the replicator equation brings the whole list of probabilities p — let's call this list —closer and closer to some stable equilibrium, say q. Then if a couple of technical conditions hold, the entropy of q relative to p keeps decreasing, and approaches zero. Remember what I told you about relative entropy. In Bayesian inference, the entropy relative to p is how much information we gain if we start with as our prior and then do an experiment that pushes us to the posterior q. So, in simple rough terms: as it approaches a stable equilibrium, the amount of information a species has left to learn keeps dropping, and goes to zero! . . . You can find [precise details] in Section 3.5, which is called "Kullback-Leibler Divergence is a Lyapunov function for the Replicator Dynamic". . . . 'Kullback-Leibler divergence' is just another term for relative entropy. 'Lyapunov function' means that it keeps dropping and goes to zero. And the 'replicator dynamic' is the replicator equation I described above. . . . [This approach] uses information geometry to make precise the sense in which evolution is a process of acquiring information Baez offers some background to this in Gavin E. Crooks' Measuring thermodynamic length and in part 1 of his series. But when we’ve got lots of observables, there’s something better than the variance of each one. There’s the covariance matrix of the whole lot of them! Each observable $X_i$ fluctuates around its mean value $x_i$… but these fluctuations are not independent! They’re correlated, and the covariance matrix says how. All this is very visual, at least for me. If you imagine the fluctuations as forming a blurry patch near the point $(x_1, \dots, x_n)$, this patch will be ellipsoidal in shape, at least when all our random fluctuations are Gaussian. And then the shape of this ellipsoid is precisely captured by the covariance matrix! In particular, the eigenvectors of the covariance matrix will point along the principal axes of this ellipsoid, and the eigenvalues will say how stretched out the ellipsoid is in each direction! As I recall, the eigenvalues will be in bits of error in terms of the units of the parameters. ### Relative Entropy in Evolutionary Dynamics. Marc Harper has a post about "Relative Entropy in Evolutionary Dynamics" (among "entropy and information" here) that is is potentially very useful for relating the Fisher Information metric to the information to be found in traversing sequence space. Harper also has a related article published as "Information Geometry and Evolutionary Game Theory," from which I'm adding the example below to a previous post. ## Tuesday, September 16, 2014 ### Adleman's K-potency and Kauffman's Atoms One of the motivations for the sequence-space probability dispersion matrix is that as a model it might estimate the computational depth of nucleotide sequences, or the relative depth between two nucleotide sequences. How deep is a given nucleotide sequence? Kauffman writes in a recent foreword that the universe has produced every kind of atom it could produce (an ergodic process, whereas enumerating the realizable proteins is a non-ergodic process), but Leonard Adleman has elsewhere written in "The Rarest Things in the Universe" (among "entropy and information" here) that atoms with higher counts of protons than we've thus far encountered could be considered to have larger depth (and thus be somewhat analogous to Kauffman's sequences). I am not a physicist, but I suppose it is possible to theorize about an atomic nucleus with a million protons. But what if I want to create one? It appears that producing transuranic elements takes huge amounts of time/energy and the greater the number of protons, the more time/energy it takes. It is even conceivable (to me at least) that there is not enough time/energy available (at least on earth) to actually produce one. Like the prime factorization of $2^{1,000,000}-1$, it may exist in theory but not in reality. On the other hand, physicists from Russia and America, using lots of time/energy, have created an atomic nucleus with 118 protons called Ununoctium. Ununoctium is analogous to Childers’ prime factorization; both exist in reality; both were very costly to create. In his 1979 paper "Time, Space, and Randomness," Adleman develops an idea about "K-potency" motivated by an analogy with thermodynamics, specifically chemical reactions that take much less time going in one direction than the other. This approach to "one-way functions" is important to crytography, incidentally. His definition for K-potency follows here: ## Monday, September 15, 2014 ### Inexplicable Caprice From Top to Bottom Oh sure natural selection's been demonstrated . . . the interesting point, however, is that it has rarely if ever been demonstrated to have anything to do with evolution in the sense of long-term changes in populations. . . . Summing up we can see that the import of the Darwinian theory of evolution is just unexplainable caprice from top to bottom. What evolves is just what happened to happen. - Stanley Salthe [There are] hundreds of other evolutionary scientists (non-creationists) who contend that natural selection is politics, not science, and that we are in a quagmire because of staggering commercial investment in a Darwinian industry built on an inadequate theory. - Suzan Mazur ## Saturday, September 13, 2014 ### Randy Olson's Creationist Shill I was tired of being told that my structuralism reduced to "creationism" by those who have no understanding of either. -- Richard Sternberg Randy Olson, in his documentary Flock of Dodos that purports to be an objective inquiry into Intelligent Design both as a (possibly) scientific enterprise and as a social phenomenon, talks about a subject interviewed at an ID convention who claimed to be a Darwinist but later seems to have not been. This subject seemed noteworthy, Olson seems to present, because it seemed unusual to have a non-creationist spouting a teach-the-controversy view, let alone attending an ID conference as something other than a heckler or guerrilla documentarian. Olson's big reveal is that this Darwinist is John Angus Campbell who is (or was) a Fellow at the Discovery Institute. Olson is vague on this point and seems to rely on the audience to assume that Campbell's warm relationship with ID is in conflict with his conception of Darwinism. Olson elsewhere does include footage of Michael Behe saying he believes in common descent and macro-evolutionary speciation events, and Olson presents Behe as the spokesman for ID in vague terms ("some say" he is the leading expert on Intelligent Design), so it would seem that Behe embraces some form of Darwinism being more or less convinced of several important tenets. Behe is certainly not Darwinist enough for Olson, since he not only denies the sufficiency of natural selection for certain macroevolutionary feats but he also thinks that the influence of an intelligent agent is better explanation that the other rivals of the selectionist point of view. (Olson's film implies that Behe is the leading idea-man of what he obviously considers an anti-evolution movement.) ## Thursday, September 11, 2014 ### Against Neo-Darwinism or Against Evolution? The nexus of Pro-Darwin lobby (teachers, pundits, parents, etc.) and biology practitioners worried about the political status of evolutionary science often work together to make this worse, and not simply by hateful negative attacks on their opposition or by failure to dumb it down sufficiently. (A point not made well by Flock of Dodos.) As with many evolution-related issues, there is at best a double-message going out there. One is that neo-Darwinism has never had any serious deficiencies and therefore never needed any balance or controversy taught, which has been a useful tactic of the NCSE for years. (Whether this is a vestigial behavior--the "pro-science" lobby has evolved much more slowly than the "anti-science" crowd--or whether this is the inherent defensiveness of a dominant paradigm is a story for another time.) The other message is that there is vigorous, healthy debate over what the processes and mechanisms of evolution are, but that since almost all of these are believers in both methodological naturalism and the power of known forces to explain everything, the commonly taught evolutionary hypotheses are unassailable facts (or should be taught as such at any rate). The former message has certainly hurt Darwinism. How much criticism has there really been against Richard Dawkins by the "pro-science" coalition for his extreme neo-Darwinistic reductionism? Randy Olson's poker-players don't seem bothered by him. The closest that Olson gets at all to noting any challenge to neo-Darwinism (or that there is any diversity in the academic ecosystem) is lumping "process structuralism" in with ID at some point (the "teach the controversy" segment, I think). The fact that Olson can implicitly charge ID as a God-Did-It approach (as his editing choices convey) but not recognize the extent to which much of evolutionary literature has boiled down to Selection-Did-It or Evolution-Did-It says much. In fact, the ideas about how it happened and the mechanisms involved are so complicated at this point, that overconfidence concerning natural selection through most of the 20th century (and continuing now) seems both naive and quaint. I was taught in college that microevolution = macroevolution, essentially, as a fact. As Stuart Newman has pointed out, this overconfidence, while achieving political mileage in jurisprudence, has hurt public perception of evolutionary teaching in general. Meanwhile Michael Ruse has attacked creationism (no doubt including ID in it) of being more selection-obsessed than the evolution crowd, without (until perhaps lately) giving any credit to this sociological effect. If people tend to conflate anti-Darwinism with anti-evolution, maybe it's because too often the "pro-science" crusaders have conflated Darwinism with evolution. The second message potentially hurts the general prospect of evolution partly because of this (wait, what do you mean it isn't as simple as natural selection and microevolution?), but also because Selection-Did-It is more obviously replaced by Evolution-Did-It. Evolution has become the Dark Energy of the 21st century. No one agrees what Dark Energy is or how it figures into physics, but Something is causing the galaxies to diverge over time; new species with novel structure and organs have appeared over time and therefore Evolution is the name given to that Power at work. The entire scientific community starts to a resemble a jury that have very conflicting ideas about how the defendant committed the crime and where he committed it, based on contradictory evidences and contradictory interpretations, but are (almost) unanimous in their belief that he is most definitely guilty based on the evidence. (Half the jury are okay his religion, half are okay with his race, and only a few don't like his face, so you can't say they are unanimously prejudiced.) But if we give the name "Evolution" to the basic pattern being investigated--the changes in biological diversity over geologic time on Earth, the explananda rather than the explanans--neither Intelligent Design in general nor Discovery Institute in particular are any opposition to this. The fact that you can be a creationist within the ID framework, as you can be an evolutionist like Michael Behe, or anything in between, is part of the guilt-by-association tactics by "pro-science" Big Darwin. What the "pro-science" lobby find so threatening about the "Big Tent" of ID is that (a) that it is mostly consonant with theism (i.e. "makes it possible to be an intellectually fulfilled theist") rather than dissonant, and (b) the usual tactics against Young Earth Creationism do not begin to address it. (Again, two messages: (1) Creationists are not to be trusted because they are evolution-denying hayseeds. (2) ID theorists like Michael Behe who largely embrace evolution are still creationists because they don't rule out theories consonant with "supernatural causation." Collectively, these messages amount to double-speak.) Certainly, you can be a skeptic of neo-Darwinism without doubting Big Evolution. What Suzan Mazur's work has achieved, perhaps more than anything else, is documenting the stifling effect the neo-Darwinian Synthesis has had on biologists and selection skeptics. But calling evolution skeptics "evolution deniers" (a trope that analogizes with Holocaust denial) is partly ugly political tactic and partly "physics envy" (the idea that biology vies with physics for ontological validity, e.g. in elevating the theoretical status of evolution to that of gravity). Many ID theoreticians believe in some version of selection-oriented evolution and common descent, many are skeptics of one or more accepted evolutionary hypotheses, and some do think the whole evolutionary narrative is a mostly unproductive concept. The crumbling of the neo-Darwinist edifice has hurt Evolution in more than just a PR sense. If science, as the ACLU has asserted through Judge Jones, is what scientists do, then neo-Darwinism is the strongest, most worked out, and most explanatory theoretical framework for evolution. If it is really as weak as it appears to be, it calls for some serious skepticism of the explanans of evolutionary science, if not the explananda. Perhaps the biggest failing of Randy Olson's Flock is the attempt to only cast Intelligent Design as a sociological phenomenon (driven by philosophical motives) and does not really get close to doing the same with his own camp, despite his belief in his own objectivity. He shows some of this at work, but doesn't make it part of his documentary's explanation. The explanation he gives concerning them is that they are so erudite (he helps make this point by displaying definitions for the big words they use) that they make poor evangelists for his gospel of truth. http://www.darwinscholars.com/how-to-enrollschedule.html http://www.evolutionnews.org/2014/06/why_does_biolog087231.html http://www.evolutionnews.org/2010/02/how_to_play_the_gene_evolution032141.html http://www.bcse-revealed.info/bcse/bcse.rev/Main/CognitiveDissonance.html http://www.bcse-revealed.info/bcse/bcse.rev/Main/FreedomPluralismAndDeception2.html http://bcse-revealed.blogspot.com/index.html http://bcse-revealed.blogspot.com/2006/11/bcse-educational-incompetence-and.html Gould's comments on von Baer's Law http://darwinianfundamentalism.blogspot.com/2007/06/abscheulich-atrocious-stephen-jay-gould.html http://www.evolutionnews.org/2011/10/wheel_of_fortune_new_work_by_t051621.html http://www.evolutionnews.org/2014/06/more_strong_exp087061.html http://www.evolutionnews.org/2009/10/dollos_law_the_symmetry_of_tim026721.html http://www.evolutionnews.org/2007/02/hoax_of_dodos_pt_1_flock_of_do003132.html http://www.suzanmazur.com/?p=20 http://www.suzanmazur.com/?p=259 ### Jack Szostak and the Creation of Life http://www.suzanmazur.com/?p=259 ## Saturday, September 6, 2014 ### links: Peer Reviewed Journal Defends Recapitulation http://ncse.com/creationism/analysis/richardson Michael K. Richardson "highly conserved" embryos no highly conserved embryos http://www.toriah.org/articles/richardson-1997.pdf http://www.evolutionnews.org/2011/06/haeckels_embryos_make_multiple047321.html#backfn6 http://www.evolutionnews.org/2011/07/three_flawed_evolutionary_mode048541.html http://www.ichthus.info/Evolution/DOCS/Richardson2.pdf http://www.talkorigins.org/faqs/wells/iconob.html#raraff2 Recapitulation is dead! Long live Recapitulation! ### Flock of Dodos Shows Randy Olson Engaging in Triviality At a high school level, the aim of the [text]book is to convey some basic concepts of biology, not to confuse students with the complexity of a subject. - Alan D. Gishlick, NCSE Unrelated to my viewing Flock of Dodos, I had recently started looking through The Origin of Animal Body Plans (Wallace Arthur, 1997) and The Shape of Life (Rudolf Raff, 1996). Figure 2-7 in Arthur shows Haeckel's embryos but attributes them to a figure from Embryos, Genes, and Evolution. Raff uses the same figure and actually does name it as ultimately from Haeckel and qualifies it as "exaggerated," but Arthur gives no indication that they are obsolete or exaggerated. Neither author uses the diagram for merely historical value but to illustrate vertebrate similarities in the phylotypic stage. One might argue that they are not textbooks, but the 2002 Biology featured above is certainly a textbook, and so was Futuyma's Evolutionary Biology, and the other textbooks highlighted by Dr. Wells. My copy of The Cell from the LIFE Science Series has drawings clearly based on Haeckel's artwork on page 103 (1964 edition), a page I clearly remember from my school library in the '80s. Figure 1-36 of Molecular Biology (1994) uses an illustration from 1874 as paradigmatic. Yet Flock would have its audience believe that these illustrations went out of fashion shortly after 1914. Science reporter James Glanz wrote ["Biology Text Illustrations More Fiction Than Fact," 4/8/01] for the New York Times in 2001 that the "drawings were reproduced in textbook after textbook for more than a century." Indeed, Glanz pointed out that one of the biology textbooks recycling Haeckel's embryo drawings was co-authored by none other than Bruce Alberts, then-head of the National Academy of Sciences [emphasis mine]: I remember seeing these same images both in college and in earlier education, and despite what Randy Olson claims, the textbooks in which I saw them used them as iconic evidences of evolutionary reality. Olson makes no bones about idolizing Stephen J. Gould, and yet Gould himself claimed less than 20 years ago that Haeckel's drawings were still being used in many "if not most" textbooks. Eugenie Scott of the NSCE had acknowledged (and defended) the fact. Even P.Z. Myers has admitted it. I'll jump ahead to my main point here, and work my way back to it. You'll mostly hear two conflicting ideas about Haeckel's embryos depending on whom you ask. Either they are being used because they are basically correct, or they haven't been used in years. (Few would probably react with as much umbrage as Stephen Gould at the obvious fakery of the images.) Olson, maker of the anti-Intelligent Design documentary Flock of Dodos, uses the issue of Haeckel's embryo drawings to present Jonathan Wells as a mass market hack, implicitly comparing his book Icons of Evolution to supermarket tabloids. Wells' criticism of the use of these embryos was published in the peer-reviewed journal The American Biology Teacher in 1999. The Discovery Institute has pointed out several current textbooks that use them. Recently I browsed through The Shape of Life, a modern evo-devo book that does point out the "hour glass" of ontogenic development, also uses a variation of Haeckel's illustrations. Olson has since defended his retention of his treatment of Wells in the film by retorting that it is a trivial issue whether Haeckel's embryos are actually still used. This however is exactly the trivial point that Olson uses for his hatchet job on Wells, to demonstrate somehow that Wells either invents things or hasn't done his homework. In fact, either Olson invented something or didn't do his homework. If this was such a trivial point, why of all the points in Icons of Evolution did Olson pick this one? In Michael Moore-esque fashion, Olson hands a biology textbook to a Darwin critic and asks him to find Haeckel's embryos, as though the existence of such a textbook was meaningful. (Perhaps this demonstrates the harm that evolutionary logic has done to thinking in general.) Why did Olson mislead the audience about a "trivial" point in a book that has little to do with explaining ID but rather criticizes the misinformation used in teaching evolutionary biology? Olson has been so on top of the "anti-science" crusade that over the years his mother sends him updates on what the poor anti-science rubes in her part of the country, which eventually led to Flock. Olson, who has spent most of his life dedicated to understanding marine ecology specifically in light of the Darwinian narrative, is yet another disinterested third party reporting objectively on Intelligent Design. About the only thing that Olson presents favorably for ID is expressing his surprise that ID conventioners seemed well-dressed, educated, and obsessed with scientific details, and that they weren't the provincial trailer trash that he very evidently was anticipating. The footage of him sitting in his hotel room the night before the convention talking in a mock country drawl makes me wonder whether his whole idea for the film had to change when he didn't find the sort of people there he hoped to find. Dr. Jonathan Wells has extended his Cracked Kettle analogy to Olson's defense of the disinformation he knowingly left in his documentary Flock of Dodos. It is worthwhile to note that soon after claiming to not want to stoop to childishly satirizing the ID group (which is laughable since the whole point of the movie is to present the ID crowd as the biggest bunch of "dodos"-- pro-evolutionary figures are criticized for not making the truth accessible to the poor unwashed), Olson immediately launches into a strawman attack on ID. He has a short interview with Michael Behe that gets into a very rough analogy, and from there starts making "sub-optimal design" arguments. If one had any doubts that Wikipedia apparently winks its eye at neo-Darwinian activists, he could look at the entry for Flock of Dodos. If there was an even-handed arbitration at the site, it would have mentioned the Discovery Institute's rebuttal to the claim that Haekel's embryo drawings aren't used. Frankly, I'm surprised that it even mentions the Institute's challenge to Olson's gross disinformation about the Discovery Institute's budget (not to mention how their budget compares to the overwhelming stacks of money that fuel the pro-Darwinian evolutionary paper mill). Wiki's misleading assertion that "[t]he film gives equal air time to both sides of the argument"is enough to telegraph that Wikipedia is promoting the film as some sort of even-handed presentation. Even Eugenie Scott acknowledged that Haeckel's embryos are still used! Actually, the rise of Intelligent Design while a thorn in the NCSE's side has been good for business. In the decade leading up to 2007, the alarm bells about a coming repressive age of theocracy drove their budget from \$250,000 to \$800,000. But the NCSE is just one lobby at the forefront. The actual money driving the entrenched paradigm is the money that pays for the thousands of papers on evolutionary science that present their findings in a neo-Darwinian framework (a la Panglossian manner highlighted by Stephen Gould in his famous "Spandrels" paper). Among the "Pulled Punches" which Olson claims, he shows Jack Cashill off the top off his head echoing Wells' dates about Gould but getting the dates wrong. He says "25 years" between 1995 and when Gould last published a rebuke of the Haeckel drawings, where Wells had in mind "over 20 years" between 1977 and 1999/2000, the latter date when Gould says Haeckel's drawings are used in "many (if not most)" textbooks. Olson refutes Cashill as a strawman for Wells in "Pulled Punches" by interviewing a former student of the late Gould who cites his lambasting the drawings in a campus lecture in 1975 (criticizing the post-1914 image recycling that Flock implies never happened). Wells might be overly judgmental about Gould's relative silence on the subject (especially during the time period he was helping "pro-science" establish U.S. law on what could be said about evolution in science classes), it would be helpful if he would give the precise dates. Again, Olson later admitted that he was wrong about the drawings not being used, but that this doesn't change anything (because being a Darwin believer means never having to say you're sorry--you're still basically right no matter how the facts turn out). What is perhaps even more ironic than Olson's accusation of harping on trivialities is the idea conveyed by Flock that the acceptance of the neo-Darwinistic narrative (and with it the unquestioning acceptance of related evolutionary hypotheses as undisputed facts) is waning because evolutionary eggheads are so far above us mentally that they can't convey these truths with the sort of catchphrases and simplistic pictures/narratives that the rest of us rubes are starving for. If Olson did indeed read Icons of Evolution (and perhaps he didn't), a central point went over his head. The reason that Haeckel's drawings weren't more criticized or noticed (at least before Richardson and Gould and Wells brought them back into the light) is because of their simplicity. They make the "truth" more obvious to the poor unwashed than it would be simply presenting the facts. ## Friday, September 5, 2014 ### Randy Olson's Flock of Anti-Creationist Statism Early in his documentary Flock of Dodos, Olson starts framing the controversy as a red/blue political issue, and his entire presentation taken as a whole seems to emotively suggest an equation: ID = Creationism = Fundamentalism = Conservatism = G.W. Bush, actually promoting the divide that he is supposedly reporting on objectively. Olson seems to go out of his way to make these impressions, at one point having the camera lingering dramatically on a picture of G.W. Bush in case the viewers haven't yet associated evolution skepticism with the political divide. Early in his presentation, he suggests that there was a time that the U.S. was "red white, and blue" before dividing into just "red and blue" states. A previous post earlier this year concerned the political significance of the phrase "Bush-appointed judge"; Olson uses the phrasing "Bush appointee" to denote the plagiaristic Judge Jones. He also manages guilt-by-association (see here and here) in linking a bunch of divisive social issues to the Discovery Institute via a "tree" analogy used in the notorious "Wedge Document," and neatly avoids the question on whether the Institute takes a stand on any of these these issues. An important nuance that is lost on most anticreationists like Olson and most of the poker-playing evolutionary Ph.D.s who rail polysyllabically against the theocratic bogeymen is that the neo-Darwinist guardians of truth are the ones who have successfully used federal power to silence opposition and criticism. And yet one of these poker-playing Darwinists opines dramatically and righteously that allowing students to be misled in school threatens "the foundations of democracy." It would seem that, if true, this would mean that democracy is best served by presenting evidence for and against. Olson presents as a sort of cynical stratagem the idea that the "teach the controversy" approach has its roots in liberal ideas of pluralism and multiculturalism (which probably motivate John Angus Campbell). Olson, on this point and others, shows his alignment with the Barbara Forrest's "trojan horse" conspiratorial propaganda (see Luskin's Salvo response), which is also set up by his colleagues' concepts of Evolutionary Wars EWI and EWII, in which a town school board embraces Intelligent Design after federal intervention in squelching creationist material (or so Flock states). Yet, he never questions nor presents questions on whether there is something inherently authoritarian about centralized government control (guided, naturally, by the poker-playing elite) of what parents choose their children to learn as science. But this is nothing new to the "pro-science" lobby. Noteworthy in the movie is that Olson claims that he would have liked to have debated two of his interviewees about evolution but that they weren't sufficiently knowledgeable. Yet, he never fires his challenges at Dr. Michael Behe. ("What scientific data supports these concepts, Dr. Behe?" is never heard.) While the film admits that Behe believes generally in macro-evolution and common descent, evolutionary ecologist Randy Olson is content to leave off the interview with the Mount Rushmore analogy, as though that represents the totality of ID concepts. He doesn't present Behe with any criticisms to the mousetrap analogy, which should be a pretty simple exercise for someone as steeped in evolutionary science as Olson. Maybe Olson was afraid of "looking like a dodo." In fact, Mount Rushmore is the strawman on which Olson will base the film's summary of ID: that it is a concpet that never gets past the subjective to the quantitative. To do this, he presents Behe as somehow the leading scientific figure in ID (curiously, an evolutionist who is ironically is representative of the what Olson depicts as a fundie conservative "anti-evolution" bloc). Would it not have been extremely informative if Olson would have interviewed Behe (or someone else) who could have answered how Behe's concept of "irreducible complexity" relates to Dembski's concept of "design inferences"? Aside from confining ID to Mount Rushmore-esque impressions, Olson interviews Dr. Jonathan Wells about one aspect (I'll discuss this grievance in a later post) of the one book mentioned that doesn't even discuss the merits of Intelligent Design. Icons of Evolution is focused on the simplistic, flimsy, and misleading teachings that "explain" the Modern Synthesis to unknowing students. It is an important book because many "pro-science" advocates state that ID is unimportant to consider because of all the things neatly explained already by the Modern Synthesis. But it begs the question why Olson avoids any meat of ID theorists before he announces his verdict.	{}
Volume 334 - The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) - Poster reception Meson electromagnetic form factors from lattice QCD C. Davies,* J. Koponen, P. Lepage, A. Lytle, A. Zimermmane-Santos on behalf of HPQCD Collaboration *corresponding author Full text: pdf Published on: 2019 May 29 Abstract Lattice QCD can provide a direct determination of meson electromagnetic form factors, making predictions for upcoming experiments at Jefferson Lab. The form factors are a reflection of the bound-state nature of the meson and so these calculations give information about how confinement by QCD affects meson internal structure. The region of high squared (space-like) momentum-transfer, $Q^2$, is of particular interest because perturbative QCD predictions take a simple form in that limit that depends on the meson decay constant. We previously showed in~\cite{jonnaff} that, up to $Q^2$ of 6 $\mathrm{GeV}^2$, the form factor for a `pseudo-pion' made of strange quarks was significantly larger than the asymptotic perturbative QCD result and showed no sign of heading towards that value at higher $Q^2$. Here we give predictions for real mesons, the $K^+$ and $K^0$, in anticipation of JLAB results for the $K^+$ in the next few years. We also give results for a heavier meson, the $\eta_c$, up to $Q^2$ of 25 $\mathrm{GeV}^2$ for a comparison to perturbative QCD in a higher $Q^2$ regime. DOI: https://doi.org/10.22323/1.334.0298 Open Access	{}
# How can I prove that every maximal ideal of $B= \mathbb{Z} [(1+\sqrt{5})/2]$ is a principal? How can I prove that every maximal ideal of $B= \mathbb{Z} [(1+\sqrt{5})/2]$ is a principal? I know if I show that B has division with remainder, that means it is a Euclidean domain. It follows that B is PID, and then every maximal ideal is principal ideal in PID. However, I haven't been able to show that $B$ has division with remainder. - Do you know about Minkowski bound on ideal norms? If so, you can use that to show that the ring is a PID. – Rankeya Nov 19 '12 at 17:09 I'm curious why the question asks about maximal ideals. Any ideas? – sperners lemma Nov 19 '12 at 17:20 It is a Dedekind domain. So, all nonzero primes are maximal. – Rankeya Nov 19 '12 at 17:24 Well, I guess it's easier to prove that $B$ is factorial. Its primes must be the following: $0$, $\sqrt{5}$, $p\in\mathbb{Z}$ prime with $p\equiv \pm 2\pmod 5$ and the divisors of primes $p\in\mathbb{Z}$ with $p\equiv \pm 1\pmod 5$ which have the form $a+b(1+\sqrt{5})/2$, $a,b\in\mathbb{Z}$. – user26857 Nov 19 '12 at 17:40 I'm sorry but i am just undergraduate student. if there is anyone to show that B has division with remainder i will be happy.because it seems only way that i can understand. – susan Nov 19 '12 at 18:39 $\phi=\frac{1+\sqrt(5)}2\\ \\ \phi^n=F_n+F_{n-1}$ where $F_n$ is the $n^{th}$ fibonacci number. For any $\frac{a+b\phi}{c+d\phi}$ with $a$ and $c$ positive (if either is negative take out the factor of $-1$), $a$ and $c$ can be written uniquely as the sum of distinct fibonaccci numbers (take the largest $F_i<a$ plus the largest $F_j<(a-F_i)$ etc.), therefore the fraction can be rewritten with the numerator and denominator polynomials in $\phi$ for which all coefficients except the term in $\phi$ are $0$ or $1$. Divide top and bottom through by $\phi$ and rewrite as $\frac{a'+b'\phi}{c'+d'\phi}$. Repeating this process will eventually yield a term in $\mathbb{Z}[\phi]$ plus a remainder. - Here's a sketch --- see how it goes. Let $\alpha,\beta$ be in $B$, $\beta\ne0$. First show that $${\alpha\over\beta}=\gamma+\delta,\quad\delta=p+q\sqrt5$$ for some $\gamma$ in $B$ and some rationals $p$ and $q$, $0\le p\lt1$, $0\le q\lt1$. Consider $\delta-\epsilon$ for the following five values of $\epsilon$, all of which are in $B$: $0,1,\sqrt5,1+\sqrt5,(1+\sqrt5)/2$. Show that for at least one of these five values of $\epsilon$ the norm of $\delta-\epsilon$ is less than $1$ in absolute value (the norm of $r+s\sqrt5$ is $r^2-5s^2$). Then we have $$\alpha=(\gamma+\epsilon)\beta+(\delta-\epsilon)\beta$$ and the norm of $(\delta-\epsilon)\beta$ is the norm of $(\delta-\epsilon)$ times the norm of $\beta$, so it's less, in absolute value, than the absolute value of the norm of $\beta$. EDIT: It's done nicely in Cohn, Advanced Number Theory, pp 108-109 (with some references to earlier pages). I'll summarize. With $\alpha,\beta$ as above, rationalize the denominator and write $${\alpha\over\beta}={A_1+A_2\omega\over C}$$ with $A_1,A_2,C$ integers and $\omega=(1+\sqrt5)/2$. We want to find $\gamma=a+b\omega$ with $a,b$ integers such that $$\|N((\alpha/\beta)-\gamma)\|\lt1$$ which is to say we want $$\|N((A_1/C)-a+((A_2/C)-b)\omega)\|\lt1$$ Computing this norm, it's $$((A_1/C)-a)^2+((A_1/C)-a)((A_2/C)-b)-((A_2/C)-b)^2$$ Choose $a,b$, respectively, as the integers closest to $A_1/C,A_2/C$, respectively, and write $$P=(A_1/C)-a,\qquad Q=(A_2/C)-b$$ Then $$-1/2\le P\le1/2,\qquad-1/2\le Q\le1/2$$ and we are looking at $$f(P,Q)=P^2+PQ-Q^2$$ Now you can use calculus to show that $$\max\|f(P,Q)\|=5/16$$ given the restriction on $P,Q$, and you're done. -	{}
## A Clever Integration Trick This trick is from Integration for Engineers and Scientists by William Squire via The Handbook of Integration by Daniel Zwillinger. Noting that \frac{1}{x} = \int\limits_{0}^{\infty} \mathrm{e}^{-xt} \mathrm{d} t we can replace $$\frac{1}{x}$$ in an integrand with its integral expression and reverse the order of integration to simplify evaluation of the integrals. Of course the integral must converge uniformly to allow us to reverse the order of integration and we must have $$t>0$$. Let us use this trick to evaluate \int\limits_{0}^{\infty} \frac{\mathrm{e}^{-ax}-\mathrm{e}^{-bx}}{x} \mathrm{d} x for $$a,b > 0$$. Using our trick yields \begin{align} \int\limits_{0}^{\infty} \frac{\mathrm{e}^{-ax}-\mathrm{e}^{-bx}}{x} \mathrm{d} x & = \int\limits_{0}^{\infty}\int\limits_{0}^{\infty} \mathrm{e}^{-xt} (\mathrm{e}^{-ax}-\mathrm{e}^{-bx}) \mathrm{d} t \mathrm{d} x \\ & = \int\limits_{0}^{\infty}\int\limits_{0}^{\infty} \mathrm{e}^{-(a+t)x}-\mathrm{e}^{-(b+t)x} \mathrm{d} x \mathrm{d} t \\ & = -\int\limits_{0}^{\infty} \frac{\mathrm{e}^{-(a+t)x}}{a+t} – \frac{\mathrm{e}^{-(b+t)x}}{b+t} \|_{0}^{\infty} \mathrm{d} t \\ & = \int\limits_{0}^{\infty} \frac{1}{a+t} – \frac{1}{b+t} \mathrm{d} t \\ & = \lim_{R \to \infty} \mathrm{ln}\frac{a+t}{b+t} \|_{0}^{R} \\ & = \mathrm{ln}\left(\frac{b}{a}\right) \end{align} The conventional way to handle this integral is to recognize that it is the Frullani integral \int\limits_{0}^{\infty} \frac{f(ax) – f(bx)}{x} \mathrm{d} x = [f(\infty) – f(0)]\mathrm{ln}\left(\frac{a}{b}\right) A simple substitution yields our result. For the Frullani integral, we must have the existence of $$f(\infty)$$ and $$f(0)$$ using the appropriate limits. For other conditions on the integral as well as proofs, see 1. On Cauchy-Frullani Integrals by A. M. Ostrowski. Use DOI 10.1007/BF02568143 with Sci-Hub to access the paper. 2. On the Theorem of Frullani by Juan Arias-De-Reyna. Use DOI 10.2307/2048376 with Sci-Hub to access the paper. ## Integrate $$\int_{0}^{\infty} \frac{\mathrm{ln}(x^{2}+a^{2})}{x^{2}+b^{2}} \mathrm{d} x$$ For $$a,b > 0$$, \int\limits_{0}^{\infty} \frac{\mathrm{ln}(x^{2}+a^{2})}{x^{2}+b^{2}} \mathrm{d} x = \frac{\pi}{b} \mathrm{ln}(a+b) \label{eq:160806a1} \tag{1} appeared on page 52 of Rediscovery of Malmsten’s integrals, their evaluation by contour integration methods and some related results by Iaroslav V. Blagouchine. This is a fascinating paper with many interesting results. In future blog posts, I will present some of Blagouchine’s results and solve some of the exercise problems that he proposed. For now, I will do this integral mainly to highlight a common trick used to evaluate contour integrals with logarithms of binomials. The trick is to begin with a different integrand f(z) = \frac{\mathrm{ln}(z+ia)}{z^{2}+b^{2}} = \frac{\mathrm{ln}(z+ia)}{(z-ib)(z+ib)} \label{eq:160806a2} \tag{2} Using the following contour we note that a first order pole at $$z=ib$$ is inside of the contour so we have Res_{z=ib}[f(z)] = \frac{\mathrm{ln}(ib+ia)}{i2b} = \frac{\mathrm{ln}(i)+\mathrm{ln}(a+b)}{i2b} = \frac{i\frac{\pi}{2}+\mathrm{ln}(a+b)}{i2b} \label{eq:160806a3} \tag{3} \begin{align} \oint\limits_{C} f(z) \mathrm{d} z & = i2\pi Res_{z=ib}[f(z)] = \frac{i\pi^{2}}{2b} + \frac{\pi}{b}\mathrm{ln}(a+b) \\ & = \lim_{R \to \infty} \int\limits_{-R}^{R} f(x) \mathrm{d} x + \int\limits_{C_{1}} f(z) \mathrm{d} z \label{eq:160806a4} \tag{4} \end{align} The second integral goes to 0 via the ML estimate. The first integral will be broken in half and we use the substitution $$y=-x$$ to obtain \int\limits_{-\infty}^{0} \frac{\mathrm{ln}(x+ia)}{x^{2}+b^{2}} \mathrm{d} x = \int\limits_{0}^{\infty} \frac{\mathrm{ln}(-y+ia)}{y^{2}+b^{2}} \mathrm{d} y \label{eq:160806a5} \tag{5} Adding the two halves of the integral together, we have the following in the numerator \mathrm{ln}(-x+ia) + \mathrm{ln}(x+ia) = i\pi + \mathrm{ln}(x-ia) + \mathrm{ln}(x+ia) = \mathrm{ln}(x^{2}+a^{2}) Now we have \oint\limits_{C} f(z) \mathrm{d} z = \int\limits_{0}^{\infty} \frac{\mathrm{ln}(x^{2}+a^{2})}{x^{2}+b^{2}} \mathrm{d} x + i\pi \int\limits_{0}^{\infty} \frac{1}{x^{2}+b^{2}} \mathrm{d} x \label{eq:160806a6} \tag{6} Equating real and imaginary parts of equations \eqref{eq:160806a6} and \eqref{eq:160806a4} yields our original result plus a bonus integral \int\limits_{0}^{\infty} \frac{1}{x^{2}+b^{2}} \mathrm{d} x = \frac{\pi}{2b} which we could have obtained via the inverse tangent function. Note that the trick allowed the limits of the integral to work out with the semi circular contour and we recovered the original integrand. This is a standard trick but surprisingly I have read some complex analysis texts that do not cover it. ## Integrate $$\int_{-1}^{1}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x$$ This integral appeared in Inside Interesting Integrals by Paul Nahin in the problem set of chapter 3. Using Wolfram Alpha, we get \int\limits_{-1}^{1}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x = \pi \label{eq:1} \tag{1} Nahin suggests the following trig substitution, $$x = \cos(2y)$$. While the form of the integrand certainly does suggest that some type of trig substitution will work, let us do it with another method. If we write the integral as \int\limits_{-1}^{1} (1+x)^{\frac{1}{2}}(1-x)^{-\frac{1}{2}} \mathrm{d} x this looks like a beta function. From Higher Transcendental Functions (Bateman Manuscript), Volume 1, Section 1.5.1, equation 10, we see \mathrm{B}(x,y) = 2^{1-x-y} \int\limits_{0}^{1} (1+t)^{x-1}(1-t)^{y-1} + (1+t)^{y-1}(1-t)^{x-1} \mathrm{d} t \label{eq:2} \tag{2} Let us begin with the original integral and the right half of the interval of integration \int\limits_{0}^{1} (1+x)^{\frac{1}{2}}(1-x)^{-\frac{1}{2}} \mathrm{d} x = \int\limits_{0}^{1}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x \label{eq:3} \tag{3} Now, let us consider \int\limits_{0}^{1} (1+x)^{-\frac{1}{2}}(1-x)^{\frac{1}{2}} \mathrm{d} x = \int\limits_{0}^{1}\sqrt{\frac{1-x}{1+x}} \mathrm{d} x \label{eq:4} \tag{4} We let $$x=-y$$ to obtain -\int\limits_{0}^{-1} \sqrt{\frac{1+y}{1-y}} \mathrm{d} y, \label{eq:5} \tag{5} which we can rewrite as \int\limits_{-1}^{0}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x \label{eq:6} \tag{6} Adding the right hand side of equation \eqref{eq:3} and equation \eqref{eq:6} yields our original integral \int\limits_{-1}^{0}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x + \int\limits_{0}^{1}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x = \int\limits_{-1}^{1}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x \label{eq:7} \tag{7} Likewise, adding the left hand sides of equations \eqref{eq:4} and \eqref{eq:3} yields \int\limits_{-1}^{0}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x + \int\limits_{0}^{1}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x = \int\limits_{0}^{1} (1+x)^{-\frac{1}{2}}(1-x)^{\frac{1}{2}} \mathrm{d} x + \int\limits_{0}^{1} (1+x)^{\frac{1}{2}}(1-x)^{-\frac{1}{2}} \mathrm{d} x If we combine this result into one integral and rearrange the integrand, we see that it is the same as the integral in \eqref{eq:2} with x=\frac{3}{2} \,\, \mathrm{and} \,\, y=\frac{1}{2} Putting it all together, we have \int\limits_{-1}^{1}\sqrt{\frac{1+x}{1-x}} \mathrm{d} x = 2\mathrm{B}\left(\frac{3}{2},\frac{1}{2}\right) = \pi ## Integrate $$\int^{\infty}_{0}\frac{e^{-px^{2}} – e^{-qx^{2}}}{x^{2}} \mathrm{d}x$$ This integral appeared in Paul Nahin’s very interesting book Inside Interesting Integrals. Nahin begins with a completely different integral and derives this one. Let us evaluate the integral directly and then redo it with Nahin’s method. We begin by breaking up the integral and looking at each piece. So we have \mathrm I = \int\limits^{\infty}_{0} x^{-2}\mathrm{e}^{-px^{2}} \mathrm{d}x. This looks very similar to a definition of the gamma function: \Gamma(z) = \int\limits^{\infty}_{0} x^{z-1}\mathrm{e}^{-x} \mathrm{d}x. We make the substitution $$y = px^{2}$$ \mathrm I = \frac{\sqrt{p}}{2} \int\limits^{\infty}_{0} \mathrm{e}^{-y} y^{-\frac{3}{2}} \mathrm{d}y. Invoking the gamma function yields \mathrm I = \frac{\sqrt{p}}{2} \Gamma\Big(-\frac{1}{2}\Big) = -\sqrt{p}\sqrt{\pi}. Treating the other part of the original integral involving $$q$$ yields our final result \int\limits^{\infty}_{0}\frac{\mathrm{e}^{-px^{2}} – \mathrm{e}^{-qx^{2}}}{x^{2}} \mathrm{d}x = \sqrt{\pi}(\sqrt{q}-\sqrt{p}). As I mentioned earlier, Nahin derived this result beginning with an entirely different integral. A casual glance at the original integral should make us suspect that this is the case as it is clear that both parts of the integrand are identical. In other words, why solve the original integral as opposed to the integral that I used at the beginning of the analysis. Such is the case with many of the results in Inside Interesting Integrals. This is the result of working backward, yielding an evaluated integral via some methods as opposed to starting from an integral that one wants to evaluate. I am not criticizing this approach, as it has resulted in an enormous number of useful integral evaluations. Indeed, it can create an unlimited number of evaluated integrals. Also, such “accidental” integrals can result from contour integration even when directly attacking a given integral. Consider that it often happens that upon the last step in evaluating an integral via contour integration, one equates real and imaginary parts in which one is the solution to the original integral while the other is a bonus. Let us now see how Nahin achieved his result. He begins with \int\limits_{0}^{\infty} \mathrm{e}^{-x^{2}} \mathrm{d}x for which Nahin derived the answer of $$\frac{1}{2} \sqrt{\pi}$$ earlier in the book. What is interesting here is that this integral can be done easily with the gamma function by letting $$x^{2} = y$$. This quickly results in \int\limits_{0}^{\infty} \mathrm{e}^{-x^{2}} \mathrm{d}x = \frac{1}{2} \int\limits_{0}^{\infty} \mathrm{e}^{-y} y^{-1/2} \mathrm{d} y = \frac{1}{2} \Gamma\Big(\frac{1}{2}\Big) = \frac{1}{2} \sqrt{\pi}. If someone saw this, then they would immediately recognize that the integral sought can be evaluated via the gamma function as I did above. Nevertheless, let us continue with Nahin’s analysis. Nahin makes a change of variable, $$x = t\sqrt{a}$$ to introduce the parameter $$a$$, and thus obtains \int\limits_{0}^{\infty} \mathrm{e}^{-at^{2}} \mathrm{d}t = \frac{1}{2}\frac{\sqrt{\pi}}{\sqrt{a}} Then he invokes a useful and interesting trick. He integrates the equation with respect to $$a$$, between two arbitrary end points, and changes the order of integration. Changing the order of integration requires some care, as it is only valid if the integral converges uniformly. Here, the integral is just a gamma function, which we know converges uniformly. This is usually the case for “well behaved”, “non-crazy” integrals. So, Nahin has for the left hand side \int\limits_{p}^{q}\left\{\int\limits_{0}^{\infty} \mathrm{e}^{-at^{2}} \mathrm{d}t\right\}\mathrm{d}a = \int\limits_{0}^{\infty}\left\{\int\limits_{p}^{q}\mathrm{e}^{-at^{2}} \mathrm{d}a\right\} \mathrm{d}t = \int\limits_{0}^{\infty}\frac{\mathrm{e}^{-pt^{2}} – \mathrm{e}^{-qt^{2}}}{t^{2}} \mathrm{d}t. The right hand side yields \int\limits_{p}^{q}\frac{1}{2}\frac{\sqrt{\pi}}{\sqrt{a}} \mathrm{d}a = \sqrt{\pi}(\sqrt{q}-\sqrt{p}). And thus we have our result.	{}
Quantum Anomalies and Quantum Symmetries In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be understood in the path intergral formulation to be a result of the non-invariance of the functional measure under the classical symmetry transformation. Although the action itself is invariant, the functional measure might not be, and therefore, if that is the case the path integral wouldn't be invariant either. For further reading you can look in wikipedia. My question is: is it possible that the action wouldn't be invariant, and the measure neither, but the path integral would? That is to say, the lack of invarince of the action and the measure would cancel each other, to form an invariant path integral, in such a way that would give have a symmetry in the quantum theory, but not in the classical one. I would guess that it isn't possible, but is there a proof? • I think I have a suggestion for a proof - in order for the theory to be invariant under the suggested transformation, all correlation functions must obey the symmetry. Therefore, by relating this correlation functions to the derivative of the partition function, you get many derivatives of the action. These derivatives must be invariant under the symmetry, and therefore, if all derivatives are invariant, you would expect the action itself to be invariant too. – itamarhason Jan 25 '16 at 8:19 • Unless the action is not analytic, then there is a contraction. Maybe you could write your proof as an answer, and we could see if it makes sense or not. – Adam Jan 25 '16 at 12:16 • @Adam - will do. – itamarhason Jan 25 '16 at 15:09 • Rethinking about it, I think my "proof" is flawed because in getting the correlation functions you take the functional derivatives with respect to an auxiliary function. The fact that these derivative should vanish isn't in itself sufficient because these derivative don't encapsulate the behavior of the derivative with respect to the fields themselves, which is what I should be interested in. – itamarhason Jan 25 '16 at 15:22 • In some situations, one can have quantum anomaly cancelled by a classical anomaly (i.e. coming from the action). An example is a Chern-Simons theory on a manifold with a boundary, with chiral fermions living on the boundary. There are also situations, if I recall correctly, when a quantum anomaly in one description of the system, say, in the UV theory, is reproduced by a classical anomaly in the IR description. – Peter Kravchuk Jan 28 '16 at 9:34 1. Traditionally, the classical action $S$ sits in the Boltzmann factor $\exp\left[\frac{i}{\hbar} S\right]$ behind an inverse power of $\hbar$ in the path integral, while the path integral measure is independent of $\hbar$. In the conventional way of counting, we say that the Jacobian $J$ from the path integral measure is a one-loop effect proportional to $\hbar$, while the variation of the classical action $S$ is tree-level, i.e. independent of $\hbar$. Anyway, the upshot is, that in a usual setting, the two variations carry different $\hbar$-orders, and cannot cancel. 2. However, in principle one may introduce a quantum action $$\tag{A} W(\hbar)~=~S+ \sum_{n=1}^{\infty}\hbar^n M_n~=~ S+\hbar M_1+{\cal O}(\hbar^2)$$ with quantum terms. Then the Boltzmann factor becomes $$\tag{B} \exp\left[\frac{i}{\hbar} W\right]~=~\exp\left[\frac{i}{\hbar} S\right]e^{iM_1}(1+{\cal O}(\hbar)),$$ so that a cancellation may formally take place between the $M_1$-action factor and the path integral measure. 3. It seems appropriate to mention that such cancellation is the main idea behind the quantum master equation (QME) $$\frac{1}{2}(W,W)~=~i\hbar\Delta W\tag{QME}$$ in the Batalin-Vilkovisky formalism. The lhs. and rhs. of the above QME are associated with the action and Jacobian, respectively, leading to a (generalized) BRST symmetry of the path integral. 4. Nevertheless, in practice in a local QFT, the BV operator (aka. the odd Laplacian) $\Delta$ is singular object. The QME is typically only satisfied if both sides of the QME are zero separately, i.e. the action and the measure parts cancel separately in practical applications. References: 1. I.A. Batalin & G.A. Vilkovisky, Gauge Algebra and Quantization, Phys. Lett. B 102 (1981) 27–31. 2. W. Troost, P. van Nieuwenhuizen & A. Van Proeyen, Anomalies and the Batalin-Vilkovisky lagrangian formalism, Nucl. Phys. B333 (1990) 727. 3. nLab. • 1. I know that the variation of the measure gives a one-loop effect, but the action's variation contributes to all loops, not only to the tree-level. I mean, a variation in the action would contribute to all loops via propagators which are induced from the action. The higher-loops contributions are induced from the action. The classical picture is induce from the action via the tree-level diagrams, but the loop diagrams are also induced from the action. Maybe you mean there is a tree level variation that cannot be removed by the measure variation - this I can accept. – itamarhason Jan 25 '16 at 15:28 • I think we can reformulate your first comment in a simpler way: The measure variation is independet of $\hbar$ while the action has an $\hbar$ coefficient, so they just cannot cancel each other. – itamarhason Jan 25 '16 at 15:34 • I think comments 2, 3 and 4 are just confusing, and 1 is a good answer by itself. – itamarhason Jan 25 '16 at 15:36 • I updated the answer. – Qmechanic Jan 25 '16 at 16:07 There is a simple proof that the cancellation is impossible (at least unless you are willing to add to the classical a term proportional to $\hbar$), I am reformulating an answer by @Qmechanic in a simpler language: The anomaly, or the measure variation which is the typical source of the anomaly, contributes a term which is independent of $\hbar$, while any variation of the action comes with a $\frac{1}{\hbar}$ coefficient. Therefore, they just cannot cancel each other.	{}
# Multiplication by a simple function and compactly supported inverse Fourier transform Let $$f\in C_c^\infty$$ be a compactly supported smooth function function with support say in $$(0,1)$$. It is clear that when I multiply $$\tau$$ with $$\hat{f}(\tau)$$ (Fourier transform of $$f$$), then inverse Fourier transform of $$\tau\hat{f}(\tau)$$ is equivalent to $$g(x)=id/dx(f(x))$$ which is clearly compactly supported with the same support at the largest. How about other powers of $$\tau$$. Let's say $$F(\tau)=\tau^r\hat{f}(\tau)$$ where $$0. Is it true that inverse Fourier transform of $$F$$ has compact support. If so, how big would be the support? Many thanks! For $$k\ge 0$$, the inverse Fourier transform of $$(i\tau)^k \hat{f}$$ is $$f^{(k)}$$ which is $$C^\infty_c$$ with a support at most as large as $$f$$. This is because $$(i\tau)^k$$ is the Fourier transform of the distribution $$\delta^{(k)}$$ with support $$\{0\}$$ so the support of $$f\ast \delta^{(k)}=f^{(k)}$$ is included in that of $$f$$. The Fourier transform of a smooth compactly supported function is entire, so $$\hat{f}(\tau)$$ is entire. For $$f\ne 0$$ and $$k\ge 0$$ then $$\hat{f}(\tau)\tau^k$$ is entire iff $$k\in \Bbb{Z}_{\ge 0}$$, ie. its inverse Fourier transform is compactly supported iff $$k\in \Bbb{Z}_{\ge 0}$$. • I think you wrote this for integer $k$. My question was for fractional $r$. – Carl Lincoln Mar 10 at 15:52 • For $k$ not an integer the inverse Fourier transform is not compactly supported. – reuns Mar 10 at 15:53	{}
# Question on tensor calculation in Reimannian geometry Given a Riemannian manfiold $M$ with metric $g=(g_{i,j})$. Let $T=T_{A,B,C,\dots}^{a,b,c,\dots}$ be a tensor on $M$. I would like to compute for example $T_{A,B,C,\dots}^{a,n,c,\dots}g_{n,m}$. We know that we should sum this over $n$ and get another tensor, but where should I put the index $m$, $$T_{A,B,C,\dots,m}^{a,n,c,\dots} \ \ \text{or} \ \ \ T_{A,m,B,C,\dots}^{a,n,c,\dots}?$$ and why should it be so? I have been confused by contraction of this kind of tensors. Thanks you for your help. - Good question. I think the answer depends on what you are reading. I propose the following: $$T_{ij} = g_{ik}T^{k}_{ \ \ \ j} =g_{jl}T_{i}^{ \ \ l}= g_{ik}g_{jl}T^{kl}$$ In other words, avoid writing indices in the same space both up and down, unless you have no intention of raising and lowering said indices. This is one fix you can use in your work. One nice thing to read about these sort of convention/notation issues is Gravitation by Misner Thorn and Wheeler. - Your answer makes perfect sense. Thank you! – M. K. Sep 10 '12 at 6:00	{}
# 9.14 Image formation by lenses (Page 7/18) Page 7 / 18 ## Virtual image An image that is on the same side of the lens as the object and cannot be projected on a screen is called a virtual image. ## Image produced by a magnifying glass Suppose the book page in [link] (a) is held 7.50 cm from a convex lens of focal length 10.0 cm, such as a typical magnifying glass might have. What magnification is produced? Strategy and Concept We are given that ${d}_{\text{o}}=7\text{.}\text{50 cm}$ and $f=\text{10}\text{.}\text{0 cm}$ , so we have a situation where the object is placed closer to the lens than its focal length. We therefore expect to get a case 2 virtual image with a positive magnification that is greater than 1. Ray tracing produces an image like that shown in [link] , but we will use the thin lens equations to get numerical solutions in this example. Solution To find the magnification $m$ , we try to use magnification equation, $m={\mathrm{–d}}_{\text{i}}/{d}_{\text{o}}$ . We do not have a value for ${d}_{\text{i}}$ , so that we must first find the location of the image using lens equation. (The procedure is the same as followed in the preceding example, where ${d}_{\text{o}}$ and $f$ were known.) Rearranging the magnification equation to isolate ${d}_{\text{i}}$ gives $\frac{1}{{d}_{\text{i}}}=\frac{1}{f}-\frac{1}{{d}_{\text{o}}}\text{.}$ Entering known values, we obtain a value for $1/{d}_{\text{i}}$ : $\frac{1}{{d}_{\text{i}}}=\frac{1}{\text{10.0 cm}}-\frac{1}{7\text{.}\text{50 cm}}=\frac{-0\text{.}\text{0333}}{\text{cm}}\text{.}$ This must be inverted to find ${d}_{\text{i}}$ : ${d}_{\text{i}}=-\frac{\text{cm}}{0\text{.}\text{0333}}=-\text{30.0 cm}.$ Now the thin lens equation can be used to find the magnification $m$ , since both ${d}_{\text{i}}$ and ${d}_{\text{o}}$ are known. Entering their values gives $m=-\frac{{d}_{\text{i}}}{{d}_{\text{o}}}=-\frac{-\text{30}\text{.}0 cm}{\text{10}\text{.}0 cm}=3\text{.}\text{00.}$ Discussion A number of results in this example are true of all case 2 images, as well as being consistent with [link] . Magnification is indeed positive (as predicted), meaning the image is upright. The magnification is also greater than 1, meaning that the image is larger than the object—in this case, by a factor of 3. Note that the image distance is negative. This means the image is on the same side of the lens as the object. Thus the image cannot be projected and is virtual. (Negative values of ${d}_{\text{i}}$ occur for virtual images.) The image is farther from the lens than the object, since the image distance is greater in magnitude than the object distance. The location of the image is not obvious when you look through a magnifier. In fact, since the image is bigger than the object, you may think the image is closer than the object. But the image is farther away, a fact that is useful in correcting farsightedness, as we shall see in a later section. A third type of image is formed by a diverging or concave lens. Try looking through eyeglasses meant to correct nearsightedness. (See [link] .) You will see an image that is upright but smaller than the object. This means that the magnification is positive but less than 1. The ray diagram in [link] shows that the image is on the same side of the lens as the object and, hence, cannot be projected—it is a virtual image. Note that the image is closer to the lens than the object. This is a case 3 image, formed for any object by a negative focal length or diverging lens. are nano particles real yeah Joseph Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master? no can't Lohitha where we get a research paper on Nano chemistry....? nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review Ali what are the products of Nano chemistry? There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others.. learn Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level learn da no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts Bhagvanji hey Giriraj Preparation and Applications of Nanomaterial for Drug Delivery revolt da Application of nanotechnology in medicine has a lot of application modern world Kamaluddeen yes narayan what is variations in raman spectra for nanomaterials ya I also want to know the raman spectra Bhagvanji I only see partial conversation and what's the question here! what about nanotechnology for water purification please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment. Damian yes that's correct Professor I think Professor Nasa has use it in the 60's, copper as water purification in the moon travel. Alexandre nanocopper obvius Alexandre what is the stm is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.? Rafiq industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong Damian How we are making nano material? what is a peer What is meant by 'nano scale'? What is STMs full form? LITNING scanning tunneling microscope Sahil how nano science is used for hydrophobicity Santosh Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq Rafiq what is differents between GO and RGO? Mahi what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq Rafiq if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION Anam analytical skills graphene is prepared to kill any type viruses . Anam Any one who tell me about Preparation and application of Nanomaterial for drug Delivery Hafiz what is Nano technology ? write examples of Nano molecule? Bob The nanotechnology is as new science, to scale nanometric brayan nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale Damian Is there any normative that regulates the use of silver nanoparticles? what king of growth are you checking .? Renato Got questions? Join the online conversation and get instant answers!	{}
## LaTeX2e News This month saw a new release of LaTeX2e. The following has been changed or added: • In addition to the yyyy/mm/dd date format, LaTeX now accepts ISO 8601 format date strings in the date argument of \ProvidesPackage , \usepackage , etc. That simply means dash insted of slash. So, today can be 2017-04-17. • The new TU encoding for specifying Unicode fonts with LuaTeX and XeTeX got extended support for the dot-under accent, \d. • Verbatim environments now use a \language setting to prevent issues with fonts that were not loaded with hyphenation disabled via \hyphenchar=-1. • \- now inserts the current font’s \hyphenchar instead of a simple -. • LaTeX now supports a default document language parameter, that may be relevant to language packages such as babel. • While LaTeX normalises the baseline spacing inside a \parbox already, it now resets \lineskiplimit in addition. Regarding changes, the latexrelease package may be used to force the older behavior. The whole announcement is here. This text was posted in German on TeXwelt.de. 17. April 2017 by stefan	{}
Properties Label 2352.2.a.bd Level $2352$ Weight $2$ Character orbit 2352.a Self dual yes Analytic conductor $18.781$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$ Related objects Newspace parameters Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2352.a (trivial) Newform invariants Self dual: yes Analytic conductor: $$18.7808145554$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{2})$$ Defining polynomial: $$x^{2} - 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1176) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$ $q$-expansion Coefficients of the $$q$$-expansion are expressed in terms of $$\beta = \sqrt{2}$$. We also show the integral $$q$$-expansion of the trace form. $$f(q)$$ $$=$$ $$q + q^{3} + ( -2 + \beta ) q^{5} + q^{9} +O(q^{10})$$ $$q + q^{3} + ( -2 + \beta ) q^{5} + q^{9} + ( -2 + 2 \beta ) q^{11} + \beta q^{13} + ( -2 + \beta ) q^{15} + ( 2 - 3 \beta ) q^{17} + ( 4 + 2 \beta ) q^{19} + ( -2 - 2 \beta ) q^{23} + ( 1 - 4 \beta ) q^{25} + q^{27} + 6 \beta q^{29} + ( 8 - 2 \beta ) q^{31} + ( -2 + 2 \beta ) q^{33} + ( -4 + 4 \beta ) q^{37} + \beta q^{39} + ( 2 - \beta ) q^{41} + 8 q^{43} + ( -2 + \beta ) q^{45} + ( 4 + 2 \beta ) q^{47} + ( 2 - 3 \beta ) q^{51} + ( -2 - 8 \beta ) q^{53} + ( 8 - 6 \beta ) q^{55} + ( 4 + 2 \beta ) q^{57} + ( 8 - 2 \beta ) q^{59} + ( -4 - 7 \beta ) q^{61} + ( 2 - 2 \beta ) q^{65} + 8 q^{67} + ( -2 - 2 \beta ) q^{69} + ( -2 + 2 \beta ) q^{71} + ( 4 + 5 \beta ) q^{73} + ( 1 - 4 \beta ) q^{75} + ( 8 - 4 \beta ) q^{79} + q^{81} + ( 4 + 8 \beta ) q^{83} + ( -10 + 8 \beta ) q^{85} + 6 \beta q^{87} + ( -2 + 9 \beta ) q^{89} + ( 8 - 2 \beta ) q^{93} -4 q^{95} + ( 12 - 3 \beta ) q^{97} + ( -2 + 2 \beta ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{3} - 4q^{5} + 2q^{9} + O(q^{10})$$ $$2q + 2q^{3} - 4q^{5} + 2q^{9} - 4q^{11} - 4q^{15} + 4q^{17} + 8q^{19} - 4q^{23} + 2q^{25} + 2q^{27} + 16q^{31} - 4q^{33} - 8q^{37} + 4q^{41} + 16q^{43} - 4q^{45} + 8q^{47} + 4q^{51} - 4q^{53} + 16q^{55} + 8q^{57} + 16q^{59} - 8q^{61} + 4q^{65} + 16q^{67} - 4q^{69} - 4q^{71} + 8q^{73} + 2q^{75} + 16q^{79} + 2q^{81} + 8q^{83} - 20q^{85} - 4q^{89} + 16q^{93} - 8q^{95} + 24q^{97} - 4q^{99} + O(q^{100})$$ Embeddings For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below. For more information on an embedded modular form you can click on its label. Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$ 1.1 −1.41421 1.41421 0 1.00000 0 −3.41421 0 0 0 1.00000 0 1.2 0 1.00000 0 −0.585786 0 0 0 1.00000 0 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles Atkin-Lehner signs $$p$$ Sign $$2$$ $$1$$ $$3$$ $$-1$$ $$7$$ $$1$$ Inner twists This newform does not admit any (nontrivial) inner twists. Twists By twisting character orbit Char Parity Ord Mult Type Twist Min Dim 1.a even 1 1 trivial 2352.2.a.bd 2 3.b odd 2 1 7056.2.a.cx 2 4.b odd 2 1 1176.2.a.j 2 7.b odd 2 1 2352.2.a.bb 2 7.c even 3 2 2352.2.q.bc 4 7.d odd 6 2 2352.2.q.be 4 8.b even 2 1 9408.2.a.ds 2 8.d odd 2 1 9408.2.a.ee 2 12.b even 2 1 3528.2.a.bl 2 21.c even 2 1 7056.2.a.cg 2 28.d even 2 1 1176.2.a.o yes 2 28.f even 6 2 1176.2.q.k 4 28.g odd 6 2 1176.2.q.o 4 56.e even 2 1 9408.2.a.dg 2 56.h odd 2 1 9408.2.a.du 2 84.h odd 2 1 3528.2.a.bb 2 84.j odd 6 2 3528.2.s.bm 4 84.n even 6 2 3528.2.s.bd 4 By twisted newform orbit Twist Min Dim Char Parity Ord Mult Type 1176.2.a.j 2 4.b odd 2 1 1176.2.a.o yes 2 28.d even 2 1 1176.2.q.k 4 28.f even 6 2 1176.2.q.o 4 28.g odd 6 2 2352.2.a.bb 2 7.b odd 2 1 2352.2.a.bd 2 1.a even 1 1 trivial 2352.2.q.bc 4 7.c even 3 2 2352.2.q.be 4 7.d odd 6 2 3528.2.a.bb 2 84.h odd 2 1 3528.2.a.bl 2 12.b even 2 1 3528.2.s.bd 4 84.n even 6 2 3528.2.s.bm 4 84.j odd 6 2 7056.2.a.cg 2 21.c even 2 1 7056.2.a.cx 2 3.b odd 2 1 9408.2.a.dg 2 56.e even 2 1 9408.2.a.ds 2 8.b even 2 1 9408.2.a.du 2 56.h odd 2 1 9408.2.a.ee 2 8.d odd 2 1 Hecke kernels This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2352))$$: $$T_{5}^{2} + 4 T_{5} + 2$$ $$T_{11}^{2} + 4 T_{11} - 4$$ $$T_{13}^{2} - 2$$ $$T_{17}^{2} - 4 T_{17} - 14$$ Hecke characteristic polynomials $p$ $F_p(T)$ $2$ $$T^{2}$$ $3$ $$( -1 + T )^{2}$$ $5$ $$2 + 4 T + T^{2}$$ $7$ $$T^{2}$$ $11$ $$-4 + 4 T + T^{2}$$ $13$ $$-2 + T^{2}$$ $17$ $$-14 - 4 T + T^{2}$$ $19$ $$8 - 8 T + T^{2}$$ $23$ $$-4 + 4 T + T^{2}$$ $29$ $$-72 + T^{2}$$ $31$ $$56 - 16 T + T^{2}$$ $37$ $$-16 + 8 T + T^{2}$$ $41$ $$2 - 4 T + T^{2}$$ $43$ $$( -8 + T )^{2}$$ $47$ $$8 - 8 T + T^{2}$$ $53$ $$-124 + 4 T + T^{2}$$ $59$ $$56 - 16 T + T^{2}$$ $61$ $$-82 + 8 T + T^{2}$$ $67$ $$( -8 + T )^{2}$$ $71$ $$-4 + 4 T + T^{2}$$ $73$ $$-34 - 8 T + T^{2}$$ $79$ $$32 - 16 T + T^{2}$$ $83$ $$-112 - 8 T + T^{2}$$ $89$ $$-158 + 4 T + T^{2}$$ $97$ $$126 - 24 T + T^{2}$$	{}
6.1. Create table¶ 6.1.1. Synopsis¶ CREATE TABLE <table_name> ( [ { <column_name> <data_type> } [, ... ] ] ) [ SHARD_SIZE [=] <duration> ] 6.1.2. Description¶ CREATE TABLE will create a new table in a QuasarDB cluster with the specified schema. A special timestamp column is automatically created, which is what new data will be indexed on. 6.1.3. Parameters¶ table_name The name of the table to be created. Can be alphanumeric, but is not allowed to start with a number. column_name The name of a column to be created in the new table. Can be alphanumeric, but is not allowed to start with a number. data_type The data type to be associated with the column. Can be any of INT64, DOUBLE, BLOB or TIMESTAMP. duration The size (as time duration) of a single shard (bucket). The syntax is described in section Durations. 6.1.4. Examples¶ Create a table with only a single column: CREATE TABLE example (my_int INT64) Create a table with multiple columns: CREATE TABLE example (my_int INT64, my_double DOUBLE, my_blob BLOB, my_ts TIMESTAMP) Create a table with a custom shard size: CREATE TABLE example (my_double DOUBLE) SHARD_SIZE = 1hour 2min 3s 6. Query language 6.2. Delete from	{}
Advertisement Remove all ads # In Your Laboratory You Trace the Path of Light Rays Through a Glass Slab for Different Values of Angle of Incidence (∠i) and in Each Case Measure the Values of the Corresponding Angle of Refraction (∠r) and Angle of Emergence (∠e) - Science Advertisement Remove all ads Advertisement Remove all ads Advertisement Remove all ads In your laboratory you trace the path of light rays through a glass slab for different values of angle of incidence (∠i) and in each case measure the values of the corresponding angle of refraction (∠r) and angle of emergence (∠e). On the basis of your observations your correct conclusion is: (a) ∠i is more than ∠r, but nearly equal to ∠e (b) ∠i is less then ∠r, but nearly equal to ∠e (c) ∠i is more than ∠e, but nearly equal to ∠r (d) ∠i is less than ∠e, but nearly equal to ∠r Advertisement Remove all ads #### Solution (a) ∠i is less than ∠r but nearly equal to ∠e. On entering a glass slab, the incident light gets refracted. According to Snell’s law, we get mu=sini/sinr For glass μ > 1 ∴sinr < sini or r < i In refraction of light through a glass slab, the emergent ray is parallel to the incident ray. Thus, ∠i = ∠e. Concept: Refraction of Light Through a Rectangular Glass Slab Is there an error in this question or solution? #### Video TutorialsVIEW ALL [1] Advertisement Remove all ads Share Notifications View all notifications Forgot password?	{}
# Reference recommendation for Projective representation, group cohomology, Schur's multiplier and central extension Recently I read the chapter 2 of Weinberg's QFT vol1. I learned that in QM we need to study the projective representation of symmetry group instead of representation. It says that a Lie group can have nontrivial projective represention if the Lie group is not simple connected or the Lie algebra has nontrivial center. So for simple Lie group, the projective representation is the representation of universal covering group. But it only discuss the Lie group, so what's about the projective representation of discrete group like finite group or infinite discrete group? I heard it's related to group cohomology, Schur's multiplier and group extension. So can anyone recommend some textbooks, monographs, reviews and papers that can cover anyone of following topics which I'm interested in: How to construct all inequivalent irreducible projective representations of Lie group and Lie algebra? How to construct all inequivalent irreducible projective representations of discrete group? How are these related to central extension of group and Lie algebra ? How to construct all central extension of a group or Lie algebra? How is projective representation related to group cohomology? How to compute group cohomology? Is there some handbooks or list of group cohomology of common groups like $S_n$, point group, space group, braiding group, simple Lie group and so on? • This answer of mine answers all these questions except for "how to compute group cohomology" (and it doesn't really call $H^2$ "group cohomology", but that's what it is). – ACuriousMind May 17 '17 at 9:02 • Having book-size sources for this kind of material would still be quite valuable @ACuriousMind – Danu May 17 '17 at 12:42 • @Danu I said nothing to the contrary; I just wanted to point out that the "non-resource recommendation" version of this question basically already exists on the site, at least for some of these questions. – ACuriousMind May 17 '17 at 13:17 • @ACuriousMind Thank you. Do you know which book can discuss the theory of projective representation thoroughly and give many examples like many textbooks of group representation for physicist. – user153663 May 18 '17 at 16:59	{}
The effect of RM models on v\sin I_{\rm s} estimates # Rossiter–McLaughlin models and their effect on estimates of stellar rotation, illustrated using six WASP systems††thanks: based on observations (under proposal 090.C-0540) made using the HARPS high resolution échelle spectrograph mounted on the ESO 3.6 m at the ESO La Silla observatory, and completed by photometry obtained the Swiss 1.2m Euler Telescope, also at La Silla. D. J. A. Brown, A. H. M. J. Triaud, A. P. Doyle, M. Gillon, M. Lendl, D. R. Anderson, A. Collier Cameron, G. Hébrard C. Hellier, C. Lovis, P. F. L. Maxted, F. Pepe, D. Pollacco, D. Queloz, B. Smalley Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK. Astrophysics Research Centre, School of Mathematics & Physics, Queen’s University, University Road, Belfast BT7 1NN, UK. Centre for Planetary Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, ON M1C 1A4, Canada Department of Astronomy & Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du 6 Août 17, 4000 Liége 1, Belgium Austrian Academy of Science, Space Research Institute, Schmiedlstraße 6, A-8042 Graz, Austria Observatoire Astronomique de l’Université de Genève, Chemin des Maillettes 51, CH-1290 Sauverny, Switzerland Astrophysics Group, Keele University, Staffordshire ST5 5BG, UK. SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK. Institut d’Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, 98bis boulevard Arago, F-75014 Paris, France Observatoire de Haute Provence, CNRS/OAMP, F-04870 St Michel l’Observatoire, France. Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, UK E-mail: d.j.a.brown@warwick.ac.uk Accepted 0000 December 00. Received 0000 December 00; in original form 0000 October 00 ###### Abstract We present new measurements of the projected spin–orbit angle for six WASP hot Jupiters, four of which are new to the literature (WASP-61, -62, -76, and -78), and two of which are new analyses of previously measured systems using new data (WASP-71, and -79). We use three different models based on two different techniques: radial velocity measurements of the Rossiter–McLaughlin effect, and Doppler tomography. Our comparison of the different models reveals that they produce projected stellar rotation velocities () measurements often in disagreement with each other and with estimates obtained from spectral line broadening. The Boué model for the Rossiter–McLaughlin effect consistently underestimates the value of compared to the Hirano model. Although differed, the effect on was small for our sample, with all three methods producing values in agreement with each other. Using Doppler tomography, we find that WASP-61 b (), WASP-71 b (), and WASP-78 b () are aligned. WASP-62 b () is found to be slightly misaligned, while WASP-79 b () is confirmed to be strongly misaligned and has a retrograde orbit. We explore a range of possibilities for the orbit of WASP-76 b, finding that the orbit is likely to be strongly misaligned in the positive direction. ###### keywords: techniques: photometric – techniques: radial velocities – techniques: spectroscopic – planetary systems – stars: rotation pagerange: Rossiter–McLaughlin models and their effect on estimates of stellar rotation, illustrated using six WASP systemsthanks: based on observations (under proposal 090.C-0540) made using the HARPS high resolution échelle spectrograph mounted on the ESO 3.6 m at the ESO La Silla observatory, and completed by photometry obtained the Swiss 1.2m Euler Telescope, also at La Silla.LABEL:lastpagepubyear: 2014 ## 1 Introduction All eight planets of the Solar system orbit in approximately the same plane, the ecliptic, which is inclined to the solar equatorial plane by only (Beck & Giles, 2005). The orbital axes for the Solar system planets therefore exhibit near spin-orbit alignment with the Sun’s rotation axis (the origin of the slight divergence from true alignment is unknown). There is no guarantee, however, that this holds true for extrasolar planets, as it is known that from binary stars that spin-orbit angles can take a wide variety of values (e.g. Hube & Couch, 1982; Hale, 1994; Albrecht et al., 2007, 2009; Jensen & Akeson, 2014; Albrecht et al., 2014). Compared to such systems, measurement of the alignment angle (‘obliquity’) for an extrasolar planet is more difficult owing to the greater radius and luminosity ratios. This is compounded by the face that the host star of a close-in exoplanet generally rotates more slowly than does the primary star in a stellar binary of the same orbital period. We are also generally limited to measuring the alignment angle as projected on to the plane of the sky, generally referred to as . Measurement of the true obliquity () requires knowledge of the inclination of the stellar rotation axis to the line of sight, , an angle that is currently very difficult to measure directly. It is possible to infer a value for using knowledge of the projected stellar rotation speed, , the stellar radius, , and the stellar rotation period, (e.g. Lund et al., 2014) , but the last of these can in turn be tricky to determine (e.g. Lendl et al., 2014). HD 209458 b was the first extrasolar planet for which was measured (Queloz et al., 2000a). Since that work the number of systems for which the projected spin-orbit alignment angle has been measured or inferred has been increasing at a steady rate, and is now closing in on 100. By far the majority of these are transiting, hot Jupiter extrextrasolara-solar planets, and for most of these the value of has been modelled using the Holt–Rossiter–McLaughlin (RM) effect (Holt, 1983; Schlesinger, 1910, 1916; Rossiter, 1924; McLaughlin, 1924), the spectroscopic signature that is produced during a transit by the occultation of the red- and blue-shifted stellar hemispheres. Other, complementary methods such as Doppler tomography (DT, Collier Cameron et al. 2010a), consideration of the gravity darkening effect (e.g. Barnes, Linscott & Shporer, 2011), modelling of photometric star-spot signatures (e.g. Nutzman, Fabrycky & Fortney, 2011; Sanchis-Ojeda et al., 2011; Tregloan-Reed et al., 2015), measurement of the chromospheric RM effect in the Ca II H & K lines (Czesla et al., 2012), and analysis of photometric variability distributions (Mazeh et al., 2015) have also contributed to the tally. While the vast majority of the measurements have been made via the RM effect, the models that have been used to model this effect have changed over time, becoming more complex and incorporating more detailed physics. The first models in widespread use were those of Ohta, Taruya & Suto (2005, 2009) and Giménez (2006), but these were superseded by the more detailed models of Hirano et al. (2011) and Boué et al. (2013), which take different approaches to the problem. A recent addition to the stable of RM models is that of Baluev & Shaidulin (2015). This assortment of models means, combined with the variety of instruments with which RV measurements are made, might be introducing biases into the parameters that we measure, particularly and . These have yet to be fully explored. In this work, we present analysis of the spin-orbit alignment in six hot Jupiter systems, found by the WASP consortium (Pollacco et al., 2006), with the aim of shedding new light on the problems discussed above. We observed WASP-61 (Hellier et al., 2012); WASP-62 (Hellier et al., 2012); WASP-71 (Smith et al., 2013) WASP-76 (West et al., 2016); WASP-78 (Smalley et al., 2012), and WASP-79 (Smalley et al., 2012). These six systems were observed with HARPS under programme ID 090.C-0540 (PI Triaud). Our earlier RM observation campaigns selected systems across a wide range of parameters and aimed to increase the number of spin-orbit measurements with as few preconceptions as possible. Here, we instead selected six particular objects. At the time, Schlaufman (2010), Winn et al. (2010) and Triaud (2011) had noticed intriguing relations between some stellar parameters and the projected spin-orbit angle. Our selection of planets, orbiting stars with around 6250 K, was meant to verify these. ## 2 Methods As in Brown et al. (2012a, b), we analyse the complete set of available data for each system: WASP photometry; follow-up photometric transit data from previous studies; follow-up spectroscopic data from previous studies; newly acquired photometric transit data, and newly acquired in-transit spectroscopic measurements of the RM effect using HARPS. New data are described in the appropriates subsections of Section 3, and are available both in the appendix and online as supplementary information. Our modelling has been extensively described in previous papers from the SuperWASP collaboration (Collier Cameron et al., 2007; Pollacco et al., 2008; Brown et al., 2012b, e.g.), but we summarize the process here for new readers. Our analysis is carried out using a Markov Chain Monte Carlo (MCMC) algorithm using the Metropolis–Hastings decision maker (Metropolis et al., 1953; Hastings, 1970). Our jump parameters are listed in Table 1, and have been formulated to minimize correlations and maximize mutual orthogonality between parameters. We use , , , and to impose uniform priors on and and avoid bias towards higher values (Ford, 2006; Anderson et al., 2011). Several of our parameters (namely impact parameter, , [Fe/H], and the Boué model parameters when appropriate) are controlled by Gaussian priors by default (see Table 2). Others may be controlled by a prior if desired, see Section 2.2. At each MCMC step, we calculate models of the photometric transit (following Mandel & Algol 2002), the Keplerian RV curve, and the RM effect (see following section). Photometric data is linearly decorrelated to remove systematic trends. Limb-darkening is accounted for by a four-component, non-linear model, with wavelength appropriate coefficients derived at each MCMC step by interpolation through the tables of Claret (2000, 2004). The RV Keplerian curve, and thus the orbital elements, is primarily constrained by the existing spectroscopic data, as our new, in-transit spectroscopy covers only a small portion of the orbital phase. Quality of fit for these models is determined by calculating . Other parameters are derived at each MCMC step using standard methods. Stellar mass, for example, is calculated using the calibration of Torres et al. (2010), with updated parameters from Southworth (2011). Stellar radius is calculated from (derived directly from the transit model) and the orbital period, via Kepler’s third law. We use a burn-in phase with a minimum of 500 steps, judging the chain to be converged (and thus burn-in complete) when for that step is greater than the median of all previous values from the burn-in chain (Knutson et al., 2008). This is followed by a phase of 100 accepted steps, which are used to re-scale the error bars on the primary jump parameters, and a production run of accepted steps. Five separate chains are run, and the results concatenated to produce the final chain of length steps. The reported parameters are the median values from this final chain, with the uncertainties taken to be the values that enclose percent of the distribution. We test for convergence of our chains using the statistics of (Geweke 1992, to check inter-chain convergence) and (Gelman & Rubin 1992, to check intra-chain convergence). We also carry out additional visual checks using trace plots, autocorrelation plots, and probability distribution plots (both one- and two-dimensional). If an individual chain is found to be unconverged then we run a replacement chain, recalculating the reported parameters and convergence statistics. This process is repeated as necessary until the convergence tests indicate a fully-converged final chain. We have used the UTC time standard and Barycentric Julian Dates in our analysis. Our results are based on the equatorial solar and jovian radii, and masses, taken from Allen’s Astrophysical Quantities. ### 2.1 Modelling spin-orbit alignment Our first model for the RM effect is that of Hirano et al. (2011). This has become the de facto standard thanks to its rigourous approach to the fitting procedure, which cross-correlates an in-transit spectrum with a template, and maximizes the cross-correlation function (CCF). This method requires prior knowledge of several broadening coefficients, specifically the macroturbulence, , and the Lorentzian () and Gaussian () spectral line dispersions. For this work we assumed km s in line with Hirano et al., and also assumed that the coefficient of differential rotation, ***Whilst several of the systems under consideration are rapidly rotating, without knowledge of the inclination of their stellar rotation axes it is difficult to place a value on .. is calculated individually for each RV data set, and depends on the instrument used to collect the data as it is a function of the spectral resolution. Boué et al. (2013) pointed out that the Hirano et al. model is poorly optimized for instruments which use a CCF based approach to their data reduction. For iodine cell spectrographs (e.g. HIRES at the Keck telescope), the Hirano et al. (2011) model works well, but for the HARPS data that we obtained for our sample the Boué et al. (2013) model (as available via the AROME library) should be more appropriate. The model defines line profiles for the CCFs produced by the integrated stellar surface out-of-transit, the uncovered stellar surface during transit, and the occulted stellar surface during transit, and assumes them to be even functions. The correction needed to account for the RM effect is calculated through partial differentiation, linearization, and maximization of the likelihood function defined by fitting a Gaussian to the CCF of the uncovered stellar surface. This approach has been tested using simulated data, but has yet to be widely applied to real observations. In this paper, we will therefore compare its results to those from the two other models. To do so, we require values for the width of the Gaussian that is fit to the out-of-transit, integrated surface CCF (), and for the width of the spectral lines expected if the star were not rotating (). The latter we set equal to the instrumental profile appropriate to each datum, whilst we use the former as an additional jump parameter for our MCMC algorithm, using the average results given by the HARPS quick reduction pipeline as our initial estimate and applying a prior using that value. The DT approach was developed by Collier Cameron et al. (2010a) for analysis of hot, rapidly rotating host stars that the RM technique is unable to deal with. It has since been applied to exoplanet hosts with a range of parameters (Collier Cameron et al., 2010b; Brown et al., 2012b; Gandolfi et al., 2012; Bourrier et al., 2015). The alignment of the system is analysed through a comparison of the in-transit instrumental line profile with a model of the average out-of-transit stellar line profile. This latter model is created by the convolution of a limb-darkened stellar rotation profile, a Gaussian representing the local intrinsic line profile, and a term corresponding to the effect on the line profile of the ‘shadow’ created as the planet transits its host star. This ‘bump’ in the profile is time-variable, and moves through the stellar line profile as the planet moves from transit ingress to transit egress. Its width tells us the width, , of the local line profile, and is a free parameter. Since this width is measured independently, we can disentangle the turbulent velocity distribution of the local profile from the rotational broadening, measuring both and directly. This gives DT an advantage over spectral analysis, as although it is possible to determine the turbulent velocity using the latter method it requires spectra with very high signal-to-noise ratio (SNR). For work such as ours it is usually necessary, therefore, to assume a value for . The path of the bump is dictated by and , and as the planet moves from transit ingress to transit egress its shadow covers regions of the stellar surface with different velocities. This leads to a relation between , , and , which must fit the observed stellar line profile when the local profile and rotational profile are convolved. We thus have two equations for two unknowns ( and , as both and can be determined from the bump’s trajectory), which are therefore well determined. Since and are independently determined using this method, it has the advantage of being able to break degeneracies that can arise between these two parameters in low impact parameter systems (Brown et al., 2012b, e.g.). We note, however, that this breaks down in systems with very slow rotation, i.e. where the uncertainty on is comparable to the rotation velocity. Another advantage that is often observed with DT is the improved precision on measurements of that it provides, as seen by Bourrier et al. (2015) for the case of the rapidly rotating KOI-12 system. This method also has potential as a confirmation method for planetary candidates, as seen with the case of recent case of HATS-14 b (Hartman et al., 2015), or conversely as a false positive identifier for difficult to confirm systems. For all of these models we separate our RV measurements by instrument, and further treat spectroscopic data taken on nights featuring planetary transits as separate data sets. Our Keplerian RV model considers these separated sets of data to be independent. To account for stellar RV noise, an additional m s is added in quadrature to the out-of-transit data; this is below the level of precision of the spectrographs used for this work. ### 2.2 Exploring system architectures As in our previous work, we explore the possible solutions for each system using a combination of parameter constraints and initial conditions. We have four independent constraints that can be applied. 1. Apply a Gaussian prior on . This indirectly controls the jump parameters and . 2. Force the planet’s orbit to be circular, . This indirectly controls the jump parameters and . 3. Force the barycentric system RV to be constant with time, , neglecting long-term trends that are indicative of third bodies. 4. Force the stellar radius, , to follow a main sequence relationship with , or use the result from spectral analysis as a prior on . We consider all 16 possible combinations of these four constraints, analysing each case independently as described above. We discuss these analyses in the following sections. Once all combinations have been examined, we identify the most suitable combination by selecting that which provides the minimal value of the reduced chi-squared statistic, . This combination is then reported as the final solution for each system. ## 3 Results ### 3.1 Wasp-61 WASP-61 b orbits a solar metallicity, moderately rotating F7 star, and was initially identified using WASP-South. Follow-up observations using TRAPPIST (Jehin et al., 2011), EulerCam (see Lendl et al. 2012 for details of the instrument and data reduction procedure), and CORALIE (Queloz et al., 2000b) showed that the signal was planetary in origin (Hellier et al., 2012). The planet has a circular orbit with a period of d, and has a relatively high density of . We observed the transit on the night of 2012 December 22 using the HARPS high-precision échelle spectrograph (Mayor et al., 2003) mounted on the 3.6-m ESO telescope at La Silla. Fortuitously, we were able to simultaneously observe the same transit photometrically using EulerCam (white light; Fig. 1). We use these new data in conjunction with all of the data presented in the discovery paper (including the original SuperWASP observations) to model the system using our chosen methods. #### 3.1.1 Hirano model Trial runs with different combinations of input constraints revealed that the impact parameter of the system is low, . As expected, a degeneracy between and was observed to be present, with the distinct crescent shaped posterior probability distribution covering a wide range of angles and extending out to unphysical values of . Our km s prior restricted the values of the two parameters as expected, but we felt that it was better to allow both to vary normally given our aim of comparing the various RM models. Tests with circular and eccentric orbital solutions showed no evidence for an eccentric orbit, with the F-test of Lucy & Sweeney (1971) returning a less than percent significance for eccentricity. This is also expected, as our new near- and in-transit RV measurements do not help to constrain the orbital eccentricity. Relaxing the stellar radius constraint led to insignificant variations in stellar density (which is computed directly from the photometric light curve, and therefore is distinct from the mass and radius calculations), but for some combinations of input constraints the value of the stellar mass varied by . Tests for long-term trends in the barycentric velocity of the system returned results with strongly varying values of both positive and negative , so we set this parameter to zero for our final runs. The selected solution therefore does not apply a prior on , assumes a circular orbit, neglects the possibility of a long-term trend in RV, and neglects the stellar radius constraint. The fit to our data returns . This particular combination of applied constraints returns an projected spin-orbit alignment angle of , an impact parameter of , and a projected rotation velocity of km s, which is in agreement with the spectroscopic value of km s determined from the HARPS spectra using km s, itself derived using the calibration of Doyle et al. (2014). The RM fit produced by the best-fitting parameters is shown in Fig. 2. #### 3.1.2 Boué model Similarly to the Hirano model tests, we found no evidence for an eccentric orbit (as expected), no reason to apply a constraint on the stellar radius, and no long-term trend in . The interaction with the prior on was more interesting; with no prior the same degeneracy between and was observed, but while applying the prior restricted the range of rotational velocities explored as expected, it led to a bimodal distribution in . Examination of the posterior probability distribution for the no-prior case revealed that this was caused by the Boué model under-predicting compared to the spectroscopic value and the Hirano model, such that the prior from spectral analysis restricted the MCMC algorithm to values within the ‘tails’ of the crescent distribution. Checking posterior distributions for other parameters reveals that the MCMC chain is well converged, and our statistical convergence tests confirm this. This highlights another degeneracy in the RM modelling problem, in addition to that between and , where orbital configurations with (,) and (,) produce the same ingress and egress velocities and the same chord length (Ohta, Taruya & Suto, 2005; Fabrycky & Winn, 2009). By extension therefore these configurations are indistinguishable when considering the two-dimensional problem, and the degeneracy can only be broken by considering the true alignment angle, . This is particularly pernicious in the case of orbits with . Like Fabrycky & Winn, we limit the inclination to the range , which leads to the distribution shown in Fig. 3, with solutions close to . Ultimately, we adopt the same set of input constraints as for the Hirano model to enable strict comparison between the two models, and acquire final results of km s (consistent with, but lower than the Hirano value as expected from our tests), , and . The resulting RM fit is shown in blue in Fig. 2, which clearly indicates that the two models are fitting the same RM effect in different ways. The Boué fit exhibits steeper ingress and egress gradients, with sharper peaks at larger than the Hirano model, which visually seems to provide a better fit to the RV data although neither model fits the second half of the anomaly particularly well. Comparing their reduced values though reveals that the Boué model gives a slightly poorer fit at , compared to the Hirano model’s . #### 3.1.3 Doppler tomography We applied the same set of constraints for our DT analysis as for the other two methods: no prior on ; ; , and no constraint on the stellar radius. The stellar parameters returned were entirely consistent with those from both the Hirano and Boué models. With results of km s, , and , we find no discrepancy between DT analysis and the two other techniques for modelling the RM anomaly. The left-hand panel of Fig. 4 shows the time series of the CCFs, with the prograde signature of the planet barely visible. No sign of stellar activity is visible in the CCF residual map. Fig. 5 shows the posterior probability distributions for all three analysis methods. Interestingly, in this case tomography seems to provide little improvement in the uncertainties on the alignment angle over the Hirano or Boué models. Instead, the improvement comes in the precision of the measurement, with the uncertainty in the stellar rotation velocity reducing by approximately percent compared to the RM modelling value. This improvement arises due to the different ways in which the different methods treat the spectroscopic data. The Hirano and Boué models are analytic approximations of the behaviour of a Gaussian fit to the composite line profile. This is a valid approach when only the RV data are available, particularly when considering HARPS data as it mimics the calculations performed by the HARPS pipeline. But with the full CCF available, the tomographic method is able to treat the various components of the composite profile explicitly, and can use information from both the time-varying and time-invariant parts of the CCF directly. ### 3.2 Wasp-62 Like WASP-61 b, WASP-62 b was discovered through a combination of WASP-South, EulerCam, and Trappist photometry, in conjunction with spectroscopy from CORALIE (Hellier et al., 2012). The host star is again a solar metallicity, F7-type star, and the planet has a circular orbit of period d. WASP-62 b is rather inflated () compared to its mass (), leading to a much lower density of . Analysis of the HARPS spectra gives km s, with km s from the calibration of Doyle et al. (2014); it is these values that we use for our prior on . HARPS was used to observe the spectroscopic transit on the night of 2012 October 12. Additional RV measurements were made using the same instruments on 2012 October 15–17 to help constrain the full RV curve. We use the full set of available data to characterize the system, including the weather-affected EulerCam light curve; as Hellier et al. (2012) note, the MCMC implementation that underlies our analysis accounts for this poorer quality data. #### 3.2.1 RM modelling Trial runs to test the effect of applying the four input constraints found that there was no long-term trend in barycentric velocity, and no evidence for an eccentric orbit, with either of the two RM models. Relaxation of the stellar radius constraint led to only minor changes in the reported stellar parameters, with stellar mass and radius being entirely consistent whether the constraint was enforced or not. Unlike the WASP-61 system, the impact parameter was found to be such that no degeneracy was expected between and . This was found to be true for the Hirano model, but our examination of the posterior probability distribution produced using the Boué model showed a long tail in extending out to values that imply very rapid rotation of the host star. In general though, we again find that the Boué model underpredicts compared to the Hirano model - as compared to km s. The Boué model therefore produces larger uncertainties in the value of in order to compensate when trying to fit the RM effect. This effect can be seen in Fig. 8, with the contours for these models being completely distinct. For both models, the alignment angle value remained pleasingly consistent across the different constraint combinations. The full sets of results, which were produced from runs using no prior on , no constraint on , , and , can be found in Table 5, and show that the larger impact parameter has enabled more stringent limits to be placed on the spin-orbit alignment angle than was the case for WASP-61. Fig. 6 shows that the two models again produce dissimilarly shaped best-fitting RM models; as with WASP-61, the Boué model has steeper ingress and egress velocity gradients, and sharper peaks. However, the angles produced by the two models are entirely consistent, with the Hirano model finding and the Boué model . #### 3.2.2 Doppler tomography Using the same set of input constraints as for our RM modelling, we again carried out DT analysis of the system, finding an alignment angle of . The planetary signature of WASP-62 is much stronger than that of WASP-61, and can be seen far more clearly in the CCF time series map (Fig. 7). For this system, the tomographic method has improved the uncertainties on by roughly a factor of compared to the Boué model, but again provides little improvement over the precision afforded by the Hirano model. All three results are consistent with alignment according to the criterion of Triaud et al. (2010), a conclusion which is supported by the trajectory of the planetary signal in Fig. 7. However, this is based on an ad hoc criterion that reflects the typical uncertainty on measurements at the time that it was formulated. Work since 2010 has improved the typical uncertainty, such that this criterion is no longer really applicable. We therefore classify WASP-62 as slightly misaligned; the resolution of the planet trajectory in our Doppler map is insufficient to distinguish this from a truly aligned orbit. As with WASP-61, it is the treatment of by the three models that is interesting here. We have already noted that the Boué model returns lower values than the Hirano model, but the DT result of falls between the two whilst being consistent with neither thanks to the small error bars on all three estimates (see Fig. 8). None of the values that we find are consistent with the spectroscopic value of km s derived from the HARPS spectra. We also note that the uncertainties in using this method are smaller than for either the Hirano or Boué models (see Table 5). ### 3.3 Wasp-71 Smith et al. (2013) presented the discovery of WASP-71 b using photometry from WASP-N, WASP-South and TRAPPIST, along with spectroscopy from CORALIE that included observations during transit made simultaneously with the TRAPPIST observations. The host star was found to be an evolved F8-type, and significantly larger and more massive than the Sun, whilst the planet was found to be inflated compared to the predictions of Bodenheimer, Laughlin & Lin (2003, e.g.), and to have a circular orbit with a period of d. The spectroscopic transit observations made using CORALIE enabled Smith et al. to measure the projected spin-orbit alignment angle of the system. They found that the system was aligned, with , and rapidly rotating at km s (calculated assuming km s following Doyle et al. 2014). We obtained additional spectroscopic data on the night of 2012 October 26, observing a complete transit, with further observations made on 2012 October 23 and 25. We combine these with the discovery photometry and spectroscopy to model the system. We do not, however, include the spectroscopic transit used by Smith et al. to measure , for two reasons. The first is that we wish to obtain an independent measurement of the spin-orbit alignment. The second is that, as noted by Boué et al. (2013), different instruments can produce different signals from the same measurement owing to their different analysis routines, and therefore RM data sets from different instruments should not be combined. Analysis of our new HARPS spectra gives km s and km s. #### 3.3.1 RM modelling Using the F-test of Lucy & Sweeney (1971) we found no indication of significant eccentricity in the system, in agreement with Smith et al. (2013), and therefore set in our final analysis. We also found no consistent evidence that there is a long-term trend in barycentric velocity, so set . The interaction between , , and the stellar radius constraint is an interesting one for this system. Relaxing the constraint on causes the stellar radius to decrease by percent, with the stellar mass increasing by approximately percent. Relaxing the constraint also leads to a significant, approximately tenfold rise in the impact parameter from to , with corresponding effect on the result for , which with the radius constraint active is almost unphysically large owing to the degeneracy that arises with both and . Smith et al. (2013) report an impact parameter of , so we chose not impose the stellar radius constraint to allow the impact parameter to fit to what appears to be the more natural value. This does mean that we find a larger, less dense planet than the Smith et al. (2013) result. We also note that applying the stellar radius constraint returns a stellar effective temperature which is K hotter than previous spectroscopic values, whilst neglecting the constraint gives a temperature more consistent with previous analyses. Once again, we find that the two different methods return similar results for the alignment angle and stellar parameters, but that the Boué model gives a more slowly rotating star than is suggested by the Hirano model (see Table 5). Fig. 9 shows the best-fitting models produced by both methods, with the Hirano model (the dashed, red line) having a shallower peak during the first half of the anomaly. There is substantial scatter in the RV measurements during this period however, and the Hirano model appears to better fit the second half of the anomaly, where there is less scatter in the radial velocities. The final solutions that we report were taken from runs with no prior on , , , and no constraint applied to the stellar radius. #### 3.3.2 Doppler tomography Whereas for the two previous systems the tomographic analysis supported the Hirano model with regards to the projected rotation velocity of the host star, for WASP-71 it is the Boué model with which DT agrees (see Fig. 10), although the value of km s that we find is significantly lower than the spectroscopic value. The other parameter values that are found through DT are substantially different to either set of RM results. The impact parameter is lower, leading to a lower value of that is consistent with (see Table 5). Particularly interesting though is the difference in the physical stellar parameters found by this method, which imply a smaller star. As implied by our result of , Fig. 11 shows that the system is well characterizedaligned, in agreement with the result from Smith et al. (2013), although we are not able to significantly improve on the precision that they report. ### 3.4 Wasp-76 WASP-76 A (West et al., 2016) is another F7-type planet-hosting star, but is rotating significantly more slowly than either WASP-61 or WASP-62. The planet is substantially bloated, with a density of only , and orbits its host every days in a circular orbit. It was discovered and characterized using data from WASPSouth, TRAPPIST, EulerCam, SOPHIE (Bouchy et al., 2009; Perruchot et al., 2011), and CORALIE. HARPS was used to observe the transit taking place on 2012 November 11, and to make additional measurements on 2012 November 12–14. We combined these measurements with the discovery paper’s photometry for our analysis, excluding two spectra that were obtained at twilight. Spectral analysis of the new spectra returned km s using the calibration of Doyle et al. (2014), leading to km s. We use this for our prior on rotation velocity. The SNR of the spectra are relatively poor however, so we increased the lengths of our MCMC phases to (minimum ) for burn-in, and for the production phase, leading to a final chain length of for the concatenated chain. We also approached the analysis of this system in a different manner to the other systems in our sample. #### 3.4.1 Hirano model We began by testing the effects of constraints , , and (see Section 2.2). We found no evidence for a long-term trend in barycentric RV, so adopted the constraint for our final solution. We also set after finding no evidence for a significantly eccentric orbit. Despite the large number of photometric light curves available for the system, we found that applying the stellar radius constraint led to increases in both and . We attribute this to a combination of poor photometric coverage of the transit ingress, and significant scatter in some of the light curves (see fig. 1 of West et al. 2016). Despite the varying stellar parameters there was no compelling reason to apply the constraint, and we therefore chose not to do so for the next phase of our analysis. ##### Exploring vsinIs Initial exploratory runs with , , no radius constraint, and no prior on consistently found a small impact parameter of , in agreement with the discovery paper value of but poorly constrained. These runs produced the expected degeneracy between and , and the associated crescent-shaped posterior probability distributions (see Fig. 14). The distribution shows a slight preference for positive , but the uncertainty on the value was large. Furthermore, our Geweke and Gelman–Rubin tests implied that the MCMC chains were poorly converged. We thus applied constraint , a prior on . The addition of this constraint leads to a bimodal distribution in , with both minima being tightly constrained (see Fig. 14). Further investigation revealed that individual chains were split roughly between the positive and negative minima in space, dependent on the chain’s exploration of parameter space during the burn-in phase; this naturally led to poor convergence when analysing the concatenated MCMC chain, but inspection of trace plots, autocorrelation data, running means, and statistics from the Geweke test showed that each individual chain was well converged. We thus ran additional chains to collect five that favoured the positive minimum and five that favoured the negative minimum, and tested the convergence of the two minima. Both were found to be well converged. We also carried out tests whereby the chain was started at ; the results matched our expectations, with each chain remaining in the associated positive / negative minimum and being well converged. As with some of our modelling of the WASP-61 (see Section 3.1.2), this is an example of the degeneracy inherent in the RM problem, whereby solutions with (, ) are indistinguishable in terms of fitting the data from solutions with (, ). Interestingly, chains that explored the positive minimum consistently returned a higher value of the impact parameter than those chains that explored the negative minimum. However, in the case of the positive minimum the median impact parameter of was consistent only with the lower end of the impact parameter given in the discovery paper, , and in the case of the negative minimum the value of did not agree with discovery paper at all. ##### Impact parameter We therefore elected to explore the option of applying an additional constraint on the system, this time on the impact parameter using the value from the discovery paper as a prior. We tested the application of this prior to cases both with and without a prior on . When we applied the prior on but not the prior on , we found very similar results to those obtained in the corresponding case without the impact parameter prior, albeit with much improved convergence of our MCMC chains. The concatenated chain showed a preference for the minimum, with sizeable uncertainty on the result; the major difference with that earlier example was the more tightly constrained impact parameter distribution. Testing chains with initial alignment of showed completely consistent results with the free case, with both cases favouring the positive minimum, albeit with substantial uncertainty on . When priors on both the impact parameter and were both applied to the free case, the MCMC chains were forced into the positive minimum. The results from the concatenated chain give an impact parameter in agreement with the discovery paper’s value, and in addition provide a more precise determination of than any of the other combinations of constraints. The gave solutions in the corresponding minima, but it is notable that the impact parameter for the negative case is significantly lower than the value expected from the discovery paper. This suggests that the positive solution should be favoured. Results from these analyses are shown in Table 3. #### 3.4.2 Boué model We investigate the system using the Boué model, following the same methodology outline for the Hirano model. We again adopt a constraint of zero drift in the barycentric velocity owing to lack of evidence to the contrary. Applying the stellar radius constraint led to increases in , , , , , and , but in several cases these parameters were unphysical. There was also no substantial improvement in fit when applying the radius constraint, and we therefore elected not to do so. We also adopted a circular solution as there was no evidence for a significantly eccentric orbit. In this we match our choice of constraints for the Hirano model, which is encouraging as it again shows that the two models are broadly consistent in their exploration of parameter space. Initial tests without a prior on also produced results consistent with those found using the Hirano model, including the crescent-shaped degeneracy between and with a preference for positive , though the stellar rotation velocity was found to be even slower at km s. When we applied the prior, we found that although convergence statistics were greatly improved, and the rotation velocity now agreed with our expectations from spectral analysis, the impact parameter was significantly lower than expected, and a bimodal distribution in was obtained. When we forced , the convergence statistics were again improved and the chains explored the expected minimum, but like the Hirano model tests the impact parameter remained lower than anticipated. Applying a prior on the impact parameter, in the absence of the prior, showed that the chains favoured the positive minimum, but with sizeable uncertainty on and a slow rotation velocity. When we apply priors on both impact parameter and , we found results consistent with the Hirano model equivalents. #### 3.4.3 Doppler tomography We adopted constraints of and , but left the stellar mass and radius freely varying, in order to be consistent with our analyses using the Hirano and Boué models. As anticipated, using the DT method substantially reduced the degeneracy between and , though it did not, for this system, remove it completely (see Fig. 14). DT again favoured the positive minimum, though more strongly than the other two models, and again returned a more slowly rotating star than anticipated. Adding a prior on , however, produced different behaviour than shown previously. With DT, adding a prior on forced the chains into the negative minimum, with no bimodal distribution observed, though once again the impact parameter strongly disagreed with the value from the discovery paper and implied a central transit. If we impose a prior on the impact parameter using the value from the discovery paper, then in the absence of a prior on we again find that the chains favour the positive minimum in , irrespective of the value of . We also find a faster value of than was returned by either the Hirano or Boué models for the same combination of priors, though the values are consistent to . If we add the prior on then the results remain consistent, but the uncertainties are reduced in magnitude, particularly for which also moves closer towards a value that implies a polar orbit. #### 3.4.4 A possible polar orbit? Consecutive analyses of WASP-76 have gradually reduced our assessment of the stellar rotation velocity. Spectral analysis of the CORALIE data by West et al. (2016) gave km s, while analysis of our new HARPS spectra returned a value of km s. In the absence of a prior on rotation, our modelling of the RM effect using any of the three methods gives a value significantly slower than this, at km s. Yet inspection of both the CORALIE and HARPS spectra reveals visible rotation (see Fig. 15), and the full width at half-maximum (FWHM) of the spectra are greater than for stars with similar () colour, such as WASP-20. This would suggest that the star is indeed oriented close to edge-on, rather than the pole-on orientation suggested by the slow rotation velocity returned by our MCMC chains. We therefore consider the possibility that the orbit is oriented at close to , with a transit chord such that the path of the planet is almost parallel to the stellar rotation axis. This solution is consistent with the path of the planetary ‘bump’ through the stellar line profile in Fig. 13, which shows little movement in velocity space. To explore this possible system configuration, we carried out additional analyses both with and without a prior on , this time forcing the MCMC chain to adopt throughout. Note that these analyses used the constraints of and , and applied no constraints on the stellar mass or radius, as before. We present these results in Table 4 and Fig. 12. We found that when applying the Boué model, the MCMC chains took approximately twice as long to converge as when applying the Hirano model. The source of this difficulty with convergence is uncertain, but seems to be related to the ratio between and . Large steps in the latter that explore rapidly rotating solutions lead to unphysical values of this ratio, such that the step fails. This restricts the set of possible solutions to a more limited area of parameter space, such that a larger percentage of possible steps lead to poor solutions, and thus convergence of the chain proceeds more slowly. The three analysis techniques generally produced consistent results. In the majority of cases, we found that the value for returned by the chains was in agreement with the discovery paper; the exceptions to this were the cases with and the prior only. With the rotation prior inactive, the only case to be consistently in agreement with predictions across all three techniques was the case with prior also inactive, and ; in the other cases, the stellar rotation was generally slower than the spectral analysis result (as noted in previous sections). These results lend some small support to the hypothesis of a polar orbit, as we note that in the case of neither prior being applied the results were consistent with both spectral analysis and the discovery paper. #### 3.4.5 A poorly constrained system? WASP-76 seems to represent a similar case to WASP-1 (Albrecht et al., 2011): a low impact parameter, combined with a poor SNR for the RM effect, leading to a weak detection. Here though, we find a three-way degeneracy between , , and that can only be broken through the application of appropriate Gaussian priors. Our results show tentative support for a strongly misaligned orbit. Applying a prior on stellar rotation or on the impact parameter produces results that suggest strong misalignment, particularly when using the DT method. Forcing the system to adopt a polar orbit, or using a polar orbit as the initial condition, reveals that this is a plausible option for the system’s configuration, though there is still substantial ambiguity in the precise orientation of the planet’s orbit. Although we have reported and discussed results for cases both with and without the various combinations of these two priors, in Section 4 we focus on the case with a prior on the impact parameter, but without a prior on . This combination maximizes the relevance of our cross-system comparison by allowing the different models to evaluate stellar rotation freely, while ensuring that the other system parameters are truly representative and derived from fully converged chains; for the WASP-76 system this necessitates the prior on . We caution readers, however, that we cannot constrain the obliquity of the planet’s orbit beyond the general statement that it is likely strongly misaligned in the positive , prograde direction. ### 3.5 Wasp-78 WASP-78 b (Smalley et al., 2012) is large-radius, low-density hot Jupiter that orbits its host star every d in a circular orbit. From the CORALIE RV data in the discovery paper, the orbit appears to be circular, and such a solution is adopted therein, but the authors state that additional RV data is required to pin-down the eccentricity. Spectral analysis shows that the host star is of spectral type F8, with K, km s, and km s. We obtained new photometry using EulerCam, in both the and bands, of transits on 2012 November 2 and 26, respectively, which we combine with the discovery photometry from WASPSouth and TRAPPIST. The -band light curve shows clear modulation, almost certainly as a result of the presence of star-spots or related stellar activity features, as this modulation is not replicated in the -band light curve (Fig. 17). Our HARPS spectroscopic transit observations were made simultaneously with the -band EulerCam observations, and used in conjunction with spectroscopy from CORALIE. Analysis of the HARPS spectra provides km s, and km s. #### 3.5.1 RM modelling As with the other systems in our sample, we find no evidence of a long-term barycentric velocity trend, and set . We also find little difference in behaviour or results between the two models; the following discussion is applicable to both. When allowing eccentricity to float we find that the MCMC algorithm returns two general sets of solutions, with the Hirano and Boué models giving comparable estimates as expected. The imposition of the stellar radius constraint leads to , but forces the stellar radius to be approximately half the value presented in Smalley et al. (2012). Furthermore, examination of Fig. 18 shows that high eccentricity orbits are a very poor fit to the RV data. We do not consider these solutions plausible. When the stellar radius constraint is removed, the free eccentricity fit returns . Testing these small eccentricity solutions using the method of Lucy & Sweeney (1971) reveals that they are not significant. Comparing eccentric and circular solutions with no other constraints applied, we find that variations in physical parameters are within the uncertainties. We thus choose to force a circular orbit as it provides the most plausible solution; the phase coverage of the HARPS data is insufficient to truly constrain any small eccentricity that might be present, and the pre-existing CORALIE RV data cannot provide a firm conclusion regarding circularity (or otherwise). We also note that hot Jupiters with M are generally observed to have zero (or small) eccentricity (Anderson et al., 2012). Application of the stellar radius constraint to a circular orbit increases the reported stellar mass, and also leads to an increased value of and a lower impact parameter. Our results in this scenario agree very well with those from Smalley et al. (2012), as expected; the host star is both too massive and too large, and inconsistent with both spectral analysis of both the existing CORALIE spectra and our new HARPS data. Conversely, if the planet’s orbit is allowed to be eccentric (against the evidence), then adding the stellar radius constraint decreases the mass of both bodies, and significantly decreases their radii. We find a moderate impact parameter of , with no correlation or degeneracy between and , so do not apply a prior using the spectroscopic . Our chosen solution is therefore a circular orbit with no long-term velocity trend, and no application of the constraints on or . The full set of results is shown in Table 5, but the alignment angles found by the Hirano and Boué models are consistent with each other, and with , implying a well-aligned orbit. We do however find that the Boué model produces a slower rotation velocity, as we found for all of the previous systems, in this case inconsistent with the spectroscopic value. This cannot, however, be as a result of a poorly constrained impact parameters; the results in Table 5 show that the impact parameter returned by the Boué model is in agreement with the results from other models, and has similar uncertainties. The form of the best-fittingting models are very similar in Fig. 19, as they were for WASP-76 (the other system with a low signal-to-noise anomaly), although in this case there are far fewer data during the transit. Our selected solutions are taken from runs for which no prior was applied to , , , and no constraint was applied to the stellar radius. #### 3.5.2 Doppler tomography We apply the same set of constraints to our tomographic MCMC analysis (Fig. 20) as for the RM modelling runs. We find that all parameters are in agreement with the results from the Hirano model and the case in which no RM modelling is carried out, and that all parameters except are in agreement with the Boué model results, though we note that the disagreement there originates with the Boué model rather than DT. Unlike for some of the other systems studied herein, we find a roughly factor of improvement in the precision of our alignment angle measurement over the RM modelling methods when using tomographic analysis (see Fig. 21 and Table 5). Acquiring simultaneous photometry and spectroscopy provides us with a means to cross-check for stellar activity signatures, as any stellar activity which affects the light curve should be visible in the CCF time series map, Fig. 20. Fig. 17 shows evidence of the presence of star spots in the -band light curve, but the -band light curve that was acquired simultaneously with our HARPS spectroscopy shows only hints of similar activity. Examination of the right-hand panel of Fig. 20 is inconclusive. ### 3.6 Wasp-79 Smalley et al. (2012) found WASP-79 b to have both a low density and a large radius, and to orbit its F5-type host star in a circular orbit with a period of d. But they were unable to fully characterize the shape and duration of the transit signature owing to a lack of high-precision follow-up photometry, having access to only a single, partial transit light curve from TRAPPIST. This limited the accuracy of the physical and orbital parameters that they were able to obtain. Addison et al. (2013) measured the spin-orbit alignment angle of the system using UCLES, modelling the RM effect during transit to obtain , indicating significant misalignment. We obtained -band EulerCam observations of the transits on the nights of 2012 November 11 and December 4 (see Fig. 22), as well as spectroscopic observations of the transit on 2012 November 13 using HARPS. We also used the data from WASPSouth, TRAPPIST, and CORALIE that was presented in Smalley et al.. Spectral analysis of the HARPS spectra provides values of km s and km s that we use as our prior on the rotation velocity. We note though that the value of is extrapolated owing to the star’s effective temperature being outwith the range used for the calibration of Doyle et al. (2014). If is fixed to , then we obtain km , which effectively places an upper limit on the stellar rotation velocity of km s. #### 3.6.1 RM modelling We find no evidence for an eccentric orbit or for a long-term barycentric velocity trend, and find no difference between the stellar parameters obtained by MCMC when run with and without the stellar radius constraint. We also find no reason to apply a prior on ; the impact parameter is sufficiently large for there to be no discrepancy between and , although we do once more see a more slowly rotating star with the Boué model than with the Hirano model. In this case the Boué model is consistent with the spectroscopic rotation velocity, whilst the Hirano model seems to be over-predicting the speed of the stellar surface, even when we consider the upper limit set by the zero macroturbulence case. Of interest are the different forms of the [-] posterior probability distributions for the two models; that for the Hirano model shows a correlation between the two parameters and a more triangular shape, whilst the distribution for the Boué model is more elliptical in shape. Our selected solutions are taken from runs for which no prior was applied to , , , and no constraint was applied to the stellar radius. Both models return strongly misaligned results for the system at very high precision: for the Hirano model, and for the Boué model, in agreement with the result of Addison et al. (2013). The reason for such strong constraints are readily apparent from Fig. 23. The RM anomaly is strongly asymmetrical and comprises only positive deviation from the out-of-transit velocity. This indicates that only one half of the star, the approaching hemisphere, is being traversed by the planet, and in combination with the angle that we find suggests a near-polar orbit for the planet. #### 3.6.2 Doppler tomography Our tomographic analysis is similarly well constrained, and returns an alignment angle of , consistent with the results from both the Boué and Hirano models. What is notable however is that the uncertainties have been reduced by a factor of over the already impressive results that we obtained with those models, and are an order of magnitude better than those obtained by Addison et al. (2013). for our DT analysis falls between those of the two RM models, and is faster than the spectroscopic result, though it is in agreement with the upper limit set by the zero macroturbulence case (see Fig. 24 and Table 5). Fig. 25 again shows the strongly asymmetric signature of a misaligned polar orbit. The planetary trajectory is unlike that for any of the other five systems, being confined to one side of the stellar spectral line and moving from right to left (although any movement through the line is slight at best). This implies either a polar orbit, or a slightly retrograde one, as suggested by the value of that we obtain. ## 4 Discussion We have obtained measurements of , , and using three different analyses of the RM effect. We show these results in Table 5, along with other relevant parameters as determined from either spectral analysis of our new HARPS data (), modelling of the available photometric and RV data (, ), or isochronal fitting (, see Section 4.2). In the following discussion we will consider our results in the context of existing literature data on spin-orbit misalignment, treating the values obtained through the DT technique as definitive. We provide a more comprehensive list of parameters in Table 7 in the appendix.	{}
Subgroup structure of special linear group:SL(2,9) View subgroup structure of particular groups \| View other specific information about special linear group:SL(2,9) This article describes the subgroup structure of special linear group:SL(2,9), which is the special linear group of degree two over field:F9. The group has order 720. Family contexts Family name Parameter values General discussion of subgroup structure of family special linear group of degree two field:F9, i.e., the group $SL(2,9)$ subgroup structure of special linear group of degree two over a finite field double cover of alternating group $2 \cdot A_n$ degree $n = 6$, i.e., the group $2 \cdot A_6$ subgroup structure of double cover of alternating group Tables for quick information FACTS TO CHECK AGAINST FOR SUBGROUP STRUCTURE: (finite group) Lagrange's theorem (order of subgroup times index of subgroup equals order of whole group, so both divide it), \|order of quotient group divides order of group (and equals index of corresponding normal subgroup) Sylow subgroups exist, Sylow implies order-dominating, congruence condition on Sylow numbers\|congruence condition on number of subgroups of given prime power order normal Hall implies permutably complemented, Hall retract implies order-conjugate Quick summary Item Value number of subgroups 588 number of conjugacy classes of subgroups 27 number of automorphism classes of subgroups PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] Sylow subgroups Compare and contrast with subgroup structure of special linear group of degree two over a finite field#Sylow subgroups We are considering the group $SL(2,q)$ with $q = p^r$ a prime power, $q = 9, p = 3, r = 2$. The prime $p = 3$ is the characteristic prime. Sylow subgroups for the prime 3 The prime 3 is the characteristic prime $p$, so we compare with the general information on $p$-Sylow subgroups of $SL(2,q)$. Item Value for $SL(2,q)$, generic $q$ Value for $SL(2,9)$ (so $q = 9, p = 3, r = 2$) order of $p$-Sylow subgroup $q$ 9 index of $p$-Sylow subgroup $q^2 - 1$ 80 explicit description of one of the $p$-Sylow subgroups unitriangular matrix group of degree two: $\{ \begin{pmatrix} 1 & b \\ 0 & 1 \\\end{pmatrix} \mid b \in \mathbb{F}_q \}$ See 3-Sylow subgroup of special linear group:SL(2,9) isomorphism class of $p$-Sylow subgroup additive group of the field $\mathbb{F}_q$, which is an elementary abelian group of order $p^r$ elementary abelian group:E9 explicit description of $p$-Sylow normalizer Borel subgroup of degree two: $\{ \begin{pmatrix} a & b \\ 0 & a^{-1} \\\end{pmatrix} \mid a \in \mathbb{F}_q^\ast, b \in \mathbb{F}_q \}$ PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] isomorphism class of $p$-Sylow normalizer It is the external semidirect product of $\mathbb{F}_q$ by the multiplicative group of $\mathbb{F}_q^\ast$ where the latter acts on the former via the multiplication action of the square of the acting element. For $p = 2$ (so $q = 2,4,8,\dots$), it is isomorphic to the general affine group of degree one $GA(1,q)$. For $q = 3$, it is cyclic group:Z6 and for $q = 5$, it is dicyclic group:Dic20. order of $p$-Sylow normalizer $q(q - 1) = p^{2r} - p^r$ 72 $p$-Sylow number (i.e., number of $p$-Sylow subgroups) = index of $p$-Sylow normalizer $q + 1$ (congruent to 1 mod p, as expected from the congruence condition on Sylow numbers) 10 Sylow subgroups for the prime 2 We are in the subcase where $\ell = 2$ ($\ell$ being the prime for which we are taking Sylow subgroups) and $q \equiv 1 \pmod 8$. The value $t$ such that $2^t$ is the largest power of 2 dividing $q - 1$ is $t = 3$. Item Value for $\ell = 2, q \equiv 1 \pmod 8$ Value for $\ell = 2, t = 3, q = 9, p = 3, r = 2$ (our case) order of 2-Sylow subgroup $2^{t+1}$ 16 index of 2-Sylow subgroup $(q^3 - q)/2^{t+1}$ 45 explicit description of one of the 2-Sylow subgroups Since multiplicative group of a finite field is cyclic, $\mathbb{F}_q^\ast$ is cyclic of order $q - 1$. Let $H$ be its unique subgroup of order $2^t$. Then, the 2-Sylow subgroup is $\{ \begin{pmatrix} a & 0 \\ 0 & a^{-1} \\\end{pmatrix} \mid a \in H \} \cup \{ \begin{pmatrix} 0 & a \\ -a^{-1} & 0 \\\end{pmatrix} \mid a \in H \}$ PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] isomorphism class of 2-Sylow subgroup dicyclic group of order $2^{t + 1}$ generalized quaternion group:Q16 explicit description of 2-Sylow normalizer Same as 2-Sylow subgroup Same as 2-Sylow subgroup isomorphism class of 2-Sylow normalizer dicyclic group of order $2^{t + 1}$ generalized quaternion group:Q16 order of 2-Sylow normalizer $2^{t + 1}$ 16 2-Sylow number (i.e., number of 2-Sylow subgroups) = index of 2-Sylow normalizer $(q^3 - q)/2^{t + 1}$ 45 Sylow subgroups for the prime 5 Here, $\ell = 5$ and we are interested in the $\ell$-Sylow subgroups. We are in the subcase $\ell$ is an odd prime dividing $q + 1$. Suppose $\ell^t$ is the largest power of $\ell$ dividing $q + 1$. In our case, $t = 1$. Item Value for generic $\ell, t, p, q, r$ Value for $\ell = 5, t = 1, q = 9, p = 3, r = 2$ order of $\ell$-Sylow subgroup $\ell^t$ 5 index of $\ell$-Sylow subgroup $(q^3 - q)/\ell^t$ 144 explicit description of one of the $\ell$-Sylow subgroups Since multiplicative group of a finite field is cyclic, $\mathbb{F}_{q^2}^\ast$ is cyclic of order $q^2 - 1$. Further, via the action on a two-dimensional vector space over $\mathbb{F}_q$, we can embed $\mathbb{F}_{q^2}^\ast$ inside $GL(2,q)$. The image of the $\ell$-Sylow subgroup of $\mathbb{F}_{q^2}^\ast$ in $GL(2,q)$ actually lands inside $SL(2,q)$, and this image is a $\ell$-Sylow subgroup of $SL(2,q)$ 5-Sylow subgroup of special linear group:SL(2,9) isomorphism class of $\ell$-Sylow subgroup cyclic group of order $\ell^t$ cyclic group:Z5 explicit description of $\ell$-Sylow normalizer PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] isomorphism class of $\ell$-Sylow normalizer Case $p = 2$: dihedral group of order $2(q + 1)$ Case $p \ne 2$: dicyclic group of order $2(q + 1)$ dicyclic group:Dic20 order of $\ell$-Sylow normalizer $2(q + 1)$ 20 $\ell$-Sylow number (i.e., number of $\ell$-Sylow subgroups) = index of $\ell$-Sylow normalizer $q(q - 1)/2$ (congruent to 1 mod $\ell$, as expected from the congruence condition on Sylow numbers) 36	{}
# markov chain example problems with solutions pdf Rain Dry 0.3 0.7 0.2 0.8 • Two states : ‘Rain’ and ‘Dry’. Markov chain as a regularized optimization problem. Matrix D is not an absorbing Markov chain.has two absorbing states, S 1 and S 2, but it is never possible to get to either of those absorbing states from either S 4 or S 5. • Transition probabilities: P(‘Rain’\|‘Rain’)=0.3 , P(‘Dry’\|� /Name/F4 b) Find the three-step transition probability matrix. /Name/F2 Since we do not allow self-transitions, the jump chain must have the following transition matrix: \nonumber P = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}. x��XK��6��W�T��K$��f�@� �[�W�m��dP��;\|H��urH6 z%>f��7�J\�Ū��ۻ�ދ��Eq�,�(1�>ʊ�w! How matrix multiplication gets into the picture. The state Layer 0: Anna’s starting point (A); Layer 1: the vertices (B) connected with vertex A; Layer 2: the vertices (C) connected with vertex E; and Layer 4: Anna’s ending point (E). ... Galton brought the problem to his mathematician friend, ... this trivial solution is the only solution, so that, since the probability ρof eventual extinction satisﬁes ψ(ρ) … Transition Matrix Example. 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 • Markov chain property: probability of each subsequent state depends only on what was the previous state: • To define Markov model, the following probabilities have to be specified: transition probabilities and initial probabilities Markov Models . de nes Markov chains and goes through their main properties as well as some interesting examples of the actions that can be performed with Markov chains. The random transposition Markov chain on the permutation group SN (the set of all permutations of N cards) is a Markov chain whose transition probabilities are p(x,˙x)=1= N 2 for all transpositions ˙; p(x,y)=0 otherwise. Graphically, we have 1 2. << /FontDescriptor 20 0 R Section 2. 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 Then we can efﬁciently ﬁnd a solution to the inverse problem of a Markov chain based on the notion of natural gradient [3]. 299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 We are making a Markov chain for a bill which is being passed in parliament house. 9 0 obj To solve the problem, consider a Markov chain taking values in the set S = {i: i= 0,1,2,3,4}, where irepresents the number of umbrellas in the place where I am currently at (home or oﬃce). 0! • For the three examples of birth-and-death processes that we have considered, the system of diﬀerential-diﬀerence equations are much simpliﬁed and can therefore be solved very easily. /Font 25 0 R 1 a) Find the transition probability matrix. /BaseFont/NTMQKO+LCIRCLE10 << /Filter[/FlateDecode] The theory of (semi)-Markov processes with decision is presented interspersed with examples. We shall now give an example of a Markov chain on an countably inﬁnite state space. Marginal Distribution of Xn - Chapman-Kolmogorov Equations - Urn Sampling - Branching Processes Nuclear Reactors Family Names Not all chains are regular, but this is an important class of chains that we shall study in detail later. A company is considering using Markov theory to analyse brand switching between four different brands of breakfast cereal (brands 1, 2, 3 and 4). >> 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.8 562.5 625 312.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 There are two states in the chain and none of them are absorbing (since$\lambda_i > 0$). 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 18 0 obj We denote the states by 1 and 2, and assume there can only be transitions between the two states (i.e. The Markov property 23 2.2. 0 0.8+! x�͕Ko1��\| Find the n-step transition matrix P n for the Markov chain of Exercise 5-2. 1! 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 The material mainly comes from books of Norris, Grimmett & Stirzaker, Ross, Aldous & Fill, and Grinstead & Snell. /BaseFont/KCYWPX+LINEW10 0 800 666.7 666.7 0 1000 1000 1000 1000 0 833.3 0 0 1000 1000 1000 1000 1000 0 0 • Weather forecasting example: –Suppose tomorrow’s weather depends on today’s weather only. Let’s understand the transition matrix and the state transition matrix with an example. Solution. /Type/Font /Type/Font in the limit, as n tends to 1. in n steps, for some n. That is, given states s;t of a Markov chain M and rational r, does << Feller semigroups 34 3.1. † defn: the Markov property A discrete time and discrete state space stochastic process is Markovian if and only if Markov chains Section 1. /FirstChar 33 The conclusion of this section is the proof of a fundamental central limit theorem for Markov chains. The course assumes knowledge of basic concepts from the theory of Markov chains and Markov processes. G. W. Stewart, Introduction to the numerical solution of Markov chains, Princeton University Press, Princeton, New Jersey, 1994. [[Why are these trivial?]] For the loans example, bad loans and paid up loans are end states and hence absorbing nodes. 23 0 obj Authors: Privault, Nicolas ... 138 exercises and 9 problems with their solutions. /LastChar 195 /FirstChar 33 0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 Numerical solution of Markov chains and queueing problems Beatrice Meini Dipartimento di Matematica, Universit`a di Pisa, Italy Computational science day, Coimbra, July 23, 2004 Beatrice Meini Numerical solution of Markov chains and queueing problems. The following topics are covered: stochastic dynamic programming in problems with - nite decision horizons; the Bellman optimality principle; optimisation … 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 The outcome of the stochastic process is gener-ated in a way such that the Markov property clearly holds. >> 761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 0 0 707.2 571.2 544 544 816 816 272 The Markov chains chapter has … To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. Understanding Markov Chains Examples and Applications. 0 +! In a Markov process, various states are defined. 343.8 593.8 312.5 937.5 625 562.5 625 593.8 459.5 443.8 437.5 625 593.8 812.5 593.8 Solution. C is an absorbing Markov Chain but D is not an absorbing Markov chain. in n steps, where n is given. (a) Simple 4-connected grid of image pixels. 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 0 0 666.7 500 400 333.3 333.3 250 1000 1000 1000 750 600 500 0 250 1000 1000 1000 7. Problem 2.4 Let {Xn}n≥0 be a homogeneous Markov chain with count-able state space S and transition probabilities pij,i,j ∈ S. Let N be a random variable independent of {Xn}n≥0 with values in N0. Let’s take a simple example. 6 0 obj 593.8 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ��Tr��=�@��K�JD)� 2��s��ٮ]��&��[o{�a?&��5寤�^E_�%�$��t��Ϣ��z$]�(!�f9� c�㉘��F��(�bX�\��yDˏ��4�П��1x��T9�Q(��T�v��lF�5�W�ꝷ��D�G��v��GG��K��x�2�J�2 For example, check the matrix below. /Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 0 1 0.4 0.2 0.6 0.8 Pn = 0.7143 0.8+0.6() 0.7 n 1 ()0.4 n 0.6 1 ()0.4 n 0.8 0.6+0.8() 0.4 n 5-5. endobj /ProcSet[/PDF/Text/ImageC] Many properties of Markov chain can be identiﬁed by studying λand T. For example, the distribution of X0 is determined by λ, while the distribution of X1 is determined by λT1, etc. rE��Hƒ�\|\|I8�ݦ[��v�ܑȎ�b��Թy ��'��Ç�kY2��xQd��W�σ�8�n\�MOȜ�+dM� �� Example 6.1.1. The outcome of the stochastic process is gener-ated in a way such that the Markov property clearly holds. • Now, µ 11 = 1/π j = 4 • For this example, we expect 4 sunny days between rainy days. ꜪQ�r�S�ɇ�r�1>�,�>��m�m�$t�#��@H��4�d"��i��Ĕ�Ƿ�'��vſV��5�kW��5�ro��"�[��3� 1^Ŕ��q�� Wֻ�غM�/Ƅ��%��[ND��6��"oT��M��(qJ��k�n֢b��N��u�^X��T��L9�ړ�;��_ۦ �6"��d^��G��7��r�$7�YE�iv6��æ�̠��C�(ӳ�. 5. 25 0 obj Sample Problems for Markov Chains 1. As an example of Markov chain application, consider voting behavior. the DP solution\|as illustrated in the example below. The Markov chains chapter has been reorganized. Statement of the Basic Limit Theorem about conver-gence to stationarity. This Markov Chain problem correlates with some of the current issues in my Organization. This article will help you understand the basic idea behind Markov chains and how they can be modeled as a solution to real-world problems. You can download the paper by clicking the button above. Since we do not allow self-transitions, the jump chain must have the following transition matrix: \nonumber P = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}. /Subtype/Type1 – If i and j are recurrent and belong to different classes, then p(n) ij=0 for all n. – If j is transient, then for all i.Intuitively, the ... problem can be modeled as a 3D-Markov Chain … Every time he hits the target his confidence goes up and his probability of hitting the target the next time is 0.9. And even if all state transitions are valid, the HMM solution can still di er from the DP solution\|as illustrated in the example below. /FontDescriptor 17 0 R About the authors. Next, we present one of the most challenging aspects of HMMs, namely, the notation. 1 a) Find the transition probability matrix. Usually they are deﬂned to have also discrete time (but deﬂnitions vary slightly in textbooks). If i = 1 and it rains then I take the umbrella, move to the other place, where there are already 3 … VENUS WINS (W) VENUS AHEAD (A) VENUS BEHIND (B) p q p p q q VENUS LOSES (L) DEUCE (D) D A B … /F4 18 0 R A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain.This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves.To see the difference, consider the probability for a certain event in the game. endstream 0 0 0 0 0 0 0 0 0 0 0 0 0 0 400 400 400 400 800 800 800 800 1200 1200 0 0 1200 1200 How to simulate one. /Widths[1000 1000 1000 0 833.3 0 0 1000 1000 1000 1000 1000 1000 0 750 0 1000 0 1000 1 0.4=! Solution. >> we do not allow 1 → 1). Transition functions and Markov semigroups 30 2.4. Branching processes. Let Nn = N +n Yn = (Xn,Nn) for all n ∈ N0. Example 2. –Given today is sunny, what is the probability that the coming days are sunny, rainy, cloudy, cloudy, sunny ? We Learn Markov Chain introducrion and Transition Probability Matrix in above video.After watching full video you will able to understand1. Compactiﬁcation of Polish spaces 18 2. How can I find examples of problems to solve with hidden markov models? The state Time reversibility. 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 979.2 489.6 489.6 Applications Markov chains can be used to model situations in many fields, including biology, chemistry, economics, and physics (Lay 288). Then we can efﬁciently ﬁnd a solution to the inverse problem of a Markov chain based on the notion of natural gradient [3]. /Name/F1 Next, we present one of the most challenging aspects of HMMs, namely, the notation. ... (along with solution) /LastChar 196 1 =1! These two are said to be absorbing nodes. 1.3. The next example is another classic example of an absorbing Markov chain. All examples are in the countable state space. the book there are many new examples and problems, with solutions that use the TI-83 to eliminate the tedious details of solving linear equations by hand. Solution. Introduction to Markov chains Markov chains of M/G/1-type Algorithms for solving the power series matrix equation Quasi-Birth-Death … 254). Examples - Two States - Random Walk - Random Walk (one step at a time) - Gamblers’ Ruin - Urn Models - Branching Process 7.3. The diagram shows the transitions among the different states in a Markov Chain. Deﬁnition: The transition matrix of the Markov chain is P = (p ij). >> We will use transition matrix to solve this problem. 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 Find the stationary distribution for this chain. /Name/F3 Transition probabilities 27 2.3. /Type/Font /Subtype/Type1 Markov processes are a special class of mathematical models which are often applicable to decision problems. The following topics are covered: stochastic dynamic programming in problems … %PDF-1.2 J. Goñi, D. Duong-Tran, M. Wang Continuous Time Markov Processes CH 5 … Markov chains Markov chains are discrete state space processes that have the Markov property. Markov chain might not be a reasonable mathematical model to describe the health state of a child. Problem 2: A two-server queueing system is in a steady-state condition 0 =1!! In the next example we examine more of the mathematical details behind the concept of the solution matrix. :��.#�ash1^�ÜǑd6�e�~og�D��fsx.v��6�uY"vXmZA\�l+��M�l]��L)�i��ZY?8�{�ez�C0JQ=�k��$BU%�� Cadlag sample paths 6 1.4. Markov processes 23 2.1. 1000 666.7 500 400 333.3 333.3 250 1000 1000 1000 750 600 500 0 250 1000 1000 1000 Markov chains can be used to model situations in many fields, including biology, chemistry, economics, and physics (Lay 288). /FontDescriptor 8 0 R /FirstChar 33 � Properties analysis of inconsistency-based possibilistic similarity measures, Throughput/energy aware opportunistic transmission control in broadcast networks. << –We call it an Order-1 Markov Chain, as the transition function depends on the current state only. 700 800 900 1000 1100 1200 1300 1400 1500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 It has a sequence of steps to follow, but the end states are always either it becomes a law or it is scrapped. endobj Example 6.1.1. The probability of going to each of the states depends only on the present state and is independent of how we arrived at that state. Solution. For this type of chain, it is true that long-range predictions are independent of the starting state. 2 MARKOV CHAINS: BASIC THEORY which batteries are replaced. Markov Chains These notes contain material prepared by colleagues who have also presented this course at Cambridge, especially James Norris. The theory of (semi)-Markov processes with decision is presented interspersed with examples. 761.6 272 489.6] /FontDescriptor 11 0 R MRF problems are predominantly gridlike, but may also be irregular, as in ﬁgure 1.1(c). There are two states in the chain and none of them are absorbing (since $\lambda_i > 0$). Either pdf, ... are examples that follow discrete Markov chain. 2.2. Solutions to Problem Set #10 Problem 10.1 Determine whether or not the following matrices could be a transition matrix for a Markov chain. 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 3200 3200 3200 3600] >> c) Find the steady-state distribution of the Markov chain. /FirstChar 33 We are interested in the extinction probability ρ= P1{Gt= 0 for some t}. most commonly discussed stochastic processes is the Markov chain. the book there are many new examples and problems, with solutions that use the TI-83 to eliminate the tedious details of solving linear equations by hand. 1 =1/4 and ! A marksman is shooting at a target. Markov Chains - 9 Weather Example • What is the expected number of sunny days in between rainy days? 1600 1600 1600 1600 2000 2000 2000 2000 2400 2400 2400 2400 2800 2800 2800 2800 3200 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 A population of voters are distributed between the Democratic (D), Re-publican (R), and Independent (I) parties. (b) Grids with greater con-nectivity can be useful—for example, to achieve better geometrical detail (see discussion later)—as here with the 8-connected pixel grid. Markov chainsThe Skolem problemLinksRelated problems Markov chains Basic reachability question Can you reach a giventargetstate from a giveninitialstate with some given probability r? Consider the Markov chain shown in Figure 11.20. Is this chain irreducible? /Widths[272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 For those that are not, explain why not, and for those that are, draw a picture of the chain. In a Markov process, various states are defined. Forward and backward equations 32 3. 812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] /F2 12 0 R Weak convergence 34 3.2. A Markov chain is a model that tells us something about the probabilities of sequences of random variables, states, each of which can take on values from some set. /Length 1026 << Layer 0: Anna’s starting point (A); Layer 1: the vertices (B) connected with vertex A; Layer 2: the vertices (C) connected with vertex E; and Layer 4: Anna’s ending point (E). endobj For an overview of Markov chains in general state space, see Markov chains on a measurable state space. Markov processes are a special class of mathematical models which are often applicable to decision problems. '� [b"{! 0 =3/4. Markov processes example 1986 UG exam. View SampleProblems4.pdf from IE 301 at Özyeğin University. 1 0.4=! 1)0.2+! A.1 Markov Chains Markov chain The HMM is based on augmenting the Markov chain. /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 ��:��ߘ&}�f�hR��N�s�+�y��lS,I�1�T�e��6}�i{w bc�ҠtZ�A�渃I��ͽk\Z\W�J�Y��evMYzӘ�?۵œ��7��L� Let’s take a simple example. 1000 800 666.7 666.7 0 1000] is an example of a type of Markov chain called a regular Markov chain. Transition diagram You have … 1! It is clear from the verbal description of the process that {Gt: t≥0}is a Markov chain. If we are in state S 2, we can not leave it. This latter type of example—referred to as the “brand-switching” problem—will be used to demonstrate the principles of Markov analysis in the following discussion. /Type/Font 0 1 Sun0 Rain1 0.80.2 0.60.4! " Section 2. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 200 Is the stationary distribution a limiting distribution for the chain? The author is an associate professor from the Nanyang Technological University (NTU) and is well-established in the field of stochastic processes and a highly respected probabilist. 1 (1!! 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000 500 333.3 250 200 166.7 0 0 1000 1000 �(�W�h/g��Sn��p�u��#K��s��-��;�m�n�/J��V�l�[�� b) Find the three-step transition probability matrix. /Filter[/FlateDecode] /BaseFont/OUBZWP+CMR10 Solutions to Problem Set #10 Problem 10.1 Determine whether or not the following matrices could be a transition matrix for a Markov chain. For example, Markov analysis can be used to determine the probability that a machine will be running one day and broken down the next, or that a customer will change brands of cereal from one month to the next. D.A. endobj Bini, G. Latouche, B. Meini, Numerical Methods for Structured Markov Chains, Oxford University Press, 2005 (in press) Beatrice Meini Numerical solution of Markov chains and queueing problems For example, from state 0, it makes a transition to state 1 or state 2 with probabilities 0.5 and 0.5. \|��q~J 0 0 4 / 5 0 1/ 5 0 1 My students tell me I should just use MATLAB and maybe I will for the next edition. << View CH5_Cont_Time_Markov_Processes_Questions_with_solutions_v4.pdf from IE 336 at Purdue University. We denote the states by 1 and 2, and assume there can only be transitions between the two states (i.e. Markov chain might not be a reasonable mathematical model to describe the health state of a child. /F1 9 0 R Here we merely state the properties of its solution without proof. Page 44 2. Discrete-time Board games played with dice. = 1 is a solution to the eigenvalue equation and is therefore an eigenvalue of any transition matrix T. 6. endobj /Subtype/Type1 My students tell me I should just use MATLAB and maybe I will for the next edition. This page contains examples of Markov chains and Markov processes in action. The conclusion of this section is the proof of a fundamental central limit theorem for Markov chains. Introduction: Markov Property 7.2. The Markov property. 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 0 100 200 300 400 500 600 15 0 obj 8.4 Example: setting up the transition matrix We can create a transition matrix for any of the transition diagrams we have seen in problems throughout the course. /BaseFont/QASUYK+CMR12 continuous Markov chains... Construction3.A continuous-time homogeneous Markov chain is determined by its inﬁnitesimal transition probabilities: P ij(h) = hq ij +o(h) for j 6= 0 P ii(h) = 1−hν i +o(h) • This can be used to simulate approximate sample paths by discretizing time into small intervals (the Euler method). These sets can be words, or tags, or symbols representing anything, like the weather. 2 1 Introduction to Markov Random Fields (a) (b) (c) Figure 1.1 Graphs for Markov models in vision. 1 0.6=! (a) Show that {Yn}n≥0 is a homogeneous Markov chain, and determine the transition probabilities. stream Markov chainsThe Skolem problemLinksRelated problems Markov chains Basic reachability question Can you reach a giventargetstate from a giveninitialstate with some given probability r? /FontDescriptor 14 0 R in n steps, where n is given. Enter the email address you signed up with and we'll email you a reset link. I would recommend the book Markov Chains by Pierre Bremaud for conceptual and theoretical background. Graphically, we have 1 2. As an example of Markov chain application, consider voting behavior. Section 4. 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 MARKOV CHAINS: EXAMPLES AND APPLICATIONS assume that f(0) >0 and f(0) + f(1) <1. Markov Chains Exercise Sheet - Solutions Last updated: October 17, 2012. Sorry, preview is currently unavailable. /Widths[3600 3600 3600 4000 4000 4000 4000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Example on Markov … /Type/Font << 0 0.2+! Matrix C has two absorbing states, S 3 and S 4, and it is possible to get to state S 3 and S 4 from S 1 and S 2. << 28 0 obj The probability of going to each of the states depends only on the present state and is independent of how we arrived at that state. 750 0 1000 0 1000 0 0 0 750 0 1000 1000 0 0 1000 1000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Problem . Solutions 5-2 P = 0.95 0.05 0 0 0 0.92 0.08 0 00 01 10 00 5-4. Note that the icosahedron can be divided into 4 layers. For example, from state 0, it makes a transition to state 1 or state 2 with probabilities 0.5 and 0.5. /Subtype/Type1 A transposition is a permutation that exchanges two cards. /LastChar 196 Figure 11.20 - A state transition diagram. Then we discuss the three fundamental problems related to HMMs and give algorithms 1A Markov process of order two would depend on the two preceding states, a Markov … Consider the Markov chain that has the following (one-step) transition matrix. << Academia.edu no longer supports Internet Explorer. We shall now give an example of a Markov chain on an countably inﬁnite state space. endobj Markov Chains - 3 Some Observations About the Limi • The behavior of this important limit depends on properties of states i and j and the Markov chain as a whole. I am looking for any helpful resources on monte carlo markov chain simulation. endobj we do not allow 1 → 1). Problem: sample elements uniformly at random from set (large but finite) Ω Idea: construct an irreducible symmetric Markov Chain with states Ω and run it for sufficient time – by Theorem and Corollary, this will work Example: generate uniformly at random a feasible solution to the Knapsack Problem • First, calculate π j. Markov chain as a regularized optimization problem. +�d��6�VJ��V�c many application examples. 777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 Consider a two state continuous time Markov chain. 656.3 625 625 937.5 937.5 312.5 343.8 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 Hidden Markov chains was originally introduced and studied in the late 1960s and early ... models is discussed and some implementation issues are considered. stream For example, the DP solution must have valid state transitions, while this is not necessarily the case for the HMMs. 1 0.2=0.8! 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 Note that the icosahedron can be divided into 4 layers. Markov Chains (Discrete-Time Markov Chains) 7.1. /FirstChar 33 We will use transition matrix to solve this problem. Notice that there are exactly N 2 transpositions. An analysis of data has produced the transition matrix shown below for … 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 /BaseFont/FZXUQJ+CMBX12 /Length 623 As such, >. '�!2��s��J��NCBNB�F�d/d��NP��>C�RF!�:��T��BRط"��}��T�Ϸ��7\q~��o��)F��\|��4��T��(2J)�)��\࣎��k>�-��4�)�[�\$��+��Q�w��m��]�!�?,�� VM��Z��Ή��B��*v?x��{�X��rl��Xq��ի_ This example demonstrates how to solve a Markov Chain problem. >> For those that are not, explain why not, and for those that are, draw a picture of the chain. In this context, the sequence of random variables fSngn 0 is called a renewal process. The course assumes knowledge of basic concepts from the theory of Markov chains and Markov processes. More on Markov chains, Examples and Applications Section 1. 489.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 611.8 816 Be transitions between the two states ( i.e use transition matrix to solve with hidden Markov models is in Markov! 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# Alink ramble (22): cluster evaluation of source code analysis ## 0x00 summary Alink is a new generation of machine learning algorithm platform developed by Alibaba based on Flink, a real-time computing engine. It is the first machine learning platform in the industry to support batch algorithm and streaming algorithm at the same time. This article and the above will lead you to analyze the implementation of clustering evaluation in alink. ## 0x01 background concept ### 1.1 what is clustering Clustering, in popular words, means that birds of a feather flock together and people flock together. Clustering is observational learning, not example learning. Clustering can be used as an independent tool to obtain the distribution of data, observe the characteristics of each cluster of data, and focus on the specific cluster for further analysis. Cluster analysis can also be used as a preprocessing step for other data mining tasks (such as classification and association rules). ### 1.2 cluster analysis method Cluster analysis can be roughly divided into the following methods: Division method • Construct various partitions and then evaluate them by some criterion,e.g.,minimizing the sum of square errors • Typical methods:k-means,k-medoids,CLARANS Hierarchical approach: • Create a hierarchical decomposition of the set of data (or objects) using some criterion • Typical methods:Diana,Agnes,BIRCH,CAMELEON Density based approach: • Based on connectivity and density functions • Typical methods:DBSCAN,OPTICS,DenClue Grid based approach: • Based on multiple-level granularity structure • Typical methods:STING,WaveCluster,CLIQUE Model based approach: • A model is hypothesized for each of the clusters and tries to find the best fit of that model to each other • Typical methods:EM,SOM,COBWEB Frequent pattern based approach: • Based on the analysis of frequent patterns • Typical methods:p-Cluster Constraint based approach: • Clustering by considering user-specified or application-specific constraints • Typical methods:COD(obstacles),constrained clustering • Objects are often linked together in various ways ### 1.3 cluster evaluation Clustering evaluation estimates the feasibility of clustering on the data set and the quality of the results produced by the clustering method. Clustering evaluation mainly includes: estimating the clustering trend, determining the number of clusters in the data set, and measuring the clustering quality. Estimate clustering trend: for a given data set, evaluate whether the data set has a non random structure. Blindly using clustering methods on data sets will return some clusters, and the mined clusters may be misleading. Cluster analysis on data sets is meaningful only if there are non random structures in the data. Clustering trend evaluation determines whether a given data set has a non random structure that can lead to meaningful clustering. A data set without any non random structure, such as evenly distributed points in the data space, although the clustering algorithm can return clusters for the data set, these clusters are random and meaningless. Clustering requires non-uniform distribution of data. Measuring the clustering quality: after using the clustering method on the data set, it is necessary to evaluate the quality of the result cluster. There are two kinds of methods: external method and internal method • External method: a supervised method requires benchmark data. A certain measure is used to judge the consistency between the clustering results and the benchmark data. • Intrinsic method: an unsupervised method without baseline data. The degree of intra class aggregation and inter class dispersion. ## 0x02 evaluation indicators supported by alink Alink document is as follows: clustering evaluation is to evaluate the effect of the prediction results of clustering algorithm, and supports the following evaluation indicators. But in fact, you can find more from its test code. Compactness (CP): the lower the CP, the closer the clustering distance within the class C P i ‾ = 1 ∣ C i ∣ ∑ x ∈ C i ∥ x i − u i ∥ \overline{CP_i}=\dfrac{1}{\|C_i\|}\sum_{x \in C_i}\\|x_i-u_i\\| CPi=∣Ci∣1x∈Ci∑∥xi−ui∥ C P ‾ = 1 k ∑ i = 1 k C P k ‾ \overline{CP}=\dfrac{1}{k}\sum_{i=1}^{k}\overline{CP_k} CP=k1i=1∑kCPk Seperation (SP): the higher the SP, the farther the clustering distance between classes S P = 2 k 2 − k ∑ i = 1 k ∑ j = i + 1 k ∥ u i − u j ∥ SP=\dfrac{2}{k^2-k}\sum_{i=1}^{k}\sum_{j=i+1}^{k}\\|u_i-u_j\\| SP=k2−k2i=1∑kj=i+1∑k∥ui−uj∥ Davies bouldin index (DB). The smaller the DB, the smaller the distance within the class and the larger the distance between classes D B = 1 k ∑ i = 1 k m a x ( C P i ‾ + C P j ‾ ∥ u i − u j ∥ ) , i ≠ j DB=\dfrac{1}{k}\sum_{i=1}^{k}max(\dfrac{\overline{CP_i}+\overline{CP_j}}{\\|u_i-u_j\\|}), i \not= j DB=k1i=1∑kmax(∥ui−uj∥CPi+CPj),i=j Calinski harabasz index (VRC). The larger the VRC, the better the clustering quality S S B = ∑ i = 1 k n i ∥ u i − u ∥ 2 SSB=\sum_{i=1}^{k}n_i\\|u_i-u\\|^2 SSB=i=1∑kni∥ui−u∥2 S S W = ∑ i = 1 k ∑ x ∈ C i ∥ x i − u i ∥ SSW=\sum_{i=1}^{k}\sum_{x \in C_i}\\|x_i-u_i\\| SSW=i=1∑kx∈Ci∑∥xi−ui∥ V R C = S S B S S W ∗ N − k k − 1 VRC=\dfrac{SSB}{SSW}\dfrac{N-k}{k-1} VRC=SSWSSB∗k−1N−k From its test code, we can find more indicators: Assert.assertEquals(metrics.getCalinskiHarabaz(), 12150.00, 0.01); Assert.assertEquals(metrics.getCompactness(), 0.115, 0.01); Assert.assertEquals(metrics.getCount().intValue(), 6); Assert.assertEquals(metrics.getDaviesBouldin(), 0.014, 0.01); Assert.assertEquals(metrics.getSeperation(), 15.58, 0.01); Assert.assertEquals(metrics.getK().intValue(), 2); Assert.assertEquals(metrics.getSsb(), 364.5, 0.01); Assert.assertEquals(metrics.getSsw(), 0.119, 0.01); Assert.assertEquals(metrics.getPurity(), 1.0, 0.01); Assert.assertEquals(metrics.getNmi(), 1.0, 0.01); Assert.assertEquals(metrics.getAri(), 1.0, 0.01); Assert.assertEquals(metrics.getRi(), 1.0, 0.01); Assert.assertEquals(metrics.getSilhouetteCoefficient(), 0.99,0.01); We need to introduce several indicators ### 2.1 contour coefficient: For each object o in D, calculate: • a(o): the average distance a(o) between O and other objects in the cluster to which o belongs. • b(o): is the minimum average distance from O to all clusters without o. The contour coefficient is defined as: s ( o ) = b ( o ) − a ( o ) m a x { a ( o ) , b ( o ) } s(o)=\dfrac{b(o)-a(o)}{max\{a(o),b(o)\}} s(o)=max{a(o),b(o)}b(o)−a(o) The value of the contour coefficient is between - 1 and 1. The value of a(o) reflects the compactness of the cluster to which o belongs. The smaller the value, the more compact the cluster. The value of b(o) captures the degree of separation of O from other clusters. The larger the value of b(o), the more separated o from other clusters. When the contour coefficient of O is close to 1, the cluster containing o is compact and O is far away from other clusters, which is a desirable case. When the value of the contour coefficient is negative, this means that in the expected case, o is closer to objects in other clusters than objects in the same cluster. In many cases, this is very bad and should be avoided. ### 2.2 Calinski-Harabaz(CH) The CH index measures the compactness within the class by calculating the sum of squares of the distance between each point in the class and the center of the class, and measures the separation of the data set by calculating the sum of squares of the distance between each center point and the center point of the data set. The CH index is obtained from the ratio of separation and compactness. Thus, the larger the CH is, the closer the class itself is, and the more scattered between classes is, that is, the better clustering result. CH and contour coefficient are applicable to the case where the actual category information is unknown. ### 2.3 Davies bouldin index (Dbi) Davidson bauding index (DBI), also known as classification accuracy index, is an index proposed by David L. Davis and Donald Bouldin to evaluate the advantages and disadvantages of clustering algorithm. This DBI is to calculate the ratio of the sum of the distance within the class to the distance outside the class to optimize the selection of K value and avoid the local optimization caused by only calculating the objective function Wn in the K-means algorithm. ### 2.4 Rand index (RI), adjusted Rand index (ARI) Where C represents the actual category information, K represents the clustering result, a represents the logarithm of elements in the same category in C and K, and b represents the logarithm of elements in different categories in C and K. The RI value range is [0,1]. The larger the value, the more consistent the clustering results are with the real situation. The larger the RI, the higher the accuracy of clustering effect, and the higher the purity in each class In order to realize that "when the clustering results are generated randomly, the index should be close to zero", the Adjusted rand index is proposed, which has higher discrimination: The value range of ARI is [− 1,1]. The larger the value, the more consistent the clustering results are with the real situation. In a broad sense, ARI measures the degree of coincidence between the two data distributions. ## 0x03 example code The cluster evaluation example code is as follows: public class EvalClusterBatchOpExp { public static void main(String[] args) throws Exception { Row[] rows = new Row[] { Row.of(0, "0,0,0"), Row.of(0, "0.1,0.1,0.1"), Row.of(0, "0.2,0.2,0.2"), Row.of(1, "9,9,9"), Row.of(1, "9.1,9.1,9.1"), Row.of(1, "9.2,9.2,9.2") }; MemSourceBatchOp inOp = new MemSourceBatchOp(Arrays.asList(rows), new String[] {"label", "Y"}); KMeans train = new KMeans() .setVectorCol("Y") .setPredictionCol("pred") .setK(2); ClusterMetrics metrics = new EvalClusterBatchOp() .setPredictionCol("pred") .setVectorCol("Y") .setLabelCol("label") .collectMetrics(); System.out.println(metrics.getCalinskiHarabaz()); System.out.println(metrics.getCompactness()); System.out.println(metrics.getCount()); System.out.println(metrics.getDaviesBouldin()); System.out.println(metrics.getSeperation()); System.out.println(metrics.getK()); System.out.println(metrics.getSsb()); System.out.println(metrics.getSsw()); System.out.println(metrics.getPurity()); System.out.println(metrics.getNmi()); System.out.println(metrics.getAri()); System.out.println(metrics.getRi()); System.out.println(metrics.getSilhouetteCoefficient()); } } Output is: 12150.000000000042 0.11547005383792497 6 0.014814814814814791 15.588457268119896 2 364.5 0.1199999999999996 1.0 1.0 1.0 1.0 0.9997530305375205 ## 0x04 overall logic The overall logic of the code is as follows: • label related index calculation operation • Use calllocalpredresult to operate on each partition • flatMap 1 is to break up the Row and get Label y • flatMap 2 is to break up Row and get y_hat, so the first two steps are to get y and y_ map of hat. These two will be broadcast to CalLocalPredResult for use. • Call CalLocalPredResult to establish confusion matrix • Use reduce to merge the results of these partition operations. • Use extractparamsfromfusionmatrix to calculate purity, NMI and other indicators according to the confusion matrix • Vector related index calculation operation • Group data by category • Group and merge, and call calcclustermetricsummary to calculate vector related indicators in a distributed manner • Traverse rows and accumulate to sumVector • Loop to calculate some statistical information • Call reducebasesemetrics and merge to form a BaseMetricsSummary • Call callsilhouettecoefficiency to calculate silhouettecoefficiency • Store data as Params • Merge output • Make a union, combine labelMetrics and vectorMetrics, and then merge and output them to the final table • Grouping merging • Output to last table The specific codes are as follows: public EvalClusterBatchOp linkFrom(BatchOperator<?>... inputs) { BatchOperator in = checkAndGetFirst(inputs); String labelColName = this.getLabelCol(); String predResultColName = this.getPredictionCol(); String vectorColName = this.getVectorCol(); DistanceType distanceType = getDistanceType(); ContinuousDistance distance = distanceType.getFastDistance(); DataSet<Params> empty = MLEnvironmentFactory.get(getMLEnvironmentId()).getExecutionEnvironment().fromElements( new Params()); DataSet<Params> labelMetrics = empty, vectorMetrics; if (null != labelColName) { // For label operation // get data DataSet<Row> data = in.select(new String[] {labelColName, predResultColName}).getDataSet(); // Use calllocalpredresult to operate on each partition labelMetrics = calLocalPredResult(data) .reduce(new ReduceFunction<LongMatrix>() { // Use reduce to merge the results of these partition operations @Override public LongMatrix reduce(LongMatrix value1, LongMatrix value2) { value1.plusEqual(value2); return value1; } }) .map(new MapFunction<LongMatrix, Params>() { @Override public Params map(LongMatrix value) { // Use extractparamsfromfusionmatrix to calculate purity, NMI and other indicators according to the confusion matrix return ClusterEvaluationUtil.extractParamsFromConfusionMatrix(value); } }); } if (null != vectorColName) { // get data DataSet<Row> data = in.select(new String[] {predResultColName, vectorColName}).getDataSet(); DataSet<BaseMetricsSummary> metricsSummary = data .groupBy(0) // Group data by category .reduceGroup(new CalcClusterMetricsSummary(distance)) // Distributed computing vector related indicators .reduce(new EvaluationUtil.ReduceBaseMetrics());// Merge DataSet<Tuple1<Double>> silhouetteCoefficient = data.map( // Calculate silhouette new RichMapFunction<Row, Tuple1<Double>>() { @Override public Tuple1<Double> map(Row value) { return ClusterEvaluationUtil.calSilhouetteCoefficient(value, (ClusterMetricsSummary)list.get(0)); } .aggregate(Aggregations.SUM, 0); // Store data as Params silhouetteCoefficient, SILHOUETTE_COEFFICIENT); } else { vectorMetrics = in.select(predResultColName) .getDataSet() .reduceGroup(new BasicClusterParams()); } DataSet<Row> out = labelMetrics .union(vectorMetrics) // Combine labelMetrics and vectorMetrics .reduceGroup(new GroupReduceFunction<Params, Row>() { // Grouping merging @Override public void reduce(Iterable<Params> values, Collector<Row> out) { Params params = new Params(); for (Params p : values) { params.merge(p); } out.collect(Row.of(params.toJson())); } }); // Output to last table this.setOutputTable(DataSetConversionUtil.toTable(getMLEnvironmentId(), out, new TableSchema(new String[] {EVAL_RESULT}, new TypeInformation[] {Types.STRING}) )); return this; } ## 0x05 for label operation ### 5.1 calLocalPredResult Because there is dataset < row > data = in select(new String[] {labelColName, predResultColName}). getDataSet();， So what we're dealing with here is y and y_hat. There are two flatmaps strung together. • flatMap 1 is to break up the Row and get Label y • flatMap 2 is to break up Row and get y_hat Both flatmaps are connected with distinguishlabelindexmap and project(0). The function of distinguishlabelindexmap is to Give each label an ID, return a map of label and ID., that is, give each ID a label. project(0) is to extract the label. So the first two steps are to get y and y_ map of hat. These two will be broadcast to CalLocalPredResult for use. The third step is to call CalLocalPredResult to establish the confusion matrix. The specific codes are as follows: private static DataSet<LongMatrix> calLocalPredResult(DataSet<Row> data) { // Break up Row and get Label y DataSet<Tuple1<Map<String, Integer>>> labels = data.flatMap(new FlatMapFunction<Row, String>() { @Override public void flatMap(Row row, Collector<String> collector) { if (EvaluationUtil.checkRowFieldNotNull(row)) { collector.collect(row.getField(0).toString()); } } }).reduceGroup(new EvaluationUtil.DistinctLabelIndexMap(false, null)).project(0); // Break up Row and get y_hat DataSet<Tuple1<Map<String, Integer>>> predictions = data.flatMap(new FlatMapFunction<Row, String>() { @Override public void flatMap(Row row, Collector<String> collector) { if (EvaluationUtil.checkRowFieldNotNull(row)) { collector.collect(row.getField(1).toString()); } } }).reduceGroup(new EvaluationUtil.DistinctLabelIndexMap(false, null)).project(0); // The first two steps are to get y and y_ map of hat. These two will be broadcast to CalLocalPredResult for use // Build the confusion matrix. DataSet<LongMatrix> statistics = data .rebalance() .mapPartition(new CalLocalPredResult()) return statistics; } CalLocalPredResult establishes the confusion matrix. • In the open function, y and y are obtained from the system_ hat. • In mapPartition function, establish confusion matrix. matrix = {long[2][]@10707} 0 = {long[2]@10709} 0 = 0 1 = 0 1 = {long[2]@10710} 0 = 1 1 = 0 The code is: static class CalLocalPredResult extends RichMapPartitionFunction<Row, LongMatrix> { private Map<String, Integer> labels, predictions; @Override public void open(Configuration parameters) throws Exception { this.labels = list.get(0).f0; this.predictions = list.get(0).f0; } @Override public void mapPartition(Iterable<Row> rows, Collector<LongMatrix> collector) { long[][] matrix = new long[predictions.size()][labels.size()]; for (Row r : rows) { if (EvaluationUtil.checkRowFieldNotNull(r)) { int label = labels.get(r.getField(0).toString()); int pred = predictions.get(r.getField(1).toString()); matrix[pred][label] += 1; } } collector.collect(new LongMatrix(matrix)); } } ### 5.2 extractParamsFromConfusionMatrix Extractparamsfromfusionmatrix here is to calculate purity, NMI and other indicators according to the confusion matrix. public static Params extractParamsFromConfusionMatrix(LongMatrix longMatrix) { long[][] matrix = longMatrix.getMatrix(); long[] actualLabel = longMatrix.getColSums(); long[] predictLabel = longMatrix.getRowSums(); long total = longMatrix.getTotal(); double entropyActual = 0.0; double entropyPredict = 0.0; double mutualInfor = 0.0; double purity = 0.0; long tp = 0L; long tpFpSum = 0L; long tpFnSum = 0L; for (long anActualLabel : actualLabel) { entropyActual += entropy(anActualLabel, total); tpFpSum += combination(anActualLabel); } entropyActual /= -Math.log(2); for (long aPredictLabel : predictLabel) { entropyPredict += entropy(aPredictLabel, total); tpFnSum += combination(aPredictLabel); } entropyPredict /= -Math.log(2); for (int i = 0; i < matrix.length; i++) { long max = 0; for (int j = 0; j < matrix[0].length; j++) { max = Math.max(max, matrix[i][j]); mutualInfor += (0 == matrix[i][j] ? 0.0 : 1.0 matrix[i][j] / total * Math.log(1.0 * total * matrix[i][j] / predictLabel[i] / actualLabel[j])); tp += combination(matrix[i][j]); } purity += max; } purity /= total; mutualInfor /= Math.log(2); long fp = tpFpSum - tp; long fn = tpFnSum - tp; long totalCombination = combination(total); long tn = totalCombination - tp - fn - fp; double expectedIndex = 1.0 * tpFpSum * tpFnSum / totalCombination; double maxIndex = 1.0 * (tpFpSum + tpFnSum) / 2; double ri = 1.0 * (tp + tn) / (tp + tn + fp + fn); return new Params() .set(ClusterMetrics.NMI, 2.0 * mutualInfor / (entropyActual + entropyPredict)) .set(ClusterMetrics.PURITY, purity) .set(ClusterMetrics.RI, ri) .set(ClusterMetrics.ARI, (tp - expectedIndex) / (maxIndex - expectedIndex)); } ## 0x06 Vector related The first two steps are distributed computing and merging: DataSet<BaseMetricsSummary> metricsSummary = data .groupBy(0) .reduceGroup(new CalcClusterMetricsSummary(distance)) .reduce(new EvaluationUtil.ReduceBaseMetrics()); ### 6.1 CalcClusterMetricsSummary Clusterevaluationutil. Was called Getclusterstatistics to calculate. public static class CalcClusterMetricsSummary implements GroupReduceFunction<Row, BaseMetricsSummary> { private ContinuousDistance distance; public CalcClusterMetricsSummary(ContinuousDistance distance) { this.distance = distance; } @Override public void reduce(Iterable<Row> rows, Collector<BaseMetricsSummary> collector) { collector.collect(ClusterEvaluationUtil.getClusterStatistics(rows, distance)); } } ClusterEvaluationUtil.getClusterStatistics is as follows public static ClusterMetricsSummary getClusterStatistics(Iterable<Row> rows, ContinuousDistance distance) { List<Vector> list = new ArrayList<>(); int total = 0; String clusterId; DenseVector sumVector; Iterator<Row> iterator = rows.iterator(); Row row = null; while (iterator.hasNext() && !EvaluationUtil.checkRowFieldNotNull(row)) { // Take out the first item that is not empty row = iterator.next(); } if (EvaluationUtil.checkRowFieldNotNull(row)) { clusterId = row.getField(0).toString(); // Remove clusterId Vector vec = VectorUtil.getVector(row.getField(1)); // Take out the Vector sumVector = DenseVector.zeros(vec.size()); // initialization } else { return null; } while (null != row) { // Traverse rows and accumulate to sumVector if (EvaluationUtil.checkRowFieldNotNull(row)) { Vector vec = VectorUtil.getVector(row.getField(1)); if (distance instanceof EuclideanDistance) { sumVector.plusEqual(vec); } else { vec.scaleEqual(1.0 / vec.normL2()); sumVector.plusEqual(vec); } total++; } row = iterator.hasNext() ? iterator.next() : null; } DenseVector meanVector = sumVector.scale(1.0 / total); // Take mean // runtime variables. Here is the second set of vectors list = {ArrayList@10654} size = 3 0 = {DenseVector@10661} "9.0 9.0 9.0" 1 = {DenseVector@10662} "9.1 9.1 9.1" 2 = {DenseVector@10663} "9.2 9.2 9.2" double distanceSum = 0.0; double distanceSquareSum = 0.0; double vectorNormL2Sum = 0.0; for (Vector vec : list) { // Loop to calculate several statistics double d = distance.calc(meanVector, vec); distanceSum += d; distanceSquareSum += d * d; vectorNormL2Sum += vec.normL2Square(); } // runtime variable sumVector = {DenseVector@10656} "27.3 27.3 27.3" meanVector = {DenseVector@10657} "9.1 9.1 9.1" distanceSum = 0.34641016151377424 distanceSquareSum = 0.059999999999999575 vectorNormL2Sum = 745.3499999999999 return new ClusterMetricsSummary(clusterId, total, distanceSum / total, distanceSquareSum, vectorNormL2Sum, meanVector, distance); } ### 6.2 ReduceBaseMetrics Here, merge to form a basemetrics summary. /** * Merge the BaseMetrics calculated locally. / public static class ReduceBaseMetrics implements ReduceFunction<BaseMetricsSummary> { @Override public BaseMetricsSummary reduce(BaseMetricsSummary t1, BaseMetricsSummary t2) throws Exception { return null == t1 ? t2 : t1.merge(t2); } } ### 6.3 calSilhouetteCoefficient The third step is to call callsilhouettecoefficiency to calculate silhouettecoefficiency. vectorMetrics = metricsSummary.map(new ClusterEvaluationUtil.SaveDataAsParams()).withBroadcastSet( silhouetteCoefficient, SILHOUETTE_COEFFICIENT); Here is the same treatment as the formula public static Tuple1<Double> calSilhouetteCoefficient(Row row, ClusterMetricsSummary clusterMetricsSummary) { if (!EvaluationUtil.checkRowFieldNotNull(row)) { return Tuple1.of(0.); } String clusterId = row.getField(0).toString(); Vector vec = VectorUtil.getVector(row.getField(1)); double currentClusterDissimilarity = 0.0; double neighboringClusterDissimilarity = Double.MAX_VALUE; if (clusterMetricsSummary.distance instanceof EuclideanDistance) { double normSquare = vec.normL2Square(); for (int i = 0; i < clusterMetricsSummary.k; i++) { double dissimilarity = clusterMetricsSummary.clusterCnt.get(i) normSquare - 2 * clusterMetricsSummary.clusterCnt.get(i) * MatVecOp.dot(vec, clusterMetricsSummary.meanVector.get(i)) + clusterMetricsSummary.vectorNormL2Sum.get(i); if (clusterId.equals(clusterMetricsSummary.clusterId.get(i))) { if (clusterMetricsSummary.clusterCnt.get(i) > 1) { currentClusterDissimilarity = dissimilarity / (clusterMetricsSummary.clusterCnt.get(i) - 1); } } else { neighboringClusterDissimilarity = Math.min(neighboringClusterDissimilarity, dissimilarity / clusterMetricsSummary.clusterCnt.get(i)); } } } else { for (int i = 0; i < clusterMetricsSummary.k; i++) { double dissimilarity = 1.0 - MatVecOp.dot(vec, clusterMetricsSummary.meanVector.get(i)); if (clusterId.equals(clusterMetricsSummary.clusterId.get(i))) { if (clusterMetricsSummary.clusterCnt.get(i) > 1) { currentClusterDissimilarity = dissimilarity * clusterMetricsSummary.clusterCnt.get(i) / (clusterMetricsSummary.clusterCnt.get(i) - 1); } } else { neighboringClusterDissimilarity = Math.min(neighboringClusterDissimilarity, dissimilarity); } } } return Tuple1.of(currentClusterDissimilarity < neighboringClusterDissimilarity ? 1 - (currentClusterDissimilarity / neighboringClusterDissimilarity) : (neighboringClusterDissimilarity / currentClusterDissimilarity) - 1); } ### 6.4 SaveDataAsParams The fourth step is to store the data as Params public static class SaveDataAsParams extends RichMapFunction<BaseMetricsSummary, Params> { @Override public Params map(BaseMetricsSummary t) throws Exception { Params params = t.toMetrics().getParams(); EvalClusterBatchOp.SILHOUETTE_COEFFICIENT); params.set(ClusterMetrics.SILHOUETTE_COEFFICIENT, silhouetteCoefficient.get(0).f0 / params.get(ClusterMetrics.COUNT)); return params; } } ## 0x06 merge output In this step, a union is made to combine labelMetrics and vectorMetrics, and then merge and output them to the final table. DataSet<Row> out = labelMetrics .union(vectorMetrics) .reduceGroup(new GroupReduceFunction<Params, Row>() { @Override public void reduce(Iterable<Params> values, Collector<Row> out) { Params params = new Params(); for (Params p : values) { params.merge(p); } out.collect(Row.of(params.toJson())); } }); this.setOutputTable(DataSetConversionUtil.toTable(getMLEnvironmentId(), out, new TableSchema(new String[] {EVAL_RESULT}, new TypeInformation[] {Types.STRING}) )); ## 0xFF reference Clustering algorithm and its evaluation index [ML] clustering evaluation index Evaluation index of clustering results Cluster evaluation index How to evaluate the clustering results? Clustering evaluation algorithm - contour coefficient Evaluation index of clustering effect ARI clustering effect evaluation index Evaluation index of clustering algorithm -- Davies bouldin index (Dbi) [weekly blog] on Davies bouldin index (DBI) Evaluation index of clustering algorithm Performance evaluation index of clustering model ★★★★★★★ thinking about life and technology ★★★★★★ Wechat public account: Rossi's thinking You can scan the following QR code (or long press the identification QR code) to follow the personal official account if you want to get the message push of personal articles written in time, or want to see the technical data recommended by individuals. Posted by chenci on Sat, 14 May 2022 16:31:35 +0300	{}
# A question about flat connection Let $E\to X$ be a complex flat vector bundle, and say $\nabla_0$ and $\nabla_1$ are two flat connections on it. Let $p:X\times[0, 1]\to X$ denote the projection onto the first factor. Is there a way to construct a flat connection $\tilde{\nabla}$ on $p^E\to X\times[0, 1]$ such that $\tilde{\nabla}\|_{X\times 0}=\nabla_0$ and $\tilde{\nabla}\|_{X\times 1}=\nabla_1$? If this is impossible, then is it possible to construct a (not necessarily flat) connection $\nabla'$ on $p^E\to X\times[0, 1]$ such that $\tilde{\nabla}\|_{X\times 0}=\nabla_0$, $\tilde{\nabla}\|_{X\times 1}=\nabla_1$ and $\textrm{ch}(\nabla')=$ the rank of $p^E\to X\times[0, 1]$? Here $\textrm{ch}(\nabla')$ is the Chern character form of $\nabla'$. Thanks. - The second question leads to secondary characteristic classes. Assuming $\nabla'=\tilde\nabla$ is any connection on $X\times[0,1]$ restricting to $\nabla_i$ on $X\times\{i\}$, $i\in\{0,1\}$, its Chern-Simons form is defined as $$\widetilde{\mathrm{ch}}(\tilde\nabla)=\int_0^1\mathrm{ch}(\tilde\nabla)\in\Omega^{\mathrm{odd}}(X;\mathbb C)\;.$$ It is closed if $\nabla_0$, $\nabla_1$ are flat. In this case, its cohomology class $\widetilde{\mathrm{ch}}(\nabla^0,\nabla^1)=[\widetilde{\mathrm{ch}}(\tilde\nabla)]\in H^{\mathrm{odd}}(X;\mathbb C)$ is independent of the choice of $\tilde\nabla$ (subject only to the boundary conditions above). If $\widetilde{\mathrm{ch}}(\nabla^0,\nabla^1)$ does not vanish, the answer to your second question is no. If it does vanish, there could still be other obstructions. - First of all thank you for your answers. Let me change my question a little bit. Let say I have only one flat connection $\nabla$ on $E\to X$. Can I construct a flat connection $\tilde{\nabla}$ on $p^E\to X\times[0, 1]$ such that $\tilde{\nabla}\|_{X\times 0}=\nabla$ and $\tilde{\nabla}\|_{X\times t}$ is any arbitrary flat connection for $0<t\leq 1$ and $\tilde{\nabla}\|_{X\times 1}$ is not $\nabla$? That means I just want to specify one flat connection. – index theory Feb 21 at 17:14 Yes, you can, if $\tilde\nabla$ itself is not flat. Easiest example: take $X=S^1$, then all connections are flat. But you can distinguish them by their holonomy, which can be any element in $GL(r,\mathbb C)$, where $r$ is the rank. If the holonomies of $\nabla_0$ and $\nabla_1$ are not conjugate, the flat connections are not isomorphic. Higher dimensional examples can be constructed using paths in the representation variety of $\pi_1(X)$. If $\tilde\nabla$ is flat, then all $\nabla_t$ are isomorphic (use parallel translation in $t$-direction to see this). – Sebastian Goette Feb 21 at 17:33 It is an instructive exercise to compute the number $\tilde{\mathrm{ch}}(\nabla^0,\nabla^1)[S^1]$ explicitly for two flat connections on $S^1\times\mathbb C\to S^1$. – Sebastian Goette Feb 21 at 17:41 Thanks, I see. Actually I really need $\tilde{\nabla}$ to be a flat connection. The real question behind this is the Riemann-Roch-Grothendieck theorem for complex flat vector bundle by Bismut-Lott. I know that you also have some work on it. In the imaginary part of this theorem, it is very interesting to me that the real analytic torsion form does not depend on the flat connection on $F\to X$, in contrast to the Bismut-Cheeger eta form which depends on more data. – index theory Feb 21 at 18:13 I mean if we look at the statement of the RRG for two flat connections, then the difference between $\displaystyle\textrm{Im(CCS)}(H(Z, F\|_Z), \nabla_k^{H(Z, F\|_Z)})-\int_{X/B}e(TZ, \nabla^{TZ})\cup\textrm{Im(CCS)}(F, \nabla_k^F)$ for $k=0, 1$ is the exterior differential of the same $T$. And I don't know whether it makes sense to say that the path joining two flat connections is not necessarily flat makes RGG theorem to be harder to prove than other secondary index theorems. In the above comment I meant $\tilde{\eta}$ also depends on $\nabla^E$, although it doesn't have to be flat. – index theory Feb 21 at 18:20 The answer to your first question is of course no. For a counter example, it is enough to consider ordinary closed 1-forms, and you see that a necessary condition for the positive answer would be that all periods of both forms are the same. In the higher rank case, periods are replaced by the monodromy. More concretely (after Anton Petrunin's comment): Consider the case of $S^1=\mathbb R/2\pi\mathbb Z$ and the trivial line bundle over it with connections $\nabla_0=d$ and $\nabla_1=d+d\varphi.$ Consider also a connection $\tilde\nabla=d+\omega$ on $\mathbb C\to S^1\times [0;1]=:\tilde M$ which restricts to $\nabla_0$ respectively $\nabla_1.$ Then, the curvature of $\tilde\nabla$ is $d\omega$, and by Stokes theorem we get $$2\pi=\int_{\partial\tilde M}\omega=\int_M d\omega.$$ Hence, the curvature of $\tilde\nabla$ does not vanish identically. - You answer is correct, but anyone who knows your terminology already knows the answer. Instead I would give an example say $\mathbb C$-bundle over $\mathbb S^1$. – Anton Petrunin Feb 21 at 20:36	{}
# Why is the dB plot of a signal usually non-positive? Almost every decibel plot of a signal is usually below 0. Why is this the case? I recently just plotted a transfer function with a very high decibel plot above 0. In power spectra of signals, 0 dB is some agreed power level. It can for example represent the level of a full-scale (FS) sinusoid. In that case it would be rare to see values above 0 dBFS (sinusoid), as it would require peak cancellation as with $1.125\sin(x) + 0.125\sin(3x)$ to stay within a numerical amplitude range of $[-1, 1]$. When a power spectrum is given in dB, the 0 dB reference should be specified. Otherwise one can't be sure what it means. $0$ dB is the limit at which the power of the signal and the power of the noise (or a standardized level) are equal: their ratio is equal to $1$, and the $\log$ is zero. Looking at a spectrum, areas with higher dBs than other are frequency bands where the presence of a useful signal is more expected. Areas with very negative dBs are suspect of having very low signal content. However, they can be a target for the detection of very weak signals of interest.	{}
This topic is 3775 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. Recommended Posts For some reason, when I put the statement "int j = 0;" along with the other variable declarations at the top of the program (e.g, "int rows, columns;" etc), it won't work properly. It only works right if I keep the statement where it is now. Could someone please explain why this is?? As for the output, it is supposed to be a matrix. Therfore, if the vaules were, rows = 4 columns = 6 theChar = A the output would look like this: AAAAAA AAAAAA AAAAAA AAAAAA -------------------------------------------------------------------------------- #include <iostream> int main() { int rows, columns; int i = 0; char theChar; std::cout << "How many rows? "; std::cin >> rows; std::cout << "How many columns? "; std::cin >> columns; std::cout << "What character? "; std::cin >> theChar; while (i < rows) { i++; int j = 0; while (j < columns) { j++; std::cout << theChar; } std::cout << "\n"; } return 0; } -------------------------------------------------------------------------------- Any help or advice will be very much appreciated! Share on other sites If you have int j = 0; in the top you should remember to set j = 0 each time you change rows. And I would probably use for loops instead of while loops for what you are trying to do[smile]. Share on other sites you could put: int j=0; at the beginning of the program but then you need to have another : j = 0; inside the loop (where it is now) try to follow the program logic, you need to set j back to zero after each iteration. here is the code: #include <iostream>int main(){int rows, columns;int i = 0;int j = 0;char theChar;std::cout << "How many rows? ";std::cin >> rows;std::cout << "How many columns? ";std::cin >> columns;std::cout << "What character? ";std::cin >> theChar;while (i < rows){i++;j = 0;while (j < columns){j++;std::cout << theChar;}std::cout << "\n";}return 0;} [Edited by - memento_mori on August 15, 2007 4:19:25 PM] Share on other sites 1. For Beginners. 2. Initialization is not the same thing as assignment. 3. For a counted number of iterations, use a for loop instead of a while loop. Share on other sites std::cin>>variable; is very bad. If I put 'a' into that line, I'll ruin your day. You need to check for the validity of input. If you get bad input, you can either throw an exception, or just demand better input. Below I use this second route - it works very well for such a simple application. Speaking of bad input, you should use safter practices. I prefer scanf and printf for such a simple application. Essentially they are the same, but printf() is good to get used to, especially if you want to print multiple variables in a single without having to constantly use <<. printf("%s, you are %d years old, and born on %d/%d in the year %d\n",name,age,day,month,year); as opposed to std::cout<<name<<" you are "<<age<<" years old, and born on "<<day<<"/"<<month<<" in the year "<<year<<endl; In addition, if you do want to do std::cin, it's easier to just add the line[code]using namespace std;[/quote]after your includes, then you don't need the std:: part. Like Zahlman said, a for loop is better than your while construction, and if those variables are only ever going to be used once, then you can nest the declaration in the loop itself. Here's an example of what I said. #include <iostream>#include <cstdio>#include <cstdlib>using namespace std;//name::function is a function stored in a "namespace"int main(int argc,char**argv[]){ char columns[255],rows[255],character[255]; int rowcount=0; int columncount=0; while(rowcount<1){//get a valid input! cout<<"How many rows? ";//no std:: needed anymore scanf("%s",rows); rowcount=atoi(rows); } while(columncount<1){ printf("\nHow many columns? "); scanf("%s",columns); columncount=atoi(columns); } printf("\nAnd what is the character? "); scanf("%s",character); printf("\n"); for(int i=0;i<rowcount;i++){ for(int j=0;j<columncount;j++) printf("%s",character); printf("\n"); } return(0);} Share on other sites Very informative. Thank you all so much. The way I have interpreted the solution, is that "int j = 0;" has to be included in the "while" statement, because you can't assign the value "0" to "int j" and keep it as "0" unless its inside the while statement. Otherwise the program won't reset "int j" to "0" as it iterates. Share on other sites This topic is 3775 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. Create an account or sign in to comment You need to be a member in order to leave a comment Create an account Sign up for a new account in our community. It's easy! Register a new account • Forum Statistics • Total Topics 628721 • Total Posts 2984394 • 25 • 11 • 10 • 16 • 14	{}
# isFibration(ToricMap) -- whether a toric map is a fibration ## Synopsis • Function: isFibration • Usage: isFibration f • Inputs: • f, , • Outputs: • , that is true if the map is a fibration ## Description A proper morphism $f : X \to Y$ is a fibration if $f_*(OO_X) = OO_Y$. A proper toric map is a fibration if and only if the underlying map of lattices is a surjection. For more information, see Proposition 2.1 in deCataldo-Migliorini-Mustata, "The combinatorics and topology of proper toric maps" arXiv:1407.3497. We illustrate this method on the projection from the first Hirzebruch surface to the projective line. i1 : X = hirzebruchSurface 1; i2 : Y = toricProjectiveSpace 1; i3 : f = map(Y, X, matrix{{1 ,0}}) o3 = \| 1 0 \| o3 : ToricMap Y <--- X i4 : isFibration f o4 = true i5 : assert (isWellDefined f and isFibration f) Here is an example of a proper map that is not a fibration. i6 : Z = weightedProjectiveSpace {1, 1, 2}; i7 : g = map(Z, X, matrix{{1, 0}, {0, -2}}) o7 = \| 1 0 \| \| 0 -2 \| o7 : ToricMap Z <--- X i8 : isFibration g o8 = false i9 : assert (isWellDefined g and isProper g and not isFibration g) To avoid repeating a computation, the package caches the result in the CacheTable of the toric map.	{}
Is Type 2 error a conditional probability? Mar 7, 2020 Is Type 2 error a conditional probability? However, with alternative hypotheses such as \mu [not equal] 72 or \mu [greater than or equal to] 72, we cannot evaluate the probability of a Type II error (fail to reject H0 when the alternative hypothesis is true). The (conditional) probability is denoted by \beta, and 1-\beta is called the power of the test. How do you calculate the probability of a Type 2 error? The probability of committing a type II error is equal to one minus the power of the test, also known as beta. The power of the test could be increased by increasing the sample size, which decreases the risk of committing a type II error. Are type 1 and 2 errors conditional probabilities? Probabilities of type I and II error refer to the conditional probabilities. A technique for solving Bayes rule problems may be useful in this context. What is the probability of a type II error symbol? beta symbol β What is a Type II Error? A Type II error (sometimes called a Type 2 error) is the failure to reject a false null hypothesis. The probability of a type II error is denoted by the beta symbol β. How do you reduce Type 2 error? While it is impossible to completely avoid type 2 errors, it is possible to reduce the chance that they will occur by increasing your sample size. This means running an experiment for longer and gathering more data to help you make the correct decision with your test results. How do you solve for Type 2 error? How to Avoid the Type II Error? 1. Increase the sample size. One of the simplest methods to increase the power of the test is to increase the sample size used in a test. 2. Increase the significance level. Another method is to choose a higher level of significance. What affects Type 2 error? A Type II error is when we fail to reject a false null hypothesis. Higher values of α make it easier to reject the null hypothesis, so choosing higher values for α can reduce the probability of a Type II error. What is the difference between Type 1 error and Type 2 error? A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population. What is the probability of a type II error? 2% in the tail corresponds to a z-score of 2.05; 2.05 × 20 = 41; 180 + 41 = 221. A type II error occurs when one rejects the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true. The probability of a type II error is denoted by beta. How does the significance level affect Type II errors? The higher significance level implies a higher probability of rejecting the null hypothesis when it is true. The larger probability of rejecting the null hypothesis decreases the probability of committing a type II error while the probability of committing a type I error increases. When is a null hypothesis a type I error? A type I error occurs when one rejects the null hypothesis when it is true. The probability of a type I error is the level of significance of the test of hypothesis, and is denoted by alpha. Usually a one-tailed test of hypothesis is is used when one talks about type I error. What’s the difference between Type I and Type II errors? CO-6: Apply basic concepts of probability, random variation, and commonly used statistical probability distributions. LO 6.28: Define a Type I and Type II error in general and in the context of specific scenarios. LO 6.29: Explain the concept of the power of a statistical test including the relationship between power, sample size, and effect size.	{}
# What was her name? I had a match with a stunning girl on tinder yesterday, I was overjoyed but then I found out that she had the most bizarre name. What was more odd was what she wrote on her profile: Welcome gentlemen to my tutorial on how to play me the right way: At the beginning of my life, I was never quite a creature with a painful and deadly bite. After that, I was never quite in possession of politeness either. With all that said, if you now break me it will be hell on earth for you. All in all, I might sound like a fearsome gal but just like you all I need is a few kisses in the right places to win me. However, that was not where it ended, the strangest thing of all was how oddly her name matched her profile. As if it were a riddle for it. Therefore I thought it was a catfish and so I decided to ignore it. Admittedly, I was a little sad but then I saw that it had great potential for a good puzzle. So my question is... What was her name? Hints: Her name is more than one word. There is a game here. Look at the last sentence of her profile to start. A big hint: One could say that she included her middle name on it. A very big hint: The number 3 is crucial to this puzzle in more ways than one. • Just to add this is not a true story. Sep 17, 2020 at 19:24 • Also I just changed in possession to lacking. Sep 18, 2020 at 16:05 • I realised a mistake I am switching back sorry Sep 18, 2020 at 17:27 • There is a 50 bounty to anyone who can provide the correct reasons for the answer! Sep 20, 2020 at 12:41 Tic Tac Toe. At the start, it’s a clean board, so there’s no hint of pain. As the game progresses, courtesy is strained as each player frustrates the other in order to keep things going. In the movie War Games, global catastrophe was averted because this game was unable to be broken. • the name has 3 words, • there is indeed a game here, • the traditional markings used in the game also correspond to the text-symbolic encodings of kisses, • the middle name was tacfully included, and • there are 3 lots of possible spaces in each cardinal direction. • "the name has 3 words" Also each word has three letters. +1 from me. Sep 20, 2020 at 7:49 • You got the right answer!! Sep 20, 2020 at 12:36 • But you need to make the clues fit... I will give you the green check, someone needs to explain how this relates to the clues. Sep 20, 2020 at 12:39 • Your reasons are not correct. Sep 20, 2020 at 12:40 • @Deepthinker101 Thanks! Have I missed all the clues, or are there specific ones you’d like me to redo? Sep 20, 2020 at 14:42 I'm going to say her name is Billie Yards General Reasoning The main profile text seems to contain several things which hint at the cue sports (snooker/pool/billiards) and billiards is the one which most sounds like a person's name. Welcome gentlemen to my tutorial on how to play me the right way: Suggestive that what we are looking for is a game (also explicitly suggested in the hints) At the beginning of my life, I was never quite a creature with a painful and deadly bite. I think this may be referring to the spider rest which is a type of rest used in cue sports but rarely (if ever) at the start of the game. After that, I was never quite lacking in politeness either. In the cue sports, missed shots are called fouls. Most players will encounter fouls during a game which sounds like they are not being polite With all that said, if you now break me it will be hell on earth for you. The shot at the start of a game to separate the balls is called a break. Also, a sequence of consecutively potted balls constitutes a break. Not completely sure about the hell on earth bit. All in all, I might sound like a fearsome gal but just like you all I need is a few kisses in the right places to win me. In the cue sports, a slight touch of a ball against another ball is known as a kiss and a few of these made during a game is usually quite helpful. • A very nice try but not the answer. Sep 18, 2020 at 17:16 I’m going to respond with more of the explanation, as I believe @Lawrence’s answer has already been identified as correct: Welcome gentlemen to my tutorial on how to play me the right way: At the beginning of my life, I was never quite a creature with a painful and deadly bite. A creature with a painful and deadly bite is a TICK (think tick bites, Lyme disease, etc.) She never quite was a TICK, so removing the last letter clues TIC as the first word. After that, I was never quite in possession of politeness either. Being in possession of politeness is the definition of having TACT. She never quite had TACT, so removing the last letter clues TAC as the second word. With all that said, if you now break me it will be hell on earth for you. Lastly, what feels like hell on earth? For one, breaking your TOE does! This clues TOE as the final word. All in all, I might sound like a fearsome gal but just like you all I need is a few kisses in the right places to win me. Hugs and kisses in text slang are clued as XOXO (X’s and O’s). If you put the X’s (or O’s) in the right places (ie. a line of three of them in a row) you can win at TIC-TAC-TOE! • Congratulations. Sep 20, 2020 at 14:12 • How do I award you the bounty but not the answer. Sep 20, 2020 at 14:14 • @Deepthinker101 Bounties can be awarded independently of green ticks. Here is more info. Sep 20, 2020 at 14:47 • Ok just wait for a day... Sep 20, 2020 at 15:25 Her name will be like: Bizarre Fearsome gal Most of the time the words are from the riddle only.. and according to the hint "The number 3 is crucial to this puzzle" the name has 3 words. • You should be able to explain the clues given in the riddle. This answer does not do that. Sep 19, 2020 at 20:06	{}
dc.contributor.author Fornasier, M. dc.contributor.author Kim, Y. dc.contributor.author Langer, A. dc.contributor.author Schönlieb, C.-B. dc.date.accessioned 2016-02-28T06:44:41Z dc.date.available 2016-02-28T06:44:41Z dc.date.issued 2012-07-19 dc.identifier.citation Fornasier M, Kim Y, Langer A, Schönlieb C-B (2012) Wavelet Decomposition Method for $L_2/$/TV-Image Deblurring. SIAM Journal on Imaging Sciences 5: 857–885. Available: http://dx.doi.org/10.1137/100819801. dc.identifier.issn 1936-4954 dc.identifier.doi 10.1137/100819801 dc.identifier.uri http://hdl.handle.net/10754/600185 dc.description.abstract In this paper, we show additional properties of the limit of a sequence produced by the subspace correction algorithm proposed by Fornasier and Schönlieb [SIAM J. Numer. Anal., 47 (2009), pp. 3397-3428 for L 2/TV-minimization problems. An important but missing property of such a limiting sequence in that paper is the convergence to a minimizer of the original minimization problem, which was obtained in [M. Fornasier, A. Langer, and C.-B. Schönlieb, Numer. Math., 116 (2010), pp. 645-685 with an additional condition of overlapping subdomains. We can now determine when the limit is indeed a minimizer of the original problem. Inspired by the work of Vonesch and Unser [IEEE Trans. Image Process., 18 (2009), pp. 509-523], we adapt and specify this algorithm to the case of an orthogonal wavelet space decomposition for deblurring problems and provide an equivalence condition to the convergence of such a limiting sequence to a minimizer. We also provide a counterexample of a limiting sequence by the algorithm that does not converge to a minimizer, which shows the necessity of our analysis of the minimizing algorithm. © 2012 Society for Industrial and Applied Mathematics. dc.description.sponsorship The work of the first three authors was supported by the FWF project Y 432-N15 START-Preis Sparse Approximation and Optimization in High Dimensions. The last author's work was supported by the DFG Graduiertenkolleg 1023 Identification in Mathematical Models: Synergy of Stochastic and Numerical Methods, the Wissenschaftskolleg (Graduiertenkolleg, Ph.D. program) of the Faculty for Mathematics at the University of Vienna (funded by the Austrian Science Fund FWF), and the FFG project 813610 Erarbeitung neuer Algorithmen zum Image Inpainting. This publication is based on work supported by award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). The results of this paper also contribute to the project WWTF Five senses-Call 2006, Mathematical Methods for Image Analysis and Processing in the Visual Arts. dc.publisher Society for Industrial & Applied Mathematics (SIAM) dc.subject Alternating minimization dc.subject Convex optimization dc.subject Image deblurring dc.subject Oblique thresholding dc.subject Total variation minimization dc.subject Wavelet decomposition method dc.title Wavelet Decomposition Method for $L_2/$/TV-Image Deblurring dc.type Article dc.identifier.journal SIAM Journal on Imaging Sciences dc.contributor.institution Technische Universitat Munchen, Munich, Germany dc.contributor.institution UC Irvine, Irvine, United States dc.contributor.institution Karl-Franzens-Universitat Graz, Graz, Austria dc.contributor.institution University of Cambridge, Cambridge, United Kingdom kaust.grant.number KUK-I1-007-43 dc.date.published-online 2012-07-19 dc.date.published-print 2012-01	{}
Find all School-related info fast with the new School-Specific MBA Forum It is currently 24 Oct 2016, 19:04 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # In triangle ABC to the right, if BC = 3 and AC = 4, then Author Message TAGS: ### Hide Tags Manager Joined: 22 Jul 2008 Posts: 94 Location: Bangalore,Karnataka Followers: 3 Kudos [?]: 161 [3] , given: 11 In triangle ABC to the right, if BC = 3 and AC = 4, then [#permalink] ### Show Tags 16 Dec 2009, 05:22 3 KUDOS 4 This post was BOOKMARKED 00:00 Difficulty: 75% (hard) Question Stats: 53% (02:27) correct 47% (01:10) wrong based on 229 sessions ### HideShow timer Statistics Attachment: Triangle.jpg [ 8.62 KiB \| Viewed 13595 times ] In triangle ABC to the right, if BC = 3 and AC = 4, then what is the length of segment CD? A. 3 b. 15/4 C. 5 D. 16/3 E. 20/3 For this problem the solution is : [Reveal] Spoiler: we have 3 similar triangles the main triangle : ABD two other triangles BC and ADC . Now to find out CD we can use the later two triangles , so by similarity we have , BC/CA = CD/AC which yields CD as 3. but the answer is wrong. where have i gone wrong? OPEN DISCUSSION OF THIS QUESTION IS HERE: in-triangle-abc-if-bc-3-and-ac-4-then-what-is-the-126937.html [Reveal] Spoiler: OA Last edited by Bunuel on 19 Dec 2012, 02:40, edited 2 times in total. Edited the question. Manager Joined: 09 May 2009 Posts: 203 Followers: 1 Kudos [?]: 210 [1] , given: 13 ### Show Tags 16 Dec 2009, 05:52 1 KUDOS kirankp wrote: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the length of segment CD? a.3 b.15/4 c.5 d.16/3 e.20/3 For this problem the solution is : we have 3 similar triangles the main triangle : ABD two other triangles BC and ADC . Now to find out CD we can use the later two triangles , so by similarity we have , BC/CA = CD/AC which yields CD as 3. but the answer is wrong. where have i gone wrong? the problem in your appraoch is that u have assumed wrong angles to be similar to check if cd=3 then bd=6 and since ac=4 and bc=3 ab and ad will be 5 hence 5^2+5^2=6^2 which is not possible now the triangle similar are DCA,ACB, DCA from tri DAB and ACB now in tri DAB and DAC =4/5*20/3=16/3 hence D OA?? _________________ GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME Senior Manager Joined: 30 Aug 2009 Posts: 286 Location: India Concentration: General Management Followers: 3 Kudos [?]: 153 [4] , given: 5 ### Show Tags 16 Dec 2009, 06:24 4 KUDOS 1 This post was BOOKMARKED kirankp wrote: In triangle ABC to the right, if BC = 3 and AC = 4, then what is the length of segment CD? a.3 b.15/4 c.5 d.16/3 e.20/3 For this problem the solution is : we have 3 similar triangles the main triangle : ABD two other triangles BC and ADC . Now to find out CD we can use the later two triangles , so by similarity we have , BC/CA = CD/AC which yields CD as 3. but the answer is wrong. where have i gone wrong? D- 16/3 we can use pythagoras theorem to solve this. AB we will be 5. Let CD = x then AD = sqrt ( 16 + x^2) in Triangle BAD we have AB^2 + AD^2 = BD^2 => 25 + 16 + x^2 = (3+x)^2 solving the above we get x= 16/3 Manager Joined: 13 Jul 2011 Posts: 151 Concentration: Operations, Strategy GMAT 1: 680 Q46 V37 WE: Engineering (Telecommunications) Followers: 1 Kudos [?]: 35 [3] , given: 42 ### Show Tags 24 Oct 2011, 22:09 3 KUDOS This is a MGMAT Question, OA is D and OE is as below. Hope it helps. Because angles BAD and ACD are right angles, the figure above is composed of three similar right triangles: BAD, ACD and BCA. [Any time a height is dropped from the right angle vertex of a right triangle to the opposite side of that right triangle, the three triangles that result have the same 3 angle measures. This means that they are similar triangles. See below for further explanation.] To solve for the length of side CD, we can set up a proportion, based on the relationship between the similar triangles ACD and BCA: BC/CA = CA/CD 3/4 = 4/CD CD = 16/3 Addendum: Let's look at how we know that triangles ACD and BCA are similar. 1) Let's say that <CDA is x degrees, and <DAC is y degrees. Since <ACD is 90 degrees, and the sum of all the interior angles in a triangle is 180, we know that x + y = 90. 2) Now let's look at <BAC. We know that <BAC + <DAC = 90, since <BAD is labeled as a right angle. We also know that <DAC is y degrees (from step 1), and that x + y = 90. Putting these facts together, we know that <BAC is x degrees. 3) We know <ACB is a right angle, since <ACD is a right angle. Since <ACB is a right angle, <BAC + <CBA = 90. Given that <BAC is x degrees, <CBA must be y degrees. 4) To summarize, <CAB has the same measure as <CDA (x degrees) , and <CBA has the same measure as <DAC (y degrees). This means that in similar triangles CAB and CAD, side BC of CAB corresponds to side CA of CAD, and side CA of CAB corresponds to side CD of CAD. Thus, BC/CA = CA/CD. Again, the correct answer is D. Senior Manager Joined: 23 Oct 2010 Posts: 386 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Followers: 21 Kudos [?]: 305 [0], given: 73 ### Show Tags 26 Oct 2011, 21:45 BC^2+Ac^2=AB^2 or 16+9=25 (1)-(2) = CD =16/3 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Senior Manager Status: mba here i come! Joined: 07 Aug 2011 Posts: 270 Followers: 42 Kudos [?]: 1018 [1] , given: 48 ### Show Tags 03 Nov 2011, 02:06 1 KUDOS all three triangles abc, acd & abd are similar. so, $$\frac{4}{3} = \frac{cd}{4}$$ ... cd = $$\frac{16}{3}$$ it can't be $$\frac{4}{3} = \frac{4}{cd}$$ ... cd = 3, because in that case $$5^2+5^2 = 6^2$$ is not true _________________ press +1 Kudos to appreciate posts Last edited by MBAhereIcome on 03 Nov 2011, 14:20, edited 1 time in total. Manager Joined: 29 Oct 2011 Posts: 184 Concentration: General Management, Technology Schools: Sloan '16 (D) GMAT 1: 760 Q49 V44 GPA: 3.76 Followers: 10 Kudos [?]: 130 [3] , given: 19 ### Show Tags 03 Nov 2011, 07:49 3 KUDOS You can immediately tell that AB=5 because ABC is a 3-4-5 triangle. Label CD x, and AD y. You get: 1) $$5^2+y^2=(3+x)^2$$ 2) $$4^2+x^2=y^2$$ Plug in the definition of $$y^2$$ from (2) into 1 and solve. You get 16/3. Intern Joined: 25 Jun 2012 Posts: 36 Followers: 0 Kudos [?]: 29 [0], given: 4 ### Show Tags 18 Dec 2012, 16:30 arjunbt wrote: This is a MGMAT Question, OA is D and OE is as below. Hope it helps. Because angles BAD and ACD are right angles, the figure above is composed of three similar right triangles: BAD, ACD and BCA. [Any time a height is dropped from the right angle vertex of a right triangle to the opposite side of that right triangle, the three triangles that result have the same 3 angle measures. This means that they are similar triangles. See below for further explanation.] To solve for the length of side CD, we can set up a proportion, based on the relationship between the similar triangles ACD and BCA: BC/CA = CA/CD 3/4 = 4/CD CD = 16/3 Addendum: Let's look at how we know that triangles ACD and BCA are similar. 1) Let's say that <CDA is x degrees, and <DAC is y degrees. Since <ACD is 90 degrees, and the sum of all the interior angles in a triangle is 180, we know that x + y = 90. 2) Now let's look at <BAC. We know that <BAC + <DAC = 90, since <BAD is labeled as a right angle. We also know that <DAC is y degrees (from step 1), and that x + y = 90. Putting these facts together, we know that <BAC is x degrees. 3) We know <ACB is a right angle, since <ACD is a right angle. Since <ACB is a right angle, <BAC + <CBA = 90. Given that <BAC is x degrees, <CBA must be y degrees. 4) To summarize, <CAB has the same measure as <CDA (x degrees) , and <CBA has the same measure as <DAC (y degrees). This means that in similar triangles CAB and CAD, side BC of CAB corresponds to side CA of CAD, and side CA of CAB corresponds to side CD of CAD. Thus, BC/CA = CA/CD. Again, the correct answer is D. where does the bolded element come from? Math Expert Joined: 02 Sep 2009 Posts: 35275 Followers: 6636 Kudos [?]: 85574 [2] , given: 10237 ### Show Tags 19 Dec 2012, 02:35 2 KUDOS Expert's post AlyoshaKaramazov wrote: where does the bolded element come from? In triangle ABC, if BC = 3 and AC = 4, then what is the length of segment CD? A. 3 B. 15/4 C. 5 D. 16/3 E. 20/3 Important property: perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. Thus, the perpendicular AC divides right triangle ABD into two similar triangles ACB and DCA (which are also similar to big triangle ABD). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles marked with red and blue on the diagram). So, $$\frac{CD}{AC}=\frac{AC}{BC}$$ --> $$\frac{CD}{4}=\frac{4}{3}$$ --> $$CD=\frac{16}{3}$$. For more on this subject please check Triangles chapter of Math Book: math-triangles-87197.html OPEN DISCUSSION OF THIS QUESTION IS HERE: in-triangle-abc-if-bc-3-and-ac-4-then-what-is-the-126937.html _________________ Re: split triangles [#permalink] 19 Dec 2012, 02:35 Similar topics Replies Last post Similar Topics: 2 E is the midpoint of AC in right triangle ABC shown above. If the area 8 22 Sep 2016, 05:05 2 In right triangle ABC, AC is the hypotenuse. If AC is 40 2 16 May 2016, 07:31 35 In right triangle ABC, BC is the hypotenuse. If BC is 13 and 15 23 Nov 2013, 11:01 5 The side lengths of triangle ABC are such that AC > BC > AB. 8 11 Mar 2013, 15:13 34 In triangle ABC, if BC = 3 and AC = 4, then what is the 35 01 Feb 2012, 16:55 Display posts from previous: Sort by	{}
Timezone: » Poster Three-dimensional spike localization and improved motion correction for Neuropixels recordings Julien Boussard · Erdem Varol · Hyun Dong Lee · Nishchal Dethe · Liam Paninski Fri Dec 10 08:30 AM -- 10:00 AM (PST) @ Neuropixels (NP) probes are dense linear multi-electrode arrays that have rapidly become essential tools for studying the electrophysiology of large neural populations. Unfortunately, a number of challenges remain in analyzing the large datasets output by these probes. Here we introduce several new methods for extracting useful spiking information from NP probes. First, we use a simple point neuron model, together with a neural-network denoiser, to efficiently map spikes detected on the probe into three-dimensional localizations. Previous methods localized spikes in two dimensions only; we show that the new localization approach is significantly more robust and provides an improved feature set for clustering spikes according to neural identity (spike sorting"). Next, we apply a Poisson denoising method to the resulting three-dimensional point-cloud representation of the data, and show that the resulting 3D images can be accurately registered over time, leading to improved tracking of time-varying neural activity over the probe, and in turn, crisper estimates of neural clusters over time. The code to reproduce our results and an example neuropixels dataset is provided in the supplementary material.	{}
# A finite group with the property that all of its proper subgroups are abelian Let $G$ be a finite group with the property that all of its proper subgroups are abelian. Let $N$ be a normal subgroup of $G$. Prove that either $N$ is contained in the center of $G$ or else $G$ has a normal abelian subgroup of prime index. I think $G$ is solvable. http://crazyproject.wordpress.com/2010/06/08/every-finite-group-whose-every-proper-subgroup-is-abelian-is-solvable/. I hope that idea maybe usefull. Help me some hints. Thanks a lot. P/s: This is a question comes from a qualifying exam in Algebra ( Wisconsin August $1979$ ) Or you could argue as follows. Suppose that $N \not \subseteq Z(G)$. Let $M$ be a maximal normal subgroup of $G$ containing $N.$ Then $M = C_{G}(N)$ as $M$ is Abelian and $M$ is proper, but $N \not \subseteq Z(G).$ Then certainly $M = C_{G}(M).$ Hence $M$ is in fact a maximal subgroup of $G,$ for if $M$ is contained in another proper subgroup $H$ of $G$ normal or not) then $H$ s Abelian, so $H \subseteq C_{G}(M) = M$ and $H = M.$ Hence $G/M$ is a simple group (as $M$ is maximal normal) with no proper non-identity subgroup (as $M$ is not contained in any proper subgroup of $G$). But $G/M$ contains a cyclic subgroup of prime order (you don't even need Cauchy's theorem to see this), so $G/M$ is in fact cyclic of prime order. • Can you explain why $G/M$ contains a cyclic subgroup of prime order? – chuyenvien94 Jan 3 '14 at 11:06 • Well, let $X$ be any finite group with more that one element. Choose $x$ to be any non-identity element of $X.$ Then $\langle x \rangle$ is cyclic of order $n >1.$ Let $p$ be a prime divisor of $n.$ Then $x^{\frac{n}{p}}$ has prime order $p.$ – Geoff Robinson Jan 3 '14 at 12:31 • I agree with you. – chuyenvien94 Jan 3 '14 at 13:40 • Use the isomorphism theorems. $M$ is not contained in any proper subgroup of $G.$ But $G/M$ has a subgroup of order $p.$ This means that $G$ has a subgroup $X$ which contains $M$ and has order $p\|M\|.$ But then $X$ must be all of $G$ and $G/M$ is cyclic of order $p.$ – Geoff Robinson Jan 3 '14 at 14:02 • @user515430 : You have a point. I was thinking that the question intended N to be proper. You need a bit more argument if that is not the intention. I deal with the case that G has a proper normal non central subgroup. Except for that case, G/Z(G) is simple. If Z(G) is non-trivial , then it's easy to finish be induction. If G is simple, then I think you might need to use Burnside's transfer theorem. If P is a non-trivial Sylow subgroup of G, then P is Abelian and not normal, so N_G(P) is Abelian, and G has a normal p- complement, contrary to simplicity. – Geoff Robinson Dec 21 '18 at 10:57 Here's how I would argue: • Show that the centralizer of $N$ in $G$ is also normal and contains $N$. So either $N$ is contained in the center, or we replace it with its centralizer, which is also a proper normal abelian subgroup of $G$. • Repeating the previous step as many times as needed ends with either the conclusion that $N$ is in the center or that $N$ is its own centralizer, and also a proper normal abelian subgroup of $G$. • In the latter case consider the homomorphism $f:G/N\to Aut(N)$ gotten by conjugation action. Show that it has to be injective. • If $G/N$ has a proper cyclic subgroup $K/N$ show that $K/N\le \ker f$. • Conclude that $G/N$ must be cyclic of prime order. • Yeah: As Geoff's answer explains, we don't need to do many iterations in step one. As $N$ grows, its centralizer can only shrink, so one round will do. – Jyrki Lahtonen Jan 3 '14 at 18:26	{}
The intersection of $[0,x)$ where $0<x\leq 1$ is $\{0\}$ [closed] I proved $\{0\}$ is contained in the intersection of $[0,x)$ where $0< x \leq 1$. But how do I show the reverse inclusion? - closed as off-topic by M Turgeon, Andrés Caicedo, Amzoti, Claude Leibovici, user127096Apr 1 '14 at 4:49 This question appears to be off-topic. The users who voted to close gave this specific reason: • "This question is not about mathematics, within the scope defined in the help center." – Andrés Caicedo, user127096 If this question can be reworded to fit the rules in the help center, please edit the question. Im sorry... but I dont know how to use matematical symbols in this app... T.T...... – user138163 Apr 1 '14 at 2:11 Oh ok I get it. You mean $\cap \{[0,x) : 0 < x \leq 1\}$. – Guest Apr 1 '14 at 2:13 Well, clearly the intersection is contained in $[0,1]$. If there was an $0 < y \leq 1$ such that $y$ was in the intersection, then you could find $0 < x < y$ for which $y \notin [0,x)$, a contradiction. Therefore the intersection is also contained in $\{0\}$. – Guest Apr 1 '14 at 2:14 @Nameless, I think you mean $[0,x) = \{y : 0 \leq y < x\}$. – Antonio Vargas Apr 1 '14 at 2:22 THANK YOU!!! Now I got it ! Thanks so much for your help :-) – user138163 Apr 1 '14 at 2:23 Notice that $0\in[0,x),\forall x\in\mathbb{R}_{>0}$. Thus $\{0\}\subseteq \cap\{[0,x):0<x\leq 1\}$. Now we want to show no other number is in the intersection. Notice that $\forall c<0$, $c\not\in[0,x)\forall x$. For the other side, assume $\exists c>0$ such that $c\in\cap\{[0,x):0<x\leq 1\}$. Then $\forall x>0,c\in[0,x)$. But if $x=\frac{c}{2}$, then $c>x\Rightarrow c\not\in[0,x)$. Contradiction.	{}
# Where is nuclear fusion occuring in the Sun? My understanding is that the sun is basically a sphere of hydrogen with a helium core, and that the hydrogen is undergoing nuclear fusion to produce helium. There are many images and cross-sectional schematics on Google but I can't find any actual numbers for the radii. Are the nuclear reactions occurring where the helium meets the hydrogen? What radius are the nuclear reaction occurring at? How thick is this spherical shell of material undergoing nuclear fusion? • "the sun is basically a sphere of hydrogen with a helium core" - no, that's not quite right. See e.g. the Wikipedia article on the solar core - the inner core drops to 33% hydrogen by mass, but it's still a far cry from pure helium. Mar 15 '19 at 12:46 There is much misconception in the question, but I'll hazard an answer. I am not going to give any links (no point linking to Wikipedia, it's just there), but I'll highlight the important terms in bold. If you want to research more, search for these. Any good general astronomy course textbook will cover these topics, too, if you want a bit more systematic approach. My understanding is that the sun is basically a sphere of hydrogen with a helium core, and that the hydrogen is undergoing nuclear fusion to produce helium. Basically, the Sun is a ball of hydrogen and helium, but this is not all there is. Being a Population I star, the Sun contains heavier elements (called metals in stellar astrophysics; anything lithium and heavier is considered metal in this sense). These elements already came with the gas cloud the Sun has formed from, and were produced by previously burst older stars. Despite low abundance, the metallicity plays an important role in the Sun's core power stability. At some depth the gas ball compresses its inner area enough to heat it up so much that hydrogen fusion into helium begins. This area is called the core. This is where practically all fusion happens, and what is responsible for the star's energy production. For a Sun-mass star and below, the proton-proton chain dominates. The pp-chain energy output is approximately proportional to $$T^4$$. The good news is, if reaction rate drops, then the outer layer of the star will compress the core, so it heats up, and the renewed energy output compensates for the compression. So this highly-sensitive dependency on the temperature is what gives the star its long term stability. It is also notable that the center of the core is hotter and therefore more energetic than its periphery, and turns hydrogen into helium faster. Absent any mixing, the core would develop an inert helium ball in the middle (helium cannot be fused by a Sun-mass star, its core is too cold for that): A pp-chain core is entirely non-convective. However, there is another multistage reaction that fuses protons into helium nuclei, the CNO cycle. This cycle requires metals ($$C$$, $$N$$ and $$O$$, naturally) be present in the core. They are not consumed, but participate in stages of the reaction and are ultimately recycled. The rate of this reaction depends on the temperature as $$T^{20}$$. It's a huge dependency! The CNO-dominant core has so much temperature gradient that it's fully convective, so it mixes the material very thoroughly. It happens so that for a star with the mass $$M=1.5 M_\odot$$ the core is fully convective, but this is not an on/off phenomenon. Even in the Sun, the CNO cycle produces roughly 10% of core's output power, and is responsible for intermittent mixing of the core material. The dependency on temperature for this reaction is so large that the reaction is practically irrelevant at $$M=0.9 M_\odot$$ and $$T=14.5\times 10^6 K$$, and becomes dominant at $$M=1.5 M_\odot$$ and $$T=17.5\times 10^6 K$$. The Sun is at the very lower end of this range. There is not a huge difference in the lifetime of the star even absent the CNO mechanism; it only changes the hydrodynamics of the core and its reactivity to temperature variation. But for the short-term stability it's very important; it amplifies the negative feedback loop that stabilizes the core reaction rate. It is probable (so models tell us) that the Sun's energy output would be much more variable on the scales of $$\sim 10^3$$ years. So we are lucky to have gotten enough "metal" in our home star, in the end--our ice ages have been bad enough already! There are many images and cross-sectional schematics on Google but I can't find any actual numbers for the radii. About $$0.2\,R_\odot$$. Are the nuclear reactions occurring where the helium meets the hydrogen? A Sun-mass star does not fuse helium. Helium fusion is a much more energetic process, and happens only in more massive and shorter-living stars. Helium is the embers of the combustion in the Sun, not its fuel. As a side note, the Sun is a very calm reactor by Earthling's standards. The core's energy output is about $$300\, W/m^3$$, far too low for any practical fusion reactor on Earth. You need a chunk of the Sun's core $$10^7\,m^3$$ in size to match the power of a large coal-fueled electrical plant, and that's the volume of a ball about $$300\,m$$ in size. No way we could contain such a fireball at 15 million K; terrestrial fusion projects aim at much higher temperatures and thus reaction rates. What radius are the nuclear reaction occurring at? In the Sun while on the main sequence, all throughout the core. The core is essentially isolated against hydrogen supply from outer layers by the radiative zone, where the high thermal gradient stabilizes the gas against convection. As the Sun exhausts its fuel in the core, it transitions into the red giant phase (and the Sun will do it twice!). This happens when the core mostly turns into unburnable helium and cools down. What was previously the hydrogen-rich material in the radiative zone collapses on the surface of the helium core, and restarts the hydrogen reaction when its temperature reaches the ignition point. This reaction occurs only on the surface of the inner helium ball, in a spherical shell. There won't be any mixing mechanism this time that could disturb the inner inert ball. All numbers come entirely off the top of my head, the best I could recall. Please double-check after me!	{}
# All Questions 14 views ### Beta Decay Energy Consider $\beta ^-$ decay. \begin{align} ^{198} Au \rightarrow ^{198} Hg + e^- + \bar{v_e} \end{align} The decay energy is given by the difference in mass between multiplied by the speed of light. ... 20 views ### The equation of the location of L1 On http://en.wikipedia.org/wiki/Lagrangian_point#L1 it says that the location of L1 can be determined as $\frac{M_1}{(R-r)^2}=\frac{M_2}{r^2}+\left(\frac{M_1}{M_1+M_2}R-r\right)\frac{M_1+M_2}{R^3}$, ... 18 views ### Collision between 2d circle and flat surface First of all I want to preface this post by saying that I am absolutely terrible at maths, my level of geometry equals being able to discern a circle from a rectangle but that's about it, as for ... 11 views ### Modern Optics (Fowles) Transmittance as a function of wavelength [on hold] I need to get the coefficient of finesse to equal ((n^2-1)/(2n))^2 from 4R/(1-R)^2 knowing that the incident beam is normal so that R=((n-1)/(n+1))^2. If this isn't possible I'm not understanding the ... 19 views ### How can I simulate a model electronic hole? Suppose I can solve time-dependent Schrödinger equation for several 1D particles (currently 3). I'd like to see, what an electronic hole is and how it behaves — in a series of numerical experiments. ... 21 views ### How does ultrasonic horn produce a convection current in the water? When I was using ultrasonic horn in a beaker, I notice that there are convection currents in the beaker and stir up my substance. I don't understand why it produce water current, I thought that it ... 21 views ### Is there a general term for the situation where an improperly chosen measurement range results in a bias? For example, consider the following measurement: A sensor can measure a specific physical quantity, and has a range of $0$ to $100$. All values above $100$ will be shown as 100. We now take the ... 25 views ### How does temperature affect photovoltaics (PV) efficiency? I know that photovoltaic panels are more efficient at lower temperatures: As the temperature increases, the output voltage decreases. I am looking for an explanation of the mechanism behind this ... 14 views ### charge on a capacitor [on hold] capacitor C1 of 1mF is charged to 100v(i.e. charge on it is 100mc).it is discoonected from the battery and connected to capaciotr C2 of 2mF .on plate of C2 is earthed .calculate the charge on each ... 44 views ### Why exactly are images formed by lenses/mirrors? I just don't get the concept behind why a lens or a mirror forms a reproduction of the object at present. Is it to do with the object blocking parts of the light source? I just don't understand why an ... 69 views ### Universal gravity at small distance Could it be that there is simply a maximum gravitational force that two bodies of finite mass can exert on one another? This would occur at $r=0$, so maybe there is some really really really small $a$ ... 29 views 10 views ### Cubic Gaussian Surface For Evaluating Electric Flux i'm working through some problem sets about Gauss' law and all the examples I have come across so far require the use of a spherical gaussian surface for a point charge, so that it is possible to say ... 88 views ### Degenerate perturbation theory applied to topological degeneracy? Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ... 22 views 1k views ### Does it make sense to open one window all the way when the other window is much smaller? I can't wrap my head around this idea because I don't know much about air flows. Say we have this imaginary apartment with two windows, one of which is two times smaller than the other: Will the ...	{}
With the return of the X-Files in form of a miniseries, I was tempted to catch up on the original run of the show, since I had only seen the occasional episode in the late 90’s or early 00’s (my mom was a big fan). Being me, I already looked up the X-Files episodes ratings on trakt.tv to see if there’s something interesting about them, but I didn’t think there was. However, when I listened to the Incomparable talking about the show, I learned that apparently X-Files can be divided into the “myth arc” and regular, more stand-alone episodes. That’s when I realized I need to get my tv show analysis boots on and try to see what I could do. To my delight, I noticed that the appropriate Wikipedia article neatly marks the myth arc episodes, ready for plucking. And then I started plucking. So I’ve been watching Marvel’s Jessica Jones over the past couple days, as one does, and I have opinions and stuff about it. However, since I believe that a plot is worth more than word stuff, I present to you my viewing expierence in data. ## Edit: 2016-12-18 02:13:19 Please note that this analysis is out of date and the code to acquire the data no longer works, since the source website has restructured and I have not found a way to reproduce the old behavior. Also, the current analysis is located at https://worldpenis.tadaa-data.de, so please go there for up to date code and analysis. It’s prettier. And better. If there’s one thing I just can’t resist, it’s publicly available tabular data containing adequate amounts of numeric values. Naturally, I couldn’t resist the World Penis Data I stumbled upon somewhere over at Reddit. So, let’s suck that data out of the web and put it into our favorite data structure. library(tRakt) # install via devtools::install_github("jemus42/tRakt") library(dplyr) library(tidyr) library(ggplot2) get_trakt_credentials(username = "Your Username") slug <- "dig" # Slug from trakt.tv show url trakt.user.ratings(type = "episodes") %>% filter(show.slug == slug) %>% arrange(season, episode) %>% select(rating, season, episode, title) %>% mutate(season = factor(season, ordered = T)) %>% rename(user.rating = rating) %>% left_join((trakt.get_all_episodes(slug) %>% select(rating, title, epnum))) %>% gather("type", value = "rating", user.rating, rating) %>% ggplot(data = ., aes(x = epnum, y = rating, colour = type)) + geom_point(size = 6, colour = "black") + geom_point(size = 5) + ylim(c(5, 10)) + scale_colour_discrete(labels = c("My Rating", "Trakt. I don’t know if you’ve noticed, but lately I’ve done a lot of stuff with tv shows. Along the way, I noticed some trends with a few shows which seemed quite interesting to me, namely some shows were going straight down the drain, at least as far as their recent ratings are concerned. The projects I’m referring to are these two: 100 Popular Shows on trakt.tv 100 Trending Shows on trakt. Analyzing TV shows seems to be what I do these days. So I wanted to keep my newfound calling going and sucked the data for about a thousand shows out of the trakt.tv API, which was nice enough to only fail on me, like, twice. So, after some time of intense data pulling, I found myself with the more or less complete data (show info, season info, episode data) for 988 shows (and that’s why I keep referring to 1000(ish)). As of today, I have my first package published on CRAN. In the grand scheme of things, that’s not really a big deal, since CRAN doesn’t have any quality standards regarding the content of a package, they just verify that the package can be installed and run without breaking horribly. Still, I’m quite happy about this minor achievement. Not because I’m particularly proud of my package, but rather since I consider it as a small verification of my ongoing path to become an R developer that doesn’t embarrass himself more than necessary. Overanalyzing tv shows has kind of become my jam. So why not totally overdo it. Note that everything I describe in this blogpost is purely for the lulz, and I don’t pretend there’s any scientific merit to it. I just like throwing maths at data. After I more or less succesfully plotted all the things, I wanted to go full blown statisticy on the subject. While my knowledge of statistics isn’t nearly as extensive as I’d like it to, I at least know a little about comparing groups. It’s been a while since I started working on a set of functions to pull data from trakt.tv. I documented part of the early process in an earlier blogpost, and since then I started aggregating my work into a proper package. Since trakt launched their new APIv2, I started to rewrite and ehance the package a little, also solidifying the whole authentication business. I have not implemented any OAuth2 methods, but since the purpose of this package is to pull a bunch of data and not to perform actions like checkins, I don’t think it’s a big deal. Remember that last post? No? Good. Then don’t scroll down. Or do. Idunno. One thing I wanted for my more-or-less-automated TV show plots was appropriate colors to differentiate seasons. I assume that’s a problem we can all relate to. Of course in the R and ggplot2 bubble, there’s the RColorBrewerpackage that provides nice and easy color palettes of varying sizes. But that’s boring. Also, repetitive. So let’s fix that. Stargate SG-1, while probably a mediocre show in the grand scheme of sci-fi shows, it’s the sci-fi show I grew up with, so I tend to enjoy rewatching parts of it occasionally. Well, at least I rewatched it twice so far. The full thing. 10 seasons. Yep. Even those last two. So this time, I wanted to cherry-pick the good™ episodes, and of course efficient cherry-picking in 2014 involves R, the trakt. Neulich hatte L3viathan seine openpaths-Locationdaten vergisted, und da ich Spaß an R habe und neulich ja schon Dinge zu ebenjenem Anwendungsfall schrob, warf ich dann mal ein paar Dinge drauf. Hier so das Ergebnis. L3vipaths This uses l3vi’s location data. For science shits ‘n giggles. Importing the data in R `r load it read it rename it convert it factor it sort it attach it library(rjson) library(ggplot2) library(maps) library(ggmap)	{}
## Introduction Human coronaviruses have emerged as significant agents in serious human disease, highlighting the need for rapid development of therapeutics. Recently, the severe acute respiratory syndrome (SARS) coronavirus-2 (SARS-CoV-2) has caused a pandemic with > 125 M individuals infected and over 2.5 M deaths globally1. Prior to this, the related human coronaviruses SARS-CoV-1 and Middle East Respiratory Syndrome coronavirus (MERS-CoV) were responsible for outbreaks of severe human coronavirus disease with significant mortality2,3. Additional human coronaviruses including NL63, OC43, and 229E elicit milder disease such as the common cold4, although more severe human diseases related to these viruses have been reported5. Human coronaviruses thus represent an important family of related viruses that impact human health worldwide with new therapies for these agents urgently needed. The recent emergence of SARS-CoV-2 variants of concern6,7 indicates that therapeutic strategies with broad antiviral activity to human coronaviruses are a high priority. SARS-CoV-2, SARS-CoV-1 and NL63 enter cells by using their Spike (S) outer protein, which interacts with angiotensin converting enzyme 2 (ACE2) on host cells8,9,10,11, while 229E and OC43 depend on host cell aminopeptidase N and glycosaminoglycans, respectively12,13. In addition, other host cell receptors contribute to SARS-CoV-2 entry, such as neuropilin-114,15. The coronavirus-bound receptor protein(s) enter cells via clathrin-mediated endocytosis16,17 or other membrane traffic mechanisms18, after which the viral RNA genome undergoes replication and expression of viral proteins, leading to assembly of viral progeny at a specialized ER-derived coronavirus replication organelle19. This is followed by coronavirus release to the extracellular milieu by a mechanism involving lysosomal exocytosis20, allowing spread of the viral particles to nearby cells21,22. Human coronavirus cellular entry, replication, assembly and egress depend on a wide range of host cell proteins and functions. For SARS-CoV-2, 26 viral proteins were found to interact with 332 host cell proteins, spanning a range of functions including membrane trafficking, centrosome structure and function, membrane transport, DNA replication and stress granule formation23. This viral protein interactome provides a rich source of information from which to identify host proteins that are functionally important for viral entry and replication and thus may serve as antiviral drug targets. Infection studies have also demonstrated conserved host-protein interaction patterns across different coronaviruses, suggesting that some host proteins can be targeted for broader antiviral activities24,25,26. The virus/host protein interactome and the identification of proteins functionally required for viral entry and replication of common cold coronaviruses may reveal important novel pan-human coronavirus antiviral drug targets. Antivirals targeting SARS-CoV-2 such as remdesivir have modest clinical benefits27, indicating a need for more effective antivirals to complement anti-inflammatory therapy approaches for the treatment of COVID-19. As the timeline for development of new drugs is ~ 10 years28, and given the current dire need for effective antiviral agents, the identification of new drugs with antiviral activity cannot provide antiviral therapies in time to address the current pandemic. Drug repurposing is a preferred method for developing rapid response therapies28,29, as it prioritizes the identification of additional drugs that can be repurposed as antivirals. Repositioning of approved drugs can be achieved either by repurposing for a related disease, repurposing of a target with a known drug for another indication, or repurposing of a drug for a novel target by taking advantage of off-target interactions. The relative prevalence of the three approaches reflects the balance of their relative feasibility and broadness of their applicability. The disease-centric approach, while the most direct and the most common, representing 59% of repositioning successes30, suffers from a more narrow generalizability in the disease space, as exemplified by the modest utility of repurposing of antivirals described above. Target-centric repurposing, while having the potential for broader application as a less direct approach, is less common since discovery of a novel link between a target and a disease is a rare finding. Even if such a link is discovered, the generalizability of the target-centric approach is limited by the drug-target coverage in the human proteome: as of 2019, only 667 of the roughly 20,000 human proteins (~ 3%) are directly targeted by FDA- approved drugs31. For that reason, drug-centric repurposing, as the least direct methodology, offers access to a much broader range of repurposing opportunities. However, since it is aimed at finding novel, off-target drug-target interactions, and therefore relies on the fundamental understanding of structural information about both the drug and the target, it has been the least prevalent repositioning approach, representing only 6% of the successes30. Successful drug repurposing discoveries to date with either of the three approaches have been largely accidental or hypothesis-driven32. Computational approaches, however, provide an alternative opportunity to identify repurposing candidates that may have been overlooked. These hypothesis-free strategies reference broad data sources to identify new protein targets, identify new compounds for a pre-selected target, or pair phenotypic signatures of a disease state with drug actions33. Notably, multiscale interactome approaches combine known relationships between disease, biological pathways, genes, proteins, and other -omic data to predict new potential indirect relationships34. Furthermore, when those interactomes are built into Graph Convolutional Networks (GCNs), they offer a systematic, Machine-Learning (ML) based approach to model the value of each relationship in the network empirically based on their intrinsic properties35,36. Such models can be applied to the target-centric repurposing approach. ML models that provide predictions for drug-targets interaction, on the other hand, and are capable of cross-screening libraries of clinically relevant compounds with large sets of proteins, can assist with the drug-centric repurposing programs37. In this study, we aimed to exploit the therapeutic potential of approved drugs by taking advantage of both the directness of the target-centric and the broader potential of the drug-centric repurposing approaches by combining GCN-based multiscale host-viral interactome approaches for target discovery with off-target interaction predictions from the PolypharmDB database37 to shortlist clinically-relevant repurposing candidates for screening in coronavirus infectivity assays. This specific combination of approaches was selected to simultaneously explore a variety of mechanistically-informed host-based targets in a focused phenotypic driven experiment. In contrast, a single-target virtual screen would require a prior target validation stage or risk having no observed activities upon experimental testing. The proposed approach maximizes the diversity of targets and compounds explored to increase the likelihood of a bioactive discovery in an experimentally efficient manner. We then examine the effectiveness of these predictions using a combination of human coronavirus entry and infection assays. We reveal several compounds that have antiviral activity, in particular capmatinib, a drug known to inhibit the receptor tyrosine kinase MET. Notably, we find that capmatinib has potent anti-human coronavirus activity in a MET-independent manner. Further, we find novel roles for human proteins such as IRAK1/4 in supporting human coronavirus infection. ## Results A total of 26 drug repurposing candidates for SARS-CoV-2 were identified using three separate approaches involving a multiscale interactome GCN and the PolypharmDB drug repurposing database37, as described in Fig. 1 and in “Materials and Methods”. Drugs assert their function by binding to proteins and regulating biological pathways. Therefore, we first constructed a multiscale interactome network to represent the known relation of 1661 drug molecules, 17,660 human proteins, 9,798 functional pathways and finally the 26 expressed proteins from SARS-CoV-2. This representation enables fine grained analysis on the probable drugs and protein targets for COVID-19, based on the assumption that the targets interacting with the viral protein nodes on the network are more likely to play a role in the potential treatment. Thus, we proposed a combined approach of node2vec and GCN to learn and generate the node embeddings in the multi-scale network. The embedding is optimized in an unsupervised manner to the objective that related nodes on the network should have higher embedding similarity (see Materials and Methods). All embeddings are then sorted by the proximity to the COVID-19 node. When first reviewing proximity distances between COVID-19 and human targets, very few had known small molecule modulators, which is an expected limitation of the target-centric drug repurposing strategy. To overcome the sparsity of drug-target interaction in the network, additionally, we further applied the drug-centric approach: off-target predictions for relevant low-data targets were retrieved from the PolypharmDB database. PolypharmDB is a database of precompiled all-by-all Drug Target Interaction (DTI) predictions performed by the MatchMaker deep-learning engine, for 8535 human proteins with 10,244 clinically-tested small molecules (see Materials and Methods). For Method 1, a target-centric approach, the top 10 drug candidates were selected among the 60 drugs with the highest proximity scores to COVID-19, as determined by the GCN approach. For Method 2, a drug-centric approach, 14 candidates were selected among single-target PolypharmDB hits for protein targets with high proximity scores to COVID-19 as determined by the GCN approach. For Method 3, an extension of the drug-centric approach, the final two candidates were selected with a variation on Method 2, which prioritizes compounds with multiple predicted interactions to GCN-identified SARS-CoV-2 targets. The compounds selected using all three methods are summarized in Table 1. Since this approach generates numerous potential hits for further validation, we chose to use a system that could be widely used and scalable without restricted access to BSL3 laboratories, as required for monitoring of SARS-CoV-2 infection. This method may bias the identification of drug compounds with pan-human coronavirus antiviral activity, rather than compounds with selective antiviral activity towards SARS-CoV-2. Thus, to examine whether the 26 selected compounds exhibit antiviral activity, we established a cell culture-based immunofluorescence (IF) screening system using the 229E human alphacoronavirus, based on detection of the 229E S protein. This assay was designed to allow ~ 100% of control cells to express the S protein following 48 h of infection, allowing robust detection of antiviral activity as reduction of S protein abundance. We validated this IF assay by treating 229E-infected cells with the nucleoside analogue prodrug remdesivir27 (Fig. S1), showing that this BSL2-based screening system allows for the safe and straightforward identification of novel antiviral compounds. Using this assay, we identified four putative antivirals within the 26 predicted hits (4/26, ~ 15%) that reduced S protein abundance following 229E infection by at least 50% (Fig. 2) with no apparent cytotoxicity. Treatment with palbociclib and anidulafungin caused partial attenuation of 229E infection, while treatment with capmatinib or polidocanol resulted in nearly 100% inhibition of 229E infection. Based on our in silico framework, these four compounds were predicted to target several host proteins, each with potential novel and noncanonical roles in supporting coronavirus infection (Table 1). Interestingly, palbociclib, capmatinib and anidulafungin were predicted to target IRAK4, either as a primary target or by a polypharmacology panel. Another compound, bortezomib, was also predicted to target IRAK4, however cytotoxicity prevented further analysis of this compound. We focused further investigation into the role of capmatinib as a potential antiviral therapeutic against human coronavirus disease, given its robust impairment of 229E infection in the IF assay. Capmatinib is an orally-available inhibitor of the receptor tyrosine kinase (RTK) MET, and is used in the clinic for the treatment of MET-amplified non-small cell lung cancer38; however, our analyses predict that capmatinib may have antiviral activity due to inhibition of targets other than MET. To further characterize the antiviral activity of capmatinib on human coronaviruses, we developed several complementary cell-based assays to probe the different aspects of infection by several different human coronaviruses, including 229E, OC43, and NL63. Noteworthy, capmatinib treatment impaired 229E viral replication in a dose-dependent manner, with concentrations as low as 1.0 µM resulting in significant attenuation of 229E S protein abundance following infection (Fig. 3A). The ability of capmatinib to impair viral replication was further confirmed using a plaque-forming unit (PFU) assay in MRC-5 cells. 229E infection of control cells resulted in the formation of distinct, large circular plaques indicating cytopathic effect (CPE) (Fig. 3B). In contrast, capmatinib treatment resulted in reduced total number and size of individual plaques; viral quantification revealed that capmatinib treatment resulted in a > 50% decrease in viral production compared to control. Importantly, this method for viral quantification is based entirely on total plaque number and does not consider plaque size, thus, these results likely represent an underestimate of the antiviral effects of capmatinib, given the differences in plaque morphology between control and treatment groups (Fig. 3B). To determine the breadth of the antiviral effects of capmatinib, we measured whether capmatinib also exhibited antiviral activity for other BSL2 human coronavirus infections, including OC43 and NL63. We adapted our MRC-5/229E plaque assay protocol for infection of LLC-MK2 cells with the alphacoronavirus NL63, which like SARS-CoV-2 depends on ACE2 for infection8. Treatment of LLC-MK2 cells with increasing concentrations of capmatinib resulted in a dose-dependent decrease in NL63 PFU with minimal cytotoxicity observed at 5 days post-infection (dpi), with > 70% reduction in PFU at 10 µM capmatinib (Fig. 3C). Consistent with results obtained with the PFU assay, qRT-PCR analysis showed that capmatinib attenuated NL63 N RNA abundance by approximately 50%, measured at 3 dpi (Fig. 3D). We also established a PFU assay based on the infection of LLC-MK2 cells with human betacoronavirus OC43. Treatment of OC43-infected LLC-MK2 cells with capmatinib resulted in a nearly 50% reduction in viral particles (Fig. 3E). As with our results obtained in the MRC-5/229E model, capmatinib treatment reduced both plaque number and the overall size of the plaques, indicating that our quantification of PFU/mL likely underestimated the actual antiviral effect of the drug. Taken together, our results from 3 different human coronaviruses and cell-based assays of coronavirus infection demonstrate that capmatinib has a broad range of antiviral activity against human coronaviruses. We next explored the mechanism of the antiviral action of capmatinib. To determine whether the potent antiviral activity of capmatinib was due to its canonical role as a MET inhibitor, we compared the effects of capmatinib with another distinct MET inhibitor, AMG-337 that has similar in vitro IC50 ≤ 1 nM for MET as capmatinib39,40. We first treated NL63-infected LLC-MK2 cells with capmatinib or an equimolar amount of AMG-337. As expected, capmatinib treatment greatly attenuated CPE as measured by PFU (Fig. 4A). In contrast, AMG-337 treatment, while similarly tolerated by the cells, did not result in an appreciable reduction in PFU. Similar results were observed in OC43-infected LLC-MK2 cells and 229E-infected MRC-5 cells; AMG-337 treatment had no effect on PFU in either case (Fig. 4B and Fig. S2). Capmatinib, but not AMG-337 was also effective at reducing 229E S protein abundance in the IF assay (Fig. 4C). Spike-pseudotyped viral inhibition assays also demonstrate the ability of capmatinib to interfere with certain aspects of viral infection. SARS-CoV-1 and SARS-CoV-2 pseudoviruses (PsV) require human ACE2 for cell entry41. Incubation of HeLa cells stably expressing ACE2 (HeLa-ACE2 cells) with capmatinib showed a potent inhibition of infection of both SARS-CoV-1 or SARS-CoV-2 PsV with half-inhibitory concentrations (IC50) of 14.1 ± 0.2 and 26.0 ± 0.1 µM, respectively (Fig. 4D). In contrast, treatment with concentrations of AMG-337 up to the mM range had no appreciable effect on PsV neutralization (Fig. 4D). Both compounds displayed minimal cytotoxicity in HeLa cells (Fig. S3). Together, these results indicate that capmatinib exhibits human coronavirus antiviral activity by inhibiting a target other than MET. Moreover, the pseudotyped virus assay selectively monitors virus uptake and reporter gene delivery, suggesting that capmatinib inhibits early stages of virus entry. We next sought to gain insight into the possible mechanism by which capmatinib exhibits human coronavirus antiviral activity. Based on MatchMaker, capmatinib was predicted to exhibit off-target interactions with IRAK4 and other protein targets (Table 1), which are part of pathways (e.g. interleukin-1 receptor) that have been broadly implicated in mediating SARS-CoV-2 infection and COVID-19 disease42,43. In addition, our in silico analyses also predicted palbociclib and anidulafungin as binders of IRAK4, and as these drugs also demonstrated antiviral activity (Fig. 2), this suggests that IRAK4 may be an important novel drug target for human coronavirus infection and that capmatinib and other drugs may exhibit antiviral activity by novel action on IRAK4. IRAK4 (Interleukin-1 receptor-associated kinase 4) is a serine/threonine kinase that forms part of the myddosome complex (consisting of MyD88 and other IRAK kinases) to transduce signals from Toll-like receptors (TLRs) or interleukin receptors44,45,46. In canonical myddosome signal transduction, activation of membrane TLRs results in recruitment of the adaptor protein MyD88 and its associated IRAKs. MyD88-bound IRAK4 recruits and phosphorylates additional IRAK kinases, such as IRAK1 and IRAK2, which can then dissociate from the myddosome and trigger a signaling cascade involving subsequent TRAF6 and TAK-1 activation44,45,46. These signaling events ultimately result in activation of the transcription factors NF-κB and MAPKs, which together contribute to the innate immune response to pathogens. Importantly, IRAK4 exhibits some functional redundancy with the related kinase IRAK147, which led us to consider inhibition of IRAK1 and IRAK4 as an antiviral mechanism for human coronavirus infection. We examined the effect of JH-I-25, a dual specific IRAK1 and IRAK4 inhibitor with no clinical relevance with IC50 values of 9.3 nM and 17.0 nM48 respectively, on human coronavirus infection. Treatment of LLC-MK2 cells with JH-I-25 (10 µM) greatly reduced CPE in cells infected with OC43 (Fig. 4F). Similar results were obtained with the IF assay in MRC-5 cells infected with 229E (Fig. 4G). To verify that our results were specific to the combined inhibition of IRAK1 and IRAK4, we silenced both using siRNA gene silencing. In concordance with results obtained from the JH-I-25 experiments, combined silencing of IRAK1 and IRAK4 attenuated 229E S protein abundance (Fig. 4H). Consistent with a role for IRAK1/4 in coronavirus infection, inhibition of p38 MAPK, known to be activated downstream of IRAK1/444,45,46, also impaired coronavirus infection (Fig. S4). Taken together, these data demonstrate that the effects of combined IRAK1/4 inhibition recapitulate the effects of capmatinib, as predicted by our in silico analyses. ## Discussion ### Computational analysis and antiviral protein target predictions In silico drug repurposing approaches have the innate advantage of accessing very large collections of information to uncover indirect associations that may have been otherwise overlooked. While the target-centric methodologies provide a more direct opportunity for drug repurposing, they are limited due to the overwhelming majority of human proteins not being targeted by existing small molecule drugs. The drug-, or structure-centric methodologies, on the other hand, while limited by the physicochemical properties of available approved drugs, provide access to a broader range of human targets. In this study, we addressed these challenges simultaneously by both exploring the targets with known approved drugs and searching for previously unappreciated modulators of undrugged targets among approved drugs. To that end, we paired two ML approaches designed for target-identification and drug-target interaction predictions, demonstrating the viability of an in silico first repurposing workflow, coupled with robust bioactivity assays. We integrated drug-target interactions, proteins and functional pathways in a multiscale interactome network. Based on the assumption that drugs take effect by binding to proteins and regulating pathways, the multiscale interactome traces the biological processes of available treatments via the interactions across proteins, functional pathways, drugs and the target disease, COVID-19. To capture this process, our approach used biased random walks and a Graph Convolutional Network (GCN) to model the correlations of nodes of multiple types and build embeddings for each drug, protein and pathway. The GCN module refines the protein and drug embeddings by further aggregating the relations in the network. GCN has been reported to be capable of encoding both graph structure and node features very efficiently. The model has a sequence of non-linear filter layers which aggregates the information of every node’s vicinity, making it effective to learn both local and global relations from lower to higher layers. The GCN embeddings were optimized in an unsupervised manner to encode the direct and indirect relations in the multiscale interactome. Then by ranking the proximity between the embeddings of candidate proteins to the target disease, the GCN model determined the potential efficacy of drugs or protein targets for this disease. ### Matchmaker, PolypharmDB, and drug repurposing The multiscale interactome GCN unveiled multiple plausible viral-host targets for repurposing leads. Rather than subjecting a single protein to a target-centric computational screen, the subsequent screening stage maximized diversity in both targets and their putative binders. Repurposing targets prioritized by the GCN were cross-referenced to PolypharmDB, a precompiled database of off-target interaction predictions between 8525 human proteins and 10,244 small molecule compounds with prior clinical evaluation. This approach contrasts sharply with disease-centric or target-centric approaches, which make up the overwhelming majority (~ 90%) of drug repurposing studies49. Evidence that capmatinib’s antiviral activity is driven by interactions other than its known target MET is provided by the lack of antiviral activity of AMG-337, another potent inhibitor of MET RTK (Fig. 4A–E). AMG-337 s is chemically distinct from capmatinib, which likely drives its differential polypharmacology. Criteria were set to maximize the diversity of compound and target selection for downstream evaluation. The recognition that polypharmacology may play a role in effective therapeutics motivated the evaluation of multiple targeted agents, leading to the nomination of capmatinib and other compounds for testing. Underappreciated polypharmacology may play a larger role in the activity of small molecule drugs; a study investigating oncology medications found for several drugs investigated that on-target interactions were inconsequential for drug activity, with off-target effects driving efficacy50. Alternatively, the use of multiple targets as separate or as combined objectives may have contributed to the success of this investigation simply by providing more possibilities for favorable outcomes. However, since few compounds are evaluated per presumed target and since these are mostly based on off-target interaction predictions, negative results obtained through this process are unable to inform on the involvement of their respective proteins on cell infectivity. Nonetheless, there may be broader opportunities within a drug-centric approach for drug repurposing, where validated therapeutic targets can be linked to small molecule drugs through approaches like PolypharmDB. To that end, several other groups have used cell-based drug screening or computational approaches to identify drug repurposing candidates for COVID-19 (reviewed by51,52,53). Our approach, which uses a unique computational pipeline for identification of clinically-relevant drugs followed by experimental testing using a broad range of coronaviruses, is complimentary to these approaches. We are encouraged that our approach identified several compounds/families of drugs that have also been identified and tested for their ability to inhibit coronavirus infection in vitro, including polidocanol54 and anidulafungin55,56. We also identified additional drugs including capmatinib and palbociclib, which to our knowledge have not been previously reported as having antiviral activity for human coronavirus infection. This may reflect certain advantages to our method, which considered > 10,000 clinically-relevant drugs, which may allow identification of molecules not considered in smaller-scale screens. ### Capmatinib as an antiviral drug for COVID-19 and other human coronavirus diseases Capmatinib was developed as a MET RTK inhibitor for the treatment of various MET-amplified tumors57. The MET proto-oncogene encodes an RTK that serves as the receptor for hepatocyte growth factor (HGF). A number of small-molecule MET inhibitors have recently been developed and are currently undergoing clinical trials to determine their efficacy in reducing cancer morbidity and mortality58,59. The availability of data on the safety of MET inhibitors in the clinic, and in particular capmatinib, provides support for this strategy of drug repurposing via polypharmacology. We observed that capmatinib exhibited antiviral activity in the low micromolar range. Indeed, using the SARS-CoV-2 and SARS-CoV-1 pseudotype virus infection assay, we determined that the IC50 for capmatinib for neutralization of infection was 14.1 ± 0.2 and 26.0 ± 0.1 µM, which is in the range reported for action of other drugs targeting SARS-CoV-2 infection when tested in Vero and Calu-3 cells in culture, including remdesivir60. Hence, capmatinib should be considered as a candidate for therapeutic testing in further preclinical and clinical trials for the treatment of human coronavirus diseases, including COVID-19. In addition, while we have not tested the action of capmatinib against SARS-CoV-2 variants that have emerged in 20216,7, the broad antiviral activity that capmatinib exhibits against 5 genetically different human coronaviruses (229E, OC43 and NL63 live virus infection and SARS-CoV-1 and SARS-CoV-2 pseudotyped virus assays) suggests that capmatinib may hold promise in broadly treating SARS-CoV-2 variants of concern, or other variants that may arise from further antigenic drift as well as other emerging viruses. To our knowledge, this is the first demonstration of antiviral activity of capmatinib in cell-based coronavirus infection assays. While this manuscript was in preparation, other computational approaches predicted binding of capmatinib to the SARS-CoV-2 S protein, viral proteases, RNA-dependent RNA polymerase and/or viral endoribonuclease61,62,63. While our analysis indicates that capmatinib may act by targeting IRAK signaling, and we find a novel requirement for IRAK1/4 in supporting human coronavirus infection, the mechanism of antiviral action of capmatinib warrants further investigation in future studies. ### Novel role for IRAK signaling in supporting human coronavirus infection Myddosome signaling is considered an essential component of the innate immune response to bacterial PAMPs, and loss of function mutations in IRAK4 or MyD88 results in a primary immunodeficiency syndrome associated with a dramatic increase in susceptibility to specific pyogenic bacterial infections64,65,66,67. In contrast, MyD88 and IRAK4 may have distinct roles in response to other pathogens, as their perturbation often does not impact susceptibility to some viral, fungal, protozoal, or other infectious agents64,65,66,67,68. Notably, MyD88 perturbation contributes to coronavirus infection and symptom severity in animal models69. However, whether and how human coronaviruses may engage TLR and IRAK signals during infection remains poorly understood. While IRAK1 and 4 are broadly expressed, in single-cell datasets deposited in the covid19atlas, IRAK1 and IRAK4 appear highly expressed in Secretory3 cells in the bronchial epithelial dataset70. Interestingly, Secretory3 cells have the highest expression of ACE2 as compared to other cell types in the primary human bronchial epithelial cell dataset, consistent with a role for IRAK1/4 in supporting coronavirus infection. Our results from two different human coronaviruses and two different host cell lines suggest that human coronavirus infection requires IRAK1 and/or IRAK4. We focused our studies on concomitant perturbation of IRAK1 and IRAK4, given the redundancy that has been reported between these kinases in some contexts71. Consistent with our results, another study performed an analysis of phosphorylated sequences within host cells and predicted activation of IRAK4 within 15 min of infection of Vero cells with SARS-CoV-2, and also revealed that a different inhibitor of IRAK1/4 impaired SARS-CoV-2 infection72. Together with the results presented here, this suggests that IRAK1/4 may contribute a non-canonical function to support human coronavirus infection. Recent work has also established that modulation of IRAK4 dependent immune responses is crucial for mounting an appropriate immune response during SARS-CoV-2 infection, supporting this observation73. As such, therapeutic modulation of IRAK signaling, and perhaps also that of TLRs and MyD88, may be a useful strategy for treatment of patients with COVID-19. In fact, a phase II clinical trial is ongoing to probe the use of the IRAK4 selective inhibitor PF-06650833 to treat COVID-19 patients with acute respiratory distress syndrome74. Supporting the role of this signaling pathway in the progression of the disease, obese individuals have increased TLR/MyD88 signaling that may predispose them to severe COVID-19 symptoms75. In this study, we use multiple methods involving a multiscale interactome GCN and the PolypharmDB drug repurposing database to identify new drug targets and drug repurposing candidates for the treatment of human coronavirus disease. We also provide evidence that several drug molecules predicted by this method have previously unknown antiviral activity against human coronavirus infection, in particular capmatinib. Further, we identify IRAK1/4 as new and unexpected coronavirus drug targets, required for coronavirus infection. This work highlights the potential of this computational approach, but it is important to note that additional pre-clinical and clinical testing is required before conclusions can be made about efficacy of treatment coronaviruses diseases in humans. Nonetheless, this indicates that the methods described herein are a novel and powerful approach for the rapid identification of new therapeutic strategies to identify antiviral drugs and could also be applied more widely for novel therapeutic intervention to other classes of disease. ## Methods ### Materials #### Viruses 229E and OC43 coronaviruses were obtained from the American Type Culture Collection (ATCC) (ATCC VR-740™ and ATCC VR-1558™). NL63 coronavirus was kindly provided by Dr. Scott Gray-Owen (University of Toronto). Original viral stocks were stored at -80ºC until use and all subsequent viral stocks were produced from the original parental stocks. #### Cell lines MRC-5 (lung fibroblast) cells were obtained from ATCC (ATCC CCL-171™). CoronaGrow LLC-MK2 (kidney epithelial) cells, a subclonal line of parental LLC-MK2 cells were obtained from VectorBuilder Inc. (Chicago, IL, Cat. No. CL0004). HEK293T cells expressing the full-length SARS-CoV-2 spike (BEI NR52310) were obtained from BEI Resources (Manassas, VA). HEK-293 T cells expressing the SARS-CoV-2 spike were kindly provided by S. Pöhlmann (Leibniz Institute for Primate Research, Göttingen, Germany). HeLa-ACE2 cells were kindly provided by D.R. Burton (The Scripps Research Institute). ### Multiscale Interactome A combined host–pathogen multiscale interactome was assembled by augmenting a pre-constructed, base human network with viral-host protein–protein interaction data. The base multiscale interactome network consisting of drug-protein interactions (8,568), human protein–protein interactions (387,626) and protein-pathway interactions (22,545) was retrieved from Ruiz et al.34, which aggregates data from multiple primary sources76,77,78,79,80,81,82,83,84,85,86. An additional 332 experimentally-derived, viral-host protein–protein interactions were added to adapt the network for SARS-CoV2 repurposing23. Then for a given viral protein that interacts with human proteins, we investigated the pathways in which these human proteins are involved. We added direct connections between viral proteins and the retrieved human functional pathways. In our experiments, adding direct connections between viral proteins and human pathways shows significant improvement in performance. Lastly, COVID-19 was introduced as a final entity to the multiscale interactome network and linked to all SARS-CoV-2 proteins. The multiscale interactome was represented as a graph G = (V, E), where individual proteins, pathways and drugs form vertices (V) and interactions form the edges (E). The goal of our approach is to learn meaningful embeddings of the nodes in the multiscale interactome network so that we can predict drug candidates or protein targets using these embeddings. To propose a proper embedding function, naively, we can introduce the bias of graph homophily, i.e. drugs/targets that connect to the viral protein via the shortest paths are the most likely to be effective. This is reflective of the assumption that drug effects propagate along the biological network to treat diseases. However, non-homophily relations can be equally important—for example, a protein can be a promising target if it is involved in several important related pathways, although it may not be directly connected to viral proteins. To address this challenge, we use graph convolutional networks to learn this hierarchy of complex relations from the interactome data. ### Graph convolutional network To prepare the Graph Convolutional Network (GCN), initial node embeddings were generated using Node2Vec87. The return parameter p and “in–out” parameter q, in Node2Vec were set to 0.25 in order to balance global and local views of the random walk process88, which helped capture the aforementioned homophily and non-homophily relations. The embedded dimensions size D was set to 64 and node2vec was applied to the multiscale interactome graph G to convergence. The Node2vec output was an embedded matrix $$H_{n} \in {\mathbb{R}}^{K,D}$$, where $$K = \left\| V \right\|$$ is the number of nodes, and each row in Hn is the learned representation for the corresponding node. These embeddings were used as the initial input feature layer, H(0), in our GCN model. The model consists of stacked multiple Graph Convolution and each one of them is defined by Eq. 135. In this model, α is the activation function ReLU, $$\tilde{A} = A + I_{N}$$ is a transformation of the multiscale interactome adjacency matrix (A) with the additional self-associating nodes (identity matrix IN), H(l) and W(l) representing layer-specific feature vectors and trainable weights, while $$\tilde{D}$$ is a diagonal degree matrix defined by $$\tilde{D}_{ij} = \sum\nolimits_{j} {\tilde{A}_{ij} }$$. $$H^{{\left( {l + 1} \right)}} = \sigma \left( {\tilde{D}^{{ - \frac{1}{2}}} \tilde{A}\tilde{D}^{{ - \frac{1}{2}}} H^{\left( l \right)} W^{\left( l \right)} } \right)$$ (1) The adjacency matrix $$A \in {\mathbb{R}}^{K,K}$$ in Eq. 1 is generated by the edges E in the multiscale interactome. Each element in A is either the connection weight or zero if there is no connection. The output features of the last layer $$H^{\left( L \right)} = \left[ {h_{1}^{\left( L \right)} ,h_{2}^{\left( L \right)} , \ldots ,h_{K}^{\left( L \right)} } \right]^{T}$$ are then normalized to produce the final embedding for each node. $$h_{i} = \frac{{h_{i}^{\left( L \right)} }}{{\left\\| {h_{i}^{\left( L \right)} } \right\\|_{2} }}$$ (2) To train the GCN model, we first compute cosine similarity between the embeddings of all nodes, $$s_{ij} = h_{i}^{T} h_{j}$$ and use a diffusion loss inspired by Liu et al.89 to train the model parameters with gradient backpropagation, $$L\left( {s_{ij} } \right) = - \frac{\alpha }{2}\left( {s_{ij} - \beta } \right)^{2} ,$$ where $$\alpha > 0$$, and β is a predefined threshold and set to 0.25 in this work. The idea of the loss function is to cluster embeddings of relevant nodes in the multiscale network and separate those irrelevant embeddings conversely. This effect can be observed from the derivative of L: $$\frac{{\partial L\left( {s_{ij} } \right)}}{{\partial s_{ij} }} = - \alpha \left( {s_{ij} - \beta } \right).$$ Therefore similarity values larger than threshold β are encouraged and embeddings of relevant nodes will cluster. Conversely, the loss function also diverges the embeddings of irrelevant nodes in the network even further away. Finally, we train the model for fixed 20 epochs and obtain the updated embeddings hi for each node. The final embeddings were then saved for further computation. Lastly, the proximity values (i.e. cosine similarities) from COVID-19 to each drug and each human protein present in the multiscale interactome were calculated and ranked to identify direct repurposing candidates and plausible targets (see section “Compound Selection”). Source code for generating the proximity values is made available at https://github.com/bowang-lab/gcn-drug-repurposing. ### Drug-target interaction predictions To identify small molecule drug candidates for host-based targets proposed by the GCN with few or no known binders, we looked up Drug Target Interaction (DTI) predictions in PolypharmDB37. PolypharmDB is a drug-repurposing database of pre-computed drug-target interaction predictions, evaluated by using the 2020Q2 beta release of MatchMaker90. Matchmaker is a deep learning model that predicts interaction of a small molecule drug/binding site pair using paired structural features of the drug with the 3D structural features of the protein binding sites. MatchMaker models with positive training examples complexes obtained by threading drug-target interaction (DTI) data91 onto 3D structures of protein–ligand binding sites obtained from the Protein DataBank92 and SwissModel93, on the basis of chemical similarity90. Negative training examples are obtained by random shuffling of positive DTI pairs, and models are trained on progressive thresholds of increasing stringency in accordance to the confidence in the source DTI and in the selection of representative 3D structures94. The compound screening library consists of 10,244 small molecule drugs, retrieved from DrugBank95 on February 19th, 2020. The library excluded compounds with fewer than four carbon atoms, or whose SMILES chemical structure was unable to be parsed by RD-KIT (Release_2018_09_1) RDKit: Open-source cheminformatics; http://www.rdkit.org)95. The screening set includes 2118 approved drugs, 2242 drugs in clinical trials and 5547 molecules in preclinical development or nutraceuticals. The protein screening library represents 29,290 pockets from 8525 human proteins obtained by the PDB92 (retrieved January 2018) and SwissModel93 database (Retrieved June 2018). Specifically, pockets correspond to binding sites of drug-like molecules observed as cocrystalized ligands in the PDB source files, or superimposed ligands from template structures from SwissModel source files. Drug-target interaction pairs were evaluated using all combinations of small molecule drugs and available binding site structures. Individual human proteins were ranked on the basis of their top-scoring pockets. Additional details related to the construction of PolypharmDB and screening libraries are available from Redka et al. 202037. ### Compound selection Small molecule repurposing candidates were selected from three methods combining the GCN network and PolypharmDB (Fig. 1) approaches. For each method, a systematic selection criterion was applied, as described below, to maximize the diversity of assayed compounds and to ensure the relevance of the hit to the infectivity-based assays, its availability, and repurposing appropriateness. Selected drugs for all three methods are provided in Table 1. For Method 1, a target-centric drug repurposing approach, compounds were selected from the top 60 drug candidates suggested directly by the GCN, on the basis of their network distance to COVID-19. Since the GCN input multiscale interactome contained a broad variety of drugs, the following criteria were applied to reduce the number of candidates from 60 to 10 compounds: 1. 1. Non-small molecule drugs, such as recombinant proteins were eliminated (e.g., peginterferon alfa-2b); 2. 2. Only one candidate was chosen if multiple drugs shared the same protein in the final node of the path to COVID-19 (e.g., only top scoring flucytosine was chosen from a total of 4 candidates connected to DNMT1); 3. 3. Candidates that were a part of networks involved with the cytokine storm, adaptive immunity, or lymphocyte response were not selected (e.g., chloramphenicol connected to CD55, CD4-positive, alpha–beta T cell cytokine production node was not selected); 4. 4. Natural amino acids (e.g., L-asparagine) and non-drug like compounds (e.g., urea and calcium chloride) were not selected; 5. 5. Only FDA approved candidates were selected. Once 10 compounds were selected in the order of their network distance to COVID-19, the selection process was completed corresponding to the last compound having a rank of 40. Methods 2 and 3, drug-centric repurposing approaches, combined the GCN for viral-host target selection and PolypharmDB to predict small molecule binders for the proposed targets. Target selection was performed by ranking human proteins in accordance with their GCN proximity scores to COVID-19. The top 100 human proteins of 17,660 represented in the network were considered in the selection process. From those 100 proteins, 66 were eliminated because they were missing from the proteome included in PolypharmDB. Out of the remaining 34 proteins, 11 proteins were eliminated because the descriptions of their functions on Uniprot or GeneCards contained terms associated with the stages of the viral infection that were outside the scope of the infectivity-based assay in MRC-5 human lung fibroblast cells used in this study: lymphocyte response, cytokine storm, natural killer cell cytotoxicity, immune synapse formation, T-cell or B-cell response. The remaining 23 proteins were manually curated to prioritize 10 proteins that were most likely to be associated with the different stages of the viral cycle, such as attachment and entry, translation, replication, assembly, or release, based either on the description of their function or previous reports. Those selected ten proteins were as follows: UGGT2, SDF2, NLRX1, MOGS, HEPACAM, IRAK4, ADAM15, CD46, LILRA3, and CHPF2. Another set of 5 proteins out of 23 proteins had functions with a potential of being involved in the viral infection of lung fibroblasts, and therefore those proteins were reserved as a supplemental list of targets if insufficient predicted binders were found for the primary list of 10 targets. That supplemental list of targets was as follows: TARS2, GOLGA3, MDN1, THUMPD2, ZBTB37. The remaining 8 of 23 proteins were removed from consideration. Following the selection of the primary list of 10 targets, Methods 2 and 3 diverge in their compound selection process. For Method 2, the top ten ranking FDA-approved small-molecule repurposing candidates for each protein (i.e. 10 single-target panels; a total of 100 candidates) were filtered to 13 compounds, as described below. For Method 3, top 25 ranking FDA-approved small-molecule candidates for a single multi-target polypharmacological panel that included all 10 proteins (i.e., a single 10-targets panel) were analysed to yield 2 additional compounds that were distinct from those that were already selected by Method 2. The analysis of the latter was based on the weighted aggregate score of all targets. Since both lists of 100 and 25 top ranking compounds were already filtered to contain only small molecules and FDA-approved drugs, for both methods, the compounds were further selected by following these criteria: 1. 1. The compound is predicted to be interacting with the target by MatchMaker, in addition to having a high rank relative to the proteome; 2. 2. The compound is drug-like (i.e., natural compounds and endogenous ligands, natural amino acids, urea, metal chelators were excluded); 3. 3. Tracer compounds or topical medications were not selected; 4. 4. Duplication of the class of drug and its indication was minimized (e.g., only two antivirals out of 9 candidates, and only one sodium glucose co-transporter-2 inhibitor out of 3 candidates in the list of top 100 by Method 1 were selected); 5. 5. The number of targets from the primary list of 10 represented in the final selection was maximized (i.e., select one candidate per target screen first, but if some targets did not result in any compounds with a significant probability of interaction predicted by MatchMaker, then select additional compounds from the supplemental list of targets; as a result, some targets are represented 2–3 times in Table 1). Following the criteria described above, 13 compounds out of 100 were selected by Method 2, and 9 compounds out of 25 were selected by Method 3. However, 7 of the repurposing candidates were common to compounds from Method 2, resulting in only 2 unique compounds (see Table 1). An additional compound scored highly for the supplemental targets of interest and was nominated to be included in the testing panel given its predicted performance and the distinct target mechanism (Table 1). ### Cell culture and human coronavirus propagation For propagation of cell lines for use in coronavirus infection experiments, cells were maintained in a standard tissue culture incubator maintained at 37 °C with 5% CO2. For infection of cells and propagation of coronaviruses, cells were maintained in a standard cell culture incubator maintained at 33 °C with 5% CO2. This temperature was determined to support optimal propagation of human coronaviruses and yielded higher viral titers than preparations of the virus grown at 37 °C. MRC-5 and LLC-MK2 cell lines were maintained in growth medium, consisting of Minimum Essential Medium Eagle (MEM), with Earle's salts, L-glutamine and sodium bicarbonate (Sigma Aldrich Cat. No. M4655) and supplemented with 10% heat-inactivated fetal bovine serum (FBS, ThermoFisher Scientific Cat. No. 10082147) and 1X penicillin–streptomycin (P/S, ThermoFisher Scientific Cat. No. 15070063). For all experiments involving coronavirus infection, cells were maintained in infection medium, which is the same as growth medium, except the concentration of heat-inactivated FBS was 2%. For plaque assays, cells monolayers were overlaid with plaque media, consisting of 2 × MEM Temin’s modification, no phenol red (ThermoFisher Scientific Cat. No. 11-935-046), 2% heat-inactivated FBS, 1 × P/S, and mixed 1:1 with pre-warmed 0.6% agarose (ThermoFisher Scientific Cat. No. 16500-500). Alternatively, see Table S1 for specific formulations of culture media. Propagation of human coronaviruses was performed based on suppliers’ instructions. Briefly, MRC-5 or LLC-MK2 cells were grown to 90% confluence in a T75 tissue culture flask in standard growth medium. Cell monolayers were washed 2 × with infection medium prior to infection. Cell monolayers were infected with 229E (MRC-5 cells), OC43 (LLC-MK2), or NL63 (LLC-MK2) at a MOI of 0.01 in a total volume of 4 mL infection medium for 2 h adsorption at 33 °C with 5% CO2. Following viral adsorption, unbound virus was aspirated, and cell monolayers were washed 2 × with infection medium, and then 12 mL fresh infection medium was added. Flasks were then placed back in the 33 °C incubator for a period of 2–4 days depending on the coronavirus strain to achieve maximal viral titer. To harvest the virus, supernatant was collected in a 15 mL conical tube and centrifuged at 1000 × g for 10 min to pellet cell debris. Viral stocks were stored as single use aliquots at − 80 °C. Viral concentration of new preparations of viral stocks were measured by PFU assay. ### Immunofluorescence detection of 229E infection Briefly, MRC-5 human lung fibroblast cells (seeded on glass coverslips) were infected with 229E at a MOI of 0.01 in the presence of drug (1–10 µM) or vehicle control for 1 h at 33 °C and 5% CO2. Following incubation, excess unbound virus was removed, and cells were incubated in fresh infection medium with drugs for an additional 48 h. This time point was chosen because it was initially determined to result in infection of ~ 100% of control cells and thus provided a baseline for examination of antiviral activity. This time point was also chosen because the infected cells remained in a virtually intact monolayer with minimal CPE—extensive CPE could lead to sampling errors and could be confounded with potential cytotoxic effects of the drugs. Drugs that caused signs of cytotoxicity (identified by DAPI staining) were excluded from further analysis as they confounded interpretation of potential antiviral effects in the IF assay. For the IF protocol, cells infected with coronaviruses were washed 2 × with PBS (with Mg2+ and Ca2+) and then immediately fixed for 1 h with 4% paraformaldehyde. This was followed by 15 min treatments with: 0.15% glycine, 0.1% triton X-100, and 3% bovine serum albumin with PBS washes in between each step. 229E S protein was detected with treating the cells with 100 µL (1:50 dilution) of the mouse anti-229E S protein antibody 9.8E1297 by the inverted drop technique for 1 h at room temperature. Following primary antibody incubation, cells were washed and treated with AlexaFluor488-conjugated anti-mouse secondary antibody (1:1000 dilution) (Cedarlane Labs Cat. No. 115–545-003) and DAPI (1 µg/mL) for 1 h at room temperature. Following another wash, coverslips were mounted on glass slides with DAKO mounting media (Agilent Technologies Cat. No. S3023) and then incubated at room temperature overnight to solidify. Slides were visualized on an inverted microscope by widefield epifluorescence (Leica DMi8 microscope, Andor Zyla 4.2-megapixel camera, run by Quorum WaveFX by Metamorph software). For each IF experiment, a total of 10–20 randomly chosen fields were selected in the DAPI channel for acquisition of the 229E S protein with a 10 × objective lens. Images were quantified by measuring the total fluorescence signal using ImageJ software (National Institutes of Health, Bethesda, MD)98. ### Human coronavirus plaque assays All coronavirus plaque assay protocols were adapted from previously described methods for measuring viral concentration using PFU assays99,100,101. Briefly, cells were grown to confluency on 6-well tissue culture plates and then infected with serially diluted virus in a volume of 300 µL for 1 h adsorption at 33 °C with 5% CO2, with gentle agitation every 15 min. Following adsorption, unbound virus was removed, and cells were washed 2 × with infection media and then overlaid with plaque media. In experiments involving the testing of potential antiviral compounds, drugs were added to the infection media during adsorption and to the plaque media. Following an incubation period of several days to establish CPE (see below for virus-specific information), cells were fixed with 10% neutral buffered formalin overnight, followed by removal of the agarose plug and counterstaining with 1% crystal violet solution to visualize the plaques. For all plaque assays, each condition was performed in technical triplicates. • 229E: Confluent monolayers of MRC-5 cells were grown on 6-well tissue culture plates and infected with serially diluted 229E virus. After washing away unbound virus, the cells were overlaid with a semi-solid agarose medium to restrict the spread of virus to adjacent cells. After 5–7 days incubation, cells were fixed and stained to quantify the number of plaques in each well. • NL63: NL63 viruses were propagated in the monkey kidney epithelial cell line LLC-MK2, which has been reported to support NL63 production102. Confluent monolayers of LLC-MK2 cells were grown on 6-well plates and infected with serially diluted NL63 virus. After washing away unbound virus, the cells were overlaid with a semi-solid agarose medium to restrict the spread of virus to adjacent cells. After 4 days incubation, cells were fixed and stained to quantify the number of plaques in each well. • OC43: We determined that OC43 viruses could be readily propagated in LLC-MK2 cells, similar to NL63 viruses. Confluent monolayers of LLC-MK2 cells were grown on 6-well plates and infected with serially diluted OC43 virus. After washing away unbound virus, the cells were overlaid with a semi-solid agarose medium to restrict the spread of virus to adjacent cells. After 4 days incubation, cells were fixed and stained to quantify the number of plaques in each well. ### qRT-PCR detection of NL63 LLC-MK2 cells seeded on 6-well tissue culture plates were infected with NL63 at a MOI of 0.01 for a 1 h adsorption period in the presence of 10 µM capmatinib in a volume of 300 µL. Following viral adsorption, cells were washed 2 × with infection media and then 500 µL fresh media/drug was added to the cells for a 3-day incubation period. To extract total NL63 RNA, 1 mL TRIzol™ Reagent (ThermoFisher Scientific) was added directly to the samples (cells + supernatant) and cells were lysed by scraping. Total RNA was purified using the Direct-zol™ RNA Miniprep Kits (Zymo Research, Irvine, CA) according to manufacturer’s instructions. Reverse transcription and qPCR were performed in a one-step reaction using Luna Universal One-Step RT-qPCR (NEB, Ipswich MA) according to manufacturer’s instructions. RT-qPCR reactions were performed on a CFX96 thermal cycler (Bio-Rad, Mississauga, ON). Experiments were performed with at least 2 technical replicates to monitor variation between wells, no template/no RT controls, and melt curves. Reactions were performed at a final volume of 20 µL with 20 ng input RNA and a primer concentration of 500 nM. All results were normalized to GAPDH RNA levels and to the infected, non-drug treated condition. Relative change in NL63 RNA was calculated using the 2−ΔΔCt method103. A minimum of 3 experimental replicates were used to assess NL63 Nucleocapsid RNA using previous established primers104. For a complete list of qPCR primers see Table S2. For thermal cycler conditions see Table S3. ### siRNA transfection siRNA transfection was performed by two individual transfections at 72 h and 48 h prior to infection or other experimental manipulation, respectively. Briefly, MRC-5 cells were grown to 40% confluency before the first round of transfection. On the day of transfection, cells were placed in fresh growth medium. A transfection master mix was made in Opti-MEM (ThermoFisher Cat. No. 31985070) by diluting stock siRNA solutions to a final concentration of 50 nM and 6.3 µL Lipofectamine RNAiMAX transfection reagent (ThermoFisher Cat. No. 13778030) per well of a 6-well tissue culture dish. Cells were transfected for 4 h before switching to fresh growth medium. For a list of siRNA sequences see Table S2. ### Pseudotyped virus particle assay SARS-CoV-2 pseudotyped viruses (PsV) were prepared using an HIV-based lentiviral system as previously described11 with few modifications. Briefly, PsVs were produced by transfection of human kidney HEK293T cells with the full-length SARS-CoV-2 spike (BEI NR52310) or SARS-CoV-1 spike (kindly provided by S. Pöhlmann, Leibniz Institute for Primate Research, Göttingen, Germany). Cells were co-transfected with a lentiviral backbone encoding the luciferase reporter gene (BEI NR52516), a plasmid expressing the Spike (BEI NR52310) and plasmids encoding the HIV structural and regulatory proteins Tat (BEI NR52518), Gag-pol (BEI NR52517) and Rev (BEI NR52519). After 24 h at 37 °C, 5 mM sodium butyrate was added to the media and the cells were incubated for an additional 24–30 h at 30 °C. Next, the PsV particles were harvested, passed through 0.45 μm pore sterile filters and finally concentrated using a 100 K Amicon (Merck Millipore Amicon-Ultra 2.0 Centrifugal Filter Units). Neutralization was determined in a single-cycle neutralization assay using HeLa-ACE2 cells (kindly provided by D.R. Burton; The Scripps Research Institute). To that end, 50 µL of twofold serial dilutions of the small molecules were incubated with 10,000 cells/well seeded the day before (100 µL/well) for 1 h at 37 °C. After 1 h incubation, 50 µL of PsVs was added to each well and incubated for 48 h-60 h in the presence of 10 µg/mL of polybrene (Sigma Aldrich, TR-1003-G). Infection levels were inferred from the amount of luminescence in relative light units (RLUs) after adding 50 µL Britelite plus reagent (PerkinElmer) to 50 µL of media containing cell (i.e. after removing 130 µL/well to account for evaporation). After 2 min incubation, the volume was transferred to a 96-well white plate (Sigma-Aldrich) and the luciferase intensity was read using a Synergy Neo2 Multi-Mode Assay Microplate Reader (Biotek Instruments). Two to three biological replicates with two technical replicates each were performed. Culture media was prepared by supplementing DMEM media with 2% inactivated FBS and 50 µg/ml of gentamicin. IC50 values were calculated using Prism. In order to confirm that the reduced infection was not related to cell toxicity, HeLa-ACE2 cell viability upon incubation with serial dilutions of the small molecules was assessed. 10,000 cells/ well of pre-seeded HeLa-ACE2 cells were co-cultured with twofold serial dilutions of the small molecules at 37 °C for 48 h-60 h under the same conditions as in the neutralization assay. Cell viability was monitored by adding 50 µL of CellTiter-Glo 2.0 reagent (Promega) to 200 µL of media containing cells. After 10 min incubation, 100 µL volume was transferred to a 96-well black plate (Sigma-Aldrich) to measure luminescence in relative light units (RLUs) using a Synergy Neo2 Multi-Mode Assay Microplate Reader (Biotek Instruments). ### Drug library Unless indicated otherwise, all compounds were purchased from MedChemExpress (Monmouth Junction, NJ) and were reconstituted according to manufacturer’s specifications. A complete list of compounds is provided in the Table S4. All compounds were reconstituted to stock concentrations of 1–10 mM and frozen in individual aliquots at − 80 °C until use. ### Statistical analysis All statistical analysis for biological experiments were performed with GraphPad Prism 9 software using student t-tests when comparing two conditions (Figs. 3B,D,E, 4B,E,F,G, S2A) or one-way ANOVA with Tukey post-hoc test when comparing multiple conditions (Figs. 3A,C, 4A,C, S4).	{}
MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4). 3 deleted 19 characters in body; edited title # Real analytic function, injective, non surjective and prevervingpreserving the rationals ? Hi, I'd like to prove the none-existence non-existence of a real analytic function, injective, non-surjective that sends rationals to rationals. Is it a classical result ? If not, any hints on how to prove it ? Thanks in advance for you helpChristian Aebi. 2 retagged 1 # Real analytic function, injective, non surjective and preverving the rationals ? Hi, I'd like to prove the none-existence of a real analytic function, injective, non-surjective that sends rationals to rationals. Is it a classical result ? If not, any hints on how to prove it ? Thanks in advance for you help Christian Aebi	{}
# How to set the maths font in Beamer when using XeLaTeX? I am using XeLaTeX with fontspec and mathdesign to set the maths font separately. This works fine in memoir, for example, but Beamer overrides my maths font settings and uses the main font as a maths font. Minimum example: \documentclass[serif]{beamer} \usepackage[utopia]{mathdesign} \usepackage[no-math]{fontspec} \setmainfont{Liberation Serif} \begin{document} \begin{frame} \frametitle{Minimum working example} \begin{itemize} \item normal text set in Liberation Serif and maths \textbf{also,} instead of Adobe Utopia as intended $v_x(t) := \lim\limits_{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t} =: \frac{\mathrm{d}v_x}{\mathrm{d}t}$ \end{itemize} \end{frame} \end{document} This produces the following output, all set in the main font: • Yes, the command that worked is \usefonttheme{professionalfonts}. Sep 5, 2015 at 10:33 • If you are using xetex you probably should be using unicode-math for changing the math font. Sep 5, 2015 at 16:30 As you found out yourself, \usefonttheme{professionalfonts} is needed to be able to use opentype fonts with beamer. However, I want to add that you probably should use unicode-math together with xelatex to change the math-fonts. \documentclass[serif]{beamer} \usefonttheme{professionalfonts} \usepackage{fontspec} \setromanfont{Linux Libertine O} \usepackage{mathtools} \usepackage{unicode-math} % check name of font for your system, this works on Ubuntu \setmathfont{TeX Gyre Pagella Math} \begin{document} \begin{frame}{Unicode-Examples} Some unicode in formulas: $$α² + β² = γ²$$ And a fraction: ½. \end{frame} \end{document} For some reason the comments containing the answer have disappeared, but I hope it is not impolite to answer my own question on the basis of those comments. The solution is to use \usefonttheme{professionalfonts} in the preamble. The minimum working example is now: \documentclass[serif]{beamer} \usepackage[utopia]{mathdesign} \usepackage[no-math]{fontspec} \setmainfont{Liberation Serif} \usefonttheme{professionalfonts}% SOLUTION % \begin{document} \begin{frame} \frametitle{Minimum working example} \begin{itemize} \item normal text set in Liberation Serif and maths \textbf{also,} instead of Adobe Utopia as intended $v_x(t) := \lim\limits_{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t} =: \frac{\mathrm{d}x}{\mathrm{d}t}$ \end{itemize} \end{frame} \end{document} Producing (having corrected the physics mistake above as well).	{}
Mathematics # An angle is equal to one-third of its supplement. Find its measure. ##### SOLUTION Let angle be $\dfrac{x}{3}$, then its supplementary will be x $x + \dfrac{x}{3} = \dfrac{4}{3} x = 180$ $x = 135^o$ $\dfrac{135}{3} = 45^o$ is measure of angle. You're just one step away Subjective Medium Published on 09th 09, 2020 Questions 120418 Subjects 10 Chapters 88 Enrolled Students 87 #### Realted Questions Q1 Single Correct Medium Find the value of $x$ and $y$. • A. $45^{\circ}, 60^{\circ}$ • B. $45^{\circ}, 45^{\circ}$ • C. $60^{\circ}, 60^{\circ}$ • D. $60^{\circ}, 45^{\circ}$ Asked in: Mathematics - Lines and Angles 1 Verified Answer \| Published on 09th 09, 2020 Q2 Subjective Medium Find the value of unknown 'x' in the following triangles. Asked in: Mathematics - Lines and Angles 1 Verified Answer \| Published on 09th 09, 2020 Q3 Subjective Medium Suppose two adjacent angles are supplementary. show that one of them is obtuse angle, then the other angle must be acute. Asked in: Mathematics - Lines and Angles 1 Verified Answer \| Published on 23rd 09, 2020 Q4 Single Correct Medium In the figure, AO=OD and OB=OC. Then • A. $\displaystyle AB=CD$ • B. $\displaystyle \angle ABC=\angle BCD$ • C. $\displaystyle \angle BAD=\angle ADC$ • D. All of these Asked in: Mathematics - Lines and Angles 1 Verified Answer \| Published on 09th 09, 2020 Q5 Subjective Medium Read the following two statements which are taken as axioms: (i) If two lines intersect each other, then the vertically opposite angles are not equal. (ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $180^0$.	{}
+0 # ½ × 8 × 4 +2 347 1 ½ × 8 × 4 May 22, 2017 #1 +2340 0 $$\frac{1}{2}84$$ simplifies to $$16$$. $$\frac{1}{2}84$$ Multiplying by 1/2 is the same as dividing by two. The rest should be fairly simple: $$\frac{1}{2}84=\frac{8*4}{2}=\frac{32}{2}=16$$ . May 22, 2017	{}
# 13.4: Concept Mapping - Connecting Ideas Visually Either individually or as a group, create a concept map on a separate piece of paper or whiteboard that relates the processes of photosynthesis and cellular respiration. The words in the word bank below should go into bubbles. Arrange these bubbles in a way that helps communicate relationships between the words, then connect the bubbles with lines that have a verb or action phrase attached to them. It might help to start by organizing the words into related groups. You can use words more than once. For example, you could group $$\ce{CO2}$$ and ATP together, then draw a line connecting them to RuBisCO and Calvin Cycle. The verb for the connecting line could be “used in”. You could then draw a line from those two that said “produces”. What would that line connect to? Word Bank: Put these terms in bubbles $$\ce{O2}$$ $$\ce{H2O}$$ $$\ce{CO2}$$ $$\ce{H+}$$ ATP Glucose Photon Electrons Chloroplast Stroma Thylakoid membrane Mitochondrion Matrix Inner mitochondrial membrane Cytoplasm High energy electron carriers $$\ce{FADH2}$$ Glycolysis Krebs cycle Electron transport chain Chemiosmosis RuBisCO Calvin cycle	{}
CAT 2016 \| Question: 71 1 vote 218 views From a circular sheet of paper with a radius $20\:\text{cm}$, four circles of radius $5\:\text{cm}$ each are cut out. What is the ratio of the uncut to the cut portion? 1. $1:3$ 2. $4:1$ 3. $3:1$ 4. $4:3$ edited 1 vote First, we can draw the diagram. We know that area of circle $= \pi \times(\text{radius})^{2}$ Four circles are cut from the circular sheet, each has a radius $= 5\;\text{cm}$ Area of cut out portion $= 4 \times \pi \times(5)^{2} = 4 \times \pi \times25 = 100 \pi$ Area of uncut portion $=$ Area of circular sheet $-$ Area of a cutout portion $\qquad \qquad \qquad \qquad= \pi \times(20)^{2}-100 \pi = 400 \pi -100 \pi = 300 \pi$ $\therefore$ The ratio of the uncut to the cut portion $= 300 \pi :100 \pi = 3:1$ Correct Answer $:\text{C}$ 10.1k points 4 8 30 edited Related questions 1 164 views Direction for questions: Answer the questions based on the following information. In a locality, there are five small cities: $\text{A, B, C, D}$ and $\text{E}$ ... ration shop is to be set up within $3 \text{ km }$ of each city, how many ration shops will be required? $1$ $2$ $3$ $4$ 1 vote 2 241 views If $\text{ABCD}$ is a square and $\text{BCE}$ is an equilateral triangle, what is the measure of $\angle \text{DEC}?$ $15^{\circ}$ $30^{\circ}$ $20^{\circ}$ $45^{\circ}$ 1 vote The figure shows a circle of diameter $\text{AB}$ and radius $6.5$ cm. If chord $\text{CA}$ is $5$ cm long, find the area of $\triangle \text{ABC}$ __________ In $\triangle \text{ABC},\:\angle \text{B}$ is a right angle, $\text{AC} = 6$ cm, and $\text{D}$ is the mid-point of $\text{AC}$. The length of $\text{BD}$ is ___________ The points of intersection of three lines $2\text{X} + 3\text{Y} – 5 = 0, 5\text{X} – 7\text{Y} + 2 = 0$ and $9\text{X} – 5\text{Y} – 4= 0$ form a triangle are on lines perpendicular to each other are on lines parallel to each other are coincident	{}
Document Detail From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine Full Text Journal Information Journal ID (nlm-ta): J Inj Violence Res Journal ID (iso-abbrev): J Inj Violence Res Journal ID (pmc): kums ISSN: 2008-2053 ISSN: 2008-4072 Publisher: Kermanshah University of Medical Sciences Article Information Download PDF Copyright © 2012, KUMS open-access: Received Day: 25 Month: 5 Year: 2010 Accepted Day: 15 Month: 7 Year: 2010 Print publication date: Month: 1 Year: 2012 Volume: 4 Issue: 1 First Page: 10 Last Page: 19 ID: 3291287 PubMed Id: 21502792 DOI: 10.5249/jivr.v4i1.85 A study of the risk of mental retardation among children of pregnant women who have attempted suicide by means of a drug overdose Dora Petika Barbara Czeizela Ferenc Bánhidyb Andrew E. Czeizela* aFoundation for the Community Control of Hereditary Diseases, Budapest, Hungary. bSecond Department of Obstetrics and Gynecology, Semmelweis University, School of Medicine, Budapest, Hungary. * Corresponding Author at: Dr. Andrew E. Czeizel, H-1026. Budapest, Törökvész lejtő 32, Hungary, Tel/Fax: +36-1-3944712, E-mail:czeizel@interware.hu(Czeizel AE.). Introduction Suicide and self-inflicted injury are classified as intentional causes of death or diseases.1-4Hungary led the world in suicide mortality with the rates of about 45 per 100 000 persons in the 1970s and 1980s, later there was a decrease in this rate but it has remained high in an international perspective. In addition, the rate of suicide attempts by means of prescription drugs has increased significantly worldwide.3,4Suicide attempts by means of drugs and other chemicals have been termed self-poisoning.6The recent self-poisoning epidemic has produced a major socio-medical problem, mostly among young females.7Such suicide attempts also occur among pregnant women.8,9It is of interest that the number of pregnant survivors of suicides has increased significantly as a result of more effective medical intervention. However, survival may be associated with a greater risk of congenital abnormalities and/or mental retardation in the fetuses/children. We have evaluated the potential to estimate the teratogenic/fetotoxic risk of these prescription drugs10Clinical trials conducted before approval and marketing of a drug generally do not include pregnant women. Thus, it is necessary to base the potential for human teratogenic/fetotoxic risk on the results of experimental animal investigations. Ideally, screening tests in laboratory animals would identify the doses of drugs that can be human reproductive or developmental toxicants/teratogens. However, current screening systems are imperfect, and multiple factors prevent direct extrapolation of results on pregnant women. Thus, the harsh reality is that humans are the ultimate test model for detection of drugs and specially the doses of drugs that are found to be human teratogens. Two types of post-marketing data of drugs have been used to estimate their human teratogenic potential. The first type of data set is obtained through case reports, clinical case series, and randomized controlled trials. However, case reports have serious selection bias, clinical case series usually do not have appropriate controls, and there are serious ethical barriers to performing randomized controlled trials on pregnant women. The second type of data set is associated with analytical epidemiological studies and/or registry/surveillance/monitoring systems.11However, identifying a possible association between the low clinical doses of drugs and structural birth defects, i.e. congenital abnormalities are confounded by the recall bias of mothers with affected children compared to mothers with healthy babies, and there is usually an inability to estimate a dose-response relationship. Although such post-marketing data can be useful in predicting human teratogenic risk of drug exposures, medical practitioners must consider the accuracy of these predictions with caution. Thus the self-poisoning model of pregnant women based on the Budapest Registry of Self-poisoned Patients12offers a unique approach for studying the potential teratogenic and fetotoxic-neurotoxic effects of drugs on the fetuses. Of 1 044 self-poisoned pregnant women, 411 delivered live-born infants between 1960 and 1993, and of these 411 children, 367 (89.3%) were evaluated for health status, in particular congenital abnormalities, birth weight and post-conceptional age, cognitive status as well as behavioral development.10 This paper summarizes the data of 27 children who were born to mothers who used the combination of amobarbital, glutethimide and promethazine (Tardyl®) for a suicide attempt during pregnancy. This medicinal product is one of the most popular prescription drugs for the treatment of insomnia in Hungary. Of these 27 children, eight (29.6%) were mentally retarded. Methods Budapest and the surrounding area have a population of about three million people. All self-poisoned patients in this area were admitted to the Department of Toxicological Internal Medicine, Korányi Hospital, Budapest.12The objective of the study was to identify pregnant women among self-poisoned females and to evaluate the effect of large doses of drugs on their exposed children. Gestational age was calculated from the first day of the last menstrual period, however, we used the term post-conceptional pregnancy age, estimated from the first day of the third week of the first lunar (28 day) pregnancy month, i.e., from the speculative day of conception. Thus the usual duration of pregnancy was 266 days and 38 pregnancy weeks. The study included three steps. First, self-poisoned pregnant women were identified among female patients in the Department of Toxicological Internal Medicine, Korányi Hospital, and their pregnancies were confirmed by gynecological examination. Each self-poisoned pregnant woman had a personal card including personal, medical, lifestyle data as well as all information regarding the self-poisoning in the study pregnancy. Doses and acute effects of the drugs used for self-poisoning were based on data obtained from three sources: (i) information obtained from the pregnant women; (ii) drug levels present in their blood and (iii) the clinical picture of intoxication. Clinical intoxication was defined as mild (not comatose at or after admission), moderate (comatose or unconscious at or after admission), severe (unconsciousness longer than one day after admission and/or need for artificial respiration), very severe (life-threatening, i.e., unconsciousness more than two days with severe complications such as uremia or multi-organ failure) and fatal. However, pregnant women whose suicides had had a fatal outcome were excluded from the study because their fetuses could not be evaluated. The study protocol was evaluated first by the Institutional Ethical Review Board, but because this methodological approach was unusual, it was forwarded to the Central Ethical Committee of Ministry of Health. This committee finally approved the study protocol with 3 criteria: (i) Self-poisoned pregnant women had to sign a consent form regarding their voluntary participation in the study and granting permission for follow-up home visits and examination of their children. (ii) Self-poisoning pregnant women had a right to refuse the collaboration at any time during the study. (iii) We had to organize a special high standard prenatal care and delivery service for self-poisoned pregnant women who decided to continue their pregnancies. Secondly, all surviving self-poisoned pregnant women were visited at home after the expected day of their deliveries to elucidate their pregnancy outcomes. Data regarding their miscarriages and still- and live-births (including birth weight and gestational age) were medically recorded in their discharge summaries because all deliveries and clinically recognized miscarriages took place in inpatient obstetric clinics and the birth attendants were obstetricians at the time of the study period. In addition, the mothers with their live-born children were invited for a thorough medical and psychometric examination at our institute. Thirdly, all exposed children and their sibs/siblings were examined by a pediatrician, medical geneticist and psychologist according to the protocol of the study. The aim of detailed medical examination was the detection of congenital abnormalities (i.e. structural birth defects) and minor anomalies (unusual morphologic variants without serious medical consequences to the children). Chromosome evaluation (karyotyping) was undertaken for children with multiple defects and/or mental retardation. The diagnosis of fetal alcohol syndrome (FAS) was based on a semi-quantitative score.13Autopsy records were available for the evaluation of deceased children. The cognitive development of children was measured by the help of the Hungarian Developmental Test14used routinely in Hungary. Children were classified into 4 groups according to their intelligence quotient (IQ): 1) above mean (110-120 IQ), 2) mean (90-109 IQ), 3) under mean (70-89 IQ) and 4) mental retardation (less than 70 IQ). There were two diagnostic criteria of mental retardation: (i) less than 70 IQ , and (ii) children were not able to attend normal primary school.15All exposed children with suspected mental retardation were followed until school age, when they were examined by official experts and they were referred to special schools for retarded students. The behavioral status of children was estimated by the psychologist using the Behavioral Style Questionnaire.16 Mothers, who could not visit our institute, were visited at home by the pediatrician and psychologist to examine exposed children and their sibs according the study protocol. Visits of families to our institute and the visits to the home of exposed children were used to check and to complete personal and lifestyle data of mothers that were collected on hospital records. Socioeconomic status of mothers was estimated based on employment status and educational level, and they were classified into three classes: high, medium and low. Smoking was classified according to the number of cigarettes smoked daily. Drinking habits were estimated on the information provided by the mothers and classified as abstinent, occasional (less than one drink per week), regular (from one drink per week to one drink/day) and hard (more than one drink/day) drinkers. If the quantity of drinking changed during the study pregnancy, we recorded the maximum. The major methodological challenge was to find appropriate controls for exposed children, and finally we used familial and population controls. The familial controls comprised of the previous and subsequent unexposed child(ren) of self-poisoned pregnant women and they were called sib controls for comparison with the exposed child. (If pregnant women repeated suicide attempts during the study period, their live-born babies were evaluated as exposed children, but these exposed children were not evaluated as sibs.) The medical condition, including birth defects and mental retardation, in addition to the cognitive status and behavioral scale of the sib controls were examined and diagnosed at the same time and place (our institute or their home) as of exposed children by the same protocol and by the same experts. Population controls included 38 151 newborns without birth defects in the Hungarian Case-Control Surveillance of Congenital Abnormalities, 1980-1996,17they were used as a reference sample (representing 1.8% of all Hungarian births) for the comparison of exposed children. Details of these materials and methods, in addition to the characteristics of self-poisoned pregnant women were described previously.10,9 The pregnant women evaluated in this paper attempted suicide with Tardyl® alone or in combination with other drugs. Tardyl® (EGIS) contains 125 mg amobarbital, 125 mg glutethimide, and 7.5 mg promethazine in one tablet, and most of these pregnant women used it as a hypnotic drug. At the statistical analysis of data, the SAS version 8.02 statistical software package was used (SAS Institute, Cary, NC). Quantitative variables of pregnant women and their children were evaluated by the Student t test and categorical variables by the chi square test. The prevalence at birth of congenital abnormalities and mental retardation in exposed children was compared with their unexposed sib controls, and odds ratios (OR) with 95% confidence interval (CI) were calculated by an unconditional multiple logistic regression model. Results Of 1044 self-poisoned pregnant women in the total sample, 74 (7.1%) used Tardyl® for their suicide attempt. Of these 74 pregnant women, one had a false address and one refused to participate, 27 decided to terminate their pregnancy (based upon socioeconomic reasons affecting their unplanned and unwanted pregnancies; in addition to the suspected teratogenic effects of the drugs used for their suicide attempts), 18 pregnancies ended in fetal death (very early loss: 12; miscarriage: 6) and 27 pregnant women delivered live-born babies. Thus, of 367 live-born and evaluated exposed children, 27 (7.4%) belonged to the Tardyl® sample. The characteristics of the 27 pregnant women who attempted suicide with Tardyl® and delivered live-born babies were compared to the Hungarian reference pregnant sample (Table 1). The mean age is lower among mothers who attempted suicide because of a larger proportion of the youngest (19 years or less) age group (37.0% vs. 8.6%), though their mean birth order was not significantly lower. The lower proportion of married women and higher proportion of low socioeconomic status were also characteristic for pregnant women who attempted suicide. There was a 2.8- and 18.5-fold higher rate of smokers and regular/hard drinkers, respectively, among self-poisoned pregnant women. Congenital abnormalities and mentally retardation did not occur among the self-poisoned pregnant women (the latter conclusion is based on their schooling and personal communication with us), i.e. the mothers of exposed children. The number of Tardyl® tablets taken by the 27 self-poisoned pregnant women ranged from 10 to 60 tablets with a mean of 24.1 + 11.5 tablets. Of these 27 pregnant women, eight combined Tardyl® with other drugs, mainly benzodiazepines, for their suicide attempt. The drug intoxication was classified as very severe in three, severe in 19, moderate in two and mild in three pregnant women. Of 27 exposed newborns, 14 (51.9%) were male. The data of birth outcomes of the 27 exposed children and their 46 unexposed sibs are shown in Table 2. These data were available for all exposed children and unexposed sibs. Two exposed children (7.4%) had congenital abnormalities, namely undescended left testicle and a multiple defect diagnosed as FAS by us. The mother of the boy affected with the undescended testis attempted suicide using 40 tablets of Tardyl® in the 20th pregnancy week (Figure 1), however, the critical period of undescended testis is during the last months of pregnancy. The exposed boy with FAS had a mild microcephaly (his first year head circumference was 40 cm) and three minor anomalies (flat occiput, smooth philtrum, thin upper lip) and his IQ was 65 and 70 in two different measurements. His hard drinker mother had a panic disorder, and she attempted suicide with 20 tablets of Tardyl® and 10 tablets of glutethimide (2,500 mg) on the 16th post-conceptional week. Six pregnant women used high doses of Tardyl® for their suicide attempt between the 3rd and 8th post-conceptional weeks, i.e., the critical period for most major congenital abnormalities; however, these six exposed children did not have any defect. Of 46 sibs, two (4.4%) were affected with defects: oesophageal atresia with tracheal fistula and FAS (he was the sib of the previously mentioned exposed child with FAS). Thus, the prevalence at birth of congenital abnormalities was not higher in exposed children than in their unexposed sibs (Table 2). Mean birth weight was similar in exposed children and their sibs (Table 2)although both had lower values than the mean birth weight of the reference Hungarian newborns (3,276 + 511 gram). Pregnancy age at delivery also did not show a significant difference between exposed children and their sibs, which was also shorter than the Hungarian population figure (37.4 + 2.0 week). Thus, the pregnancy week specific birth weights did not indicate any intrauterine fetal growth retardation. The rate of low birth weight and preterm birth was also similar in exposed children and in their sibs. Of 27 exposed children, eight (29.6%) had the diagnosis of mental retardation and they attended a special school for mentally retarded children. In general their IQs were measured twice or more with nearly similar findings. Only two exposed children: a boy with FAS (who was mentioned previously) and a girl had once 65 IQ and on another measurement 70 IQ. The main data of these eight exposed children are shown in Table 3. Of their eight mothers, six used only Tardyl® for their suicide attempt, three took 20 tablets. (One box of Tardyl® contains 20 tablets) Of these eight pregnant women, one was classified as hard and five as regular drinkers, but we were able to diagnose FAS only in one exposed child (and his sib) of a hard-drinker mother. Of these eight exposed children, six had normal karyotypes; the other two children were without any visible defects but were housed in a special institution and thus chromosome examination was not allowed. Other syndromes were also not identified in these exposed children. Eight mentally retarded exposed children had 20 sibs, but two were excluded as exposed children because their mothers attempted suicide in two different pregnancies (Figure 1). The mother of these two exposed children was not a drinker, but was a heavy smoker and her children showed an association between the maternal suicide attempt with Tardyl® during pregnancy and some neurotoxic effects of the high doses of Tardyl®. Of her five unexposed children, four had normal cognitive status, and the IQ was measured as 115 in the fifth child, i.e. her son. However, the two exposed children were mentally retarded, and one of them had been placed in a young offenders institution for repeated offences by the time he was 15 years old. Of the unexposed 46 sibs, none had mental retardation (Table 2); all sibs attended normal primary schools. The cognitive status and behavioral scale measurements were planned for all exposed children and their unexposed sibs, but IQ could only be tested in 22 exposed children and 20 unexposed sibs, while the behavioral scale was measured in 16 exposed children and 16 unexposed sibs (Table 4). The calculated mean IQ was lower in exposed children than in their unexposed sibs. The timing of suicide attempts showed that the high doses of Tardyl® were associated with a high risk for mental retardation when exposure occurred between the 14th and 20th post-conceptional weeks, i.e. in the second trimester of pregnancy (Table 5). In addition, we evaluated the cognitive status of the exposed children and their sibs according to the drinking habits of self-poisoned pregnant women (Table 5). Exposed children and their sibs who were born to mothers without a drinking habit had a higher mean IQ than exposed children and their sibs born to alcohol drinking mothers. However, a lower mean IQ was also found in exposed children compared to their unexposed sibs who were born to the same non-drinker mothers and this suggests that there may be a neurotoxic effect of Tardyl®. Behavioral scales also showed some differences between exposed children and unexposed sibs (Table 4). Of eight mentally retarded exposed children, five had severe and one had moderate behavioral deviation (it was not possible to estimate behavioral status in another mentally retarded boy). In addition two other exposed children had moderate behavioral deviation. On the other hand, of 16 sibs, none had severe and only one had a moderate behavioral deviation. Thus, of 27 exposed children, 8 were mentally retarded (29.6%) while of 46 sibs, none were mentally retarded (Χ[\documentclass[12pt]{minimal} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{} \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{} \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n} \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $${\mathrm{_{{1}}^{{2}}}}$$ \end{document} ])=79.7, p<0.0001). Furthermore, moderate behavioral deviations occurred in 2 other exposed children and in one control sib. If we evaluate these 10 exposed children together, the percentage figure is 37.0% in the group of exposed children, while the similar figure was 2.1% in the total group of unexposed sibs based on one child with moderate behavior deviation (OR with 95% CI: 27.6, 3.3-232.4). Finally we make a comparison of exposed children born to mothers who attempted suicide with Tardyl® and with the components of Tardyl® separately (Table 6). There was no mentally retarded exposed child in the group exposed to amobarbital or glutethimide; one exposed child in the group exposed to promethazine was mentally retarded but the boy had a genetic X -linked fragile X chromosome.Table 7 shows the maternal characteristics in these study groups. The drinking and smoking habits during the study pregnancy were not significantly different in the three components of Tardyl® separately and together in Tardyl®. The mean maternal age and birth order did also not differ significantly among pregnant women who used these drugs and Tardyl® for their suicide attempt. Discussion Pregnant women who attempted suicide with Tardyl® showed the general characteristics of self-poisoned pregnant women, i.e. many of them were young, unmarried and had low socioeconomic status, as well as often being smokers and/or drinkers.10 Our data did not indicate the “classical” human teratogenic effect of the high doses of Tardyl® (its mean dose was 24-folds higher than the usual clinical dose) because there was no difference in the prevalence at birth of congenital abnormalities between exposed children and their unexposed sibs. The intrauterine fetal development based on pregnancy aged specific birth weight also did not show a significant difference between exposed children and their sibs. However, of 27 exposed children, eight (29.6%) were diagnosed as mentally retarded and they attended special schools. Mental retardation did not occur among 46 unexposed sibs born to the same mothers. The recorded incidence of mental retardation in school-age (6-18 years) children is about three percent in Hungary,18thus the occurrence of mental retardation was about ten-fold higher in exposed children born to the mothers who had attempted suicide with Tardyl®. Of seven mentally retarded children who were evaluated for behavioral development,5 had severe and one moderate behavioral deviation. In addition, two other exposed children showed moderate behavioral deviation. Thus, of 27 exposed children, ten (37.0%) showed mental retardation and/or severe/moderate behavioral deviation and these findings suggest a possible neurotoxic effect of Tardyl® (i.e., the combination of amobarbital, glutethimide and promethazine). These results of our study were supported by the lack of familial occurrence of mental retardation in these families. Neither the mothers nor the 46 unexposed sibs of these eight exposed children suffered from any mental retardation. The fathers of exposed children were not examined, but the mothers stated that they did not suffer from mental retardation. Several environmental agents induce congenital abnormality syndromes (such as FAS, fetal rubella, varicella, hydantoin, valproate, methylmercury effect, iodine deficiency, etc) and these syndromes include both structural defects and mental retardation. In this study we did not find structural defects in the eight exposed children who were mentally retarded. Exposed children and their sibs were examined thoroughly in the study but only FAS was diagnosed: in one exposed boy and one sib, the brother of this exposed boy. Low birth weight and/or preterm birth is associated with a higher rate of mental retardation and behavioral deviation.15Of eight exposed children with mental retardation, two (25.0%) had preterm birth with low birth weight. However, of their 18 sib controls, five (27.8%) had low birth weight. In addition there was no significant difference in the rate of preterm birth and low birth weight between exposed children and sib controls, thus these confounder factors cannot explain the higher risk for mental retardation in exposed children. In addition, we have to consider an obvious interaction between alcohol abuse and Tardyl®, because five out of the eight exposed children diagnosed with mental retardation were born to drinker mothers. However, the drinking habits may have been exaggerated in this study because pregnant women who attempted suicide with drugs frequently combined this course of action with concomitant alcohol abuse, and these pregnant women were diagnosed as drinkers, though in general they were not hard or regular drinkers. In addition, the phenotypic features of these mentally retarded children did not fit the well-known pattern of FAS.13,19FAS was diagnosed only in one exposed boy and in his brother born to the same mother. Exposed children and their sibs were born to the same mothers in general with a similar drinking habit in their pregnancies, nevertheless the mean IQ was significantly lower in exposed children than in their unexposed sib controls born to both the same drinker or non-drinker mothers. On the other hand some interaction between the effect of Tardyl® and alcohol seems to be plausible, but the mental retardation inducing effect of this medicinal product cannot be explained only by the concurrent effect of alcohol. We did not find a higher rate of mental retardation in exposed children born to mothers who attempted suicide with either amobarbital,20 glutethimide21or promethazine22taken separately, compared with the data of their sibs in the previous studies of these drugs. Thus only the combination of the three drugs in Tardyl® produced a high risk for mental retardation and very low IQ. We hypothesized that the three components of Tardyl® may result in additive or potentiated drug interactions.23,24Glutethimide can stimulate hepatic microsomal enzyme production, thus self-induction of its own metabolites, and has frequent interactions with other drugs (e.g., oral anticoagulants) and alcohol.25 Another important argument for the potential neurotoxic effect of Tardyl® is that its association with mental retardation in the exposed children occurred when pregnant women attempted suicide with Tardyl® between the 14th and 20th post-conceptional weeks of pregnancy. Otaka and Schull26studied the critical period of mental retardation among 1 600 children exposed to radiation from the atomic bomb attack on Japan and found it to be between 8th to 15th post-conceptional weeks. This period corresponds to the time when major proliferation of neuroblasts occurs in the brain of human fetuses. Thus the final conclusion of this study is that maternal exposure to high doses of Tardyl®, due to the interaction of its component drugs, may induce mental retardation. As far as we know drug induced mental retardation without structural defects has not been described until now.27,28 There are many strengths of the self-poisoning model, e.g., there is the potential to estimate a dose-response relationship; one can establish the absence of birth defects after high doses of a drug used during the critical period of embryonic development; there is a potential to examine the neurotoxic effect of drugs following fetal exposure. A further strength of this project is that stresses the clinical and social importance of the self-poisoned pregnant women.9 Among the limitations of the study we can mention here that Tardyl® is a popular hypnotic drug in Hungary and some other Central-Eastern European countries, but not in the Western part of Europe. However, the recognition of the potential for a drug effect on the origin of mental retardation appears to be important from both clinical and theoretical points of view. In conclusion, the results of this study did not show the classical teratogenic, i.e. congenital abnormality inducing effect of high doses of a combination of amobarbital, glutethimide and promethazine (a popular hypnotic drug, Tardyl® in Hungary) in children born to mothers who attempted suicide with this drug during pregnancy. There was no intrauterine growth retardation in children after the suicide attempt of their mothers with high doses of Tardyl®. However, the findings of the study showed a statistically significant association between a higher risk for mental retardation and high doses of Tardyl® when exposure was during the second trimester of pregnancy. Notes Funding:None Competing interests:None declared Ethical approval:Central Ethical Committee, Hungarian Ministry of Health. Acknowledgements The project was supported by IARC, Lyon and the work of Erzsébet H Puhó regarding mathematical calculations of our data set was sponsored by Richter Gedeon Pharmaceutical Ltd, Budapest, Hungary. We thank the contribution for our previous co-workers: P Bácskai, A Glauber, A Lendvay, G Molnár, I Szekeres, I Szentesi, L Tímár, and M Tomcsik. We also very much appreciated the editorial assistance of A. Bendich. References 1. Scheidemann ES (eds): Suicidology, Contemporary Development. New York: Grune and Stratton, 1976. 2. Weckstein L. Handbook of Suicidology. Principles, Problems and Practice.New York: Brunner-Mazel, 1980. 3. Hawton K, Van Heeringen K. The International Handbook of Suicide and Attempted Suicide. Chichester: Wiley, 2000. 4. Bertolote JM,Fleischmann A. Suicidal behaviour prevention: WHO perspectives on research.Am J Med Genet C Semin Med GenetYear: 2005Month: 2 Day: 15 133C181215645530 5. Värnik P,Sisask M,Värnik A,Laido Z,Meise U,Ibelshäuser A,et al. Suicide registration in eight European countries: a qualitative analysis of procedures and practicesForensic Sci IntYear: 2010Month: 10 2021869220483553 6. Skegg K. Self-harmLancetYear: 2005Month: 10 Day: 22 366949514718316243093 7. King RA, Apter A. Suicide in Children and Adolescents. Cambridge: Cambridge Univ Press, 2003. 8. Kleiner GJ, Greston WM (eds): Suicide in Pregnancy.Boston: John Wright, 1984. 9. Czeizel AE. Attempted suicide and pregnancyJ Inj Violence ResYear: 2011Month: 1 31455421483214 10. Czeizel AE,Gidai J,Petik D,Timmermann G,Puhó EH. Self-poisoning during pregnancy as a model for teratogenic risk estimation of drugsToxicol Ind HealthYear: 2008Month: 2 241112818818178 11. Czeizel AE. The estimation of human teratogenic/fetotoxic risk of exposures to drugs on the basis of Hungarian experience:a critical evaluation of clinical and epidemiological models of human teratologyExpert Opin Drug SafYear: 2009Month: 5 8328330319505262 12. Czeizel AE. Budapest Registry of Self-poisoned PatientsMutat ResYear: 1994Month: 4 3122157637510828 13. Vitéz M,Korányi G,Gönczy E,Rudas T,Czeizel A. A semiquantitative score system for epidemiological studies of fetal alcohol syndromeAm J EpidemiolYear: 1984Month: 3 119330186702808 14. Szegal B. Diagnostic of psychomotor developmentHung PsycholYear: 19803714888 15. Czeizel A,Lányi-Engelmayer A,Klujber L,Métneki J,Tusnády G. Etiological study of mental retardation in Budapest, HungaryAm J Ment DeficYear: 1980Month: 9 85212087446579 16. Lendvay A,Czeizel AE. A behavioural teratologic study on offspring of self-poisoned pregnant womenActa Paediatr HungYear: 1992324347691304192 17. Czeizel AE,Rockenbauer M,Siffel C,Varga E. Description and mission evaluation of the Hungarian case-control surveillance of congenital abnormalities, 1980-1996TeratologyYear: 2001Month: 5 6351768511320528 18. Czeizel A,Sankaranarayanan K,Szondy M. The load of genetic and partially genetic diseases in man. III. Mental retardationMutat ResYear: 1990Month: 10 23222913032215538 19. Jones KL,Smith DW,Ulleland CN,Streissguth P. Pattern of malformations in offspring of chronic alcoholic mothersLancetYear: 1973Month: 6 Day: 9 178151267714126070 20. Petik D,Timmermann G,Czeizel AE,Acs N,Bánhidy F. A study of the teratogenic and fetotoxic effects of large doses of amobarbital used for a suicide attempt by 14 pregnant womenToxicol Ind HealthYear: 2008Month: 2 241798518818184 21. Petik D,Ács N,Bánhidy F,Czeizel AE. A study of the effects of large doses of glutethimide that were used for self-poisoning during pregnancy on human fetusesToxicol Ind HealthYear: 2008Month: 2 241697818818183 22. Petik D,Ács N,Bánhidy F,Czeizel AE. A study of the potential teratogenic effect of large doses of promethazine used for a suicide attempt by 32 pregnant womenToxicol Ind HealthYear: 2008Month: 2 241879618818185 23. Hanstein PD. Drug Interactions, 5th ed. Philadelphia: Lea and Febiger, 1985. 24. Gorrod IW, Beckett AH (eds): Drug Metabolism in Man. London: Taylor and Francis, 1978. 25. Nicholson AN. The use of short- and long-acting hypnotics in clinical medicineBr J Clin PharmacolYear: 198111161S69S6133538 26. Otake M,Schull WJ. In utero exposure to A-bomb radiation and mental retardation: a reassessmentBr J RadiolYear: 1984Month: 5 57677409146539140 27. Shepard TH, Lemire RJ. Catalog of Teratogenic Agents,11th ed. Baltimore: Johns Hopkins Univ. Press, 2004. 28. Briggs GG, Freeman RK, Yaffe SJ. Drugs in Pregnancy and Lactation, 7th ed. Philadelphia: Lippincott Williams and Wilkins, 2005. 29. Czeizel AE,Petik D,Puhó E. Smoking and alcohol drinking during pregnancy:the reliability of retrospective maternal self-reported informationCentr Eur J Public HealthYear: 2004Month: 12 12417983 Figures [Figure ID: F1] Figure 1:Family tree of two exposed children born to a mother who attempted suicide with Tardyl® in their two pregnancies. Tables [TableWrap ID: T1] Table 1: Main variables of 27 pregnant women who attempted suicide during pregnancy with Tardyl® (amobarbital 125 mg, glutethimide 125 mg, promethazine 7.5 mg in one tablet) alone or with other drugs and delivered live-born babies, and a reference sample of Hungarian pregnant women who delivered newborns without birth defects in the Hungarian Case-Control Surveillance of Congenital Abnormalities, 1980-199617 Variables Tardyl®(N=27) Hungarian pregnant women(N=38,151) Comparison Age, yr (mean, S.D.) 22.4 5.4 25.4 4.9 t=2.9; P=0.004 Birth order (mean, S.D.) 1.6 0.9 1.7 0.9 t=0.9; p=0.35 Married (%) 63.0 96.1 x [\documentclass[12pt]{minimal} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{} \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{} \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n} \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $${\mathrm{_{{1}}^{{2}}}}$$ \end{document} ]=79.7 P<0.0001 Socioeconomic status (%) High 7.4 38.0 Medium 22.2 30.6 x [\documentclass[12pt]{minimal} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{} \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{} \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n} \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $${\mathrm{_{{2}}^{{2}}}}$$ \end{document} ]=20.3 P<0.0001 Low 70.4 31.4 Smoker (%) 51.9 18.9* Regular/hard drinker (%) 29.6 1.6* These figures were based on a sub-sample in which 3,022 mothers were visited at home and data were obtained by cross interview of family members29 [TableWrap ID: T2] Table 2: Comparison of birth outcomes in exposed children born to pregnant women who attempted suicide with Tardyl® during pregnancy and in their unexposed sibs Variables Exposed children(N=27) Unexposed sibs(N=46) Comparison Categorical No. % No. % OR 95% CI Congenital abnormalities 2 7.4 2 4.4 1.8 0.2 – 13.9 Mental retardation 8 29.6 0 0.0 Χ[\documentclass[12pt]{minimal} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{} \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{} \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n} \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $${\mathrm{_{{1}}^{{2}}}}$$ \end{document} ]=79.3 p<0.0001 Low birth weight (less than 2500 g) 4 14.8 7 15.2 1.0 0.3 – 3.8 Preterm birth (less than 35th week) 6 22.2 8 17.4 1.6 0.6 – 5.5 Quantitative Mean S.D. Mean S.D. t = p = Birth weight (g) 2,883 55 2,895 67 0.10 0.94 Pregnancy age (wk) 36.4 2.8 36.8 2.9 0.08 0.79 Bold numbers show significant association [TableWrap ID: T3] Table 3: Data of exposed children with mental retardation and moderate behavioral deviation Period/Number Suicide attempt Exposed children IQ Mental retardation Tardyl (tbl) Other drugs Pregnancy Age (wk) Sex Birth weight(g) Pregnancy age (wk) Defect (Minor anomaly) Karyo-type Age of diag-nosis(yr) Estimated etiology I/41 30 Yes 20 M 2,650 39 0 (0) 65 46,XY 15 Tardyl phenobarbital I/86 40 0 20 M 2,000 33 Undescended testicles (0) 60 46,XY 13 Tardyl® II/29 20 AA 18 F 2,850 35 0 (NE) 65 NE 6 Tardyl® II/81 30 AA 18 M 2,550 36 0 (NE) 55 NE 6 Tardyl® II/107 40 0 14 F 2,750 37 0 (NE) 65,70 NE 6 Tardyl® III/107 20 AA 17 F 2,550 37 0 (enamel hypoplasia) 55 46,XX 6 Tardyl® III/572 20 Yes* 16 M 2,500 38 FAS 65,70 46,XY 6 Tardyl®+Glutethimide/alcohol III/603 20 AA 16 F 1,500 30 0 (low broad nasal bridge, umbilical hernia) 60 46,XX 6 Tardyl® Moderate behavioral deviation II/91 20 0 21 F 2,400 31 0 (NE) 85 NE 6 Tardyl® III/185 20 AA 28 F 3,450 39 0 (low broad nasal bridge, enamel hypoplasia) 85 46,XX 6 Tardyl® * Valeriana compsitaR (Phenobarbital 600 mg + Valeriana 3.000 mg). AA= alcohol abuse and suicide attempt together M= Male, F= Female / FAS= Fetal alcohol syndrome / NE= no examination [TableWrap ID: T3-2] Continue table 3: Data of exposed children with mental retardation and moderate behavioral deviation Behavioral deviation Mother Remarks * Age(yr) Drinking Smoking (cig/d) Health Severe 21 0 40 Repeated suicide 6 sibs: one of them I/86,another sib: 115 IQ NE 24 0 40 Repeated suicide 6 sibs: one of them I/41,another sib: 115 IQ Severe 19 Regular 20 - EC in foster home,1 sib Severe 19 Regular 20 - EC in foster home,no sib Mild 28 0 0 - 2 sibs,one: 100 IQ Severe 18 Regular 30 Repeated suicide 1 sib Moderate 25 Hard 20 Panic disorder 2 sibs: 100 IQ,85 IQ Severe 22 Regular 10 - 2 sibs Moderate 24 0 20 - 2 sibs: 100 IQ;85 IQ Moderate 22 Regular 0 - 2 sibs,one: 100 IQ Glutethimide 2.500 mg *** See Figure 1 [TableWrap ID: T4] Table 4: Comparison of cognitive status and behavioral scale in exposed children born to pregnant women who attempted suicide with Tardyl® during pregnancy and in their unexposed sibs Cognitive status (IQ) Exposed children(N=22) Unexposed sibs(N=20) Behavioral scale Exposed children(N=16) Unexposed sibs(N=16) Above mean (110-120) 3 4 Normal 4 9 Mean (90-109) 7 12 Mild 4 6 Under mean (70-89) 4 4 Moderate 3 1 Mental retardation (less than 70) 8 0 Severe 5 0 Mean ± S.D. 82.2 ± 20.0(t=3.8) 100.0 ± 9.7(p=0.04) Distribution χ[\documentclass[12pt]{minimal} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{} \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{} \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n} \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $${\mathrm{_{{3}}^{{2}}}}$$ \end{document} ] = 8.3 p=0.03 [TableWrap ID: T5] Table 5: Association between the occurrence of different categories of cognitive status in exposed children and the time of suicide attempts with Tardyl® according to pregnancy age periods, in addition distribution of different categories of cognitive status in exposed children and their sibs according to the drinking habit of self-poisoned pregnant women Cognitive status (Estimated mean IQ) Pregnancy age periods (wk) Self-poisoned pregnant women 7 12 (N=8) 13 24 (N=13) 25 38 (N=6) Non-drinker Drinker Exposed children(N=19) Sibs(N=34) Exposed children(N=8) Sibs(N=12) No. No. No. No. No. No. No. Above mean 1 0 2 3 4 0 0 Mean 5 0 2 7 9 0 3 Under mean 0 3 1 1 1 3 3 Mental retardation 0 8 0 3 0 5 0 Subtotal * 6 11 5 14 14 8 6 IQ, Mean 100.3 69.5 103.0 95.4 103.2 82.5 92.5 S.D. 7.2 11.5 12.5 11.8 7.7 5.0 8.2 Comparison χ[\documentclass[12pt]{minimal} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{} \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{} \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n} \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $${\mathrm{_{{4}}^{{2}}}}$$ \end{document} ] = 30.8; p < 0.0001 Exposed children Fisher p < 0.0001 χ[\documentclass[12pt]{minimal} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \DeclareFontFamily{T1}{linotext}{} \DeclareFontShape{T1}{linotext}{m}{n} { <-> linotext }{} \DeclareSymbolFont{linotext}{T1}{linotext}{m}{n} \DeclareSymbolFontAlphabet{\mathLINOTEXT}{linotext} \begin{document} $${\mathrm{_{{3}}^{{2}}}}$$ \end{document} ] = 9.3, p = 0.02; Fisher p = 0.02 Evaluated number of exposed children Bold numbers show significant associations [TableWrap ID: T6] Table 6: Occurrence of mental retardation, in addition to the distribution of cognitive status with mean IQ and behavioral scale in exposed children born to mothers who attempted suicide during pregnancy with amobarbital, glutethimide, promethazine and Tardyl® (including these three drugs) Variables Amobarbital (N=14) Glutethimide (N=16) Promethazine(N=32) Tardyl®(N=27) No. % No. % No. % No. % Mental retardation (instead of MR) 0 0.0 0 0.0 1 3.1 8 29.6 Cognitive status Above mean 0 0.0 1 7.7 5 20.0 3 13.6 Mean 9 81.8 10 76.9 13 52.0 7 31.8 Under mean 2 18.2 2 15.4 6 24.0 4 18.2 MR 0 0.0 0 0.0 1* 4.0 8 36.4 Subtotal 11 100.0 13 100.0 25 100.0 22 100.0 IQ, mean ± S.D. 96.4 ± 8.4 100.4 ± 10.8 98.4 ± 11.2 82.2 ± 20.0 Behavioral scale Normal 5 62.5 8 72.7 11 55.0 4 25.0 Mild 2 25.0 2 18.2 9 45.0 4 25.0 Moderate 0 0.0 1 9.1 0 0.0 5 31.3 Severe 1 12.5 0 0.0 0 0.0 5 31.3 Subtotal 8 100.0 11 100.0 20 100.0 16 100.1 *His brother was also mentally retarded; mental retardation of this sib pair was caused by X-linked fragile X chromosome [TableWrap ID: T7] Table 7: Comparison of maternal characteristics of pregnant women who attempted suicide with amobarbital, glutethimide and promethazine (i.e. the components of Tardyl®) separately, and Tardyl® Variables Amobarbital(N=14) Glutethimide(N=16) Promethazine(N=32) Tardyl®(N=27) Age, yr (mean, S.D.) 22.8 6.1 26.1 7.5 22.9 5.3 22.4 5.4 Birth order (mean, S.D.) 1.5 0.8 2.0 1.3 1.9 1.2 1.6 0.9 Married (%) 50.0 50.0 53.1 63.0 Socioeconomic status (%) High 7.1 12.5 9.4 7.4 Medium 35.7 37.5 37.5 22.2 Low 57.1 50.0 53.1 70.4 Smoker (%) 57.1 43.8 62.5 51.9 Regular/hard drinker (%) 21.4 31.3 8.8 29.6 Article Categories: Injury &Violence Drug Interaction Amobarbital Glutethimide Promethazine Combination Teratogenic Effect Fetal Neurotoxic Effect Mental Retardation Previous Document: The impact of child safety promotion on different social strata in a WHO Safe Community. 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## Politics Three new polls today, each of them interesting in their own respects. Just when you thought it was safe to use the word “Pennsylvania” without using the word “polling” in the same sentence, Rasmussen has a new, post-primary survey out in Pennsylvania that shows Hillary Clinton leading John McCain by 5 points, but Barack Obama trailing him by 1 point. Bolstering Clinton’s electability arguments, The Pennsylvania polls have somewhat consistently shown her outperforming Barack Obama in the state, usually by margins of about 3-6 points. What’s interesting is the question of whether the Democrats left Pennsylvania in a better place than they found it. Strategic Vision showed consistent deterioration in the Democrats’ numbers over time, whereas Rasmussen’s previous poll of the state, conducted 4/9, showed Clinton and Obama with 9 and 8 point leads, respectively. Rasmussen also has new numbers from Massachusetts, Obama +12, Clinton +19. This is actually the first Massachusetts poll to show Obama with a double-digit advantage in the state, as SurveyUSA’s fieldwork had consistently shown a tight race between he and McCain. Since Massachusetts has such strong Democratic voter ID (although it also has large numbers of independents), this may be a consequence of support tending to get more partisan over time. Finally, in Oklahoma, a somewhat dated Sooner Poll shows John McCain ahead of both Democrats by enormous margins: Obama by 41 points and Clinton by 30. We are working on more detailed versions of our regression model to help explain why, for instance, the Democrats can be competitive in Indiana, but are losing Oklahoma by such wide margins. Also, the Gallup daily tracker shows further, post-Pennsylvania movement toward Clinton, somewhat defying my prediction from yesterday. The Rasmussen daily tracker, however, is unbudging. Nate Silver is the founder and editor in chief of FiveThirtyEight. Filed under , , , All Politics ### The Eagles, Cowboys And Giants Look Good Next To The Disaster In D.C.Sep 4, 2015 Never miss the best of FiveThirtyEight.	{}
Kaon-nucleon scattering to one-loop order in heavy baryon chiral perturbation theory # Kaon-nucleon scattering to one-loop order in heavy baryon chiral perturbation theory Bo-Lin Huang Yun-De Li Department of Physics, Yunnan University, Kunming 650091, China August 24, 2019 ###### Abstract We calculate the T-matrices of kaon-nucleon () and antikaon-nucleon () scattering to one-loop order in SU(3) heavy baryon chiral perturbation theory (HBPT). The low-energy constants (LECs) and their combinations are then determined by fitting the phase shifts of scattering and the corresponding data. This leads to a good description of the phase shifts below 200 MeV kaon laboratory momentum. We obtain the LEC uncertainties through statistical regression analysis. We also determine the LECs through the use of scattering lengths in order to check the consistency of the HBPT framework for different observables and obtain a consistent result. By using these LECs, we predict the elastic scattering phase shifts and obtain reasonable results. The scattering lengths are also predicted, which turn out to be in good agreement with the empirical values except for the isospin-0 scattering length that is strongly affected by the resonance. As most calculations in the chiral perturbation theory, the convergence issue is discussed in detail. Our calculations provide a possibility to investigate the baryon-baryon interaction in HBPT. PACS numbers 13.75.Jz,12.39.Fe,12.38.Bx ###### pacs: Valid PACS appear here preprint: APS/123-QED ## I Introduction Chiral perturbation theory (ChPT) is the effective field theory of quantum chromodynamics (QCD) at energies below the scale of chiral symmetry breaking GeVmach2011; sche2012. As we all know, the relativistic framework for baryons in ChPT does not naturally provide a simple power-counting scheme as for mesons because of the baryon mass, which does not vanish in the chiral limit. Relativistic (such as infrared regularizationbech1999 and the extended on-mass-shell schemegege1999; fuch2003) and heavy baryonjenk1991; bern1992 approaches have been proposed and developed to solve the power-counting problem. Recently, the relativistic approaches have made some progress. For some observables, the chiral series even show a better convergence than the heavy baryon approachren2012; alar2013. However, the heavy baryon chiral perturbation theory (HBPT) is still a reasonable and useful tool in the study of the meson-baryon scattering. The expansion in HBPT is expanded simultaneously in terms of and , where represents the meson momentum or its mass or the small residue momentum of baryon in the nonrelativistic limit and denotes the baryon mass in the chiral limit. Over the years, the low-energy processes have been widely investigated in the SU(2) HBPT. Fettes et al. have investigated pion-nucleon scattering up to the fourth orderfett1998; fett2000. The low-energy constants (LECs) of the SU(2) chiral pion-nucleon Lagrangian were determined by fitting various empirical phase shifts. The threshold parameters were also predicted in Refs. fett1998; fett2000. Krebs, Gasparyan, and Epelbaum calculated the chiral three-nucleon force at fifth order by using the LECs from scattering at fourth orderkreb2012, and Entem et al. considered peripheral nucleon-nucleon scattering at fifth order through using these LECsente2015. These predictions are in good agreement with the data. For processes involving kaons or hyperons, the situation is more complicated. One has to use the SU(3) HBPT in comparison to the SU(2) sector of scattering. These involve several new problems. First, there are more unknown LECs needed to be determined through experimental data which are insufficient at present. Second, the kaon mass is larger than the pion mass duo to broken SU(3) symmetry. In fact, the pertinent expansion parameter results in a low convergence rate. Third, the and scattering are inelastic and elastic at low energies, respectively. These involve inconsistent predictions duo to the dynamical differences between and scattering. However, Kaiser achieved some success when analyzing the and scattering lengths in SU(3) HBPTkais2001. Then Liu and Zhu generalized this method to the predictions of meson-baryon scattering lengthsliu20071; liu20072; liu2011; liu2012. They obtained reasonable results. But higher-order corrections are needed to consider due to the complicated convergence. That leads to involving more LECs and needs more experimental meson-baryon scattering lengths which are unavailable for now. In this paper, we will determine the LECs by fitting the phase shifts of the elastic scattering and make predictions up to one-loop order, as the scattering in the framework of SU(2) HBPT. In Sec. II, we summarize the Lagrangians involved in the evaluation up to one-loop order contributions. In Sec. III, we present the T-matrices of the elastic and scattering. In Sec. IV we explain how we calculate the phase shifts and the scattering lengths. Section V contains the results and discussions and also includes a brief summary. Appendix A contains the amplitudes from one-loop diagrams. Apppendix B contains the threshold T-matrices and the relation between the threshold T-matrices with the s-wave scattering lengths. ## Ii Lagrangian Our calculation of the elastic and scattering is based on the effective SU(3) chiral Lagrangian in HBPT L=Lϕϕ+LϕB. (1) Here, the SU(3) matrix and represent the pseudoscalar Goldstone fields () and the octet baryons fields, respectively. The lowest-order effective SU(3) chiral Lagrangians for meson-meson and meson-baryon interaction takes the formbora1997 L(2)ϕϕ=f24tr(uμuμ+χ+), (2) L(1)ϕB = tr(i¯¯¯¯B[v⋅D,B])+Dtr(¯¯¯¯BSμ{uμ,B}) (3) +Ftr(¯¯¯¯BSμ[uμ,B]), where denotes the covariant derivative [Dμ,B]=∂μB+[Γμ,B] (4) and is the covariant spin operator à la Pauli-Lubanski Sμ=i2γ5σμνvν, (5) with [Sμ,Sν]=iϵμνσρvσSρ,{Sμ,Sν}=12(vμvν−gμν), (6) where is the completely antisymmetric tensor in four indices, . The chiral connection and the axial vector quantity contain even number meson fields and odd number meson fields, respectively. The SU(3) matrix collects the pseudoscalar Goldstone fields. The parameter is the pseudoscalar decay constant in the chiral limit. The axial vector coupling constants and can be determined by fitting the semileptonic decays ()bora1999. The combination with results in explicit chiral symmetry breaking. The complete heavy baryon Lagrangian at next-to-leading order can be written as L(2)ϕB=L(2,1/M0)ϕB+L(2,ct)ϕB, (7) where denotes corrections of dimension two with fixed coefficients and stems from the expansion of the original relativistic leading-order Lagrangian bora1997. These read L(2,1/M0)ϕB = D2−3F224M0tr(¯¯¯¯B[v⋅u,[v⋅u,B]]) (8) −D212M0tr(¯¯¯¯BB)tr(v⋅uv⋅u) −DF4M0tr(¯¯¯¯B[v⋅u,{v⋅u,B}]) −12M0tr(¯¯¯¯B[Dμ,[Dμ,B]]) +12M0tr(¯¯¯¯B[v⋅D,[v⋅D,B]]) −iD2M0tr(¯¯¯¯BSμ[Dμ,{v⋅u,B}]) −iF2M0tr(¯¯¯¯BSμ[Dμ,[v⋅u,B]]) −iF2M0tr(¯¯¯¯BSμ[v⋅u,[Dμ,B]]) −iD2M0tr(¯¯¯¯BSμ{v⋅u,[Dμ,B]}), where denotes the baryon mass in the chiral limit. The remaining heavy baryon Lagrangian proportional to the low-energy constants can be obtained from the relativistic effective meson-baryon chiral Lagrangianolle2006 L(2,ct)ϕB = bDtr(¯¯¯¯B{χ+,B})+bFtr(¯¯¯¯B[χ+,B]) (9) +b0tr(¯¯¯¯BB)tr(χ+)+b1tr(¯¯¯¯B{uμuμ,B}) +b2tr(¯¯¯¯B[uμuμ,B])+b3tr(¯¯¯¯BB)tr(uμuμ) +b4tr(¯¯¯¯Buμ)tr(Buμ)+b5tr(¯¯¯¯B{v⋅uv⋅u,B}) +b6tr(¯¯¯¯B[v⋅uv⋅u,B])+b7% tr(¯¯¯¯BB)tr(v⋅uv⋅u) +b8tr(¯¯¯¯Bv⋅u)tr(Bv⋅u) +b9tr(¯¯¯¯B{[uμ,uν],[Sμ,Sν]B}) +b10tr(¯¯¯¯B[[uμ,uν],[Sμ,Sν]B]) +b11tr(¯¯¯¯Buμ)tr(uν[Sμ,Sν]B). The first three terms proportional to the LECs result in explicit symmetry breaking. Notice that the LECs have dimension . ## Iii T-Matrices We are considering only elastic kaon-nucleon and antikaon-nucleon scattering in the center-of-momentum system (CMS) with . The T-matrix takes the following form: T(I)KN,¯¯¯¯KN = (EN+MN2MN){V(I)KN,¯¯¯¯KN(q) (10) +iσ⋅(q′×q)W(I)KN,¯¯¯¯KN(q)}, with the nucleon mass, the nucleon energy, and the total isospin of the kaon-nucleon system. Furthermore, refers to the non-spin-flip kaon-nucleon or antikaon-nucleon amplitude, and refers to the spin-flip kaon-nucleon or antikaon-nucleon amplitude. Now, we calculate the T-matrices order by order. Note that we choose for the sake of convenience throughout this paper. The leading-order amplitudes corresponding to diagrams (1a) and (1b) in Fig. 1 (including also the crossed diagram) read V(1)KN(q)=13f2K[−3w+(D2+3F2)q2zw], (11) W(1)KN(q)=−D2+3F23wf2K, (12) V(0)KN(q)=(2D2−6DF)q2z3wf2K, (13) W(0)KN(q)=−2D2−6DF3wf2K, (14) V(1)¯¯¯¯KN(q)=12f2K[w−(D−F)2q2zw], (15) W(1)¯¯¯¯KN(q)=−(D−F)22wf2K, (16) V(0)¯¯¯¯KN(q)=16f2K[9w−(D+3F)2q2zw], (17) W(0)¯¯¯¯KN(q)=−(D+3F)26wf2K, (18) where denotes the kaon CMS energy and the angular variable between and . We also take the renormalized kaon decay constant instead of (the chiral limit value). At next-to-leading order , one has the contribution from the second row diagrams of Fig. 1 (including also the crossed diagrams) involving the vertices from the Lagrangian and . First, for the vertices from the , we have V(1)KN(q) = 16M0f2K(D2+3F2)[−w2+2(z+2)q2 (19) −3(1+z)D2+3F2q2−2z(1+z)q4w2], W(1)KN(q) = −13M0f2K(D2+3F2)[1−(1+z)q2w2], (20) V(0)KN = 13M0f2K(D2−3DF)[−w2+2(z+2)q2 (21) −2z(1+z)q4w2], W(0)KN=−13M0f2K(2D2−6DF)[1−(1+z)q2w2], (22) V(1)¯¯¯¯KN = −14M0f2K[(D−F)2w2+2z(D−F)2q2 (23) −(1+z)q2], W(1)¯¯¯¯KN(q)=−(D−F)22M0f2K, (24) V(0)¯¯¯¯KN(q) = −112M0f2K[(D+3F)2w2 (25) +2z(D+3F)2q2−9(1+z)q2], W(0)¯¯¯¯KN(q)=−(D+3F)26M0f2K. (26) Second, for the vertices from the , we introduce αη=4bDm2η+3b0(m2π+m2η), απ=4bDm2π+3b0(m2π+m2η) (27) to make the following expressions more compact. The amplitudes read V(1)KN = −1f2K[4(bD+b0)m2K+(C1+C2)w2−C1zq2] (28) +zq212w2f2K[(D+3F)2αη+3(D−F)2απ], W(1)KN = −1f2KC3−112w2f2K[(D+3F)2αη (29) +3(D−F)2απ], V(0)KN = 1f2K[4(bF−b0)m2K+(C4+C5)w2−C4zq2] (30) +zq212w2f2K[9(D−F)2απ−(D+3F)2αη], W(0)KN = −1f2KC6−112w2f2K[9(D−F)2απ (31) −(D+3F)2αη], V(1)¯¯¯¯KN = 1f2K[(2bF−2bD−4b0)m2K−12(C1+C2 (32) −C4−C5)w2+12(C1−C4)zq2] +zq22w2f2K(D−F)2απ, W(1)¯¯¯¯KN=12f2K(C3+C6)+12w2f2K(D−F)2απ, (33) V(0)¯¯¯¯KN = −1f2K[2(3bD+bF+2b0)m2K+12(3C1+3C2 (34) +C4+C5)w2−12(3C1+C4)zq2] +zq26w2f2K(D+3F)2αη, W(0)¯¯¯¯KN=12f2K(3C3−C6)+16w2f2K(D+3F)2αη, (35) where C1=−4b1−4b3−2b4, C2=−4b5−4b7−2b8, C3=4b10+b11, C4=−4b2+4b3−2b4, C5=−4b6+4b7−2b8, C6=−4b9−b11. (36) The six combinations of LECs are introduced in order to reduce the number of LECs. At the third order , we have the one-loop diagram contributions and the counterterm contributions. The nonvanishing one-loop diagrams generated by the vertices of and are shown in Fig. 2. The counterterm contribution estimated from resonance exchange was found to be much smaller than the chiral loop contribution in the case of threshold scatteringbern1993; bern1995. Kaiser assumed that similar features hold for threshold and scattering and also achieved some successkais2001. Liu and Zhu also ignored the counterterm contributions when they calculated meson-baryon scattering lengthsliu20071. Later, Liu and Zhu claimed that the counterterm contributions are larger than the one-loop diagrams contributions in some T-matrices in Ref. liu20072. But, Liu and Zhu did not consider the resonance contribution when determining the LECs and their combinations in Ref. liu20072. However, we are not considering the counterterm contributions when calculating T-matrices at in this paper. The nonvanishing one-loop amplitudes corresponding to loop diagrams are too tedious; thus, we present these amplitudes separately in Appendix A. In loop calculations, we use dimensional regularization and the minimal subtraction scheme to evaluate divergent loop integralshoof1979; bern19951; mojz1998; bouz2000; bouz2002. We use in all loops instead of corresponding decay constants in respective loops. The difference appears at higher order. ## Iv Calculating phase shifts and Scattering lengths The partial wave amplitudes , where refers to the orbital angular momentum and to the spin, are given in terms of the invariant amplitudes via f(I)l±s(q) = EN+MN16π(w+EN)∫+1−1dz[V(I)KN,¯¯¯¯KN(q)Pl(z) (37) +q2W(I)KN,¯¯¯¯KN(q)(Pl±1(z)−zPl(z))], where are conventional Legendre polynomials. For the energy range considered in this paper, the phase shifts are evaluated from (for discussions about the phase shifts, see Refs. gass1991; fett1998) δ(I)l±s(q)=arctan(qRef(I)l±s(q)). (38) Based upon relativistic kinematics, there is a relation between the CMS on-shell momentum and the momentum of the incident kaon in the laboratory system , q2=M2Nq2Km2K+M2N+2MN√m2K+q2K. (39) Near threshold the scattering length for s waves and the scattering volume for p waves is given byeric1988 a(I)l±s=limq→0q−2l−1% tanδ(I)l±s(q). (40) ## V Results and Discussion Before calculating the phase shifts and the threshold parameters, we have to determine the LECs. There are 14 unknown LECs in and also need to be determined. Fortunately, after the regrouping, we determine only and the six LEC combinations which were defined by Eq. (III). Throughout this paper, we use MeV, MeV, MeV, MeV, MeV, MeV, and pdg2014, and for the axial vector coupling constants we use and . We also take as the chiral symmetry breaking scale. We first determine , , and through the formulas of the octet-baryon masses and given in Ref. bern19951. We take in the loops in these formulas, respectively. The baryon masses MeV, MeV, MeV, and MeV and the pion-nucleon () term hofe2015 are used to fit these four parameters. We obtain M0=646.30±47.72MeV, bD=0.043±0.008GeV−1, bF=−0.498±0.003GeV−1, b0=−1.003±0.047GeV−1 (41) with . In our fitting, the new from Ref. hofe2015 is taken; thus, we obtain different values than those in Ref. liu20071. Note that the uncertainty of the th LEC (here, refers to one of the , , and ) is purely the statistical uncertainty that is a measure of how much this particular parameter can change while maintaining a good description of the fitted data, as detailed in Refs. doba2014; carl2015. We now determine the six LEC combinations by using the phase shifts of the SP92 solution, GW Institute for Nuclear Studies, for kaon-nucleon () scattering analysisSAID; hysl1992. Since the SP92 give no uncertainties for the phase shifts, we set a common uncertainty of to all values before the fitting procedure. For the parameters , we use the data of the S11, P11 and P13 waves between 50 and 90 MeV (15 data points in total) to fit. As to the , we fit the data of the S01, P01 and P03 waves at MeV. The resulting LECs are given by C1=1.99±0.11GeV−1, C2=−0.45±0.11GeV−1, C3=6.36±0.09GeV−1, (42) with and C4=3.01±0.21GeV−1, C5=−5.10±0.21GeV−1, C6=−5.13±0.12GeV−1, (43) with . For the uncertainties, see the above description. The corresponding S- and P-wave phase shifts are shown in Fig. 3. For the P01 wave, the description of the phase shifts is surprisingly good even at higher and lower energies. The remaining waves are also in good agreement with the empirical phase shifts below 150 MeV and purely overestimated at large kaon momentum. However, to sum up, we obtain a good description for these six lowest partial waves in this one-loop order calculation of the scattering up to surprisingly large kaon momenta. In order to check the consistency of the ChPT framework for different observables, we now determine the low-energy constants by the scattering lengths. However, there are six LEC combinations , but only four scattering lengths can be used. At this time, we take the threshold T-matrices to calculate the scattering lengths; see Appendix B. For comparison, we use the two scattering lengths and from the SP92hysl1992 to determine the two LEC combinations and . The resulting LECs are given by C12=C1+C2=1.59GeV−1, C45=C4+C5=−1.99GeV−1. (44) The LEC combination determined by the phase shifts from Eq. (V) is , while the from Eq. (V) is . The results are consistent with the LEC combinations determined by the scattering lengths from Eq. (V) within the limit of error. In the following, we make predictions for the scattering through the above LECs determined by the phase shifts and the corresponding data. At present, the existing empirical phase shifts of the scatteringarme1969; hemi1975; gopa1977; ks20131; ks20132 are all above the kaon laboratory momentum of 200 MeV (corresponding to the CM energy of around 1460 MeV); thus, the resulting S- and P-wave phase shifts are shown in Fig. 4 without the empirical phase shifts. From the plot of Fig. 4, none of the phase shifts shows the resonant behavior. The recent multichannel partial-wave analysis for scattering KS2013ks20131; ks20132 includes a variety of resonances, such as the S01, S11, P01, P03, P11, and P13 wave including the , , , , and resonances, respectively. But all the resonances considered by the KS2013 do not contribute to the phase shifts below the CM energy of 1460 MeV , because they are so far away. Thus, the predictions for the phase shifts of the partial waves in the scattering are reasonable. However, as we all know, there exists the resonance as a quasibound state below the threshold energy in a S01 wave. To solve this problem, the solution is given by the nonperturbative resummation approach with a phenomenologically successful description of the scattering amplitudekais1995; oset1998; olle2001; lutz2002 (for a review on this issue, see Ref. hyod2012). Now let us apply the above LECs to estimate the kaon-nucleon and antikaon-nucleon scattering lengths. We have two approaches to predict the scattering lengths. One is through the use of the Eq. (40) and the LECs from Eqs. (V) and (V). As before, we do not fit data below MeV (for , ); hence, the scattering lengths are predictions. The scattering lengths are obtained by using an incident kaon momentum MeV and approximating its value at the threshold. As a result, no errors are provided. We present the values of the scattering lengths as “Prediction A” in Table 1. The other is through the use of the formalism in Appendix B and the LECs from Eq. (V). We show the values of the scattering lengths as “Prediction B” in Table 1. The values purely have slightly difference than Ref. liu20071 because different data are taken. In addition, for comparison, the various empirical values are also shown in Table 1. We successfully predict the isospin-1 scattering lengths. For the isospin-0 scattering length, we obtain very small negative values differing from the empirical values. However, the error will cover the difference. As expected, we fail to predict the isospin-0 scattering length that is dominated by the resonance. The situation is the same as the prediction for the phase shifts of the scattering. From this, it would be more reliable to predict the et al. scattering, although no empirical data are available. These works will be presented in our next publication. Finally, we discuss the convergence. This issue is addressed for scattering in Fig. 5. For S01, the leading order is zero. The second-order contribution is much bigger than the third order and describes well the partial wave. For S11, we find that there is sizeable cancellation between the second and the third orders. This feature has also occurred in the chiral expansion of a threshold T-matrixkais2001. For P-waves, the second order is much more important than the others in all partial waves and nearly describes well the empirical phase shifts. The situation is simpler than the scatteringfett1998. According to these results, a higher-order calculation is needed. In summary, we have calculated the T-matrices for and scattering to one-loop order in SU(3) HBPT. We then fit the , the SP92 phase shifts of scattering, and the corresponding data to determine the LECs. This leads to a good description of the phase shifts below 200 MeV kaon momentum in the laboratory frame. We also discuss the LEC uncertainties through statistical regression analysis. In order to check the consistency of the ChPT framework for different observables, we determine the LECs by the scattering lengths, make a comparison with the LECs determined by the phase shifts, and obtain a consistent result. By using these LECs, we predict the scattering phase shifts and obtain a reasonable result. The s-wave scattering lengths are predicted with the energy-dependent solution (Prediction A) and in the case of the threshold T matrices (Prediction B). As expected, we fail to predict the isospin-0 scattering length which is dominated by the resonance. This issue can be successfully solved by the nonperturbative resummation approach, and that is not the focus of this paper. Finally, we check the convergence of the scattering and find that the large cancellations occurred between the second and third orders in the S11 wave. In order to determine accurately the LECs and make better predictions, higher-order calculations are needed in SU(3) HBPT. In addition, the prediction for the octet meson and octet baryon interaction ( such as and scattering) will be calculated in the next publication. We also expect our calculations to provide a possibility to investigate the baryon-baryon interaction in HBPT. ###### Acknowledgements. This work is supported by the National Natural Science Foundation of China under Grants No. 11465021 and No. 11065010. B. L. H. thanks Norbert Kaiser (Technische Universität München), Yan-Rui Liu (Shandong University) and Jia-Qing Zhu (Yunnan University) for very helpful discussions. ## Appendix A One-loop amplitudes In this Appendix, we present the nonvanishing amplitudes from nonvanishing one-loop diagrams. The amplitudes are shown one diagram by one diagram (but similar diagrams are grouped together) due to the expressions being too tedious. For giving the expressions as many details as possible, we use several functions in the following expressions. The normal unit step function θ(x)={1x>0,0x<0 (45) is used. We also define Q2=2q2(z−1), (46) r(m)=√\|1−4m2Q2\|. (47) Figures 2(a)-2(d): V(1)KN = zq2144π2w2f4K{αDFπ[w3−wm2π+πm3π+(3wm2π−2w3)lnmπλ−2(w2−m2π)3/2lnw+√w2−m2πmπ] (48) +αDFK[w3−wm2K+πm3K+(3wm2K−2w3)lnmKλ−2(w2−m2K)3/2lnw+√w2−m2KmK] +αDFη[w3−wm2η+πm3η+(3wm2η−2w3)lnmηλ−2(m2η−w2)3/2(arccoswmη)θ(m2η−w2) −2(w2−m2η)3/2(lnw+√w2−m2ηmη)θ(w2−m2η)]}, W(1)KN=−V(1)KNzq2, (49) V(0)KN = zq2144π2w2f4K{βDFπ[w3−wm2π+πm3π+(3wm2π−2w3)lnmπλ−2(w2−m2π)3/2lnw+√w2−m2πmπ] (50) +βDFK[w3−wm2K+πm3K+(3wm2K−2w3)lnmKλ−2(w2−m2K)3/2lnw+√w2−m2KmK] +βDFη[w3−wm2η+πm3η+(3wm2η−2w3)lnmηλ−2(m2η−w2)3/2(arccoswmη)θ(m2η−w2) −2(w2−m2η)3/2(lnw+√w2−m2ηmη)θ(w2−m2η)]}, W(0)KN=−V(0)KNzq2, (51) V(1)¯¯¯¯KN = zq296π2w2	{}
# If $P \ne NP$, is every language not contained in $NP$ $NP$-hard? The other day, a student asked me whether, if $P \ne NP$, whether any language outside of $NP$ is known to be $NP$-hard. I wasn't sure if • This is definitely known to be true, • This is definitely known to be false, or • This depends on another set of complexity assumptions that do not immediately follow from $P \ne NP$ (that is, even if we knew $P \ne NP$, this would still be an open question) None of the texts on complexity I looked into seemed to answer this question (though it is quite possible that I simply missed it). Does anyone know which of the above three is true, or know a good reference where I could look up the answer? (Note: This earlier question is related, but I'm considering solely questions outside of $NP$ (so the existing answer doesn't really help) and am not restricting this to just the decidable languages) Thanks! - I think that it's the case that this is definitely known to be true, but I'm not certain enough to make this an answer. – Keith Irwin Dec 13 '11 at 6:24 The answer to this question should not depend on wether P=NP. – Raphael Dec 13 '11 at 6:58 Are you asking if every language outside NP is NP-hard? Or are you asking if there exists some language outside NP that is NP-hard? I cannot tell from the wording... – Srivatsan Dec 13 '11 at 7:26 What happens, say, if you take the language of all $x$ such that $\|x\| \in K$, for some undecidable $K$? – Yuval Filmus Dec 13 '11 at 7:58 @SRivastan- The question is whether every language outside NP is NP-hard. – templatetypedef Dec 13 '11 at 8:18 show 3 more comments ## 4 Answers So it looks like the answer to this question is as follows: If $P \ne NP$, then there exists a language not contained in NP that is not NP-hard. This follows from Mahaney's theorem, which says that $P = NP$ iff there is some sparse language L such that SAT is polynomial-time reducible to L. In particular, this says that if $P \ne NP$, then SAT is not polynomial-time reducible to any sparse language. So consider the unary halting language $UNARYHALT$ consisting of unary encodings of TM/string pairs where the given TM halts on the particular input. This language is sparse, since for any length there is either zero or one strings in the language with that length. Moreover, this language is undecidable by a reduction from the halting problem, so it cannot be in NP. Therefore, if $P \ne NP$, by Mahaney's theorem this language is not NP-hard, because there is no polynomial-time reduction from SAT to it. - add comment It seems that the probabilistic method works. Consider $\{0,1\} \times \{0,1\} \times \dots$ as a probability space, corresponding to throwing a coin countably many times (product measure). Any event $a \in \{0,1\} \times \{0,1\} \times \dots$ encodes a subset $L \subseteq \{0,1\}^{\ast}$, the consecutive bits decide if $\epsilon \in L, 0 \in L, 1 \in L, 00 \in L, \dots$. We will now select random $L$, equivalently random $a$, and check its properties. With probability 1, $L \notin \mathsf{NP}$ (since $\mathsf{NP}$ is countable), even more: with probability 1, $L$ is undecidable. Now, suppose you have a reduction $f \colon A^{\ast} \to \{0,1\}^{\ast}$ that attempts to reduce SAT to $L$. Since $\mathsf{P} \neq \mathsf{NP}$ by assumption, the image of $f$ must be infinite; otherwise you could convert the reduction to a decision procedure for $SAT$. However, for any $x$, it must hold $x \in SAT \iff f(x)\in L$, and that happens with probability 1/2. Since there are infinitely many values for $f(x)$, the probability that $f$ is a valid reduction from SAT to $L$ is 0. Since there are countably many reductions, and countable intersection of sets of measure 1 has measure 1, the overall probability of $L$ satisfying all conditions is 1. So a "generic" random language is neither decidable nor $\mathsf{NP}$-hard, unless $\mathsf{P} = \mathsf{NP}$. It is possible to convert this proof to diagonalization: on $2i$-th stage, you diagonalize against $i$-th $\mathsf{NP}$ problem; on $2i+1$-th stage, you diagonalize against $i$-th polynomial time reduction with infinite image. This gives a constructive example; with more careful bookkeeping you can get a decidable example. - @templatetypedef: No, there's definitely uncountably many NP-hard languages. Pick arbitrary language $L$ and then $M=0\cdot L \cup 1\cdot SAT$ is NP-hard by reduction from SAT to $M$: $f(x) = 1 x$. In your argument, a pair does not specify the NP-hard language completely, outside the image of the reduction. – sdcvvc Jan 17 at 9:27 Excellent point. I stand corrected! – templatetypedef Jan 17 at 16:57 add comment The answer to this question depends on the complexity assumptions. • If $\mathrm P = \mathrm {NP}$, then every nontrivial language $L$ is $\mathrm{NP}$-hard. [A language is said to be nontrivial if it contains at least one yes instance and at least one no instance.] To reduce a given $\mathrm {NP}$ problem $A$ to $L$, we simply ignore $L$ and use the polynomial-time algorithm for $A$ -- this is guaranteed to exist under our assumption. • Assuming $\mathrm{NP} \neq \text{co-}\mathrm{NP}$, no problem in $\text{co-}\mathrm{NP}$ would be $\mathrm{NP}$-hard. - So even if P != NP, we cannot say for certain whether every language outside NP is NP-hard, since it depends on whether NP = co-NP? It seems like there might be some other known result that would show this result either way. – templatetypedef Dec 13 '11 at 8:19 @templatetypedef Yes, this does not answer your question completely because I need the stronger hypothesis that NP $\neq$ coNP (although most people believe this stronger assumption anyway). – Srivatsan Dec 13 '11 at 8:30 Any co-NP-complete problem, for example the set of Boolean formula tautologies, is NP-hard. The definition NP-hardness allows arbitrary oracle ("Turing" or "Cook") reductions, not just many-one ("Karp") reductions. – Colin McQuillan Dec 13 '11 at 9:07 @Colin, You raise a nice point. Indeed under the Turing (Cook) reductions, coNP-complete problems are NP-complete as well. However, without explicit qualification, I always take NP-complete in the sense of Karp reductions (as my post shows :-)). However I will be happy to see answers from the other point of view. :) – Srivatsan Dec 13 '11 at 9:16 "NP-complete" is always Karp, "NP-hard" is always Turing. – Colin McQuillan Dec 13 '11 at 9:28 show 7 more comments Take any undecidable language L and let L' be the language of pairs (n,x) with x in L and n=2^\|x\| in unary. Then L' is in P/poly but not in NP. If L' is NP-hard then NP$\subset$P/poly and the polynomial hierarchy collapses by the Karp-Lipton theorem. - This is not a complete answer to the question, however, because we may have NP $\subseteq$ P/poly but P$\neq$NP. – Colin McQuillan Dec 13 '11 at 9:27 add comment	{}
# Jtag debugging AVR Can anyone advise what hardware and software is required for debugging AVR in circuit. Normal ISP programmers have no JTAG debugging capabilities. For this you will need slightly more expensive hardware. A JTAG in circuit emulator will enable you to let your circuit communicate with your PC while you are running the firmware. This way you can set breakpoints, watch the memory, enable/disable pins and see the exact status of your micro controller. The ISP programmers from EMSL and Adafruit will not let you do this. One of the cheapest programmers that have in-circuit emulation capabilities is the AVR Dragon. It will cost you about $50,-. It is cheap for a reason though: it's too easy to overload the circuit and break the programmer. If you get one I recommend that you find some form of protection like a DragonRider or a DragonHide. (I already killed my first dragon which is surprisingly easy to do) A more robust solution would be an AVR-JTAG-ICE-MKII but this thing is much more expensive. You can also try and build one yourself. Another option for hardware may be the Bus Pirate at$27.15(sold though seedstudio) which also do other things. I haven't used it for JTAG yet, but this is what the manual says: link. For the hardware, see my answer to a similar question. For the software, you can start with AVR Studio on Windows. If you're using Linux for your development platform, then read this Linux Journal article.	{}
# Regularity results for quasilinear elliptic equations in the Heisenberg group @article{Manfredi2007RegularityRF, title={Regularity results for quasilinear elliptic equations in the Heisenberg group}, author={Juan J. Manfredi and Giuseppe Mingione}, journal={Mathematische Annalen}, year={2007}, volume={339}, pages={485-544} } We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group $${\mathbb{H}}^n$$ . The model case is the non-degenerate p-Laplacean operator $$\sum_{i=1}^{2n} X_i \left( \left(\mu^2+ \left\| {\mathfrak{X}}u \right\|^2\right)^\frac{p-2}{2} X_i u\right) =0,$$ where $$\mu > 0$$ , and p is not too far from 2. BETA #### Citations ##### Publications citing this paper. SHOWING 1-10 OF 24 CITATIONS ## $C^{1,\alpha}$-Regularity for variational problems in the Heisenberg group VIEW 6 EXCERPTS CITES BACKGROUND & RESULTS HIGHLY INFLUENCED ## On the $C^{1,\alpha}$ Regularity of $p$-Harmonic Functions in the Heisenberg Group VIEW 5 EXCERPTS CITES METHODS HIGHLY INFLUENCED ## OPTIMAL PARTIAL REGULARITY FOR NONLINEAR SUB-ELLIPTIC SYSTEMS RELATED TO HÖRMANDER' S VECTOR FIELDS • 2011 VIEW 7 EXCERPTS CITES BACKGROUND HIGHLY INFLUENCED ## Mean Value Property and Harmonicity on Carnot-Carathéodory Groups VIEW 2 EXCERPTS CITES BACKGROUND HIGHLY INFLUENCED ## Variational approach to the asymptotic mean-value property for the p-Laplacian on Carnot groups Tomasz Adamowicz, Antoni Kijowski, Andrea Pinamonti, Ben Warhurst • 2019 VIEW 2 EXCERPTS CITES BACKGROUND ## Regularity of quasilinear sub-elliptic equations in the Heisenberg group VIEW 2 EXCERPTS CITES BACKGROUND & METHODS ## Optimal partial regularity for nonlinear sub-elliptic systems with Dini continuous coefficients in Carnot groups • 2016 #### References ##### Publications referenced by this paper. SHOWING 1-10 OF 29 REFERENCES ## Multiple integrals in the calculus of variations VIEW 6 EXCERPTS HIGHLY INFLUENTIAL ## Differentiability of solutions for the non-degenerate p-Laplacian in the Heisenberg group VIEW 9 EXCERPTS HIGHLY INFLUENTIAL ## Regularity for quasilinear equations and $1-$quasiconformal maps in Carnot groups VIEW 9 EXCERPTS HIGHLY INFLUENTIAL ## An embedding theorem and the harnack inequality for nonlinear subelliptic equations VIEW 6 EXCERPTS HIGHLY INFLUENTIAL ## Direct Methods in the Calculus of Variations VIEW 4 EXCERPTS HIGHLY INFLUENTIAL ## Hypoelliptic second order differential equations VIEW 4 EXCERPTS HIGHLY INFLUENTIAL ## Regularity of quasi-linear equations in the Heisenberg group VIEW 13 EXCERPTS HIGHLY INFLUENTIAL ## Doctoral dissertation L. Capogna • Purdue University, • 1996 VIEW 10 EXCERPTS HIGHLY INFLUENTIAL VIEW 1 EXCERPT ## J A. Domoko • J. Manfredi, C-regularity for p-harmonic functions in the Heisenberg group for p near 2. In “The p-Harmonic Equation and Recent Advances in Analysis”, ed. P. Poggi-Corradini, Contemporary Mathematics 370, American Mathematical Society, • 2005 VIEW 1 EXCERPT	{}
# Properties Label 348726.x Number of curves $2$ Conductor $348726$ CM no Rank $1$ Graph # Related objects Show commands for: SageMath sage: E = EllipticCurve("x1") sage: E.isogeny_class() ## Elliptic curves in class 348726.x sage: E.isogeny_class().curves LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality 348726.x1 348726x1 $$[1, 0, 1, -548006, -145152520]$$ $$56402207875/4451328$$ $$1436388784379200512$$ $$[2]$$ $$5836800$$ $$2.2278$$ $$\Gamma_0(N)$$-optimal 348726.x2 348726x2 $$[1, 0, 1, 549434, -653486728]$$ $$56844576125/604685088$$ $$-195124438928012019552$$ $$[2]$$ $$11673600$$ $$2.5744$$ ## Rank sage: E.rank() The elliptic curves in class 348726.x have rank $$1$$. ## Complex multiplication The elliptic curves in class 348726.x do not have complex multiplication. ## Modular form 348726.2.a.x sage: E.q_eigenform(10) $$q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + q^{12} - 2q^{13} - q^{14} + q^{16} - 6q^{17} - q^{18} + O(q^{20})$$ ## Isogeny matrix sage: E.isogeny_class().matrix() The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering. $$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$ ## Isogeny graph sage: E.isogeny_graph().plot(edge_labels=True) The vertices are labelled with LMFDB labels.	{}
# How to find standard electrode potential of a reaction resulting from two different reactions? Q1) Calculate $$E_{\ce{Cu+}\|\ce{Cu}}^o=E_o$$. Given that- $$E_{\ce{Cu^2+}\|\ce{Cu}}^o=E_1$$ and $$E_{\ce{Cu+}\|\ce{Cu^2+}}^o=E_2$$ Method 1- $$(i)\quad\ce{Cu^2+} + 2e^-\to \ce{Cu} \quad... \Delta G_1=-2FE_1$$ $$(ii)\quad\ce{Cu+}\to\ce{Cu^2+}+e^-\quad...\Delta G_2=-FE_2$$ Required reaction is the "addition" of these two so- $$\ce{Cu+}+e^-\to\ce{Cu}$$ $$E_o=2E_1+E_2$$ Method 2- Just directly add the two reactions, which gives us $$E_o=E_1+E_2$$ Q2) Calculate standard cell potential of the following reaction- $$14\ce{H+}+6\ce{Cl-}+\ce{Cr2O7^2-}\to 3\ce{Cl2}+2\ce{Cr^3+}+7\ce{H2O}$$ Given that $$E_{\ce{Cr2O7^2-}\|\ce{Cr^3+}}^o=E_1$$ and $$E_{\ce{Cl-}\|\ce{Cl2}}^o=E_2$$ Method 1- Use the same process as done in the above example i.e. write expressions of $$\Delta G$$ of reduction of dichromate and oxidation of chloride, multiply them by suitable coefficients so as to get the desired chemical equation. This gives us $$E_o=\frac{E_1+3E_2}{6}$$. Method 2- Just directly add the two reactions, which gives us $$E_o=E_1+E_2$$ According to my textbook Method 1 is correct for the first question while Method 2 is correct for the second. Why? • Arithmetics with E is the same as with DeltaG, except the extra multiplicator n (resp. nF ). so if you are going to honor the energy conservation law, when doing additions and subtractions with potentials, you always have to implicitly or explicitly involve the n multiplicators. As energy = charge . potential. Aug 10 '21 at 12:05 • @Poutnik yeah then why does that not work with the second question? Method 1 should have been correct according to what you say but actually method 2 is the correct one. Aug 10 '21 at 12:29 • There is another factor that you use another multiple of Delta G or of nFE, if you use multiplied chemical equation, like $\ce{2 Cu+ + 2e- -> 2 Cu}$ instead of $\ce{Cu+ + e- -> Cu}$ Aug 10 '21 at 12:40 • Define $E_2$ for Q. 2. Standard electrode potential is an $intensive$ property. Aug 15 '21 at 5:57 • @Apurvium Sorry, that was a typo, corrected. Aug 15 '21 at 7:07 Q2) Calculate standard cell potential of the following reaction- $$14\ce{H+}+6\ce{Cl-}+\ce{Cr2O7^2-}\to 3\ce{Cl2}+2\ce{Cr^3+}+7\ce{H2O}$$ Given that $$E_{\ce{Cr2O7^2-}\|\ce{Cr^3+}}^o=E_1$$ and $$E_{\ce{Cl-}\|\ce{Cl2}}^o=E_2$$ The half-cell reactions are:$$14\ce{H+}+6\ce{e-}+\ce{Cr2O7^2-}\to 2\ce{Cr^3+}+7\ce{H2O};~~~~~~~~~~n_1=6$$ $$3[\ce{2Cl-}\to \ce{Cl2}+\ce{2e-}];~~~~~~~~~~n_2=6$$ Note that, before arriving the final equation, you have to balance the charges and then cancel out the electrons by multiplying with appropriate coefficient. As $$G$$ is a state function: $$\Delta G^0_1+\Delta G^0_2=\Delta G^0$$ $$\implies -n_1FE^0_1+(-n_2FE^0_2)=-nFE^0$$ $$\implies E^o=\frac{6E^0_1+6E^0_2}{6}=E^0_1+E^0_2$$ Q1) Calculate $$E_{\ce{Cu+}\|\ce{Cu}}^o=E_o$$. Given that- $$E_{\ce{Cu^2+}\|\ce{Cu}}^o=E_1$$ and $$E_{\ce{Cu+}\|\ce{Cu^2+}}^o=E_2$$ Similarly, the half-cell reactions are: $$(i)\quad\ce{Cu^2+} + 2e^-\to \ce{Cu} \quad... \Delta G^0_1=-2FE^0_1$$ $$(ii)\quad\ce{Cu+}\to\ce{Cu^2+}+e^-\quad...\Delta G^0_2=-FE^0_2$$ Required reaction is the "addition" of these two so- $$\ce{Cu+}+e^-\to\ce{Cu};~~~~~~~~~~n=1$$ $$\Delta G^0_1+\Delta G^0_2=\Delta G^0$$ $$\implies -2FE^0_1+(-FE^0_2)=-FE^0$$ $$\implies E^o=\frac{2E^0_1+E^0_2}{1}=2E^0_1+E^0_2$$ Therefore, we can always get the correct result by equating the values of $$\Delta G$$. • Oh! I made a silly mistake. Sorry for wasting your time Aug 15 '21 at 16:59	{}
1. ## Geometry type question a rectangular garden measures 5mx4m its area is to be tripled by extending each dimension by the same amount. How much should each dimension extend? 2. Hello, mcinnes! Did you make a sketch? A rectangular garden measures 5m x 4m. Its area is to be tripled by extending each dimension by the same amount. How much should each dimension extend? Code: : - - x+5 - - : - ------------- - x \| \| : - --------- _ * - - - - * \| : : \| \| : \| \| \| x+4 4 \| 20 m² \| 4 \| \| \| : : \| \| : \| \| \| : - --------- - ------------* - : - 5 - : : - 5 - : x : The original garden is 5 by 4 and has an area of 20 m². The new garden is $(x+5)$ by $(x+4)$ and has an area of 60 m². There is our equation . . . . $(x+5)(x+4) \:=\:60 \quad\Rightarrow\quad x^2 + 9x - 40 \:=\:0$ Quadratic Formula: . $x \;=\;\frac{-9 \pm\sqrt{241}}{2}$ The positive root is: . $x \;=\;\frac{-9 + \sqrt{241}}{2} \;\approx\;3.262\text{ m}$	{}
HOSTING A TOTAL OF 318 FORMULAS WITH CALCULATORS ## Volume Of General Cone and Pyramid A pyramid has a base and triangular sides which rise to meet at the same point. The base may be any polygon such as a square, rectangle, triangle, etc. ## $\frac{1}{3}\mathrm{ah}$ here,a = area of base, h = height ENTER THE VARIABLES TO BE USED IN THE FORMULA Similar formulas which you may find interesting.	{}
User:Pramodkumartk/Temp/Report of OER WS-27-29Feb12.doc Report of Workshop on Development Of Open Educational Resources In Vocational Education A three days workshop was held at Seminar Hall , Indian Institute of Education, Kothrud, Pune to orient the OER Course teams in the areas of ICT Applications, Rural Technology and Hospitality and Tourism Management during 27,28 and 29th February 2012. Twenty five participants including three course Team Leaders and their team members were present with other Experts of Open Educational Resources. The workshop sessions were co-ordinated by Prof. M.N Deshmukh who has played a major role in the design of the workshop. On 27th February 2012 the session began with the welcome address by Mr. Sanjay Kumar Sinha , Regional Director. Thereafter objectives of the workshop and the significance of OER development for Vocational Education were elaborated by the Project Co-ordinator Ms. Koushalya Barik , Assistant Director ( Vocational )NIOS, Noida. The programme was inaugurated by Prof. Ram Takwale, Ex. V.C , IGNOU. In his inaugural address he briefly described the history of OER movement . He emphasised that creating OER based educational system should be our ultimate aim.He hoped that this workshop will help in development of Role based and concept based OERs with lot of activities through which the distance learners can enhance their capabilities. Breaking the ice Prof.M.N.Deshmukh, Secretary, i-consent and mentor of the project explained in detail the proposed plan of action (as per annexure-1)to the participants. He also motivated the participants to actively participate in the sessions . After tea break Prof. S.C. Agarkar, HBCSE, Mumbai gave a detailed presentation on the term OER starting with the terms’ Open Resource’ and ‘Educational Resource’. He also shared his experience in the field of Open Educational Resources. In the afternoon session Prof.M.N.Deshmukh explained the significance of Content Analysis in the development of OER. Then the participants analysed the syllabus and presented their content analysis by writing down the Concepts involved, Objectives and learning activities proposed. Feedback was taken from the participants and the session ended by assigning the task for preparation of content analysis for the entire course. On 28th February 2012, Dr.Jayashree Shinde , Head of Department of Educational Technology,SNDT University , Mumbai gave an online presentation through two way video conferencing from the University campus in Mumbai. She discussed on the importance of ADDIE Model and the usefulness of this model in the development of OERs. This session was supported by Prof. Veena Deshmukh , Director ,CDE, SNDT University ,Mumbai. After the tea break Prof. Deshmukh gave a detailed explanation on the concept mapping and the modalities of Assessment and Evaluation Procedure which needs to be incorporated in the OERs. She also presented some Sample OERs prepared by some students and teachers for the sake of clarity . In the post lunch session the participants were asked to prepare Concept Maps on the topics for which the content analysis is complete .The participants were enriched by the inputs received from Prof. Ram Takwale who joined this session to interact with the participants. Towards the end of the day , the teams demonstrated one concept map each from their selected topic. They also continued their work of completing the integrated syllabi. On 29th February morning Mr. M.N.Deshmukh, Sr. Scientific Officer, HBCSE, Mumbai interacted with the participants giving his experience of OER project of Homi Bhabha Centre for Science Education, Mumbai. He also gave some inputs on systematic preparation of OER . After this sharing of experience Dr.Savithri Singh,Principal Acharya Narendra Dev college took over for her session on Wiki. She emphasised the need of making the OER to be Open in its complete sense( deviating from mere access of the material) and how Wikieducator can be used in achieving this goal. She also demonstrated the use of Wiki educator as a platform for OER. Mr. S.K.Prasad SAP,NIOS , Noida gave his observations on the use of Wikipedia and the e-platform creation through which the participants can be linked for meaningful interaction. In the post lunch session the participants practised with Wikieducator with inputs from Dr. Singh. Majority of the participants created their user account on wikieducator and also demonstrated some wiki skills. As the participants were asked to prepare at least one specimen OER, the groups were busy in making one OER based on the concept map and the content analysis. The group representative presented an OER each at the end of this session. They also used wikieducator to present this OER. This was followed by Valedictory function in which feedback on the Action plan was taken from the participants by Prof.M.N.Deshmukh. He also asked the participants to complete the work of preparation of Integrated syllabus by 5th March and Plan for the next activity as per action plan to which all participants agreed. The course team leaders accordingly shall prepare for the next workshop in the month of March involving 25 teachers in each group for final development of the OERs. It has also come out from the workshop that a page on wikieducator can be during the development of OERs. All participants expressed their gratitude to the NIOS for enriching their knowledge and skills in this emerging area of OER development. Mr. Pramod Kumar T.K. Assistant Director , NIOS RC Pune co-ordinated the administrative aspects of the workshop.	{}
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# ag.algebraic geometry – Projective modules restricted to flush curves Answer Hello pricey customer to our community We will proffer you an answer to this query ag.algebraic geometry – Projective modules restricted to flush curves ,and the respond will breathe typical via documented info sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning in regards to the respond to this query. ## ag.algebraic geometry – Projective modules restricted to flush curves I requested this query on Stack Exchange, however nobody answered this. I need to show a coherent sheaf $$M$$ on $$X$$ is domestically free if and provided that that is undoubted for $$M\|_{X’}$$ , for all flush curves $$X’$$ mapping to $$X$$. I cerebrate the provided that path is patent. For the if path, a coherent module is flat if and solely whether it is projective, for Dedekind domains if and provided that torsion free as effectively. So I’m considering of utilizing Tor$$_1$$. There is native gauge for flatness, however I’m not positive if this may ameliorate. This is used on the birth of the proof of Proposition 5.13 of Gaitsgory’s lecture notes. we are going to proffer you the answer to ag.algebraic geometry – Projective modules restricted to flush curves query through our community which brings all of the solutions from a number of dependable sources.	{}
On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu? Result n = 495 #### Solution: $C_{{ 4}}(12)=\dbinom{ 12}{ 4}=\dfrac{ 12! }{ 4!(12-4)!}=\dfrac{ 12 \cdot 11 \cdot 10 \cdot 9 } { 4 \cdot 3 \cdot 2 \cdot 1 }=495 \ \\ \ \\ n={ { 12 } \choose 4 }=495$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you! Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! Tips to related online calculators Would you like to compute count of combinations? ## Next similar math problems: 1. Quiz or test I have a quiz with 20 questions. Each question has 4 multiple choice answers, A, B, C, D. THERE IS NO WAY TO KNOW THE CORRECT ANSWER OF ANY GIVEN QUESTION, but the answers are static, in that if the "correct" answer to #1 = C, then it will always be equal Adam has half the money in his right pocket than in his left pocket. If he transferred 40 crowns from the left pocket to the right, he would have the same in both pockets. Calculate how many crowns does Adam have in his left pocket more than in his right? 3. Average height There are twice as many girls in the class as there are boys. The average height of girls is 177 cm, boys 186 cm. What is the average height of students in this class? 4. A particle A particle moves in a straight line so that its velocity (m/s) at time t seconds is given by v(t) = 3t2-4t-4, t>0. Initially the particle is 8 meters to the right of a fixed origin. After how many seconds is the particle at the origin? 5. Students Students Aleš, Bohouš, Cyril, and Dušan were on a brigade. They divided the total revenue as follows: Aleš received two-fifths of the revenue, Bohouš received one-sixth of the revenue, Cyril received three-tenths of the revenue, and Dušan received the res 6. Energy consumption The device is connected to 230V and draws 3.5A current. Power consumption is 1932kJ. How many minutes has this device been in operation? 7. All use computer It is reported that 72% of working women use computers at work. Choose 3 women at random, find the probability that all 3 women use a computer in their jobs. 8. The test The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer 9. Slow saving in banks How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest? 10. What is What is the annual percentage increase in the city when the population has tripled in 20 years? 11. Magnified cube If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube. 12. Viewing angle The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? 13. Triangle from median Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5. 14. The modulus Find the modulus of the complex number 2 + 5i 15. The half life The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives? 16. Half of halves Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part? 17. Closed circuit In a closed circuit, there is a voltage source with U1 = 12 V and with an internal resistance R1 = 0.2 Ω. The external resistance is R2 = 19.8 Ω. Determine the electric current and terminal voltage.	{}
Univariate Newton-Raphson method¶ This notebook introduces Newton's method given a univariate, i.e. single variable, optimization example where it is the objective to compute $f(x)=\sqrt[b]{x}$ while $b\in\mathbb{N}$ which is considered constant. This scenario suits numerical optimization as it suffices to incrementally approach a solution posed by its inverse $f^{-1}(x)=x^b$ being an exponential function. Note: The analytical solution $f(x)=\sqrt[b]{x}=x^{1/b}$ is straightforward and more elegant when implemented as x**(1/b) because it does not require additional libraries such that it should always be preferred over the below jaunt. last update: 30/09/2020 Author Christopher Hahne, PhD Cost function¶ Optimization generally involves the definition of a cost (or loss) function prior to the actual minimization to assess each intermediate result candidate $x_k, \, k \in \mathbb{N}$ by analyzing how much it deviates from the point of convergence. We employ the squared loss here as it is differentiable and given by $$L(x_k)=\left( f^{-1}(x_k)-x)\right)^2=\left(x_k^b-x\right)^2$$ where $x$ represents the requested input which is constant. Dual differentation of the loss function is an important requirement for the Newton method. The first-order derivative can be given by $$\frac{\partial}{\partial x_k} L(x_k)=2b\left(x_k^{b+1}-x_kx\right)$$ of our cost function is obtained from the chain rule and written as Similarly, we obtain the second-order derivative given by $$\frac{\partial^2}{\partial^2 x_k} L(x_k)=2b\left((b+1)x_k^b-x\right)$$ which is implemented as Newton-Raphson method¶ Using Newton's method, we aim to converge to $f'(x)=0$ which may be achieved by second-order Taylor expansion yielding $$x_{k+1} = x_k - \frac{f'(x_k)}{f''(x_k)}=x_k-\left(\frac{\partial}{\partial x_k} L(x_k)\right)\left(\frac{\partial^2}{\partial^2 x_k} L(x_k)\right)^{-1}$$ which is implemented hereafter with a tolerance value and maximum iteration number as break conditions. For sake of benchmarking, the binary search algorithm is used in the following. Validation¶ The requested input $x\in\mathbb{R}_+$ for root computation and respective exponent $b\in\mathbb{N}$ are set hereafter and can be varied to see their effects on the computational process. From the plot below, it can be observed that the Newton method generally converges to a more accurate result with fewer iterations whereas the binary search yields good first approximates oscillating around the convergence point $x$.	{}
### Burning Down One night two candles were lit. Can you work out how long each candle was originally? ### Percentage Unchanged If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ? ### Digit Sum What is the sum of all the digits in all the integers from one to one million? # Rough Root ##### Age 14 to 16 ShortChallenge Level Squaring the options $\dfrac{10 000}{2012}\approx\dfrac{10000}{2000}=5$, so $\sqrt{\dfrac{10000}{2012}}\approx\sqrt5$ (We should really check how good this approximation is. See below (or click here) for comparison). So one of the options should square to a number close to $5$. Squaring them gives: $1.9^2=3.61$ which is too small $2.2^2=4.84$ which is too small $2.5^2=6.25$ which is too big so $2.7^2$ will definitely be too big. $2.2$ is too small and $2.5$ is too big. To find which is closer to $\sqrt5$, test a number in between. If $2.3$ is too big, then we will know that $\sqrt5$ is between $2.2$ and $2.3$, so it is definitely closer to $2.2$ than to $2.5$. $2.3^2=2.3\times2+2.3\times0.3=4.6+0.69=5.29$, which is too big. So $2.2$ is the closest. Estimating the square root $10 000=100^2$ $\dfrac{100}?\times\dfrac{100}?=\dfrac{10000}{?\times?}$ where $?\times?$ is close to $2012$ $40^2=1600$ and $50^2=2500$. Try $45^2=2025$ $\therefore\dfrac{100}{45}\times\dfrac{100}{45}=\dfrac{10000}{2025}\approx\dfrac{10000}{2012}$ (We should really check how close this approximation is. See below (or click here) for comparison) So $\sqrt{\dfrac{10000}{2012}}\approx\dfrac{100}{45}=\dfrac{20}{9}=2.\dot2$ So $2.2$ is the closest. How close are our approximations? The difference between $\dfrac{10 000}{2012}$ and $5$ is: \begin{align}\frac{10000}{2000}-\frac{10000}{2012}&=1000\left(\frac{1}{2000}-\frac1{2012}\right)\\ &=10000\left(\frac{2012-2000}{2000\times2012}\right)\\ &=\frac{10000\times12}{2000\times2012}\\ &=\frac{10\times6}{2012}=\frac{30}{1006}<\frac{30}{1000}=0.03\end{align} So really we were looking for a number whose square was somewhere between $5$ and $5.03$. Squaring the options gave results far less precise than this, so this approximation was good enough for this situation. The difference between $\dfrac{10 000}{2012}$ and $\dfrac{10000}{2025}$ is: \begin{align}\dfrac{10 000}{2012}-\dfrac{10000}{2025}&=10000\left(\dfrac1{2012}-\dfrac{1}{2025}\right)\\ &=10000\left(\frac{2025-2012}{2012\times2025}\right)\\ &=\frac{10000\times13}{2025\times2012}<\frac{10000\times13}{2000\times2000}=\frac{13}{2\times200}<\frac{16}{400}=\frac4{100}=0.04\end{align} So the square of $2.\dot2$ is too large, by up to $0.04$. We can write this as $2.\dot2^2-c^2<0.04$, where $c$ is the exact value of $\sqrt{\dfrac{10000}{2012}}$ We can factorise $2.\dot2^2-c^2$ as the difference of two squares: $2.\dot2^2-c^2=(2.\dot2+c)(2.\dot2-c)$, so $(2.\dot2+c)(2.\dot2-c)<0.04$ $2.\dot2-c$ must be very close to $0$, because the product is close to $0$, and $(2.\dot2+c)$ is not particularly close to $0$. This is good, because if $2.\dot2$ is a good approximation, then $2.\dot2-c$ is close to $0$. In fact, $(2.\dot2+c)$ must be more than $2$, since $c$ is positive. So $2.\dot2-c$ must less than $0.02$, to give a product of less than $0.04$ (since $2\times0.02=0.04$). So $2.\dot2$ is an over-estimation by less than $0.02$, which means that the true value of $c$ is somewhere between $2.\dot2-0.02=2.20\dot2$ and $2.\dot2$. So $2.2$ is defiitely the closest of the options. Our approximation was actually far better than the question required. You can find more short problems, arranged by curriculum topic, in our short problems collection.	{}
Tag Info 13 The concept is based on the convolution theorem, which states that for two signals $x(t)$ and $y(t)$, the product of their Fourier transforms $X(f)$ and $Y(f)$ is equal to the Fourier transform of the convolution of the two signals. That is: $$\mathcal{F}\{x(t) * y(t)\} = \mathcal{F}\{x(t)\}\mathcal{F}\{y(t)\}$$ You can read more on the derivation of ... 7 If your signal is real-valued, then it's spectrum is conjugate symmetric. That means, that negative frequencies (or frequencies from $\frac{f_s}{2}$ up to $f_s$) are mirrored. Thus we can always neglect frequencies above Nyquist range. Although, if your signal is complex valued, then such symmetry won't exist, and frequencies above $\frac{f_s}{2}$ contain ... 7 The answer is: yes, sampling in the frequency domain causes aliasing in the time domain, exactly like the dual case: sampling in the time domain causes aliasing in the frequency domain. There are many ways to see this. One standard way is to sample the discrete-time Fourier transform (DTFT) of a discrete-time signal by multiplying it with a Dirac comb and ... 6 I think you made a mistake between the power spectrum and the Fourier Transform. This is the right form of the Convolution Theory (Nothing is squared): $$\lvert Y(\omega)\rvert = \lvert H(\omega) X(\omega)\rvert$$ Try this and it will work for you on MATLAB. MATLAB Code % Calculating the Magnitude of the Filtered Signal vFilterCoeff = [1; 2; 3; 4; 5]; ... 6 Essentially, the reason why you need two tones is to ensure that a normal human voice can't replicate the tones. As such, by simultaneously generating a tone from a high-frequency group and low-frequency group, it is highly improbable that a human voice can replicate a sound from such differing ends of the frequency spectrum at the same time. If we were ... 6 Since what interests you is the "embedded system" part, and since you have a low budget (this excludes anything that requires proprietary compilers), I'd recommend building yourself a board with an ARM MCU and a codec, like this one. There's less than $50 of parts - the processor, the codec and the bare minimum to get them to work. I'm recommending this ... 6 A canonical implementation of a digital filter has the minimum number of delay elements. The same filter cannot be implemented with less memory. Since memory is often not the only concern, a canonical implementation is not necessarily always the best implementation on a given platform. 6 The etymology refers to the canon, as a rule or a body of rules, or axiomatic or universal standards. It exists in arts: sculpture, music, script writing, etc. The notion of canon law is also used in the domain of religion: a "set of ordinances and regulations [...] for the government of a Christian organization or church and its members". In ... 5 Your counterexample to the book's assertion is confusing between two different uses for$n$. There was a question earlier in which some user (endolith? datageist?) gave an answer containing a detailed description of what exactly this confusion is and how to interpret the results correctly. My cursory search has not found this great answer, and so I will ... 5 The usual way to estimate the amplitude of a particular frequency is to use the Goertzel algorithm. There is a good write-up by Rick Lyons here. Even though Rick's writeup is about single tone detection, it can be applied when multiple tones are present, too. 5 This is related to Chirp Z-transform (CZT) (refer to the Bluestein's algorithm). Using this identity, the CZT can be expressed in terms of a convolution. Hence, it can be efficiently implemented using FFT. 5 Matlab’s ‘upsample()’ command does not “pad” a sequence with zero-valued samples. The ‘upsample()’ command “stuffs” a sequence with zero-valued samples. “Zero padding” and “zero stuffing” are two different operations. “Zero padding” means appending a sequential string (a sequence) of zero-valued samples to the beginning or end of a sequence. I believe ... 5 The general topic of finding similarities between signals is wide ranging: are the signals of same sampling, length, offset, shift or scale? where do they take their values (discrete, real, complex)? are they stationary? noisy? what do you consider similar (whole signals, chunks, specific features)? which are the invariances looked for? and most important:... 5 The denominator (recursive coefficients Ai) look OK: the poles of your system are at 45 degree angles ($\pi/4$), with magnitude 0.68 (which is not very aggressive for a notch filter; in my opinion they should be more like 0.9). But your numerator has its roots very near$z=1$, which corresponds to frequency 0 instead of the desired$\pi/4$for implementing ... 5 a Digital Signal Processor is one that has, in its instruction set, some instructions and addressing modes that are optimized for processing digital signals. usually these optimizations can be shown around what is needed to perform the dot-product needed for an FIR filter. $$y[n] = \sum\limits_{i=0}^{L-1} h[i]\,x[n-i]$$ to do this in, say,$L$... 5 8+ high quality inputs for beamfroming and "...beginner friendly..." are competing requirements. There will soon be the audioinjector which attaches on Raspberry Pi and would be a relatively pain-free option for what you mention. You can program the Raspberry in a number of different ways including "low-level" C to high level Python or ... 5 It is a symmetric odd-sized FIR smoothing kernel, belonging to the class of Pascal or binomial filters that somehow sample a Gaussian kernel. Plus, its coefficients are simple dyadic integers, that can be implemented as bit-shifts 1/4 1/2 1/4. The coefficients sum to one, hence it is unit gain at DC. In simpler word: (one of) the simplest real smoother ... 5 I myself recently graduated from Applied Mathematics and began PhD in signal processing. I do Stochastic Geometry modeling of wireless networks in particular, which is quite mathematical subject. It involves measure theory, probability theory, Fourier Analysis etc. etc. The area of Signal Processing is very broad indeed. It of course depends if you want to ... 4 Just change the code to the following: x = randn(1,1000); h = [1 2 3 4 5]; y = conv(x,h); plot((abs(fft(h,1024))).*(abs(fft(x,1024)))); % It's \|H(w)\|\|X(w)\| hold on plot(abs(fft(y,1024)),'--r') By mistake you raised the DFT of an impulse response to the second power. You could see that magnitudes are bit off, but peaks and valleys are more-less at the same ... 4 Suppose you have given an input signal to a system: $$x(n)=\begin{cases} 1, & \mbox{if } n=0 \\ 0, & \mbox{if } n\ne 0 \end{cases}$$ Then the output response of that system is known as the impulse response. In your example$h(n) = \frac{1}{2}u(n-3)$. This means that if you apply a unit impulse to this system, you will get an output signal$... 4 First, use a timer and an ISR to get accurate timing (don't forget to configure the NVIC so that this timer interrupt takes over any other ISR that would be running). Only this will ensure a consistant sample rate. Little variations in timing would create noticeable degradations of audio quality. In particular, in your current example, unless the "filters" ... 4 Finding the phase response of a biquad at a specific frequency is simple. Recall the transfer function of a biquad: $$H(z) = \frac{b_0 + b_1z^{-1} + b_2z^{-2}}{a_0 + a_1z^{-1} + a_2z^{-2}}$$ The frequency response of a system can be calculated by letting $z = e^{j\omega}$, where $\omega$ is a normalized frequency in the range $[-\pi, \pi)$. SO, it would ... 4 This code is splitting a stereo signal with left and right components into a stereo signal with mid and side components, scaling the mid and side components and converting back to left and right components. To convert left (L) and right (R) stereo into mid (M and side (S): $$M = \frac{L + R}{2}$$ $$S = \frac{L - R}{2}$$ And back: $$L = M + S$$ $$R ... 4 assuming finite power signals:$$ \lVert x \rVert^2 \triangleq \lim_{N \to \infty} \ \frac{1}{2N+1} \sum\limits_{n=-N}^{+N} \big\|x[n] \big\|^2 \ < +\infty $$this is a Hilbert Space sorta thingie. define inner product:$$ \langle x,y \rangle \triangleq \lim_{N \to \infty} \ \frac{1}{2N+1} \sum\limits_{n=-N}^{+N} x[n] \cdot \overline{y}[n] where \$\... 4 if you are searching for similarity between two signals in frequency domain, you can go for coherence. Coherence indicates frequency components common to both signals 4 Hopefully you'll get a bunch of answers here from the very general to the super specific. I'll put in my two cents here. The recommendations I would make are from the field of radar and communication systems. These systems tend to exercise almost all aspects of signal processing: Signal generation and mixing Sampling, decimating/upsampling Signal ... 3 It's been a while, but if anyone would like a working fixed-point implementation (no floats/doubles) in C you might take a look at: http://www.ti.com/ww/cn/uprogram/share/ppt/c6000/Chapter17.ppt‎ – Slide 14. It looks like it will work beautifully and efficiently in even a low-powered micro-controller. (In which case some of the ‘int’ variables in that TI C ... 3 There is no easy answer to that question. Plenty of algorithms exists which are suitable to that task. Nowadays Non-negative Matrix Factorisation (NMF) is getting more and more popular in this field of research. If you have enough of resources and knowledge then you can try it. It's just a 'fancy' SVD decomposition with some 'constraints and tweaks'. Some ... Only top voted, non community-wiki answers of a minimum length are eligible	{}
Symplectic and Poisson structures on some loop groups.(English)Zbl 0820.58021 Maeda, Yoshiaki (ed.) et al., Symplectic geometry and quantization. Papers presented at the 31st Taniguchi international symposium on symplectic geometry and quantization problems held at Sanda, Japan, July 12-17, 1993 and a satellite symposium held at Keio University, Yokohama, Japan, from July 21-24, 1993. Providence, RI: American Mathematical Society. Contemp. Math. 179, 173-192 (1994). The author’s abstract: Drinfeld has given an idea of multiplicative Poisson structures on Lie groups. The essential derivative of a multiplicative Poisson structure at the unit element of a group defines a Lie algebra structure on the dual space of the Lie algebra of the group. It is known that classical $$r$$-matrices give multiplicative Poisson structures. In this paper we find classical $$r$$-matrices of some loop groups and study dual Lie algebra structures defined by them”. For the entire collection see [Zbl 0810.00022]. MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 22E67 Loop groups and related constructions, group-theoretic treatment 53D50 Geometric quantization	{}
### Artificial IntelligenceAIMA Exercises Using the data from the family tree in Figure family2-figure, or a subset thereof, apply the algorithm to learn a definition for the ${Ancestor}$ predicate. Using the data from the family tree in Figure family2-figure, or a subset thereof, apply the algorithm to learn a definition for the ${Ancestor}$ predicate. Submit Solution	{}
# Problem in solving ODE from NDSolve I have a problem in solving a type of ODE from NDSolve. Specifically I want to know the solution at time T (say T=50). The number of differential equations increases at each iteration. This equations involves one parameters, and I want the solution of the differential equations at each iteration. T = 10; nu = 0.2; n = 5; vars = Table[Subscript[x, j][t], {i, n}, {j, i}]; eqns = Table[{ Subscript[x, j]'[t] == Subscript[x, j][t] (1 - Subscript[x, j][t] - nu Sum[Subscript[x, k][t] Boole[k != j], {k, i}]), Subscript[x, j][0] == 0.3}, {i, n}, {j, i} ]; The variable eqns gives exactly the process of iteration that I need sol = NDSolve[eqns, Table[Subscript[x, j], {i, n}, {j, i}], {t, 0, T}, DependentVariables -> vars] But Mathematica gives the message NDSolve::ndode: Input is not an ordinary differential equation. >> I don't understand how to fix it. I believe it violates some operation NDSolve. • It is not clear to me what you are trying to do, but I can say with reasonable confidence that your NDSolve arguments are invalid. I recommend that you state clearly the problem you are trying to solve. – bbgodfrey Aug 19 '16 at 3:55 • The sentence "The number of differential equations increases at each iteration" isn't clear. Do you want to increase n at some point? – Chris K Aug 19 '16 at 18:24 If you are attempting to solve ODEs one through five in sequence, one way to do so is GraphicsGrid[{Table[s = NDSolve[eqns[[n]], vars[[n]], {t, 0, T}]; Plot[Evaluate[vars[[n]] /. s], {t, 0, T}, PlotRange -> All], {n, 5}]}, ImageSize -> Large] Alternatively, the solutions can be presented in a single plot. Show @@ Table[s = NDSolve[eqns[[n]], vars[[n]], {t, 0, T}]; Plot[Evaluate[vars[[n]] /. s], {t, 0, T}, PlotRange -> All], {n, 5}] Not surprisingly, all curves for each value of n coincide.	{}

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