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http://ncl.ucar.edu/Document/Functions/Built-in/solve_linsys.shtml
[ "", null, "NCL Home > Documentation > Functions > General applied math\n\n# solve_linsys\n\nComputes the solution to a real system of linear equations.\n\n## Prototype\n\n```\tfunction solve_linsys (\nA [*][*] : numeric,\nB : numeric\n)\n\nreturn_val [dimsizes(B)] : float or double\n```\n\n## Arguments\n\nA\n\nA two-dimensional (N, N) coefficient matrix.\n\nB\n\nA one- or two-dimensional array containing the right hand side matrix. If B is one-dimensional, it must be of length N. If it is two-dimensional, it must be B(NRHS, N) where NRHS is the number of right hand sides.\n\n## Return value\n\nReturns an array dimensioned the same as B.\n\nThe return type is floating point if the input is floating point, and double if the input is of type double.\n\n## Description\n\nThis function computes the solution to a real system of linear equations A * x = B where B may have multiple right-hand-sides. An LU decomposition with partial pivoting and row interchange is used to factor A as A = P * L * U where P is a permutation matrix, L is the unit lower tridiagonalar matrix, and U is the upper triangular matrix. The factored form is then used to solve the system of equations.\n\n## Examples\n\nExample 1:\n\nSolve the system A * x = B where B is one-dimensional:\n\n``` 3 2 -1 2 0\nA = 1 4 0 2 B = 0\n2 1 2 -1 1\n1 1 -1 3 0\n\n```\nIn NCL:\n``` A = (/ (/3.0, 2.0, -1.0, 2.0/), \\\n(/1.0, 4.0, 0.0, 2.0/), \\\n(/2.0, 1.0, 2.0,-1.0/), \\\n(/1.0, 1.0, -1.0, 3.0/) /)\n\nB = (/0.0, 0.0, 1.0, 0.0/) ; this is treated as a one-dimensional\n; column vector (special case)\n\nx = solve_linsys(A, B) ; x will be one-dimensional [x(N)]\n```\nNote: the following would also work:\n``` NRHS = 1\nN = 4\nB = new ((/NRHS,N/), \"float\") ; \"double\" also\nB(0, 0) = 0.0\nB(0, 1) = 0.0\nB(0, 2) = 1.0\nB(0, 3) = 0.0\n```\nExample 2:\n\nThe same as Example 1, but with multiple right hand sides:\n\n``` nrhs = 3\nn = 4\nb = new ((/nrhs,n/), \"float\") ; \"double\" also\nb(0,:) = (/0.0, 0.0, 1.0, 0.0/)\nb(1,:) = (/-2.0, 1.0, 3.0, 4.0/)\nb(2,:) = (/2.0, 2.0, 0.0, 0.0/)\n\nx = solve_linsys(A, B) ; x will be 2D: x(3, 4)\n```\n\n## Errors\n\ninfo\n= 0 : successful exit\n\n< 0: the i-th argument had an illegal value\n\n> 0: U(i, i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed." ]
[ null, "http://ncl.ucar.edu/Images/NCL_NCAR_NSF_banner.png", null ]
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https://www.tutorpace.com/calculus/differential-calculus-online-tutoring
[ "# Differential Calculus\n\n## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.\n\n#### SIGN UP FOR A FREE TRIAL\n\nDifferential calculus is one of sub field of calculus which is concerned with the study of rate at which quantity changes. The object of study of differential calculus is derivative of a function .Differentiation is a process of finding Derivative. Differential calculus is connected with fundamental theorem of calculus. Differentiation is used in many applications. For example, in physics the derivative of velocity with respect to time is acceleration.  Derivative of a function f(x) is defined by d/ d x (f(x).\n\nProblem 1: Compute the derivative of the function f(x) = 5x^3 - 9x +8cos x\n\nSolution: Given the function f(x) = 5x^3 - 9x +8cos x\n\n=> To find derivative of 5x^3 subtract one from the variable power and multiply the original power by the variable.\n\n=> Here 3 is the power of x. subtract one from 3. (3-1 = 2)\n\n=> Now multiply the original power by the variable, which gives 5. 3x^2 = 15x^2\n\n=> Now take -9x, we get the derivative as -9\n\n=> For 8 cos x = - 8 sin x (since cos x = - sin x)\n\n=> Therefore, the derivative of 5x^3 - 9x +8cos x is 15x^2 -9 – 8 sin x\n\nProblem 2: Compute the derivative of the function f(x) = (x^2 + 1) ^5\n\nSolution: Given the function f(x) = (x^2 + 1) ^5\n\n=> To find derivative of this function take (x^2 + 1) as y\n\n=> So y^5 = 5y^4       (as per power rule of derivative)\n\n=> Now find the derivative of y = x^2 + 1 = 2x      (power rule)\n\n=> Derivative d f(x) / d x= 5y^4. 2 x\n\n=> We know y = (x^2 + 1)\n\n=> Therefore, Derivative of f(x) = 5(x^2 + 1) ^4. 2x = 10x(x^2 + 1)^4." ]
[ null ]
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https://maternityandbabyshoppingmart.com/6-popular-equations-tables-and-graphs-worksheets/
[ "HomeLesson Worksheet ➟ 0 9+ Fresh Equations Tables And Graphs Worksheets\n\n# 9+ Fresh Equations Tables And Graphs Worksheets\n\nGet thousands of teacher-crafted activities that sync up with the school year. Some of the worksheets for this concept are Concept 7 writing linear equations Matching representations patterns functions and algebra 8 Solving equations using tables and graphs 1 7 words equations tables graphs Lesson practice b equationstables and graphs Introduction.", null, "Two Pages Of Graphing Equations Using Tables Of Values Some Of These Could Be Graphed With The Slope And Y Intercept The Equations Values Worksheet Graphing Equations tables and graphs worksheets\n\n### You can choose from up to four types of equations depending on the sophistication of your students.\n\nEquations tables and graphs worksheets. Be sure to plot all points from the table and draw a line connecting the points. Y-2 1 0 2 Graph. Substitute the x values of the equation to find the values of y.\n\nStudents analyze relationships between two variables using equations tables and graphs in this sixth-grade algebra worksheet. Some of the worksheets for this concept are Independent and dependent variables Linear relationships tables equations and graphs Practice writing rules equations from tables graphs Lesson 8 3 of 5 for problem solving and data analysis Tables graphs and equations of linear. Equations Tables And Graphs.\n\n1 Ha 2 Em 3 Co 4 Kd 5 Lk 6 Jg 7 Ol 8 Ae 9 Rh How to use this activity Materials scissors worksheets glue and construction paper optional Put students in pairs and hand them just the graphs and equations pgs 2 3. The Videos Games Quizzes and Worksheets make excellent materials for math teachers math educators and parents. Each problem in this two-page math worksheet describes a real-world scenario and provides a simple equation that models the scenario.\n\nJust substitute the given x and y to see if the equation works. This product is suitable for Preschool kindergarten and Grade 1The product is available for instant download after purchase. Graph the Line Using Slope and y.\n\nPractice graphing linear equations by completing the function table graph using slope and y-intercept graph horizontal and vertical lines and find ample MCQs to reinforce the concept with these graphing linear equation worksheets. Examples videos worksheets and activities to help Algebra 1 students learn how to connect tables graphs and equations as well as how to write equations to connect pictures. To graph a linear equation first make a table of values.\n\nGet thousands of teacher-crafted activities that sync up with the school year. Y-2 -7 1 6 0 -5 -4 2 -3 Graph. Matching Graphs Verbal Descriptions Equations and Tables This product is specifically designed as an informal assessment of TEKS 66C represent a given situation using verbal descriptions tables graphs and equations in the form y kx or y x b It may however be used in other grade lev.\n\nEquations Tables And Graphs. If playback doesnt begin shortly try restarting your device. Use this version or check out other variations created.\n\nUsing the information from the table graph the line of the equations on the coordinate plane below. Words Equations Tables And Graphs. Math workbook 1 is a content-rich downloadable zip file with 100 Math printable exercises and 100 pages of answer sheets attached to each exercise.\n\nComplete the tables plot the points and graph the lines. Students will practice using the equation. Use a linear function to graph a line.\n\nEquations Tables Graphs Worksheet Use the representation given to complete the other two representations. Complete the function tables and graph quadratic graphing linear equations functions math equation worksheets free distance learning worksheetore commoncoresheets matching graphs tessshlo nar with rtopia 32 using a table of values worksheet resource plans writing snowtanye com create junior high line sumnermuseumdc org answers Complete The Function Tables And Graph Quadratic Graphing. Complete the table for and graph the resulting line.\n\nGraphs Tables And Equations. Example of graphing a line solved for y using a table of values. Some of the worksheets for this concept are Graphing lines Concept 7 writing linear equations Linear systems using graphs tables student work Kuta software Graphing linear equations using a table of values date period Lesson 8 3 of 5 for problem solving and data analysis.\n\nY 3x 2 -1 Table. Equations Tables And Graphs – Displaying top 8 worksheets found for this concept. Assume your own values for x for all worksheets provided here.\n\nThis worksheet includes the task of completing a function table from a linear equation and graphing the line that it describes. Some of the worksheets for this concept are Independent and dependent variables Linear relationships tables equations and graphs Practice writing rules equations from tables graphs Lesson 8 3 of 5 for problem solving and data analysis Tables graphs and equations of linear. Graphs Tables And Equations – Displaying top 8 worksheets found for this concept.\n\nTell whether the ordered pair is a solution of the equation. Graphing Linear Equations using XY Tables Part 1. Complete the table for and graph the resulting line.\n\nAd The most comprehensive library of free printable worksheets digital games for kids. Learn to graph linear functions by plotting points on the grid. X y-2 1 0 2 Graph.\n\nDisplaying top 8 worksheets found for – Equations Tables And Graphs. Write solution if it works and not a solution if it doesnt. Graphing Linear Function Worksheets.\n\nConnecting Tables Graphs and Equations. Complete the table for and graph. Write equations from tables and graphs Worksheet.\n\nDisplaying top 8 worksheets found for – Words Equations Tables And Graphs. Tables pg 4 and the slips of paper to record their a Answer Key. Ad The most comprehensive library of free printable worksheets digital games for kids.\n\nRelate Tables Graphs and Equations.", null, "Equations Tables Graphs Worksheet Answer Key In 2021 Equations Graph Worksheet Algebra Worksheets Equations tables and graphs worksheets", null, "Linear Equations And Their Graphs Worksheets Graphing Linear Equations Linear Function Linear Equations Equations tables and graphs worksheets", null, "Graphing Linear Equations Practice Worksheet Graphing Linear Functions Worksheet Did You Kn In 2020 Graphing Linear Equations Graphing Functions Practices Worksheets Equations tables and graphs worksheets", null, "Table Graph Equation Worksheet Graphing Linear Equations Linear Equations Worksheet Writing Equations Equations tables and graphs worksheets" ]
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https://www.teachoo.com/4140/767/Ex-13.5--15---Probability-that-student-is-not-a-swimmer-is-1-5/category/Ex-13.5/
[ "Ex 13.5\n\nChapter 13 Class 12 Probability\nSerial order wise", null, "", null, "", null, "Solve all your doubts with Teachoo Black (new monthly pack available now!)\n\n### Transcript\n\nEx 13.5, 15 The probability that a student is not a swimmer is 1/5 . Then the probability that out of five students, four are swimmers is (A) 5C4 (4/5)^4 1/5 (B) (4/5)^4 1/5 (C) 5C1 1/5 (4/5)^4 (D) None of theseIf a trial is Bernoulli, then There is finite number of trials They are independent Trial has 2 outcomes i.e. Probability success = P then Probability failure = q = 1 – P (4) Probability of success (p) is same for all trials Let X : be number of swimmers Picking a student is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒^(𝒏−𝒙) 𝒑^𝒙 Here, n = number of students = 5 Given probability that student is not a swimmer is 1/5 So, q = 1/5 ∴ p = 1 – q = 1 – 1/5 = 4/5 Hence, P(X = x) = 5Cx (𝟒/𝟓)^𝒙 (𝟏/𝟓)^(𝟓 − 𝒙) We need to find the Probability of that out of five students, four are swimmers i.e. P(X = 4) P(X = 4) = 5C4 (4/5)^4 (1/5)^(5 − 4) = 5C4 (𝟒/𝟓)^𝟒 𝟏/𝟓 = 5C1 𝟏/𝟓 (𝟒/𝟓)^𝟒 Hence, option (A) & (C) both are correct", null, "" ]
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https://yummysaves.savingadvice.com/2008/09/
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122.178.223.244\n)\n\n => Array\n(\n => 195.181.164.65\n)\n\n => Array\n(\n => 106.195.12.187\n)\n\n => Array\n(\n => 124.253.48.48\n)\n\n => Array\n(\n => 103.140.30.214\n)\n\n => Array\n(\n => 180.178.147.132\n)\n\n => Array\n(\n => 138.197.139.130\n)\n\n => Array\n(\n => 5.254.2.138\n)\n\n => Array\n(\n => 183.81.93.25\n)\n\n => Array\n(\n => 182.70.39.254\n)\n\n => Array\n(\n => 106.223.87.131\n)\n\n => Array\n(\n => 106.203.91.114\n)\n\n => Array\n(\n => 196.70.137.128\n)\n\n => Array\n(\n => 150.242.62.167\n)\n\n => Array\n(\n => 184.170.243.198\n)\n\n => Array\n(\n => 59.89.30.66\n)\n\n => Array\n(\n => 49.156.112.201\n)\n\n => Array\n(\n => 124.29.212.168\n)\n\n => Array\n(\n => 103.204.170.238\n)\n\n => Array\n(\n => 124.253.116.81\n)\n\n => Array\n(\n => 41.248.102.107\n)\n\n => Array\n(\n => 119.160.100.51\n)\n\n => Array\n(\n => 5.254.40.91\n)\n\n => Array\n(\n => 103.149.154.25\n)\n\n => Array\n(\n => 103.70.41.28\n)\n\n => Array\n(\n => 103.151.234.42\n)\n\n => Array\n(\n => 39.37.142.107\n)\n\n => Array\n(\n => 27.255.186.115\n)\n\n => Array\n(\n => 49.15.193.151\n)\n\n => Array\n(\n => 103.201.146.115\n)\n\n => Array\n(\n => 223.228.177.70\n)\n\n => Array\n(\n => 182.179.141.37\n)\n\n => Array\n(\n => 110.172.131.126\n)\n\n => Array\n(\n => 45.116.232.0\n)\n\n => Array\n(\n => 193.37.32.206\n)\n\n => Array\n(\n => 119.152.62.246\n)\n\n => Array\n(\n => 180.178.148.228\n)\n\n => Array\n(\n => 195.114.145.120\n)\n\n => Array\n(\n => 122.160.49.194\n)\n\n => Array\n(\n => 103.240.237.17\n)\n\n => Array\n(\n => 103.75.245.238\n)\n\n => Array\n(\n => 124.253.215.148\n)\n\n => Array\n(\n => 45.118.165.146\n)\n\n => Array\n(\n => 103.75.244.111\n)\n\n => Array\n(\n => 223.185.7.42\n)\n\n => Array\n(\n => 139.5.240.165\n)\n\n => Array\n(\n => 45.251.117.204\n)\n\n => Array\n(\n => 132.154.71.227\n)\n\n => Array\n(\n => 178.92.100.97\n)\n\n => Array\n(\n => 49.48.248.42\n)\n\n => Array\n(\n => 182.190.109.252\n)\n\n => Array\n(\n => 43.231.57.209\n)\n\n => Array\n(\n => 39.37.185.133\n)\n\n => Array\n(\n => 123.17.79.174\n)\n\n => Array\n(\n => 180.178.146.215\n)\n\n => Array\n(\n => 41.248.83.40\n)\n\n => Array\n(\n => 103.255.4.79\n)\n\n => Array\n(\n => 103.39.119.233\n)\n\n => Array\n(\n => 85.203.44.24\n)\n\n => Array\n(\n => 93.74.18.246\n)\n\n => Array\n(\n => 95.142.120.51\n)\n\n => Array\n(\n => 202.47.42.57\n)\n\n => Array\n(\n => 41.202.219.253\n)\n\n => Array\n(\n => 154.28.188.182\n)\n\n => Array\n(\n => 14.163.178.106\n)\n\n => Array\n(\n => 118.185.57.226\n)\n\n => Array\n(\n => 49.15.141.102\n)\n\n => Array\n(\n => 182.189.86.47\n)\n\n => Array\n(\n => 111.88.68.79\n)\n\n => Array\n(\n => 156.146.59.8\n)\n\n => Array\n(\n => 119.152.62.82\n)\n\n => Array\n(\n => 49.207.128.103\n)\n\n => Array\n(\n => 203.212.30.234\n)\n\n => Array\n(\n => 41.202.219.254\n)\n\n => Array\n(\n => 103.46.203.10\n)\n\n => Array\n(\n => 112.79.141.15\n)\n\n => Array\n(\n => 103.68.218.75\n)\n\n => Array\n(\n => 49.35.130.14\n)\n\n => Array\n(\n => 172.247.129.90\n)\n\n => Array\n(\n => 116.90.74.214\n)\n\n => Array\n(\n => 180.178.142.242\n)\n\n => Array\n(\n => 111.119.183.59\n)\n\n => Array\n(\n => 117.5.103.189\n)\n\n => Array\n(\n => 203.110.93.146\n)\n\n => Array\n(\n => 188.163.97.86\n)\n\n => Array\n(\n => 124.253.90.47\n)\n\n => Array\n(\n => 139.167.249.160\n)\n\n => Array\n(\n => 103.226.206.55\n)\n\n => Array\n(\n => 154.28.188.191\n)\n\n => Array\n(\n => 182.190.197.205\n)\n\n => Array\n(\n => 111.119.183.33\n)\n\n => Array\n(\n => 14.253.254.64\n)\n\n => Array\n(\n => 117.237.197.246\n)\n\n => Array\n(\n => 172.105.53.82\n)\n\n => Array\n(\n => 124.253.207.164\n)\n\n => Array\n(\n => 103.255.4.33\n)\n\n => Array\n(\n => 27.63.131.206\n)\n\n => Array\n(\n => 103.118.170.99\n)\n\n => Array\n(\n => 111.119.183.55\n)\n\n => Array\n(\n => 14.182.101.109\n)\n\n => Array\n(\n => 175.107.223.199\n)\n\n => Array\n(\n => 39.57.168.94\n)\n\n => Array\n(\n => 122.182.213.139\n)\n\n => Array\n(\n => 112.79.214.237\n)\n\n => Array\n(\n => 27.6.252.22\n)\n\n => Array\n(\n => 89.163.212.83\n)\n\n => Array\n(\n => 182.189.23.1\n)\n\n => Array\n(\n => 49.15.222.253\n)\n\n => Array\n(\n => 125.63.97.110\n)\n\n => Array\n(\n => 223.233.65.159\n)\n\n => Array\n(\n => 139.99.159.18\n)\n\n => Array\n(\n => 45.118.165.137\n)\n\n => Array\n(\n => 39.52.2.167\n)\n\n => Array\n(\n => 39.57.141.24\n)\n\n => Array\n(\n => 27.5.32.145\n)\n\n => Array\n(\n => 49.36.212.33\n)\n\n => Array\n(\n => 157.33.218.32\n)\n\n => Array\n(\n => 116.71.4.122\n)\n\n => Array\n(\n => 110.93.244.176\n)\n\n => Array\n(\n => 154.73.203.156\n)\n\n => Array\n(\n => 136.158.30.235\n)\n\n => Array\n(\n => 122.161.53.72\n)\n\n => Array\n(\n => 106.203.203.156\n)\n\n => Array\n(\n => 45.133.7.22\n)\n\n => Array\n(\n => 27.255.180.69\n)\n\n => Array\n(\n => 94.46.244.3\n)\n\n => Array\n(\n => 43.242.178.157\n)\n\n => Array\n(\n => 171.79.189.215\n)\n\n => Array\n(\n => 37.117.141.89\n)\n\n => Array\n(\n => 196.92.32.64\n)\n\n => Array\n(\n => 154.73.203.157\n)\n\n => Array\n(\n => 183.83.176.14\n)\n\n => Array\n(\n => 106.215.84.145\n)\n\n => Array\n(\n => 95.142.120.12\n)\n\n => Array\n(\n => 190.232.110.94\n)\n\n => Array\n(\n => 179.6.194.47\n)\n\n => Array\n(\n => 103.62.155.172\n)\n\n => Array\n(\n => 39.34.156.177\n)\n\n => Array\n(\n => 122.161.49.120\n)\n\n => Array\n(\n => 103.58.155.253\n)\n\n => Array\n(\n => 175.107.226.20\n)\n\n => Array\n(\n => 206.81.28.165\n)\n\n => Array\n(\n => 49.36.216.36\n)\n\n => Array\n(\n => 104.223.95.178\n)\n\n => Array\n(\n => 122.177.69.35\n)\n\n => Array\n(\n => 39.57.163.107\n)\n\n => Array\n(\n => 122.161.53.35\n)\n\n => Array\n(\n => 182.190.102.13\n)\n\n => Array\n(\n => 122.161.68.95\n)\n\n => Array\n(\n => 154.73.203.147\n)\n\n => Array\n(\n => 122.173.125.2\n)\n\n => Array\n(\n => 117.96.140.189\n)\n\n => Array\n(\n => 106.200.244.10\n)\n\n => Array\n(\n => 110.36.202.5\n)\n\n => Array\n(\n => 124.253.51.144\n)\n\n => Array\n(\n => 176.100.1.145\n)\n\n => Array\n(\n => 156.146.59.20\n)\n\n => Array\n(\n => 122.176.100.151\n)\n\n => Array\n(\n => 185.217.117.237\n)\n\n => Array\n(\n => 49.37.223.97\n)\n\n => Array\n(\n => 101.50.108.80\n)\n\n => Array\n(\n => 124.253.155.88\n)\n\n => Array\n(\n => 39.40.208.96\n)\n\n => Array\n(\n => 122.167.151.154\n)\n\n => Array\n(\n => 172.98.89.13\n)\n\n => Array\n(\n => 103.91.52.6\n)\n\n => Array\n(\n => 106.203.84.5\n)\n\n => Array\n(\n => 117.216.221.34\n)\n\n => Array\n(\n => 154.73.203.131\n)\n\n => Array\n(\n => 223.182.210.117\n)\n\n => Array\n(\n => 49.36.185.208\n)\n\n => Array\n(\n => 111.119.183.30\n)\n\n => Array\n(\n => 39.42.107.13\n)\n\n => Array\n(\n => 39.40.15.174\n)\n\n => Array\n(\n => 1.38.244.65\n)\n\n => Array\n(\n => 49.156.75.252\n)\n\n => Array\n(\n => 122.161.51.99\n)\n\n => Array\n(\n => 27.73.78.57\n)\n\n => Array\n(\n => 49.48.228.70\n)\n\n => Array\n(\n => 111.119.183.18\n)\n\n => Array\n(\n => 116.204.252.218\n)\n\n => Array\n(\n => 73.173.40.248\n)\n\n => Array\n(\n => 223.130.28.81\n)\n\n => Array\n(\n => 202.83.58.81\n)\n\n => Array\n(\n => 45.116.233.31\n)\n\n => Array\n(\n => 111.119.183.1\n)\n\n => Array\n(\n => 45.133.7.66\n)\n\n => Array\n(\n => 39.48.204.174\n)\n\n => Array\n(\n => 37.19.213.30\n)\n\n => Array\n(\n => 111.119.183.22\n)\n\n => Array\n(\n => 122.177.74.19\n)\n\n => Array\n(\n => 124.253.80.59\n)\n\n => Array\n(\n => 111.119.183.60\n)\n\n => Array\n(\n => 157.39.106.191\n)\n\n => Array\n(\n => 157.47.86.121\n)\n\n => Array\n(\n => 47.31.159.100\n)\n\n => Array\n(\n => 106.214.85.144\n)\n\n => Array\n(\n => 182.189.22.197\n)\n\n => Array\n(\n => 111.119.183.51\n)\n\n => Array\n(\n => 202.47.35.57\n)\n\n => Array\n(\n => 42.108.33.220\n)\n\n => Array\n(\n => 180.178.146.158\n)\n\n => Array\n(\n => 124.253.184.239\n)\n\n => Array\n(\n => 103.165.20.8\n)\n\n => Array\n(\n => 94.178.239.156\n)\n\n => Array\n(\n => 72.255.41.142\n)\n\n => Array\n(\n => 116.90.107.102\n)\n\n => Array\n(\n => 39.36.164.250\n)\n\n => Array\n(\n => 124.253.195.172\n)\n\n => Array\n(\n => 203.142.218.149\n)\n\n => Array\n(\n => 157.43.165.180\n)\n\n => Array\n(\n => 39.40.242.57\n)\n\n => Array\n(\n => 103.92.43.150\n)\n\n => Array\n(\n => 39.42.133.202\n)\n\n => Array\n(\n => 119.160.66.11\n)\n\n => Array\n(\n => 138.68.3.7\n)\n\n => Array\n(\n => 210.56.125.226\n)\n\n => Array\n(\n => 157.50.4.249\n)\n\n => Array\n(\n => 124.253.81.162\n)\n\n => Array\n(\n => 103.240.235.141\n)\n\n => Array\n(\n => 132.154.128.20\n)\n\n => Array\n(\n => 49.156.115.37\n)\n\n => Array\n(\n => 45.133.7.48\n)\n\n => Array\n(\n => 122.161.49.137\n)\n\n => Array\n(\n => 202.47.46.31\n)\n\n => Array\n(\n => 192.140.145.148\n)\n\n => Array\n(\n => 202.14.123.10\n)\n\n => Array\n(\n => 122.161.53.98\n)\n\n => Array\n(\n => 124.253.114.113\n)\n\n => Array\n(\n => 103.227.70.34\n)\n\n => Array\n(\n => 223.228.175.227\n)\n\n => Array\n(\n => 157.39.119.110\n)\n\n => Array\n(\n => 180.188.224.231\n)\n\n => Array\n(\n => 132.154.188.85\n)\n\n => Array\n(\n => 197.210.227.207\n)\n\n => Array\n(\n => 103.217.123.177\n)\n\n => Array\n(\n => 124.253.85.31\n)\n\n => Array\n(\n => 123.201.105.97\n)\n\n => Array\n(\n => 39.57.190.37\n)\n\n => Array\n(\n => 202.63.205.248\n)\n\n => Array\n(\n => 122.161.51.100\n)\n\n => Array\n(\n => 39.37.163.97\n)\n\n => Array\n(\n => 43.231.57.173\n)\n\n => Array\n(\n => 223.225.135.169\n)\n\n => Array\n(\n => 119.160.71.136\n)\n\n => Array\n(\n => 122.165.114.93\n)\n\n => Array\n(\n => 47.11.77.102\n)\n\n => Array\n(\n => 49.149.107.198\n)\n\n => Array\n(\n => 192.111.134.206\n)\n\n => Array\n(\n => 182.64.102.43\n)\n\n => Array\n(\n => 124.253.184.111\n)\n\n => Array\n(\n => 171.237.97.228\n)\n\n => Array\n(\n => 117.237.237.101\n)\n\n => Array\n(\n => 49.36.33.19\n)\n\n => Array\n(\n => 103.31.101.241\n)\n\n => Array\n(\n => 129.0.207.203\n)\n\n => Array\n(\n => 157.39.122.155\n)\n\n => Array\n(\n => 197.210.85.120\n)\n\n => Array\n(\n => 124.253.219.201\n)\n\n => Array\n(\n => 152.57.75.92\n)\n\n => Array\n(\n => 169.149.195.121\n)\n\n => Array\n(\n => 198.16.76.27\n)\n\n => Array\n(\n => 157.43.192.188\n)\n\n => Array\n(\n => 119.155.244.221\n)\n\n => Array\n(\n => 39.51.242.216\n)\n\n => Array\n(\n => 39.57.180.158\n)\n\n => Array\n(\n => 134.202.32.5\n)\n\n => Array\n(\n => 122.176.139.205\n)\n\n => Array\n(\n => 151.243.50.9\n)\n\n => Array\n(\n => 39.52.99.161\n)\n\n => Array\n(\n => 136.144.33.95\n)\n\n => Array\n(\n => 157.37.205.216\n)\n\n => Array\n(\n => 217.138.220.134\n)\n\n => Array\n(\n => 41.140.106.65\n)\n\n)\n```\nArchive for September, 2008: Yummy Saves\n << Back to all Blogs Login or Create your own free blog Layout: Blue and Brown (Default) Author's Creation\nHome > Archive: September, 2008", null, "", null, "", null, "# Archive for September, 2008\n\n## Just try to use coupons and price match at Walmart - dare ya...\n\nSeptember 19th, 2008 at 12:29 am\n\nMonday I tried to pricematch and use coupons at walmart. The \"cashier police\" stopped me from doing that as that's one deal on top of another .. and once can't do that. Since I've done this many times at Walmart I let them reverse the items (all 9 boxes of cling wrap) and just bought the other items I wanted.\n\nI didn't feel like waiting around for a manager and the supervisor (err.. other employee?) had backed up the cashier's statement.\n\nSo when I came home I sent walmart an email asking for clarification of policy.\n\nToday ... manager at walmart called. Assured me the cashier was wrong and i was right .. and that they have been SPOKEN TO (uh huh). One can use coupons on price matched items.\n\nSo I asked if I could come by tonight and do it with no problem - he assured me I could and I have the name of the manager and the assistant working tonight.\n\nMy guess is that emails to head office get logged and the manager gets a black mark for them and a really big black mark if I have to write another email tonight. He assured me that I should phone him if I run into any other issues and he'll handle it \"quicker than head office\".\n\nStill he was very nice and I did get his phone number.. just in case. I'm keeping that number.\n\nSo on the way home I go there and get my cling wrap.\n\nGot to the cash, not a bad line up.. only two in front of me though dyno-boy on cash is straightening the baby clothes on the hangers before he takes them off of the hangers (it was interesting to watch...). Anyways the customer service manager - hey it said so on her tag- came over and took over cash. She assured me no problem about the price matching and coupons. Totally not an issue.\n\nI smile and hand her over the 9 coupons I had - I bought nine boxes of cling wrap (price match for \\$1 and \\$1 off coupon .. the sort of deal one gets to like).\n\nAnd of course you know what happened then don't you?\n\nYup she tried to tell me that it is one per purchase (you KNEW that was coming didn't you??). So I tell her yup, 9 coupons, I'm purchasing 9 items what's the problem. She looked dubious and she paged someone. I said, well if you want you can do it in 9 transactions. She didn't like that answer much. (and yes I'd have used my debit card for each transaction *grins*). Finally she gets an answer but not before she suspends my transaction and has dyno boy start on the next order.\n\nLuckily for her she didn't end up up having to do 9 transactions for me as someone on the other end of the phone authorized her doing them on one bill. She took me to the cash at customer service so I'd not have to wait any longer. She was very pleasant but .. come on .. shouldn't a customer service manager know policy?\n\nNever mind .. that last question was rhetorical\n\nGawd saving money is hard work.\n\nYvonne" ]
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https://www.aiproblog.com/index.php/forums/topic/simple-linear-regression-with-python-numpy-matplotlib/
[ "# Simple linear regression with Python, Numpy, Matplotlib\n\nHome Forums Linear Regression Simple linear regression with Python, Numpy, Matplotlib\n\nViewing 1 post (of 1 total)\n• Author\nPosts\n• #1452\n\nBackground info / Notes:\nFind a line that models the relationship between a dependent variable and an independent variable.\n\nEquation:\ny = α + b*x\n\nIn English: y is the dependent variable: what we are trying to predict, α is a constant: y at x = 0, b is a coefficient: slope of the line, x is the independent variable: what we think predicts y\n\nEquation:\n[SUM(Y) * SUM(X^2)] – [SUM(X) * SUM(XY)]\nα = ________________________________________\nn[SUM(X^2)] – [SUM(X)]^2\n\nn[SUM(XY)] – [SUM(X) * SUM(Y)]\nb = ___________________________________\nn[SUM(X^2)] – [SUM(X)]^2\n\nSUM = Summation\nn = sample size\n\nR-Squared:\nTells us how good our prediction is, closer to 1 the better.\nEquation:\n\nSUM(Y – Yi)^2\nR^2 = 1 – _______________________________\nSUM(Y – Yavg)^2\n\nY = the actual data point\nYi = the predicted Y value\nYavg = the average Y value\n\nConvert the equations to code (we can leverage the numpy dot function for SUM(XY) and SUM(X^2)):\nn = X.size\nsumY = Y.sum()\nsumX = X.sum()\nsumXY = X.dot(Y)\nsumX2 = X.dot(X)\n\ndenominator = (n * sumX2) – (sumX ** 2)\na = ((sumY * sumX2) – (sumX * sumXY)) / denominator\nb = ((n * sumXY) – (sumX * sumY)) / denominator\n\nSSres = Y – predictedY\nSStot = Y – Y.mean()\nrSquared = 1 – (SSres.dot(SSres) / SStot.dot(SStot))\n\nYou can view the code and dataset on github here.\n\nThe full code:\n\n``````import numpy as np\nimport matplotlib.pyplot as plt\n\n# create arrays for the data points\nX = []\nY = []\n\nx, y = line.split(',')\nX.append(float(x))\nY.append(float(y))\n\n# change to numpy array\nX = np.array(X)\nY = np.array(Y)\n\n# view the data\nplt.figure(1)\nplt.scatter(X, Y)\nplt.title(\"The data we're trying to model\")\n\n# use variables so that the sum, dot, and denominator is only calculated once\nn = X.size\nsumY = Y.sum()\nsumX = X.sum()\nsumXY = X.dot(Y)\nsumX2 = X.dot(X)\n\ndenominator = (n * sumX2) - (sumX ** 2)\na = ((sumY * sumX2) - (sumX * sumXY)) / denominator\nb = ((n * sumXY) - (sumX * sumY)) / denominator\nprint(\"the value of a is: \", a)\nprint(\"the value of b is: \", b)\n\n# calculate predicted Y array\npredictedY = a + b * X\n\n# calculate the r-squared value\nSSres = Y - predictedY\nSStot = Y - Y.mean()\nrSquared = 1 - (SSres.dot(SSres) / SStot.dot(SStot))\nprint(\"the value of R-squared is: \", rSquared)\n\n# view the data and the line\nplt.figure(2)\nplt.scatter(X, Y)\nplt.plot(X, predictedY)\nplt.title(\"The data and our line\")\nplt.show() ``````\n\nIf you use the same data set you should see the following:", null, "", null, "Viewing 1 post (of 1 total)\n• You must be logged in to reply to this topic." ]
[ null, "https://www.aiproblog.com/wp-content/uploads/SLRpythonFig1.png", null, "https://www.aiproblog.com/wp-content/uploads/SLRpythonFig2.png", null ]
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https://deepai.org/publication/fixed-points-of-the-set-based-bellman-operator
[ "DeepAI\n\n# Fixed Points of the Set-Based Bellman Operator\n\nMotivated by uncertain parameters encountered in Markov decision processes (MDPs), we study the effect of parameter uncertainty on Bellman operator-based methods. Specifically, we consider a family of MDPs where the cost parameters are from a given compact set. We then define a Bellman operator acting on an input set of value functions to produce a new set of value functions as the output under all possible variations in the cost parameters. Finally we prove the existence of a fixed point of this set-based Bellman operator by showing that it is a contractive operator on a complete metric space.\n\n01/22/2020\n\n### Bounding Fixed Points of Set-Based Bellman Operator and Nash Equilibria of Stochastic Games\n\nMotivated by uncertain parameters encountered in Markov decision process...\n07/15/2022\n\n### Set-based value operators for non-stationary Markovian environments\n\nThis paper analyzes finite state Markov Decision Processes (MDPs) with u...\n01/30/2022\n\n### The Geometry of Robust Value Functions\n\nThe space of value functions is a fundamental concept in reinforcement l...\n11/01/2019\n\n### Generalized Mean Estimation in Monte-Carlo Tree Search\n\nWe consider Monte-Carlo Tree Search (MCTS) applied to Markov Decision Pr...\n09/01/2021\n\n### On the Existence of the Augustin Mean\n\nThe existence of a unique Augustin mean and its invariance under the Aug...\n07/13/2018\n\n### On the Complexity of Iterative Tropical Computation with Applications to Markov Decision Processes\n\nWe study the complexity of evaluating powered functions implemented by s...\n03/26/2022\n\n### Getting more from the skyline operator through restricted skylines, regret minimizing sets and skyline ordering: a survey on their properties and comparison\n\nGiven a set of multidimensional points, the skyline operator returns a s...\n\n## 1 Introduction\n\nMarkov decision processes (MDPs) is a widely used mathematical framework for control design in stochastic environments, eg. density control of a swarm of agents (Açikmeşe and Bayard, 2012; Demir et al., 2015). It is also a fundamental framework for reinforcement learning, robotic motion planning and stochastic games (Filar and Vrieze, 2012; Li et al., 2019). An MDP can be solved for different objectives including minimum average cost, minimum discounted cost, reachability, among others (Puterman, 2014). Given an objective, solving an MDP is equivalent to computing the optimal policy and the optimal value function of a decision maker over the state space. Among different algorithms for computing the optimal policy, most are based on the Bellman equation that characterizes the value function as its fixed point.\n\nIn applications, it is common to encounter MDPs with uncertainties. When modeling an environment as a stochastic process, sampling techniques are often used to determine process parameters such as process costs or probabilities; such models are inherently uncertain. Another source of uncertainty is in stochastic games, where the cost and probability parameters change with respect to another decision maker’s strategy. While existing works focus on certain perturbations in MDPs\n\n(Bielecki and Filar, 1991; Altman and Gaitsgory, 1993; Abbad and Filar, 1992), these results do not generalize to the analysis of overall behaviour of the MDP under all possible cost parameters in a compact set.\n\nAdditionally, how uncertainty in MDP cost parameters affect the outcome of value iteration type methods is not well studied. Dynamic programming on bounded MDPs is studied in Givan et al. (2000) for specifically interval sets, however convergence of over general compact sets is not considered. While computation of the fixed points of Bellman operator is the topic of numerous studies (Delage and Mannor, 2010), most focus on the convergence analysis of value iteration and its stopping criteria (Ashok et al., 2017; Eisentraut et al., 2019). However, they do not consider the relationship between bounds on the optimal value function and the uncertainty in cost. Similarly motivated, Haddad and Monmege (2018) analyzes entry-wise uncertain transition kernels by using graph-based MDP transformations. While we also derive bounds of an MDP due to uncertain parameters, we differ in our approach: our set-based framework allows for direct extraction of the value iteration trajectories with respect to the set of cost parameters. This differentiates our work from Haddad and Monmege (2018) due to their graphical abstraction of MDP, which allows for derivation of bounds but not extraction of value function trajectories.\n\nContributions: We characterize the solutions of a family of MDPs at once, represented as sets of MDPs. More specifically, we: (i) develop a characterization of MDPs with uncertain cost parameters; (ii) propose a set-based Bellman operator over non-empty compact sets; (iii) establish the contractivity of this set-based Bellman operator with the existence of a unique compact fixed point set.\n\n## 2 Review of MDPs and Bellman Operator\n\nNotation: Sets of elements are given by . We denote the set of matrices of rows and columns with real (non-negative) valued entries as . Elements of sets and matrices are denoted by capital letters, , while sets are denoted by cursive letters,\n\n. The ones column vector is denoted by\n\n.\n\n### 2.1 Mdp\n\nWe consider a discounted infinite-horizon MDP defined by for a decision maker, where\n\n1. denotes the finite set of states.\n\n2. denotes the finite set of actions. Without loss of generality, assume that every action is admissible from each state .\n\n3. denotes the transition kernel. Each component is the probability of arriving in state by taking state-action . Matrix is column stochastic and element-wise non-negative — i.e. , , .\n\n4. denotes the cost of each pair .\n\n5. denotes the discount factor.\n\nAt each time step , the decision maker chooses an action based on its current state . The state-action pair\n\ninduces a probability distribution\n\n, where is the probability that the decision maker arrives at at time step . The state-action also induces a cost that must be paid by the decision maker.\n\nAt each time step, the decision maker chooses a policy that dictates the action chosen at each state . We denote policy as a function , where denotes the probability that action is chosen at state . We also denote in shorthand, a probabilistic distribution vector over the action space at each state . We denote the set of all feasible policies of an MDP by . In our context, it suffices to consider only deterministic, stationary policies i.e. is a time invariant function that returns for exactly one action, and for all other possible actions. The set of all such policies is denoted by .\n\nWe denote the policy matrix induced by a policy as , where\n\n (Mπ)s′,sa={π(s,a)s′=s0s′≠s.\n\nEvery stationary policy induces a stationary Markov chain (El Chamie et al., 2018), given by . We denote the set of all policy matrices induced by stationary policies as .\n\nFor an MDP , we are interested in minimizing the discounted infinite horizon expected cost, defined with respect to a policy as\n\n V⋆s0=minπ∈ΠEπs0{∞∑t=0γtC(st,at)},∀ s0∈[S] (1)\n\nwhere is the discount factor of future cost, and are the state and action taken at time step , and is the state that the decision maker starts from at .\n\nThe minimum expected cost is called the optimal value function. The policy that achieves the optimal value function is called an optimal policy. In general, is unique while is not. It is well known that the set of optimal policies always includes at least one deterministic stationary policy (Puterman, 2014, Thm 6.2.11) — i.e. for each , returns for exactly one action, and for all other possible actions.\n\n### 2.2 Bellman Operator\n\nDetermining the optimal value function of a given MDP is equivalent to solving for the fixed point of the associated Bellman operator, for which a myriad of techniques exist (Puterman, 2014). We introduce the Bellman operator here as well as relating its fixed point to the corresponding MDP problem.\n\n[Standard Bellman Operator] For a discounted infinite horizon MDP , its associated Bellman operator is given component-wise by\n\n (fC(V))s:=mina Csa+γ∑s′,aPs′saVs′, ∀s∈[S].\n\nThe fixed point of the Bellman operator is a value function that is invariant under the operator. [Fixed Point] Let be an operator on the metric space , is a fixed point of if it satisfies\n\n V⋆=F(V⋆). (2)\n\nIn order to show that the Bellman operator has a unique fixed point, we consider the following operator property. [Contraction Operator] Let be a complete metric space. An operator is a contracting operator if it satisfies\n\n d(F(V),F(V′))\n\nThe Bellman operator is known be a contraction operator on the complete metric space . From the Banach fixed point theorem (Puterman, 2014), it has a unique fixed point. Because the optimal value function is given by the unique fixed point of the associated Bellman operator, we use the terms optimal value function and fixed point of interchangeably.\n\nIn addition to obtaining , MDPs are also solved to determine the optimal policy, . We note that because every feasible policy induces a Markov chain, every feasible policy also induces a unique stationary value function which satisfies\n\n V=MπCT1S+γMπPTV, (3)\n\nwhere is the policy matrix induced by a feasible policy . Given a feasible policy , we can equivalently solve for the stationary value function as . From this perspective, the optimal value function is the minimum vector among the finite set of stationary value functions generated by the set of all policies .\n\nFrom the optimal value function , we can also derive a deterministic optimal policy from the Bellman operator as\n\n π⋆(s,a)=⎧⎨⎩1a=argmin¯a∈[A] Cs¯a+γ∑s′Ps′,s¯aV⋆s′0otherwise, ∀ s∈[S]. (4)\n\nWhile the optimal policy does not need to be deterministic and stationary, the optimal policy derived from (4) will always be deterministic.\n\n### 2.3 Termination Criteria for Value Iteration\n\nAmong different algorithms to determine the fixed point of the Bellman operator, value iteration (VI) is a commonly used and simple technique in which the Bellman operator is iteratively applied until the optimal value is reached — i.e. starting from any value function and , we apply\n\n Vk+1s=mina Csa+γ∑s′,aPs′,saVks′,∀s∈[S]. (5)\n\nThe iteration scheme given by (5) converges to the fixed point of the corresponding discounted infinite horizon MDP. The stopping criteria of VI can be considered the over-approximation of the optimal value function. (Puterman, 2014, Thm. 6.3.1) For any initial value function , let be the value function trajectory from (5). Whenever there exists , such that , then is within of the fixed point , i.e. . Lemma 2.3 connects relative convergence of the sequence to absolute convergence towards by showing that the former implies the latter.\n\nIn general, the stopping criteria differ for different MDP objectives (see Haddad and Monmege (2018) for recent results on stopping criteria for reachability).\n\n## 3 Set-based Bellman Operator\n\nThe standard Bellman operator with respect to a fixed cost parameter is well studied. Motivated by a family of MDPs corresponding to a compact set of cost parameters with all other data parameters remaining identical, we lift the Bellman operator to operate on sets rather than individual vectors in . For the set-based operator, we analyze its set-based domain and prove that it is a contraction operator. We also prove the existence of a unique fixed point set for a set-based Bellman operator and relate its properties to the fixed point of the standard Bellman operator.\n\n### 3.1 Set-based operator properties\n\nWe define a new metric space based on the Banach space to serve as our set-based operator domain (Rudin and others, 1964), where is the collection of non-empty compact subsets of equipped with partial order: for , if . The metric is the Haussdorf distance (Henrikson, 1999) defined as\n\n dH(V,V′)=max{ supV∈VinfV′∈V′∥∥V−V′∥∥∞, (6) supV′∈V′infV∈V∥∥V−V′∥∥∞}.\n\nSince is a complete metric space, is a complete metric space with respect to .\n\n(Henrikson, 1999, Thm 3.3) If is a complete metric space, then its induced Hausdorff metric space is a complete metric space. On the metric space , we define a set-based Bellman operator. [Set-based Bellman Operator] For a family of MDP problems, , where is a compact set, its associated set-based Bellman operator is given by\n\n FC(V)=cl⋃(C,V)∈C×VfC(V),∀ V∈H(RS)\n\nwhere is the closure operator. As we take the union of an uncountably many bounded sets, the resulting set may not be bounded, and therefore it is not immediately obvious that maps into the metric space . We show this is true in Proposition 3.1. If is compact, for all , . For a non-empty set of some finite dimensional real vector space, let us define its diameter to be denoted as . The diameter of any compact set in a metric space is bounded.\n\nWe take any non-empty compact set . As , it suffices to prove that is closed and bounded. The closedness is guaranteed by the closure operator. A subset of a metric space is bounded iff its closure is bounded. Hence, to prove the boundedness, it suffices to prove that . Consider any two cost-value function pairs, , they must satisfy\n\n fC(V)−fC′(V′)=(fC(V)−fC′(V))+(fC′(V)−fC′(V′)),\n\nwhere the norm of the second term must be upper bounded by due to contraction properties of . Let . For the first term, we take to be the optimal strategy corresponding to , then\n\n ∥fC(V)−fC′(V)∥∞ ≤ ∥∥M¯πCT1S+γM¯πPTV−M¯π(C′)T1S−γM¯πPTV∥∥ ≤\n\nTherefore, we have that . Since it holds for all then as and are bounded. ∎ Proposition 3.1 shows that is an operator from to . Having established the space which it operates on, we can draw many parallels between and . Similar to the existence of a unique fixed point for operator , we consider whether a fixed point set of which satisfies exists, and if it is unique. To take the comparison further, since is the optimal value function for an MDP problem defined by , how does relate to the family of optimal solutions that corresponds to the MDP family ?\n\nTo prove the unique existence of , we utilize the Banach fixed point theorem (Puterman, 2014), which states that a unique fixed point must exist for all contraction operators on complete metric spaces. First, we show that is a contraction as defined in Definition 2.2 on the complete metric space .\n\nFor any and closed and bounded, is a contracting operator under the Hausdorff distance.\n\nConsider , , to see that is a contraction, we need to show\n\n supV∈FC(V)inf¯V∈FC(¯V)∥∥V−¯V∥∥∞\n\nFirst we note that taking () of a continuous function over a set is equivalent to taking the () over the closure of . Let and , then due to continuity of norms (Rudin and others, 1964, Thm 4.16),\n\n supV∈FC(V)inf¯V∈FC(¯V)∥∥V−¯V∥∥=supV∈GC(V)inf¯V∈GC(¯V)∥∥V−¯V∥∥.\n\nTherefore, it suffices to prove\n\n supfC(V)∈GC(V)inff¯C(¯V)∈GC(¯V)∥∥fC(V)−f¯C(¯V)∥∥∞\n supf¯C(¯V)∈GC(¯V)inffC(V)∈GC(V)∥∥fC(V)−f¯C(¯V)∥∥∞\n\nFor any , ,\n\n inf(¯C,¯V)∈CׯV∥∥fC(V)−f¯C(¯V)∥∥∞ (9a) = inf(¯C,¯V)∈CׯV∥MπCT1S+γMπPTV− (9b) (M¯π(¯C)T1S+γM¯πPT¯V)∥∞, (9c) ≤ inf(¯C,¯V)∈CׯV∥M¯πCT1TS+γM¯πPTV− (9d) (M¯π(¯C)T1TS+γM¯πPT¯V)∥∞, (9e) ≤ (9f)\n\nwhere corresponds to the optimal policy for the MDP and corresponds to the optimal policy for the MDP in (9b). In (9c) we replaced by by noting that and is optimal, therefore must result in a larger value function (similar to the proof of Prop. 3.1). In (9e) we note that the infimum of expression over set must be upper bounded by when . In (9f), we used the fact that .\n\nTaking the over and ,\n\nTherefore . Since , is a contracting operator on .∎\n\nThe contraction property of implies that repeated application of the operator to any will result in closer and closer sets in the Hausdorff sense of distance to a fixed point set. It is then natural to consider if there is a unique set which all converges to.\n\nThere exists a unique fixed point to the set-based Bellman operator as defined in Definition 2.2, such that , and is a closed and bounded subset of . Furthermore, for any iteration starting from arbitrary , , the sequence converges in the Hausdorff sense i.e. . As shown in Proposition 3.1, is a contracting operator. From the Banach fixed point theorem (Puterman, 2014, Thm 6.2.3), there exists a unique fixed point , and any arbitrary will generate a sequence that converges to the fixed point. ∎\n\nThe fixed point of Bellman operator on metric space corresponds to the optimal value function of the MDP associated with cost parameter . Because there is no direct association of an MDP problem to the set-based Bellman operator , we cannot claim the same for . However, does have many interesting properties on , in parallel to operator on , especially in terms of the value iteration method (5). Suppose that instead of a fixed cost parameter, we have that at each iteration , a that is random chosen from a compact set of costs, , then it is interesting to ask if contains all the limit points of . Indeed, we can infer from Theorem 3.1 that the sequence converges to under the Hausdorff metric. Furthermore, even when itself does not converge, it must converge to the set under the Hausdorff metric— i.e. .\n\n## 4 Conclusion\n\nWe summarize our results on set-based Bellman operator: for a compact cost function set , converges to to a unique compact set which contains all the fixed points of for all fixed . Furthermore, also contains the limit points of for any , , given that converges. Even if the limit does not exist, must asymptotically converge to in the Hausdorff sense. Future work includes extending the uncertainty analysis to consider uncertainty in the transition kernel to fully capture learning in a general stochastic game.\n\n## References\n\n• M. Abbad and J. A. Filar (1992) Perturbation and stability theory for markov control problems. IEEE Trans. Autom. Control. Cited by: §1.\n• B. Açikmeşe and D. S. Bayard (2012) A markov chain approach to probabilistic swarm guidance. In American Control Conference, pp. 6300–6307. Cited by: §1.\n• E. Altman and V. A. Gaitsgory (1993) Stability and singular perturbations in constrained markov decision problems. IEEE Trans. Autom. Control 38 (6), pp. 971–975. Cited by: §1.\n• P. Ashok, K. Chatterjee, P. Daca, J. Křetínskỳ, and T. Meggendorfer (2017) Value iteration for long-run average reward in markov decision processes. In International Conference on Computer Aided Verification, pp. 201–221. Cited by: §1.\n• T. R. Bielecki and J. A. Filar (1991) Singularly perturbed markov control problem: limiting average cost. Annals of Op. Res. 28 (1), pp. 153–168. Cited by: §1.\n• E. Delage and S. Mannor (2010) Percentile optimization for markov decision processes with parameter uncertainty. Op. Res. 58 (1), pp. 203–213. Cited by: §1.\n• N. Demir, U. Eren, and B. Açikmeşe (2015) Decentralized probabilistic density control of autonomous swarms with safety. Autonomous Robots 39 (4), pp. 537 –554. Cited by: §1.\n• J. Eisentraut, J. Křetínskỳ, and A. Rotar (2019) Stopping criteria for value and strategy iteration on concurrent stochastic reachability games. arXiv preprint arXiv:1909.08348. Cited by: §1.\n• M. El Chamie, Y. Yu, B. Açıkmeşe, and M. Ono (2018) Controlled markov processes with safety state constraints. IEEE Trans. Autom. Control 64 (3), pp. 1003–1018. Cited by: §2.1.\n• J. Filar and K. Vrieze (2012) Competitive markov decision processes. Springer Science & Business Media. Cited by: §1.\n• R. Givan, S. Leach, and T. Dean (2000) Bounded-parameter markov decision processes. Artificial Intelligence 122 (1-2), pp. 71–109. Cited by: §1.\n• S. Haddad and B. Monmege (2018) Interval iteration algorithm for mdps and imdps. Theoretical Computer Science 735, pp. 111–131. Cited by: §1, §2.3.\n• J. Henrikson (1999) Completeness and total boundedness of the hausdorff metric. In MIT Undergraduate Journal of Mathematics, Cited by: §3.1, §3.1.\n• S. H. Q. Li, Y. Yu, D. Calderone, L. Ratliff, and B. Açikmeşe (2019) Tolling for constraint satisfaction in markov decision process congestion games. In American Control Conference, pp. 1238–1243. Cited by: §1.\n• M. L. Puterman (2014) Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons. Cited by: §1, §2.1, §2.2, §2.2, §2.3, §3.1, §3.1.\n• W. Rudin et al. (1964) Principles of mathematical analysis. Vol. 3, McGraw-hill New York. Cited by: §3.1, §3.1." ]
[ null ]
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https://homework.cpm.org/category/ACC/textbook/acc7/chapter/9%20Unit%2010/lesson/CC3:%209.2.4/problem/9-114
[ "", null, "", null, "### Home > ACC7 > Chapter 9 Unit 10 > Lesson CC3: 9.2.4 > Problem9-114\n\n9-114.\n\nSimplify each of the following expressions.\n\n1. $4x^3y · 3xy^2$\n\nCombine like terms.\n\n$(4)(3)x^{(3 + 1)}y^{(1 + 2)}$\n\n$12x^{4}y^{3}$\n\n1. $6a^5b^2 · 3ab^2$\n\nSee (a).\n\n$18a^{6}b^{4}$\n\n1. $m^2n · 9mn$\n\nSee part (a).\n\n1. $\\frac { 3 ^ { 5 } \\cdot 8 \\cdot 5 ^ { 3 } } { 3 ^ { 2 } \\cdot 2 ^ { 3 } \\cdot 5 ^ { 3 } \\cdot 3 ^ { 3 } }$\n\nRewrite this expression with the lowest base numbers possible\n\n$\\frac{(3^{5})(2^{3})(5^{3})}{(3^{2})(2^{3})(5^{3})(3^{3})}$\n\nCombine numbers with the same base.\n\n$(3^{(5 − 2 − 3)}) · (2^{(3 − 3)}) · (5^{(3 − 3)})$\n\n$(3^0) · (2^0) · (5^0)$\n\nAny number to the zero power has the value of $1$.\n\n$1$\n\n1. $\\frac { m ^ { 4 } \\cdot n } { n ^ { 3 } }$\n\nSee (d).\n\n$\\frac{m^{4}}{n^{2}}$\n\n1. $\\frac { 9 a ^ { 4 } b ^ { 2 } } { 15 b }$\n\nSee (d)." ]
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SMAK/8hRgLL8S6SwvMcWDQzvascJkuopwm+szYqyA2SH3kRum89v6EE33NrjKLdwLy0Ffh2G4qUg32uVon3YtWxXrWXUEd8FCqftTH765n3cuqEC7zXUczvGyW8W5TzFrwvFmda1k/5wn0wEqelQJ7qWX/XlHC9Jr6z9hLrr0LRKws9tPhJS4FKutaTFjbUcSQcIhO48vcP7F9sZHWJhA58zshvpW/D9SoNNFAIMkRXQ27yHInWkL+ADa2LqTyGCXv+6ciz9GLs7aWfxLT3s4GIAxq8x5n2oALpQCB38X7PeXlw5bNM/2mmfdY59jz/38HjPr7BfFwVk4ejeXxG4NhHeN2XJJr/AOWJlfWOK/IO7D0v8fbv4z0Xnvlv3vNAfsf07+exh6ic+cR5Ae9jPVbYvijwbhDvMZv32jMmz0fy/FsK1P+TmZ9rCjz7VF7nm72ou7vElAfK6RGWq0/4tzL9PwJ1Au/04zH3QnDrLyRaCvkVvtvZRd7tRL7/13gOzv2l9OwGRPndXCBfuO8nipSFfbffKpBmBtNMLXKtk5gOsUTDlKYU/WmhZ2MIvbNCefqQ00BmaG3tE9Nozab2HCLoNY5G7Fp3owNp0T0wpgzFoFLYjB6Mnfn/VeYRDc6lEi0aM9GxEDZhwybcZxeoBfHbYMVT2ABZLX8bCqam/WlMPr4i+eF7Q4rkGaMbtuS76QqUWcJpxOud/HY69cfm91iS6IWedY38xgUsDuXxVd7+/VlvhrNsXmR5oSG+nedMi7EyJ/P4ZCoSqx2PyFjHE5Ry6ppb31c639P2tIirPCX4VxKtBgjMo/W1PZ/9Uzy2wrnODvRWYA6HCQEr3JbDigIWHIJGtyWxX0GPgA+U89Ysq3JRRyXGWrJZx1BA3vYyciiVsLWO8rgd03YG6vBRVODvcu6D7+MevosMFTYowntQcPw7Xt6+4xDnElrmyOsJLG8onU85dXIrJ1+2TXHzdQzzNTNG0Z1MRWwyvYAhq34sy+Ub/BbfiCnT8/jemjYy40PxHrTQQ+iqoFtoNK2PI9kQ7BtDtLDkf+6QiA806D8q4X7PsdFMDED5X83GaIFEa7uPpxxPUsAwv9O9cgZ+xgZ/R/4iNuA2ktN0yc++57pZz2BjEfIQuKMFisUjWCI7xcmDK+PZ+LrXQgO8k5Nmd8fC/j6f3ffQxE3qkw4QKkj8Jv7+kff6MJXDHzLNZVSQfNgpi4VKneuheJjPY8t5MvfPoQJkn/dwrx52eN/Dt0jYq1incc4H+X6XkbAv9JTmDsfrcEGJ5eBiJz4b0OwoE6FvN84zVgz2/UKp2I1ltAOf78tU9A/y6rDN77leHd6dym09CXGYo1TdSDKczfLYieV3GdOc79WhfRwyv5RpbZ14gG3M9Z4HzObrvJh81Xn58pXJcY6XZq8i3w6I+rSYNJ93PAgdou52xQAQ+kBgKt1icV6GIbRKFhS5DhqDtwcg/2igPsftMyVa/jXDjxgW5ZU8dnbAbbmazzWPv3B7TqIS00wLxMeOtH58wHrbtBf5X+TkwZW5bMh90niNx+fTMsJ8BLMc5aAv+CS9Bkv4PHNYlktIpo+wrp8ZOHcij83l/0nOsTbut+X8hkN+9nlej7G0xCGkE7l9Cb0IHSyTu0ggQqKPc69+m5ZoOTiGHoV5zO+kfqzLackHvM7n9g2S78I4WnpOKLXUq8OoEyfxnYEcd2G63aiItbKePM93i/7w7xm5m+lOdK5tn/XPVBiX8ZyX6alq4/UPCTwL7v8vL1+TuB+KcqhLwN77Nf6eUEKZTQ54C1EPz1JaUgw0oW/oRUlg2V5cJE2t89HH4T5q300DUPZoHBpp3TweOD6dpPftwHtKxlhLL3M7zl39TU8Bgqvwq45VWA7K6a6B5VoT2P9bx5rsSx3awfG2LA0cn0Kiv9Xb30yLKMuyWUhLb8uY+6Sc56ktMW9Qlmx/+gOB4w+R3DeR9fvdq0g8C3jfH5dxT6Q71lEGXqVC8MF+qstx5fG04wWqLaH+LCVxAkMdi1eoWL0WOOde/m7r7NveO+biLXrAzohRxEL5Wu7UK1/p2oyKwTpes4WK+ogSPJH+PBoHSnwMgULRL4Qeck03SnhseiXRzgbxMDZSxQjIRr+jEX8wcBxW0jkFnqm/Yee1XynhaG7sn0Fr3Y+E7o7xSNh+8IXesQdo2XzMs0pgOW1HC/8fZea/EjETbzl5b+jDdWwjG+dpQUAUgsf+GmhA4SlBlwC6CeBih2v1iAq+5yaSWafk+9r9et1CIqnzvrMsLbZVtCi/U+I94fL9AOsBvAD3U2Hqr9EdWQlH2u/rELVfx0PR+weQjLO08oHhzjUk5juxdci2aU1F6sPdVJifCRwL5etAyceCvOwd+yy/ZVjyCGJDtwCi8A8t0Hb+kt/w1x3FxSrcwEyJjw1SKCpiZbkNUKjRapJ8UE9fAGviSoeQYXku4wf+ai8UljQVgNmelfgTiSJJB7rsu6T8/stNaNW6VuC32OgsCxAXgv4w8c+1THc3G3jr3kMU9GllNN7AFWwwk16D9b2YhlJilCrrceiLhZ4sUDcLwbpGf+80pCdy/3SpzOp5SckPLQzFBXQ7+xMBJe0JiVzXeEfnUvF4usg9j3eIK81fBGIhIvxyqVwAq1uXMT/FWueZP8P8WgLzyxJW7OZMm6FX5EQqP4gHedF7t+uKKJZJpwxD9WFXfjdZJ13I6j/Cy9dYenf8fPllfadThw5mHZoRk2d8n2OoKEyi9wWWOUZ9wN3/fxLFZWj/uaLfCT2k9Q7nR+AT+v5s4NNO5QSp3sCPI4TFrNCVBAgGQTBnOhbs1AEue7dhKddDcDLFByL7vyw9o5mHsnFBfy2Gtu1GBeyjtDhmUukpB3EL8/y0DEJ3yyJbobIsFWioD2KjbUdVII5hCZ9tl148R2/ec7H3D+/Xj0jGu7Px372AEjhC8gFwv+bvoxL1Ce9A6/3+CtdlfP+PxRybwW/Px3HSc8hZG7/9s5xyK/ZuE166uHNQhhO8c690lA6LYwKeDHjIEIB7tqeYjGd5tku+L38W0+9PBXtujBJyNQkdVvr/UuGCAYKA1/kyMF5DxSAk9BcC+6C9fs2z8rDvssBHBFxVwPqp7qdnRV6OYkOOhV2WD3DZ9+WDfZtKSZKNACwjuPxulsi1HipTuG2voyJzjuOt+G82pMky84358Z+UvFswUaB+FPKgDFRZHk6yhJvddjesIrmfxkb9mQrlLdGH57CW4mkkzY+TBBbFXOMztEThfXrEsW7RdQOX/cR+IPRuWq7dfKcZEtmdjlLhA11hiB9AVx2i4D9EMjy1l+82UeQcxGu8QuPCkm1XgXwlWc7IF0ZOTAmktYGHs0jCwJtMj2NHSj641QW6l+5gvUM3GQJz0RXWQkLfSqlJsaEI/a8kR/+jQXAV+o7gEkRf4BdjyBxE9KCEg6T6E8v4cR0vPYOjBgJtzsddI4XXhk94FsgvJN//Xw5gZaCf7mj+XyDR+OjeAIQxu49lYPu+OyTvUrWKRZzClw4oA+scS7FURcK6SuGh2JPfQkbyoyKg/F1c5L2Ugg5aZPUSjhOwM9+JxA/Vs+WNbo6LJBri9ouYdLYb4SXvuawCcBjLaWUF6/JKWqpryzgHwai3OSQICxf90RjG+ZyTrt3xMoUwxClnW286vPplFVeLmwsQ+h+db+JNtmeH0ZvldtHVOJb8K3z+JOuntcqhPP1Qes7SZ2daRJ5ukXyA73S2Ux9QalL0Br2xkBBA9ZeYY0fzY/lpDJkDP6FLKjUAz3ujQ2YDjVX8qEfHNFZoQOACnik9I2t7a9kulfUnl7mOjXBvrldXgTKw0elLnEbYTuoyJuacTZ3ycz0WwLiYc6ZQibya/3eSfDQxJtV5lMdhrf+A+xE1vW8FnnEFSQllHJo2eRRJqU16Dvfzgbw9zXNs95Gr6CHP+3H7C95zXeeU38H94G0q1zho8Ej0CSo2/ph7G/W+eUybMc6rD1lHWdk65t7betcOKQhW6XhM8rP8uXBHDZxHb8iD/D2f+6Gc7FqgDOyshlYpvVYpSbGhCd0O8elNANzj1EIH0ipevJGU/Rx6K+okP3TMfS/Q2g8gma8ONKC9xfW0gEAMN/XhOi1lpE1Lz0AsDEeyE7Xc5+x/mL8TAoQKIjuJ2+5qfU84SpAfXTyWFu2+TkNvXaVv0Br7jSP4/6pDin3FUsfiDAUens73PUcKj2e3jf43aFmGukg+T6JEEOTtged6vsBztffxOftSJ9P0PgBwU3/CMyDWkZxPCNSHL3h1QBzP0XHSc6w3vAC7sx17rEi+YO3b2QWP8IwU6+GZS0+DW9b4P9/zBMV5by6nV+g6Cfe3KxQlo7f91a+wgt9awCoKWfbHSt9dmO8VrGUjdj01fFikGGJUS9I6hA3Kd6Uy0dYWi9lgurOR9QYns4FLBOoUvAovelb1+ZJ3PW5FTwkaW7g1f+aR80zWL/R7wmWJvkaMrf86FYGF9LZYPMWG9Bg2pldTYRlH5RPW3WtsNF1X6eUSng4XZT+Lv2OkbxMPZfme9yPBQIGzUd/HOXkBcZQy2uFJWuoXBAh1IrevlfA0txNIdgfwHSxwjkHhCc15kKLy9Eg/fw/38N1/gs/2WYcwf05FBvVkRyp9GP+Ncd8Y5vaW5GeNBG6gVwZu9XtZHkizN89JUZl9roR8WSt9Ar/FQ6lkH+5Y578LnIeI/RlUsnBea8z1URf+UKaCrFBUlNCFHzg+kMvYKMW5YGHJ3yzR0JvVXgPUHEhf7rKmdpUjH0PLuEbcilH93c8PMkFUMmaz+hLFAtbk2bJ+P7V1B5Y6ZrsupkxDQ4CaS3hmt6xPLZBuCQndXmszkqePZ+ideMuziibz3EMCxPQyFZ63A+ckaeH5i6y8SOsObtmjqBRkJD9TnY+H+Qyb0AK8xiub5hiLtNqpey4xoovqFF7ncIcMrKcDBHaHsy/pvOOQJY5vDv26OzvvAwqDndp2ZsxzQcnBzHbbsq5d6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null ]
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https://www.hpmuseum.org/forum/archive/index.php?thread-7550.html
[ "# HP Forums\n\nFull Version: Heads up for a hot new root seeking algorithm!!\nYou're currently viewing a stripped down version of our content. View the full version with proper formatting.\nPages: 1 2\nThe famous Russian mathematician Ostrowski, who taught for many years at the University of Basil, Switzerland, proposedf an enhancement to Newton’s root seeking algorithm. Ostrowski suggested that each iteration offers two refinements for the root—one of them being intermediate per each iteration. The Ostrowski algorithm matches Halley’s root seeking algorithm in its third order rate of convergence. Recently, the Ostrowski algorithm inspired many mathematicians to device root-seeking algorithms with two or more refinements to the root per iteration.\n\nI recently applied Ostrowski’s approach to the Illinois algorithm (an improved version of the False Position algorithm) and was able to obtain better rates of convergence than with the Illinois algorithm. I posted the pseudo-code for this algorithm on this web site. I was a little baffled as to why Ostrowski improved only the Newton’s method and did not become more ambitious to enhance Halley’s method!\n\nA few days ago, I decided to experiment with applying Ostrowski’s approach to Halley’s algorithm. Since the latter method is a bit more advanced than Newton’s method (requiring the calculations of approximations for the first AND second derivatives), applying the Ostrowski approach was NOT trivial. I decided, nevertheless, to give it a go. I started with a simple improvement to Halley’s method, but that did not yield better calculations. After two or three incarnations, I was able to find a satisfactory marriage between Ostrowski and Halley. I plan to publish a report on my website and include a comparison between the methods of Newton, Halley, Ostrowski, and my new Ostrowski-Halley method. The results will include testing these algorithms with two dozen functions and reporting the number of function calls AND iterations.\n\nI am happy to report that the new Ostrowski-Halley method competes well with Halley’s method and its cousin the Ostrowski method. The competition is stiff between these three algorithms., but the Ostrowski-Halley method shows good promise. Stay tuned for my announcement of posting a paper on this subject in my personal web site.\n\nNamir\nHi Namir, very promising! Do you have any stict proof of convergence? Also, interesting woul be an estimate for the achievable convergence rate (and how this depends on type/smoothness etc. of the function to be \"rooted\").\n\nAnyways, am curious to read your paper and the comparison with the original algorithms.\n\nJuergen\n(01-10-2017 06:30 PM)Namir Wrote: [ -> ]The famous Russian mathematician Ostrowski, who taught for many years at the University of Basil, Switzerland, proposedf an enhancement to Newton’s root seeking algorithm. Ostrowski suggested that each iteration offers two refinements for the root—one of them being intermediate per each iteration. The Ostrowski algorithm matches Halley’s root seeking algorithm in its third order rate of convergence. Recently, the Ostrowski algorithm inspired many mathematicians to device root-seeking algorithms with two or more refinements to the root per iteration.\n\nI recently applied Ostrowski’s approach to the Illinois algorithm (an improved version of the False Position algorithm) and was able to obtain better rates of convergence than with the Illinois algorithm. I posted the pseudo-code for this algorithm on this web site. I was a little baffled as to why Ostrowski improved only the Newton’s method and did not become more ambitious to enhance Halley’s method!\n\nA few days ago, I decided to experiment with applying Ostrowski’s approach to Halley’s algorithm. Since the latter method is a bit more advanced than Newton’s method (requiring the calculations of approximations for the first AND second derivatives), applying the Ostrowski approach was NOT trivial. I decided, nevertheless, to give it a go. I started with a simple improvement to Halley’s method, but that did not yield better calculations. After two or three incarnations, I was able to find a satisfactory marriage between Ostrowski and Halley. I plan to publish a report on my website and include a comparison between the methods of Newton, Halley, Ostrowski, and my new Ostrowski-Halley method. The results will include testing these algorithms with two dozen functions and reporting the number of function calls AND iterations.\n\nI am happy to report that the new Ostrowski-Halley method competes well with Halley’s method and its cousin the Ostrowski method. The competition is stiff between these three algorithms., but the Ostrowski-Halley method shows good promise. Stay tuned for my announcement of posting a paper on this subject in my personal web site.\n\nNamir\n\nKeep them coming. I hope you don't mind if one or more of your algorithms end up implemented in newRPL (proper credit will be given, of course!). Always interesting to discover something new in a subject that seemed closed already.\nSince it's on-topic:\n\nhttp://ojs.excelingtech.co.uk/index.php/...ew/430/294\n\nThere's a lot of operations in each iteration, but smaller number of evaluations to find the root. Considering that newRPL has relatively slow CORDIC transcendental functions, evaluation is heavy and one of these could perhaps be beneficial, but have you ever tested if it's actually worth it? Sometimes they just want to prove a theoretical point, but they are not really better than plain Newton.\n(01-10-2017 10:14 PM)Claudio L. Wrote: [ -> ]Since it's on-topic:\n\nhttp://ojs.excelingtech.co.uk/index.php/...ew/430/294\n\nThere's a lot of operations in each iteration, but smaller number of evaluations to find the root. Considering that newRPL has relatively slow CORDIC transcendental functions, evaluation is heavy and one of these could perhaps be beneficial, but have you ever tested if it's actually worth it? Sometimes they just want to prove a theoretical point, but they are not really better than plain Newton.\n\nI looked at the article and my new method does not involve as much calculations per iterations! I think my new algorithm has the same order of convergence as Halley, which is third order.\n\nAlso the author of teh article is improving on Ostrowski (who improved on Newton). My new algorithms improves on Halley's method using Ostroskwi's approach.\n\nAnyway, thanks for the articles. A few years ago I did a survey of recent algorithms that were inspired by Ostrowski. I found algorithms with three or more intermediate refinements for the root per iterations. While the number of iterations of these algorithms decreased (compared to Newton or Halley), the number of function calls went up! So I am conscious that the number of function calls, per iteration, should not get out of hand.\n\nNamir\n(01-11-2017 08:05 PM)Namir Wrote: [ -> ]\n(01-10-2017 10:14 PM)Claudio L. Wrote: [ -> ]... but have you ever tested if it's actually worth it? Sometimes they just want to prove a theoretical point, but they are not really better than plain Newton.\n\nI think my new algorithm has the same order of convergence as Halley, which is third order.\n\nBut again Namir, as you wrote \"you think it is of 3rd order\", but do you know for sure by means of a strict mathematical proof? Mathematics can't go without that ;-) A modification of a 3rd order algorithm does not necessarily result in an algorithm of the same convergence behavior. Did you try to adopt the proves of Halley/Ostrowski to your new algorithm? This would indeed make your work complete!\n\nJuergen\n(01-17-2017 09:13 PM)JurgenRo Wrote: [ -> ][quote='Namir' pid='66624' dateline='1484165132']\n\nI think my new algorithm has the same order of convergence as Halley, which is third order.\n\nBut again Namir, as you wrote \"you think it is of 3rd order\", but do you know for sure by means of a strict mathematical proof? Mathematics can't go without that ;-) A modification of a 3rd order algorithm does not necessarily result in an algorithm of the same convergence behavior. Did you try to adopt the proves of Halley/Ostrowski to your new algorithm? This would indeed make your work complete!\n\nJuergen\n[/quote\n\nThe new algorithm matches or slightly improve on Halley. Sicne Halley is third order, the new algorithm could not be second or fourth order. I am saying 3rd order by induction.\n\nNamir\n(01-17-2017 10:42 PM)Namir Wrote: [ -> ]The new algorithm matches or slightly improve on Halley. Sicne Halley is third order, the new algorithm could not be second or fourth order. I am saying 3rd order by induction.\n\nNamir\n\nAnd how do you define \"it matches\"? what criteria is used? What parameters? In what cases? all possible expressions??\nIMHO induction is not applicable here...\n\nCheers,\nÁM\nThe paper pointed by Claudio shows how the authors use a numerical computation to ascertain the order of convergence of the algorithm. I think that such approach can be used here to estimate the order of convergence of Namir's algorithm not needing a, perhaps cumbersome, rigorous demonstration. Provided, of course, you have a math software capable to work with high precision numbers (say Mathematica).\n\nKnowing the order of convergence, the efficiency index can be calculated, perhaps a better metric to compare algorithms.\n\nIn any way, AFAIK, the basic (Newton based) Ostrowsky's algorithm has a convergence order of 4, not 3.\n(01-18-2017 05:47 AM)Ángel Martin Wrote: [ -> ]\n(01-17-2017 10:42 PM)Namir Wrote: [ -> ]The new algorithm matches or slightly improve on Halley. Sicne Halley is third order, the new algorithm could not be second or fourth order. I am saying 3rd order by induction.\n\nNamir\n\nAnd how do you define \"it matches\"? what criteria is used? What parameters? In what cases? all possible expressions??\nIMHO induction is not applicable here...\n\nCheers,\nÁM\n\nI fully agree with Ángels rating. I do not see how Induction could do the work here. Also, the convergence rate might (and likely will) depend on the properties of the function to be \"rooted\" (smoothness for example). That is why a \"demonstration\" of convergence with a couple of functions is not reliable at all. Then again it would be legitimate to say, that you guess that the scheme is of 3rd order (for sufficient smooth?) functions but that a rigorous proof is still missing ...\n\nJuergen\nMy study compared the number of iterations and functions for the method of Newton, Halley, Ostrowski, and my new algorithm. I used two dozen tes functions. The last three method generally had close number of iterations and function calls. Since Halley has been discussed on several books (and Wikipedia) to be third order, then Ostrowski and my new algorithm should have the same convergence rate. When you compare Newton's method with the other three, you can see that Newton's method is slower.\n\nI am not sure that Ostrowski's method has an order 4 of convergence. Any reference that confirm this?\n\nNamir\n(01-18-2017 11:53 PM)Namir Wrote: [ -> ]I am not sure that Ostrowski's method has an order 4 of convergence. Any reference that confirm this?\n\nNamir\n\nThe paper I cited, shows at the very top on page 78 (it's actually the third page) that plain Newton has order 2, Ostrowski has order 4, and another formula has order 8. It says \"it's well established\", so I guess it must be true.\n(01-19-2017 03:23 AM)Claudio L. Wrote: [ -> ]\n(01-18-2017 11:53 PM)Namir Wrote: [ -> ]I am not sure that Ostrowski's method has an order 4 of convergence. Any reference that confirm this?\n\nNamir\n\nThe paper I cited, shows at the very top on page 78 (it's actually the third page) that plain Newton has order 2, Ostrowski has order 4, and another formula has order 8. It says \"it's well established\", so I guess it must be true.\n\nYes the paper states, on page 78, that Ostrowski's convergence is of order 4. The author is mistaken!! I tested 24 functions and compared Newton, Halley, Ostrowski, and my new Ostrowski-Halley method. The methods of Halley and Ostrowski often found the root in the same number of iterations. If Ostrowski's method is order 4, I didn't see it in the test results. My new algorithm did, in general a little bit better than Halley and Ostrowski (after all it's a combination of these two methods).\n\nMany mathematicians have, somewhat recently, improved on Ostrowski's method to yield algorithms with high to very high convergence rates. That's nice and dandy, but it comes at the cost of very high number of function calls, making the simpler (and slower converging) algorithms more practical if one regards the number of function calls as the cost of doing business in finding roots.\n\nNamir\n(01-19-2017 05:26 AM)Namir Wrote: [ -> ]Yes the paper states, on page 78, that Ostrowski's convergence is of order 4. The author is mistaken!!\n\nhttp://folk.uib.no/ssu029/Pdf_file/Varona02.pdf states that the order of convergence of Newton's is 2, Halley's 3 and Ostrowsky's 4.\n\nhttp://www.sciencedirect.com/science/art...2706006716 states that the basic Ostrowsky's method has order of convergence 4.\n\nhttp://www.sciencedirect.com/science/art...2111008078 states again that the order of convergence of Ostrowsky method is 4. It also says that the Ostrowsky's method is optimal in the sense that it satisfies the Kung-Traub conjecture (which states that the maximum attainable order of convergence for an algorithm with $$n$$ function evaluations is $$2^{n-1}$$, neither Halley's nor Newton's are optimal in such sense.\n\nI'm not sure about the first reference, but the other two are peer reviewed publications, so I assume them to be safe sources.\n\nI cannot find now your algorithms description (didn't they were in this thread or in another one?) so, how many function evaluations do they need on each iteration?\n\nObtaining the computational order of convergence COC of your algorithm seems not to be a hard task (only 3 iterations are needed for some test function/root combinations). Such COC combined with the number of function evaluations needed on each iteration will give us all a much better indication of your algorithm performance.\n\nRegards.\n\nEdit: I located your algorithm in the other thread (sorry I forgot it). It needs four function evaluations on each iteration. Supposing its order of convergence is 4, its efficiency index is $$\\sqrt{4}=1.4142...$$. As Ostrowsky's algorithm only requires 3 function evaluations on each iteration and it has an order of convergence of 4, its efficiency index is $$\\sqrt{4}=1.5874...$$, which is better. If the order of convergence of your algorithm is not 4, but 3, then the situation is even worse. To compete with the Ostrowsky's algorithm (in terms of the efficiency index) we need your algorithm to be of order 6-7. For comparison, the efficiency index of Newton's is also 1.4142... and that for Halley is 1.44225...\n(01-19-2017 10:44 AM)emece67 Wrote: [ -> ]\n(01-19-2017 05:26 AM)Namir Wrote: [ -> ]Yes the paper states, on page 78, that Ostrowski's convergence is of order 4. The author is mistaken!!\n\nhttp://folk.uib.no/ssu029/Pdf_file/Varona02.pdf states that the order of convergence of Newton's is 2, Halley's 3 and Ostrowsky's 4.\n\nhttp://www.sciencedirect.com/science/art...2706006716 states that the basic Ostrowsky's method has order of convergence 4.\n\nhttp://www.sciencedirect.com/science/art...2111008078 states again that the order of convergence of Ostrowsky method is 4. It also says that the Ostrowsky's method is optimal in the sense that it satisfies the Kung-Traub conjecture (which states that the maximum attainable order of convergence for an algorithm with $$n$$ function evaluations is $$2^{n-1}$$, neither Halley's nor Newton's are optimal in such sense.\n\nI'm not sure about the first reference, but the other two are peer reviewed publications, so I assume them to be safe sources.\n\nI cannot find now your algorithms description (didn't they were in this thread or in another one?) so, how many function evaluations do they need on each iteration?\n\nObtaining the computational order of convergence COC of your algorithm seems not to be a hard task (only 3 iterations are needed for some test function/root combinations). Such COC combined with the number of function evaluations needed on each iteration will give us all a much better indication of your algorithm performance.\n\nRegards.\n\nEdit: I located your algorithm in the other thread (sorry I forgot it). It needs four function evaluations on each iteration. Supposing its order of convergence is 4, its efficiency index is $$\\sqrt{4}=1.4142...$$. As Ostrowsky's algorithm only requires 3 function evaluations on each iteration and it has an order of convergence of 4, its efficiency index is $$\\sqrt{4}=1.5874...$$, which is better. If the order of convergence of your algorithm is not 4, but 3, then the situation is even worse. To compete with the Ostrowsky's algorithm (in terms of the efficiency index) we need your algorithm to be of order 6-7. For comparison, the efficiency index of Newton's is also 1.4142... and that for Halley is 1.44225...\n\nThank you for the interesting information. I will look at the various articles you mentioned in your links.\n\nI have a question for you. Given a function f(x) with an initial guess x0 and a specified tolerance. If I apply root-seeking algorithm AL1, which has an efficient index EI1, and it takes N1 iterations to refine the root. Can I predict the number of iterations N2 for another algorithm AL2 with an efficiency index EI2? If we can do that, then we can estimate the efficiency index EI3 of algorithm AL3, compared with algorithm AL1, given the number of iterations N1 and N3 for both methods (which the initial guess and tolerance being the same) and an Efficiency Index EF1 for AL1.\n\nNamir\n(01-19-2017 03:23 AM)Claudio L. Wrote: [ -> ]\n(01-18-2017 11:53 PM)Namir Wrote: [ -> ]I am not sure that Ostrowski's method has an order 4 of convergence. Any reference that confirm this?\n\nNamir\n\nThe paper I cited, shows at the very top on page 78 (it's actually the third page) that plain Newton has order 2, Ostrowski has order 4, and another formula has order 8. It says \"it's well established\", so I guess it must be true.\n\nYou have to distinguish between local- and global error. Plain Newton is simply Tayler series Expansion of 1st order:\n\nf(x_(n+1)) = f(x_n) + hf'(x_n) + (1/2)h^2f''(ceta),\n\nwhere h= x_(n+1)-x_n, ceta in (x_n+1,x_n) and R:=(1/2)h^2f''(ceta) is the term defining the local error (of each step). That is, locally plain Newton is o(h^2), i.e. quadratic. The global error though (the accumulated error of all N steps ) is o(Nh^2)=o(h), i.e. linear behavior. Normally you are interested in the total accumulated error, i.e. in the global error. So to my understanding plain Newton is a linear scheme.\n\nJuergen\nUsing Taylor series can easily explain the order of convergence for Newton, Halley, and Halston. But as the algorithms becomes more complication, generating one or more additional intermediate guesses per iteration, this get complicated.\n\nI was asking in a previous message whether the number of iterations can be estimated using the efficiency index, if we know the number of iterations achieved by another algorithm with a known efficiency index--- for solving the root of the same function, using the same initial guess and tolerance value for the refined root.\n\nMy own perception is that the efficiency index is a qualitative indicator that gives you a general idea about the convergence rate. I doubt there exists a general formula for what I am asking above.\n\nNamir\n(01-20-2017 01:24 AM)Namir Wrote: [ -> ]My own perception is that the efficiency index is a qualitative indicator that gives you a general idea about the convergence rate. I doubt there exists a general formula for what I am asking above.\n\nThat's also my perception.\n\nRegarding your question, seeing that algorithms can behave very differently (even with different orders of convergence) upon different functions and even around different roots of the same function, I also doubt that there's a way to ascertain the required number of iterations for a given algorithm to converge to a given root of a given function.\n\nI think that what we can do is to build tables such that given here http://article.sapub.org/10.5923.j.ajcam...01.03.html in order to \"have a feeling\" about the behaviour of an algorithm compared to others.\n\nRegards.\nIf you download the ZIP file from my web site, you get the report and an Excel file that has worksheets for the dozen test functions. What I observed is that in the majority of the cases, the methods of Halley and Ostrowski give the same results or don't differ by more than one iteration (both require three function calls per iteration). The results DO SHOW a consistent improvement over Newton's method. You can say that the methods of Halley and Ostrowski have a higher convergence rate than that of Newton. My new algorithm (which uses the Ostrowski's approach to enhance Halley) shows several cases where either the number of iterations or both the number of iterations AND number of function calls is less than that of Halley and Ostrowski. Since I developed the new algorithm using an empirical/heuristic approach I did not yield a long set of mathematical derivations that indicate the convergence rate. It may well be at least one order more than that of Ostrowski's method. It's hard to measure ... compared to, say determining the order of array sorting methods where you can widely vary the array size and calculate the number of array element comparisons and number of element swaps. See my article about enhancing the CombSort method where I was able to calculate the sort order of this method in Tables 3 and 4 of the article.\n(01-20-2017 08:59 AM)emece67 Wrote: [ -> ]\n(01-20-2017 01:24 AM)Namir Wrote: [ -> ]My own perception is that the efficiency index is a qualitative indicator that gives you a general idea about the convergence rate. I doubt there exists a general formula for what I am asking above.\n\nThat's also my perception.\n\nRegarding your question, seeing that algorithms can behave very differently (even with different orders of convergence) upon different functions and even around different roots of the same function, I also doubt that there's a way to ascertain the required number of iterations for a given algorithm to converge to a given root of a given function.\n\nI think that what we can do is to build tables such that given here http://article.sapub.org/10.5923.j.ajcam...01.03.html in order to \"have a feeling\" about the behaviour of an algorithm compared to others.\n\nRegards.\n\nRegarding the link to the article you mentioned in your message. Can you check the new algorithm by the author Thukral. I implemented equation 7 in the article and got bizarre results! Perhaps I am doing something wrong? When I replaced the second subtraction in equation 7 with a multiplication, the algorithm worked but was painfully slow to converge!\n\nI suspect typos om the article since the title has one \" Nonlinear Equations of Type f(0)=0\" instead of \" Nonlinear Equations of Type f(x)=0\".\n\nNamir\nPages: 1 2\nReference URL's\n• HP Forums: https://www.hpmuseum.org/forum/index.php\n• :" ]
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https://stats.stackexchange.com/questions/379293/vae-with-mixture-of-gaussian-prior
[ "# VAE with mixture of gaussian prior\n\nI try to understand this paper where they try to use a mixture of Gaussian as a prior, instead of the standard gaussian. There are several things unclear to me though:\n\n1. They say that they set $$\\pi_k = \\frac{1}{K}$$ and draw $$z$$ from Cat($$\\pi$$). But later in equation 5 they parameterize $$p_\\beta(z_k = 1|x, w)$$ by a neural network, and also condition it on the inputs. How does that fit together?\n2. Also in equation 5 they calculate a KL divergence. What is this KL divergence explicitly though? How to optimize it?\n3. They don't write how to optimize the $$z$$-prior term in equation 4. Is there a closed form solution similar to the $$w$$-prior term? Or how would one do that?\n\n## 1 Answer\n\n1. Cat($$\\pi$$) is the prior distribution on $$z$$. $$p_\\beta(z|x,w)$$ is the variational approximation of the posterior of $$z$$.\n\n2. It's the KL between the variational approximation of the posterior of $$x$$ (technically it's just one factor of the mean field variational approximation) and the conditional prior of $$x$$. These are both normal distributions, so computing the KL is easy and differentiable.\n\n3. I believe $$p(z)$$ is just Cat($$\\pi$$), so the KL can be written in closed form.\n\n• So 2. simply with the reparametrization trick? And for 3. what is the closed form of the KL? – Luca Thiede Nov 30 '18 at 19:31" ]
[ null ]
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https://www.dworksheets.com/grade2/match-objects-3dshapes.htm
[ "## Circle Similar Object for 3D Geometry Shape\n\nName\nDate", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Answers Key", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "# Worksheet for matching Objects for given 3D Geometry Shapes\n\nMatch objects for 3d geometry shapes worksheet with answers to practice & learn 2nd grade math problems on geometry is available online for free in printable & downloadable (pdf & image) format. Tap on PRINT, PDF or IMAGE button to print or download this 2nd grade geometry worksheet for circle the similar objects for the given 3D geometric shapes.\n\nHow to Use this Worksheet\n\nIn this 3D geometry shapes worksheet, there are 8 questions with 1 solved example. To practice this worksheet, students are required to circle the similar objects for given 3d geometric shapes as like in the above solved example.\n\nAnswers Key\n\nTeachers, tutors, parents or students can check or validate the completed math workbook of 2nd grade math questions on matching 3D geometry shapes with objects by using the corresponding answers key." ]
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https://math.stackexchange.com/questions/1637959/how-should-i-prove-the-following-algebraic-topology-and-homeomorphism
[ "# How should I prove the following? Algebraic topology and homeomorphism\n\nI am struggling immensely with topology since the start of the course, probably due to its extremity; the explanations are either \"very rough\" or \"very strict and rigid and hard to comprehend.\" Either 0 or 100, no 40 or 50. As a complete newbie, here's a question I am approaching which I managed 20% (if, at all).\n\nThe question is with respect to the following diagram:", null, "Here is the question\n\nFor any $f: X \\rightarrow S^1$, define $\\bar{f}: f^* \\mathbb{R} \\rightarrow \\mathbb{R}$ and $q:f^* \\mathbb{R} \\rightarrow X$, and $p: \\mathbb{R} \\rightarrow S^1$ specifically, $t \\rightarrow e^{2 \\pi i t}$. Prove that for any $x \\in X$, the inverse image $q^{-1}(x) \\subset f^* \\mathbb{R}$ is homeomorphic to $\\mathbb{Z}$ with the discrete topology. $f^*\\mathbb{R}$ is the pullback of $p$ on $f$, defined $f^*\\mathbb{R}= \\{(x,t) \\in X \\times \\mathbb{R} : f(x) = p(t) \\in S^1\\}$\n\n1.$\\,$My remark about topology's extremity; homeomorphism. Sure, I get the \"vague\" idea that it is a type of mapping and just as how say coffee cups can be transformed into a torus but not a sheet of paper, homeomorphic (topological) spaces are \"equivalent.\" That is, a \"homeomorphism exists\" between them. But specifically, what are they? My notes gives me the example $[0,1)$ and $(0,1]$ are homeomorphic with $x \\rightarrow 1-x$.\n\na) I thought homemorphisms are defined in \"topological\" spaces, $[0,1)$ and $(0,1]$ seem to me just \"sets.\" What is the topology defined on them?\n\nb)Sure $x \\rightarrow 1-x$ is a \"map\" but I mean, how does this relate to the \"intuitive rough explanation\" of transforming a torus and a coffee cup? $[0,1)$ is just an interval, a straight line so... a straight line transformed to a straight line? Is that what's going on here?\n\nThen the stuff gets very rigid; homeomorphisms are bijective continuous maps. Well, I can perhaps try to ram the definition down my throat without a great understanding of it, but while people told me \"topology is pretty much about drawing stuff out\" I can't imagine anything as to what \"homeomorphism\" is.\n\nOkay, back to the question, what I figured so far\n\n$(\\mathbb{Z}, \\tau _{disc})$, $\\tau_{disc}$ is the power set, so essentially, this topological space has elements which are all open(right?). So, the homeomorphism between the subset $Q=\\{q^{-1}(x): x \\in X\\}$ should have its preimage i.e. Q to be an open set itself(by definition of \"continuity\" of a map for topological spaces, which a homeomorphism must satisfy).\n\nis all. I get stuck here; I mean, I don't know what $X$ is, I don't know what topology is defined on it(is there? Or do I have the liberty of coming up with whatever that's convenient?) and I have no means of deducing that $Q$ is open. Well, can I define a discrete topology on $Q$ too? That should make every element or subset open in $Q$.\n\nAnd even if I manage to show \"continuity\" I don't know how \"bijectivity\" can be shown.\n\nThe issue is, I really have no means of finding a \"homeomorphism\" in general. How do people show these? A good guess? Intuition? Years of practice? I don't immediately see \"hmm, ah, a map like this might work...or if not, probably this one..yeah that works\"\n\nWould someone please show me how this can be solved? Thank you so much in advance\n\n• What is $f^\\ast\\Bbb R$?\n– Pedro\nFeb 2, 2016 at 21:35\n• Hi just added the definition to it. Feb 2, 2016 at 21:36\n• A few remarks. 1) Intuitively, a homeomorphism is like a \"continuous deformation\". For example, you can deform a half-sphere into a circle. And indeed, they are homeomorphic. a) $[0,1)$ and $(0,1]$ have a natural topology: the topology generated by intersections of open intervals $(a,b)$ with those sets. Such intersections might not be open intervals, because if $0\\in(a,b)$, $0\\in(a,b)\\cap[0,1)$, which is thus $[0,\\max\\{1,b\\})$. b) $x\\mapsto1-x$ is like taking a line segment and flipping it and superimposing it with itself. Might not be what you thought of with \"deformation\" in 1), but it is… Feb 2, 2016 at 21:44\n• … still a homeomorphism. In general, if you deform continuously and bijectively, or translate, or rotate, you are likely to get a homeomorphism. Feb 2, 2016 at 21:45\n• Of course, be careful with \"deformations\": contracting a circle to a point is certainly a continuous deformation, but definitely not a homeomorphism. Feb 2, 2016 at 21:46\n\nIt seems to me that you have all the correct ideas about topology. Topology works best as a mixture of intuition and precision. The fuzzy intuitive dreaming is fun, but it needs to interact correctly with the precise and rigid part. For instance, dreamy intuition can be a helpful step in formulating a precise mathematical description of what is true and what is not true. On the other hand, precise calculation might be helpful in dreaming up the correct picture.\n\nIn your penultimate paragraph where you write \"...I really have no means of finding a homeomorphism...\", you then go on to give a precisely correct description of how one proves that two spaces are homeomorphic: you must somehow dream up an appropriate formula for a homeomorphism, write that formula down precisely, and then prove that the formula you wrote down satisfies the definition of a homeomorphism. Keep in mind, the property that two spaces $X,Y$ are homeomorphic is an existential property:\n\n• $X$ and $Y$ are homeomorphic if there exists a homeomorphism $h:X \\to Y$.\n\nLike any existential property, there are often (usually) no shortcuts to dreaming up a precise description of the appropriate object whose existence is being asserted, and then proving that this object satisfies all the properties needed. But you might have to do some precise work to aid the dreaming up stage.\n\nFor the mathematical question you asked, before you can \"see\" or \"dream up\" or \"intuit\" a correct formula for a homeomeomorphism from the space $q^{-1}(x)$ to the space $\\mathbb{Z}$, you first need to very carefully pick apart the meaning of the expression $q^{-1}(x)$ for $x \\in X$. To do this you should follow your nose through the trail of definitions, aided by your background knowledge of complex numbers, trigonometry, etc.\n\n• First, apply $f$ to $x$, and you get $f(x) \\in S^1$. Give the point a name, perhaps $z=f(x)$.\n• Next, use the definition of $S^1$ to write an expression for $z$. For this problem, the most convenient and appropriate expression might be $$z = f(x) = \\cos(2 \\pi t_0) + i \\sin(2 \\pi t_0) = e^{2 \\pi it_0}, \\quad t_0 \\in [0,1)$$ The reason this is the most convenient and appropriate expression is because it matches up with the description of the map $p$. The number $t_0$ is of course a well-defined number depending only on $z$.\n• Next, use the definition of $p$ and your knowledge of trigonometry etc. to write an expression for $p^{-1}(z)$: $$p^{-1}(z) = \\{t_0 + 2 \\pi n \\, \\bigm| \\, n \\in \\mathbb{Z}\\}$$\n• Next, use the definitions of $f^*\\mathbb{R}$, of $\\bar f$, and of $q$, to show that $$q^{-1}(x) = \\{(x,t) \\, \\bigm| \\, t \\in p^{-1}(z)\\} = \\{(x,t_0 + 2 \\pi n) \\, \\bigm| \\, n \\in \\mathbb{Z} \\}$$\n\nNow can you write down a formula for a homeomorphism $q^{-1}(x) \\mapsto \\mathbb{Z}$?\n\n• Thanks for all the help, so now I need some map $(x,t) \\rightarrow k$ where $k \\in \\mathbb{Z}$ yes? My issue is, because I don't know what $X$ is(real?complex?integers? rational? irrational?) I need to come up with a map that regardless of whatever the elements of $x$ is, it will take $(x,t)$ and spit out an integer... yes? Does something like a step function(maybe floor or ceiling function) qualify as a map..? But then I guess it's not bijective... Feb 3, 2016 at 17:40\n• @JohnTrail notice how all points of $q^{-1}(x)$ have $x$ as their first component and a number as the second. You can very well neglect the first component: $q^{-1}(x)$ is clearly in bijection with the set $p^{-1}(z)$ via the projection onto the second component, and I claim this map is a homeomorphism if on $q^{-1}(x)$ we place the topology induced on it by the product topology on $f^\\ast\\mathbb R$ and on $p^{-1}(z)$ that induced by the euclidean topology on $\\mathbb R$. Which btw are both discrete topologies. Can you see a way of extracting an integer from an element of $p^{-1}(z)$,… Feb 3, 2016 at 22:23\n• …directly from the way Lee has written the elements of that set? HINT: they depend on an integer parameter… Feb 3, 2016 at 22:24\n• Following up on the further hint of @MickG, what you need is some map $(x,t_0+2\\pi n) \\mapsto k$ where $k \\in \\mathbb{Z}$. Feb 4, 2016 at 15:01" ]
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https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.leastsq.html
[ "# scipy.optimize.leastsq¶\n\nscipy.optimize.leastsq(func, x0, args=(), Dfun=None, full_output=0, col_deriv=0, ftol=1.49012e-08, xtol=1.49012e-08, gtol=0.0, maxfev=0, epsfcn=None, factor=100, diag=None)[source]\n\nMinimize the sum of squares of a set of equations.\n\nx = arg min(sum(func(y)**2,axis=0))\ny\n\nParameters: func : callable should take at least one (possibly length N vector) argument and returns M floating point numbers. It must not return NaNs or fitting might fail. x0 : ndarray The starting estimate for the minimization. args : tuple, optional Any extra arguments to func are placed in this tuple. Dfun : callable, optional A function or method to compute the Jacobian of func with derivatives across the rows. If this is None, the Jacobian will be estimated. full_output : bool, optional non-zero to return all optional outputs. col_deriv : bool, optional non-zero to specify that the Jacobian function computes derivatives down the columns (faster, because there is no transpose operation). ftol : float, optional Relative error desired in the sum of squares. xtol : float, optional Relative error desired in the approximate solution. gtol : float, optional Orthogonality desired between the function vector and the columns of the Jacobian. maxfev : int, optional The maximum number of calls to the function. If Dfun is provided then the default maxfev is 100*(N+1) where N is the number of elements in x0, otherwise the default maxfev is 200*(N+1). epsfcn : float, optional A variable used in determining a suitable step length for the forward- difference approximation of the Jacobian (for Dfun=None). Normally the actual step length will be sqrt(epsfcn)*x If epsfcn is less than the machine precision, it is assumed that the relative errors are of the order of the machine precision. factor : float, optional A parameter determining the initial step bound (factor * || diag * x||). Should be in interval (0.1, 100). diag : sequence, optional N positive entries that serve as a scale factors for the variables. x : ndarray The solution (or the result of the last iteration for an unsuccessful call). cov_x : ndarray Uses the fjac and ipvt optional outputs to construct an estimate of the jacobian around the solution. None if a singular matrix encountered (indicates very flat curvature in some direction). This matrix must be multiplied by the residual variance to get the covariance of the parameter estimates – see curve_fit. infodict : dict a dictionary of optional outputs with the key s: nfev The number of function calls fvec The function evaluated at the output fjac A permutation of the R matrix of a QR factorization of the final approximate Jacobian matrix, stored column wise. Together with ipvt, the covariance of the estimate can be approximated. ipvt An integer array of length N which defines a permutation matrix, p, such that fjac*p = q*r, where r is upper triangular with diagonal elements of nonincreasing magnitude. Column j of p is column ipvt(j) of the identity matrix. qtf The vector (transpose(q) * fvec). mesg : str A string message giving information about the cause of failure. ier : int An integer flag. If it is equal to 1, 2, 3 or 4, the solution was found. Otherwise, the solution was not found. In either case, the optional output variable ‘mesg’ gives more information.\n\nNotes\n\n“leastsq” is a wrapper around MINPACK’s lmdif and lmder algorithms.\n\ncov_x is a Jacobian approximation to the Hessian of the least squares objective function. This approximation assumes that the objective function is based on the difference between some observed target data (ydata) and a (non-linear) function of the parameters f(xdata, params)\n\nfunc(params) = ydata - f(xdata, params)\n\n\nso that the objective function is\n\n min sum((ydata - f(xdata, params))**2, axis=0)\nparams\n\n\n#### Previous topic\n\nscipy.optimize.golden\n\n#### Next topic\n\nscipy.optimize.least_squares" ]
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https://www.hindawi.com/journals/je/2013/840596/
[ "/ / Article\n\nResearch Article | Open Access\n\nVolume 2013 |Article ID 840596 | https://doi.org/10.1155/2013/840596\n\nKrishnendu Bhattacharyya, Md. Sharif Uddin, \"Reactive Solute Diffusion in Boundary Layer Flow through a Porous Medium over a Permeable Flat Plate with Power-Law Variation in Surface Concentration\", Journal of Engineering, vol. 2013, Article ID 840596, 7 pages, 2013. https://doi.org/10.1155/2013/840596\n\n# Reactive Solute Diffusion in Boundary Layer Flow through a Porous Medium over a Permeable Flat Plate with Power-Law Variation in Surface Concentration\n\nRevised05 Feb 2013\nAccepted05 Feb 2013\nPublished28 Feb 2013\n\n#### Abstract\n\nThe solute diffusion in boundary layer flow of an incompressible fluid through a porous medium over a porous flat plate with first-order chemical reaction and with variable surface concentration is studied. The reaction rate of the solute is also takenasvariable. The self-similar ordinary differential equations are obtained from the governing partial differential equations using similarity transformations, and then those self-similar equations are solved by shooting technique using forth-order Runge-Kutta method. The analysis shows that the velocity increases with the increase of permeability of the porous medium, whereas the concentration decreases. The thicknesses of momentum and solute boundary layers reduce for suction, and the effect of blowing is opposite. For the inverse variation of wall concentration along the surface, mass absorption at the surface is found in all cases, and in direct variation mass transfer is found. For increase of both the Schmidt number and the reaction rate parameter, the concentration as well as the solute boundary layer thickness decreases.\n\n#### 1. Introduction\n\nThe study of the steady flow of viscous incompressible fluid has acquired significant attention because of its wide range of engineering applications, and the flow over a flat plate is one of such important problems in fluid dynamics. Blasius first investigated the steady laminar boundary layer viscous flow over a flat plate. The numerical solution for Blasius problem was obtained by Howarth . The existence of a solution for the flow past a flat plate was established by Abu-Sitta . Further some important aspects of boundary layer flow over flat plate were studied by Bataller , Cortell , Wang , Bhattacharyya and Layek , Bhattacharyya et al. , and Bhattacharyya .\n\nThe solute transfer analysis in fluid flow has great importance in expansion of the theory of separation processes and chemical kinetics. Chambré and Young presented the diffusion of a chemically reactive species in a laminar boundary layer flow past a flat plate. The mass transfer effects on the flow over an impulsively started infinite vertical plate under various physical conditions were discussed by Soundalgekar , Soundalgekar et al. and Das et al. . Whereas Afzal and Hussain and Yao studied the mixed convection flows on a flat plate. Fan et al. reported the similarity solution of diffusion of chemically reactive species in mixed convective flow over a horizontal moving plate. Anjalidavi and Kandasamy studied the effects of chemical reaction, heat and mass transfer on laminar flow along a semi-infinite horizontal plate. Makinde and Ogulu investigated the MHD flow with heat and mass transfer past a vertical porous plate in presence of thermal radiation with variable viscosity fluid. Ibrahim and Makinde illustrated the effect of thermal radiation on chemically reacting MHD boundary layer flow of heat and mass transfer past a porous vertical flat plate. The effects of chemical reaction on flow due to the stretching/shrinking of flat sheet were discussed by Andersson et al. , Chamkha et al. , El-Aziz , Bhattacharyya and Layek [23, 24], Bhattacharyya [25, 26], and Bhattacharyya et al. [27, 28].\n\nMass and heat transfer phenomenon in porous medium grabbed the attention of modern researchers due to its huge applications in chemical industries, reservoir engineering, and many other technological processes. Also, a better understanding of convection through porous medium can benefit several areas like insulation design, underground nuclear waste storage sites, grain storage, heat exchangers, filtering devices, metal processing, catalytic reactors, and so forth. Lai and Kulacki showed the coupled heat and mass transfer by mixed convection from a vertical plate in a saturated porous medium. Postelnicu studied the influence of chemical reaction on heat and mass transfer by natural convection from vertical surface in porous media with the Soret and Dufour effects. Mukhopadhyay and Layek described the effects of thermal radiation on forced convective flow and heat transfer over a porous flat plate in a porous medium. Makinde investigated the MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux. Recently, Bhattacharyya et al. have discussed the effects of velocity and thermal slips on the boundary layer flow and heat transfer over a permeable plate in porous medium.\n\nIn this paper, the effect of diffusion of reactive solute on boundary layer flow over a permeable flat plate in porous medium with power-law surface concentration will be discussed. The reaction rate is taken as variable. Using similarity transformations, self-similar ordinary differential equations are obtained from the governing partial differential equations. The transformed ODEs are then solved numerically using well-known shooting method for the solution of boundary value problems. Obtained numerical results are presented in some figures for various values of physical parameter, and the flow and solute transfer characteristics are discussed in detail.\n\n#### 2. Formulation of the Problem\n\nConsider the steady two-dimensional laminar boundary layer flow of viscous incompressible fluid and solute transfer with first-order chemical reaction over a permeable flat plate in porous medium with the surface concentration varying as , where is a real constant and is a power-law exponent that signifies the change of amount of solute along the surface. The external flow consists of a uniform-free stream velocity parallel to the plate and concentration . The -axis is taken along the plate and the -axis is considered normal to the plate. A sketch of the physical flow problem through porous medium is plotted in Figure 1(a). The governing equations for the flow and the solute distribution may be written in usual notation as where is the velocity component in direction, is the velocity component direction, ) is the kinematic fluid viscosity, is the fluid density, is the coefficient of fluid viscosity, is the permeability of the porous medium, is the concentration, and is the diffusion coefficient. is the variable reaction rate and is given by is the reference length, and is a constant.\n\n##### 2.1. Boundary Conditions\n\nThe appropriate boundary conditions for the velocity components and the concentration are given by where is prescribed suction or blowing through the porous plate and is given by /, is a constant with for suction, and for blowing.\n\n#### 3. Method of Solution\n\nWe now introduce the stream function as Now, using relation (6), (1) is automatically satisfied and (2) and (3) become\n\nThe boundary conditions in (4) for the flow reduce to\n\n##### 3.1. Similarity Technique\n\nWe shall introduce the dimensionless variables for and as given below where the similarity variable is defined as , being the local Reynolds number.\n\nIn view of relations in (9) we finally obtain the self-similar equations in the following form: where is the local Darcy number, is a constant, is the Schmidt number, and is the reaction rate parameter. It is important to note that the chemical reaction is of destructive type if , the chemical reaction is of constructive type if , and when , it is the case for non-reactive solute.\n\nEquation (10) can be written as where is the permeability parameter of the porous medium (Mukhopadhyay and Layek ).\n\nThe boundary conditions (8) and (5) finally become where is the suction or blowing parameter, (i.e., ) is corresponding to suction, and (i.e., ) is corresponding to blowing.\n\n##### 3.2. Numerical Method\n\nThe nonlinear self-similar coupled ordinary differential equations (12) and (11) along with the boundary conditions (13) and (14) form a boundary value problem (BVP) and are solved using shooting method [8, 32, 33], by converting it into an initial value problem (IVP). In this method, we have to choose a suitable finite value of , say . We set the following first-order systems: with the boundary conditions To integrate (15) and (16) with (17) as an IVP the values for , that is, and , that is, are needed, but no such values are given. The initial guess values for and are chosen and applying fourth-order Runge-Kutta method a solution is obtained. We compare the calculated values of and at with the given boundary conditions and and adjust values of and using “secant method” to give better approximation for the solution. The step size is taken as . This process is repeated until we get the results asymptotically correct up to the desired accuracy of level.\n\n#### 4. Results and Discussion\n\nThe computed solutions of self-similar ODEs are obtained for several values of parameters involved, namely, the permeability parameter , the suction or blowing parameter , the Schmidt number Sc, the reaction rate parameter , and power-law exponent . The variations in velocity and temperature distributions for the variations in the parameters are presented in some figures. Also, to ensure the accuracy of numerical scheme, a comparison of the velocity profile for and (i.e., for nonporous medium) with the available data provided by Granger in Figure 1(b) and those are found in excellent agreement.\n\nThe velocity and concentration distributions for several value of the permeability parameter are plotted in Figures 2, 3(a) and 3(b). The increase in permeability of the porous medium causes the enhancement of the velocity at a fixed (Figure 2), because the momentum boundary layer thickness is reduced due to the increase in . Two figures of concentration profiles (Figures 3(a) and 3(b)) are shown: one for direct variation of surface concentration () and the other for inverse variation of surface concentration (). For direct variation solute transfer is found from the surface to the fluid, and for inverse variation solute absorption at the surface occurs with concentration overshoot. In both cases, the concentration decreases with increase of permeability parameter. The concentration overshoot reduces with permeability of the porous medium.\n\nNext, the effect of suction or blowing through the permeable plate is discussed. For various values of the suction or blowing parameter , the dimensionless velocity and concentration profiles are plotted in Figures 4, 5(a), and 5(b). For the increase of applied suction, the velocity at a fixed point increases, and, with increasing blowing, the velocity decreases. On the other hand, the concentration decreases with suction and increases with blowing. The concentration overshoot in inverse variation of surface concentration reduces with suction and enhances with blowing. Also, it is important to note that fluid suction causes reduction in solute boundary layer thickness and due to blowing it becomes thicker.\n\nThe effect of the Schmidt number Sc on the solute distribution for positive (direct variation) and negative (inverse variation) values of is depicted in Figures 6(a) and 6(b), respectively. In both cases, with increasing values of Sc, the concentration at a point and solute boundary layer thickness rapidly decrease. Schmidt number is inversely proportional to the diffusion coefficient and so increase of Schmidt number means a decrease in diffusion coefficient, which acts to reduce the solute boundary layer thickness. Here also, concentration overshoot is found when the surface concentration varies inversely along the plate and the overshoot, that is, mass absorption is suppressed with the increase in the Schmidt number Sc. Actually, due to increasing Schmidt number the rate of mass transfer from the surface to the fluid increases.\n\nThe first-order chemical reaction of solute affects the diffusion dynamics. In Figures 7(a) and 7(b), the reactive concentration profiles for several values of reaction rate parameter of the first-order reaction are illustrated. In both cases, positive and negative values of , the concentration overshoot is observed. For direct variation () the overshoot can be seen only for higher negative values reaction rate parameter, that is, for higher constructive chemical reaction. But, for inverse variation () the overshoot is appeared in destructive reaction, and it reduces with higher destructive chemical reaction. Thus destructive reaction causes mass transfer from the surface and constructive reaction results mass absorption at the surface. Also, due to increase in , the solute boundary layer thickness reduces.\n\nNow, it is important to note down the influence of variable surface concentration on the solute distribution. The graphical representations of the concentration profiles for different values of are demonstrated in Figures 8(a) and 8(b). For direct variation, the concentration and solute boundary layer thickness decrease with mass transfer from the surface when increases, that is, when the concentration increases along the surface. For inverse variation, the concentration along the surface decreases with increasing magnitude of , and the effect of inverse variation is opposite to that of direct variation. Also, in inverse variation the mass absorption is found and with increasing magnitude of mass absorption becomes larger.\n\nThe local skin friction coefficient for various values of permeability parameter and suction or blowing parameter is plotted in Figure 9. It is worth noting that the local skin friction coefficient increases with increase suction parameter and permeability parameter, whereas it reduces with increasing blowing.\n\n#### 5. Concluding Remarks\n\nThe investigation focuses on the reactive species diffusion with first-order reaction in boundary layer flow over a porous flat plate in porous medium with power-law variation in surface concentration. Using similarity transformations, self-similar equations are obtained from the governing equations, and then those are solved by shooting method. The study reveals that, with the increase permeability of the porous medium, the velocity increases and the concentration decreases. The suction through the porous plate causes decrease in the momentum and solute boundary layer thicknesses, while due to blowing both boundary layers become thicker. For the increase in Schmidt number and reaction rate parameter the concentration reduces. Due to inverse variation of surface concentration (negative value of power-law exponent of surface concentration) mass absorption at the surface is observed in all cases, and mass transfer from the surface is found for direction variation (positive value of power-law exponent of surface concentration). But for higher constructive chemical reaction, mass absorption is seen even in direct variation of surface concentration along the surface.\n\n#### Acknowledgment\n\nThe authors are thankful to the referee for his valuable comments and suggestions, which definitely helped to improve the paper.\n\n1. H. Blasius, “Grenzschichten in Flüssigkeiten mit kleiner Reibung,” Zeitschrift für Mathematik und Physik, vol. 56, pp. 1–37, 1908. View at: Google Scholar\n2. L. Howarth, “On the solution of the laminar boundary layer equations,” Proceedings of the Royal Society of London A, vol. 164, pp. 547–579, 1938. View at: Google Scholar\n3. A. M. M. 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Makinde, “On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 19, no. 3-4, pp. 546–554, 2009. View at: Publisher Site | Google Scholar\n33. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Steady boundary layer slip flow and heat transfer thorough porous medium over a flat plate subjected to suction/blowing,” Journal of Petroleum Science and Engineering, vol. 78, pp. 304–309, 2011. View at: Google Scholar\n34. R. A. Granger, Fluid Mechanics, Dover, New York, NY, USA, 1995." ]
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https://socratic.org/questions/how-do-you-simplify-root3-16-root3-54
[ "# How do you simplify root3(16) +root3(54) ?\n\nJun 12, 2017\n\nSee a solution process below:\n\n#### Explanation:\n\nFirst, rewrite the expression by rewriting each radical using this rule for radicals:\n\n$\\sqrt[n]{\\textcolor{red}{a}} \\cdot \\sqrt[n]{\\textcolor{b l u e}{b}} = \\sqrt[n]{\\textcolor{red}{a}} \\cdot \\sqrt[n]{\\textcolor{b l u e}{b}}$\n\n$\\sqrt{16} + \\sqrt{54} \\implies \\sqrt{\\textcolor{red}{8} \\cdot \\textcolor{b l u e}{2}} + \\sqrt{\\textcolor{red}{27} \\cdot \\textcolor{b l u e}{2}} \\implies$\n\n$\\left(\\sqrt{\\textcolor{red}{8}} \\cdot \\sqrt{\\textcolor{b l u e}{2}}\\right) + \\left(\\sqrt{\\textcolor{red}{27}} \\cdot \\sqrt{\\textcolor{b l u e}{2}}\\right) \\implies$\n\n$2 \\sqrt{\\textcolor{b l u e}{2}} + 3 \\sqrt{\\textcolor{b l u e}{2}}$\n\nWe can factor and combine:\n\n$\\left(2 + 3\\right) \\sqrt{\\textcolor{b l u e}{2}} \\implies$\n\n$5 \\sqrt{\\textcolor{b l u e}{2}}$" ]
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https://forums.phpfreaks.com/profile/166578-steeve_84/
[ "", null, "", null, "# steeve_84\n\nNew Members\n\n9\n\n## Community Reputation\n\n0 Neutral\n\n• Rank\nNewbie\n1. Hi! Thanks for all reply, I solved it. \\$link = new mysqli(\\$host,\\$user,\\$pass,\\$mydb); \\$link->query (\"DELETE FROM \" .\\$table. \"\"); if ((\\$handle = fopen(\\$file, \"r\")) !== FALSE) { while ((\\$data = fgetcsv(\\$handle, 10000, \";\")) !== FALSE) { if( count(\\$data) !== 36 ) continue; \\$i=0; foreach(\\$data as \\$elem){ \\$data[\\$i] = str_replace(\"'\",\"\",\\$elem); \\$i++; } \\$sql = \"INSERT IGNORE INTO \" .\\$table. \" VALUES ('\" . implode(\"','\", \\$data) . \"');\"; // echo \\$sql.\"<br \\>\"; \\$link->query (\\$sql) or die (\\$link->error); } fclose(\\$handle); }\n2. I know it, but I want to skip rows, where doesn't match column numbers. Now this rows are 1. and 6434, but the at next time can it be the 6328. or other.\n3. OK, changed to: \\$sql=\"INSERT IGNORE INTO \" .\\$table. \"VALUES (\" . implode(\"';'\", \\$data) . \");\"; \\$link->query (\\$sql) or die (\\$link->error); You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '0';'';'';'';'';'';'0';'0';'0';'0';'Engedményekhez';'';'';'LOR';'';'0';'';'0';'';' at line 1 If I import the source file at phpmyadmin sql says invalid number of columns.\n4. I'm so sorry. Changed: <?php \\$row = 1; \\$host = \"localhost\"; \\$user = \"root\"; \\$pass = \"pass\"; \\$mydb = \"database\"; \\$table = \"gumiflex\"; \\$link = new mysqli(\\$host,\\$user,\\$pass,\\$mydb); \\$link->query (\"DELETE FROM \" .\\$table. \"\"); if ((\\$handle = fopen(\"ftp://user:[email protected]/data.csv\", \"r\")) !== FALSE) { while ((\\$data = fgetcsv(\\$handle, 10000, \";\")) !== FALSE) { if( count(\\$data) !== 36 ) continue; \\$num = count(\\$data); \\$row++; for (\\$c=0; \\$c <= \\$num; \\$c++) { \\$link->query (\"INSERT IGNORE INTO \" .\\$table. \"VALUES (\" . implode(\"';'\", \\$data) . \"\") or die (\\$link->error); } } fclose(\\$handle); } ?> You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '0';'';'';'';'';'';'0';'0';'0';'0';'Engedményekhez';'';'';'LOR';'';'0';'';'0';'';' at line 1\n5. Hi! I make an another script to import data to my db, but its too wrong... I don't have any idea to solve this. I can't import the fields because at source file are some rows with invalid number of columns, but the scipt don't skip this rows, only write data to the screen but the insert script isn't work. Help Pls! <?php \\$row = 1; \\$host = \"localhost\"; \\$user = \"root\"; \\$pass = \"pass\"; \\$mydb = \"database\"; \\$table = \"gumiflex\"; \\$link = new mysqli(\\$host,\\$user,\\$pass,\\$mydb); \\$link->query (\"DELETE FROM \" .\\$table. \"\"); if ((\\$handle = fopen(\"ftp://user:[email protected]/data.csv\", \"r\")) !== FALSE) { while ((\\$data = fgetcsv(\\$handle, 10000, \";\")) !== FALSE) { if( count(\\$data) !== 36 ) continue; \\$num = count(\\$data); \\$row++; for (\\$c=2; \\$c <= \\$num; \\$c++) { echo \\$data[\\$c].\";\"; \\$link->query (\"INSERT IGNORE INTO \" .\\$table. \"VALUES\" .\\$data[\\$c]); } } fclose(\\$handle); } ?>\n6. Thanks for reply. I make this change, but nothing happens. No errors, simply writes 'OK'.\n7. So.. I changed the code for continue when the column number different from 35, but the data dont writed to table, only the delete query works. <?php \\$addauto = 1; \\$delimiter = ';'; \\$csoport_kod = new mysqli('localhost', 'root', '', '2012'); \\$csoport_kod->query(\"DELETE FROM gf1\"); \\$i=1; if ((\\$handle = fopen(\"ftp://2012.com/gf1.csv\", \"r\")) !== FALSE) { while ((\\$data = fgetcsv(\\$handle, 10000, \\$delimiter)) !== FALSE) { if (count(\\$data) !== 35) continue; foreach(\\$data as \\$i => \\$content) { \\$data[\\$i] = \\$csoport_kod->real_escape_string(\\$content); } \\$csoport_kod->query (\"INSERT INTO gf1 VALUES('\" . implode(\"','\", \\$data) . \"');\"); } fclose(\\$handle); } echo 'OK' ?> At the source file the first and 4637. rows have different columns. If I delete this rows the script works, but its not automatic :/\n8. Thx for your reply, The source file I can't change... I make this change, but isnt working... Any other ideas?\n9. Hi, I have a problem with importing .csv file. The content of file have some rows with invalid culomn number. Can I skip rows with this error? My code is: <?php \\$addauto = 1; \\$delimiter = ';'; \\$csoport_kod = new mysqli('localhost', 'root', '', '2012'); \\$csoport_kod->query(\"DELETE FROM gf1\"); \\$i=1; if ((\\$handle = fopen(\"ftp://2012.com/gf1.csv\", \"r\")) !== FALSE) { while ((\\$data = fgetcsv(\\$handle, 10000, \\$delimiter)) !== FALSE) { foreach(\\$data as \\$i => \\$content) { \\$data[\\$i] = \\$csoport_kod->real_escape_string(\\$content); } \\$csoport_kod->query (\"INSERT ignore INTO gf1 VALUES('\" . implode(\"','\", \\$data) . \"');\"); } fclose(\\$handle); } echo 'OK' ?> THX!\n×\n\n• #### Activity\n\n• Chat\n×\n• Create New..." ]
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https://www.springerprofessional.de/en/an-introduction-to-hodge-structures/1924562
[ "main-content\n\n## Swipe to navigate through the chapters of this book\n\n2015 | OriginalPaper | Chapter\n\n# An Introduction to Hodge Structures\n\nAuthors: Sara Angela Filippini, Helge Ruddat, Alan Thompson\n\nPublisher: Springer New York\n\n## Abstract\n\nWe begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kähler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This will lead us to the more general definition of a variation of Hodge structure and the Gauss-Manin connection. We then review the basics about mixed Hodge structures with a view towards degenerations of Hodge structures; including the canonical extension of a vector bundle with connection, Schmid’s limiting mixed Hodge structure and Steenbrink’s work in the geometric setting. Finally, we give an outlook about Hodge theory in the Gross-Siebert program.\nFootnotes\n1\nA third characterization of Hodge structures is given in terms of certain representations of $$\\mathrm{Res}_{\\mathbb{C}/\\mathbb{R}}\\mathbb{C}^{{\\ast}}$$ (see, for example, ). More precisely, a rational Hodge structure of weight n on a $$\\mathbb{Q}$$-vector space H can be identified with an algebraic representation $$\\rho: \\mathbb{C}^{{\\ast}}\\rightarrow GL(H_{\\mathbb{R}})$$, where $$H_{\\mathbb{R}}:= H \\otimes _{\\mathbb{Q}}\\mathbb{R}$$, such that the restriction of ρ to $$\\mathbb{R}^{{\\ast}}$$ is given by $$\\rho (\\lambda ) =\\lambda ^{n}$$. From this point of view, it is clearly completely natural to use constructions from multi-linear algebra to produce new Hodge structures.\n\n2\nNote that here we use the original notation by Steenbrink ; the two indices p, q are swapped in .\n\nLiterature\n1.\nBarth, W.P., Hulek, K., Peters, C.A.M., van de Ven, A.: Compact Complex Surfaces. Volume 4 of Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Fogle, A Series of Modern Surveys in Mathematics, 2nd edn. Springer, Berlin/New York (2004)\n2.\nCarlson, J., Müller-Stach, S., Peters, C.A.M.: Period Mappings and Period Domains. Volume 85 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (2003)\n3.\nClemens, C.H.: Degeneration of Kähler manifolds. Duke Math. J. 44(2), 215–290 (1977)\n4.\nDeligne, P.: Théorie de Hodge II. Inst. Hautes Études Sci. Publ. Math. 40, 5–57 (1971)\n5.\nDeligne, P.: Comparaison avec la théorie transcendante. In: Groupes de Monodromie en Géométrie Algébrique. Volume 340 of Lecture Notes in Mathamatics, pp. 116–164. Springer, Berlin/Heidelberg (1973)\n6.\nDeligne, P.: Le formalisme des cycles évanescents. In: Groupes de Monodromie en Géométrie Algébrique. Volume 340 of Lecture Notes in Mathamatics, pp. 82–115. Springer, Berlin/Heidelberg (1973)\n7.\nDeligne, P.: Théorie de Hodge III. Inst. Hautes Études Sci. Publ. Math. 44, 5–77 (1974)\n8.\nDeligne, P.: Local behavior of Hodge structures at infinity. In: Mirror Symmetry, II. Volume 1 of AMS/IP Studies in Advanced Mathematics, pp. 683–699. American Mathematical Society, Providence (1997)\n9.\nGriffiths, P.: Periods of integrals on algebraic manifolds. I. Construction and properties of the modular varieties. Am. J. Math. 90, 568–626 (1968) MATH\n10.\nGriffiths, P.: Periods of integrals on algebraic manifolds. II. Local study of the period mapping. Am. J. Math. 90, 805–865 (1968) MATH\n11.\nGriffiths, P.: On the periods of certain rational integrals. I, II. Ann. Math. (2) 90, 460–495, 496–541 (1969)\n12.\nGriffiths, P.: Periods of integrals on algebraic manifolds. III. Some global differential-geometric properties of the period mapping. Inst. Hautes Études Sci. Publ. Math. 38, 125–180 (1970)\n13.\nGriffiths, P.: Periods of integrals on algebraic manifolds: summary of main results and discussion of open problems. Bull. Am. Math. Soc. 76, 228–296 (1970)\n14.\nGross, M.: Mirror symmetry and the Strominger-Yau-Zaslow conjecture. In: Current Developments in Mathematics 2012, pp. 133–191. International Press, Somerville (2013)\n15.\nGross, M., Katzarkov, L., Ruddat, H.: Towards mirror symmetry for varieties of general type (February 2012, preprint). arXiv:1202.4042\n16.\nGross, M., Siebert, B.: Affine manifolds, log structures, and mirror symmetry. Turkish J. Math. 27(1), 33–60 (2003)\n17.\nGross, M., Siebert, B.: Mirror symmetry via logarithmic degeneration data I. J. Differ. Geom. 72(2), 169–338 (2006)\n18.\nGross, M., Siebert, B.: Mirror symmetry via logarithmic degeneration data II. J. Algebraic Geom. 19(4), 679–780 (2010)\n19.\nGross, M., Siebert, B.: An invitation to toric degenerations. In: Geometry of Special Holonomy and Related Topics. Volume 16 of Surveys in Differential Geometry, pp. 43–78. International Press, Somerville (2011)\n20.\nKempf, G., Knudsen, F., Mumford, D., Saint-Donat, B.: Toroidal Embeddings I. Volume 339 of Lecture Notes in Mathematics. Springer, Berlin/Heidelberg (1973)\n21.\nKulikov, V.: Mixed Hodge Structures and Singularities. Volume 132 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge/New York (1998)\n22.\nMalgrange, B.: Intégrales asymptotiques et monodromie. Ann. Sci. École Norm. Sup. (4) 7, 405–430 (1974)\n23.\nMorrison, D.: The Clemens-Schmid exact sequence and applications. In: Griffiths, P. (ed.) Topics in Transcendental Algebraic Geometry (Princeton, 1981/1982). Volume 106 of Annals of mathematics studies, pp. 101–119. Princeton University Press, Princeton (1984)\n24.\nMorrison, D.: Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians. J. Am. Math. Soc. 6(1), 223–247 (1993)\n25.\nPeters, C.A.M., Steenbrink, J.H.M.: Mixed Hodge Structures. Volume 52 of Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Fogle, A Series of Modern Surveys in Mathematics. Springer, Berlin (2008)\n26.\nRuddat, H., Siebert, B.: Canonical coordinates in toric degenerations. (September 2014, preprint). arXiv:1409.4750\n27.\nRuddat, H.: Log Hodge groups on a toric Calabi-Yau degeneration. In: Mirror Symmetry and Tropical Geometry. Volume 527 of Contemporary Mathematics, pp. 113–164. AMS, Providence (2010)\n28.\nRuddat, H., Sibilla, N., Treumann, D., Zaslow, E.: Skeleta of affine hypersurfaces. Geom. Topol. 18(3), 1343–1395 (2014)\n29.\nSchmid, W.: Variation of Hodge structure: the singularities of the period mapping. Invent. Math. 22, 211–319 (1973)\n30.\nSteenbrink, J.H.M.: Limits of Hodge structures. Invent. Math. 31(3), 229–257 (1975)\n31.\nvan Geemen, B.: Kuga-Satake varieties and the Hodge conjecture. In: Gordon, B.B., Lewis, J.D., Müller-Stach, S., Saito, S., Yui, N. (eds.) The Arithmetic and Geometry of Algebraic Cycles (Proceedings of the NATO Advanced Study Institute held as part of the 1998 CRM Summer School at Banff, AB, 7–19 June 1998). Volume 548 of NATO Science Series C: Mathematical and Physical Sciences, pp. 51–82. Kluwer, Dordrecht (2000)\n32.\nVarčenko, A.N.: Asymptotic behaviour of holomorphic forms determines a mixed Hodge structure. Dokl. Akad. Nauk SSSR 255(5), 1035–1038 (1980) MathSciNet\n33.\nVoisin, C.: Hodge Theory and Complex Algebraic Geometry. I. Volume 76 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (2007)\nTitle\nAn Introduction to Hodge Structures\nAuthors\nSara Angela Filippini\nHelge Ruddat\nAlan Thompson" ]
[ null ]
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https://wiki.seg.org/wiki/AVO_equations
[ "# AVO equations\n\nSeries", null, "Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store\n\nConsider the two elastic half-space layers in Figure 11.2-3e. The Zoeppritz equations (14) can be solved for the reflected and refracted P- and S-wave amplitudes, A1, B1, A2, and B2. However, our interest in exploration seismology is largely the angle-dependency of the P-to-P reflections given by the coefficient A1. Specifically, we wish to infer or possibly estimate elastic parameters of reservoir rocks from reflection amplitudes and relate these parameters to reservoir fluids.\n\nThe exact expression for A1 derived from the solution of the Zoeppritz equations (13) is complicated and not intuitive in terms of its practical use for inferring petrophysical properties of reservoir rocks. The first approximation to the Zoeppritz equation for P-to-P reflection amplitude is given by Bortfeld as\n\n $R(\\theta _{1})={\\frac {1}{2}}\\ln \\left({\\frac {\\alpha _{2}\\rho _{2}\\cos \\theta _{1}}{\\alpha _{1}\\rho _{1}\\cos \\theta _{2}}}\\right)+\\left[2+{\\frac {\\ln \\left({\\frac {\\rho _{2}}{\\rho _{1}}}\\right)}{\\ln \\left({\\frac {\\alpha _{2}}{\\alpha _{1}}}\\right)-\\ln \\left({\\frac {\\alpha _{2}\\beta _{1}}{\\alpha _{1}\\beta _{2}}}\\right)}}\\right]{\\frac {\\beta _{1}^{2}-\\beta _{2}^{2}}{\\alpha _{1}^{2}}}\\sin ^{2}\\theta _{1}.$", null, "(14)\n\n $CE={\\frac {1}{\\sqrt {1+A^{-1}z}}},$", null, "(13a)\n $CE(\\theta )={\\frac {1}{\\sqrt {1+A^{-1}z/\\cos ^{2}\\theta }}},$", null, "(13b)\n\nThe arrangement of the two terms on the right-hand side of equation (14) is based on separating the acoustic (the first term) and the elastic (the second term) effects on reflection amplitudes. As such, equation (14) does not explicitly indicate angle- or offset-dependence of reflection amplitudes; therefore, its practical implementation for AVO analysis has not been considered.\n\nInstead, we shall use the approximation provided by Aki and Richards as the starting point for deriving a series of practical AVO equations. Now that we only need to deal with the P-to-P reflection amplitude A1, we shall switch to the conventional notation by replacing A1 with R(θ) as the angle-dependent reflection amplitude for AVO analysis.\n\nBy assuming that changes in elastic properties of rocks across the layer boundary are small and propagation angles are within the subscritical range, the exact expression for R(θ) given by the Zoeppritz equation can be approximated by \n\n $R(\\theta )=\\left[{\\frac {1}{2}}{\\Big (}1+\\tan ^{2}\\theta {\\Big )}\\right]{\\frac {\\Delta \\alpha }{\\alpha }}-\\left[4{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta \\right]{\\frac {\\Delta \\beta }{\\beta }}+\\left[{\\frac {1}{2}}{\\Big (}1-4{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta {\\Big )}\\right]{\\frac {\\Delta \\rho }{\\rho }},$", null, "(15)\n\nwhere α = (α1 + α2)/2, average P-wave velocity and Δα = (α2α1), β = (β1 + β2)/2, average S-wave velocity and Δβ = β2β1, ρ = (ρ1 + ρ2)/2, average density and Δρ = ρ2ρ1, and θ = (φ1 + φ2)/2, average of the incidence and transmission angles for the P-wave (Figure 11.0-2e).\n\nFigure 11.2-8 shows the angle-dependent reflection amplitude associated with an interface with contrast in P- and S-wave velocities and densities based on the exact Zoeppritz equation, the Bortfeld approximation described by equation (14), and the Aki-Richards approximation described by equation (15) . Note that these approximations closely follow the exact solution within the range of angles of incidence that are achievable by the recording of seismic data used in exploration. For very shallow reflectors, however, the approximate solutions would deviate from the exact solution significantly at very wide angles of incidence.\n\nNote that the Aki-Richards approximation to the angle-dependent reflection amplitude R(θ) given by equation (15) has three parts in terms of Δα/α which describes the fractional change in P-wave velocity across the layer boundary and hence may be referred to as the P-wave reflectivity, Δβ/β which describes the fractional change in the S-wave velocity across the layer boundary and hence may be referred to as the S-wave reflectivity, and Δρ/ρ which describes the fractional change in density across the layer boundary.\n\nIn practice, we do not observe the separate effects of P-wave reflectivity Δα/α, S-wave reflectivity Δβ/β and fractional change in density Δρ/ρ on the reflection amplitudes R(θ). Instead, we observe changes in reflection amplitudes as a function of angle of incidence. In fact, it is the elastic parameters such as the P-wave reflectivity Δα/α, S-wave reflectivity Δβ/β and fractional change in density Δρ/ρ that we wish to estimate from the observed angle-dependent reflection amplitudes. To use the Aki-Richards equation (15) in the inversion of reflection amplitudes for these elastic parameters, we first need to recast it in successive ranges of angle of incidence. This change of philosophy in arranging the terms in the Aki-Richards equation (15) was first introduced by Shuey and led to practical developments in AVO analysis. The new arrangement in terms of successive ranges of angle of incidence is given by\n\n $R(\\theta )=\\left[{\\frac {1}{2}}\\left({\\frac {\\Delta \\alpha }{\\alpha }}+{\\frac {\\Delta \\rho }{\\rho }}\\right)\\right]+\\left[{\\frac {1}{2}}{\\frac {\\Delta \\alpha }{\\alpha }}-4{\\frac {\\beta ^{2}}{\\alpha ^{2}}}{\\frac {\\Delta \\beta }{\\beta }}-2{\\frac {\\beta ^{2}}{\\alpha ^{2}}}{\\frac {\\Delta \\rho }{\\rho }}\\right]\\sin ^{2}\\theta +\\left[{\\frac {1}{2}}{\\frac {\\Delta \\alpha }{\\alpha }}\\right]{\\big (}\\tan ^{2}\\theta -\\sin ^{2}\\theta {\\big )}.$", null, "(16)\n\nAnother practical matter of concern is that the Aki-Richards equation (15) or any of its modifications that we shall derive in this section describe the modeled reflection amplitudes as a function of angle of incidence. However, the observed reflection amplitudes are available from CMP data as a function of offset. A need then arises either to transform the model equation for the reflection amplitudes from angle to offset coordinates or to actually transform the CMP data from offset to angle coordinates. While the first approach is theoretically appealing, the practical schemes are based on the latter approach. We have already discussed such a transformation in the radon transform — the Radon transform using the linear moveout equation or its robust variation in the form of slant stacking. Figure 11.2-9 shows Zoeppritz amplitude curves as a function of angle of incidence and offset .\n\nBased on the theoretical conjecture made earlier by Koefoed that the elastic property that is most directly related to angular dependence of reflection coefficient R(θ) is Poisson’s ratio σ, Shuey introduced a variable transformation from S-wave velocity β to σ. The relationship between the two variables is given by equation (L-49) which we rewrite below as\n\n $\\beta ^{2}={\\frac {1}{2}}\\left({\\frac {1-2\\sigma }{1-\\sigma }}\\right)\\alpha ^{2}$", null, "(17a)\n\nto perform the necessary differentiation\n\n ${\\frac {\\Delta \\beta }{\\beta }}={\\frac {\\Delta \\alpha }{\\alpha }}-{\\frac {1}{2}}{\\frac {\\Delta \\sigma }{(1-\\sigma )(1-2\\sigma )}}.$", null, "(17b)\n\nThe compressional-wave velocity α is given by equation (3b) and the shear-wave velocity β is given by equation (L-47) which is rewritten below as\n\n $\\beta ={\\sqrt {\\frac {\\mu }{\\rho }}},$", null, "(17c)\n $\\alpha ={\\sqrt {\\frac {\\lambda +2\\mu }{\\rho }}}.$", null, "(3b)\n\nwhere μ is Lamé’s constant.\n\nWe also define the P-wave reflection amplitude RP at normal incidence as\n\n $R_{P}={\\frac {1}{2}}\\left({\\frac {\\Delta \\alpha }{\\alpha }}+{\\frac {\\Delta \\rho }{\\rho }}\\right).$", null, "(18)\n\nSubstitute equations (17a), (17b), and (18) into the Aki-Richards equation (16) and perform some algebraic simplification to obtain\n\n $R(\\theta )=R_{P}+\\left[{\\frac {1}{2}}{\\frac {\\Delta \\alpha }{\\alpha }}-\\left(2{\\frac {\\Delta \\alpha }{\\alpha }}+{\\frac {\\Delta \\rho }{\\rho }}\\right)\\left({\\frac {1-2\\sigma }{1-\\sigma }}\\right)+{\\frac {\\Delta \\sigma }{(1-\\sigma )^{2}}}\\right]\\sin ^{2}\\theta +\\left[{\\frac {1}{2}}{\\frac {\\Delta \\alpha }{\\alpha }}\\right](\\tan ^{2}\\theta -\\sin ^{2}\\theta ).$", null, "(19)\n\nDefine a new term H\n\n $H={\\frac {\\Delta \\alpha /\\alpha }{\\Delta \\alpha /\\alpha +\\Delta \\rho /\\rho }},$", null, "(20)\n\nand by way of equation (18) note that\n\n ${\\frac {\\Delta \\alpha }{\\alpha }}=2\\,R_{P}H.$", null, "(21a)\n\nNext combine equations (20) and (21a) to obtain\n\n ${\\frac {\\Delta \\rho }{\\rho }}=2\\,R_{P}(1-H).$", null, "(21b)\n\nFinally, substitute equations (21a) and (21b) into the second term on the right-hand side of equation (19) to obtain\n\n $R(\\theta )=R_{P}+\\left[R_{P}H_{0}+{\\frac {\\Delta \\sigma }{(1-\\sigma )^{2}}}\\right]\\sin ^{2}\\theta +\\left[{\\frac {1}{2}}{\\frac {\\Delta \\alpha }{\\alpha }}\\right](\\tan ^{2}\\theta -\\sin ^{2}\\theta ),$", null, "(22)\n\nwhere\n\n $H_{0}=H-2(1+H){\\frac {1-2\\sigma }{1-\\sigma }}.$", null, "(23)\n\nEquation (22) is known as Shuey’s three-term AVO equation. The first term RP is the reflection amplitude at normal incidence. At intermediate angles (0 < θ < 30 degrees), the third term may be dropped, thus leading to a two-term approximation\n\n $R(\\theta )=R_{P}+G\\sin ^{2}\\theta ,$", null, "(24)\n\nwhere\n\n $G=R_{P}H_{0}+{\\frac {\\Delta \\sigma }{(1-\\sigma )^{2}}}.$", null, "(25)", null, "Figure 11.2-9  Reflection and refraction amplitude curves as a function of offset and angle of incidence. P1, S1: reflected P- and S-waves, P2, S2: transmitted P- and S-waves. .\n\nEquation (24) is known as Shuey’s two-term AVO equation. In practice, amplitudes picked along a moveout-corrected event on a CMP gather plotted against sin2 θ can be fitted to a straight line. The slope of the line gives the AVO gradient attribute and the ordinate at zero angle gives the AVO intercept attribute. The AVO gradient given by equation (25) is directly related to change in Poisson’s ratio Δσ, which in turn, is directly related to fluid saturation in reservoir rocks. The AVO intercept attribute represents the reflectivity RP at normal incidence. Therefore, the AVO intercept attribute, in lieu of conventional stack, can be used as input to derive the acoustic impedance attribute (acoustic impedance estimation), which is indirectly related to porosity in reservoir rocks.\n\nShown in Figure 11.2-10a is a portion of a section derived from 2-D prestack time migration. The objective is to identify fluid-saturated reservoir zones at the apex and the flanks of the structural closure. This image section is derived from the stacking of common-reflection-point (CRP) gathers associated with the prestack time-migrated data. The CRP gather in Figure 11.2-10b shows three events with amplitude variations with offset which are plotted in Figure 11.2-10c. By using Shuey’s equation (24), the AVO gradient and intercept sections are computed from the CRP gathers as shown in Figures 11.2-11 and 11.2-12, respectively. Note that the gradient section exhibits a group of AVO anomalies in the vicinity of the structural apex, possibly indicating fluid-saturated reservoir rocks.\n\nAt large angles of incidence beyond 30 degrees, the third term in equation (22) gradually becomes dominant. Note that this term is related directly to fractional change in P-wave velocity, Δα/α. So, not only the reflection traveltimes at far offsets (normal moveout) corresponding to large angles of incidence, but also the reflection amplitudes at large angles of incidence make the biggest contribution to the resolution needed to estimate the changes in P-wave velocities.\n\nThe two-term equation (24) can be specialized for a specific value of Poisson’s ratio, σ = 1/3 and H0 = −1 so that equation (25) takes the form\n\n $G=-R_{P}+{\\frac {9}{4}}\\Delta \\sigma ,$", null, "(26)\n\nwhich can be solved for the change in Poisson’s ratio across a layer boundary\n\n $\\Delta \\sigma ={\\frac {4}{9}}(R_{P}+G).$", null, "(27)\n\nThis is the AVO attribute equation for estimating changes in Poisson’s ratio . Actually, as described by equation (27), this attribute is the scaled sum of the AVO intercept RP and AVO gradient G attributes.\n\nBy recasting the first-order approximation to the Zoeppritz equation, Wiggins and Spratt derived a practical expression for S-wave reflectivity. First, drop the term with tan2 θ in equation (16) and rearrange the remaining terms to obtain\n\n $R(\\theta )=\\left[{\\frac {1}{2}}\\left({\\frac {\\Delta \\alpha }{\\alpha }}+{\\frac {\\Delta \\rho }{\\rho }}\\right)\\right]+\\left\\{\\left[{\\frac {1}{2}}\\left({\\frac {\\Delta \\alpha }{\\alpha }}+{\\frac {\\Delta \\rho }{\\rho }}\\right)\\right]-8{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\left[{\\frac {1}{2}}\\left({\\frac {\\Delta \\beta }{\\beta }}+{\\frac {\\Delta \\rho }{\\rho }}\\right)\\right]\\right\\}\\sin ^{2}\\theta +\\left[2{\\frac {\\beta ^{2}}{\\alpha ^{2}}}{\\frac {\\Delta \\rho }{\\rho }}-{\\frac {1}{2}}{\\frac {\\Delta \\rho }{\\rho }}\\right]\\sin ^{2}\\theta$", null, "(28)\n\nsuch that, much like the definition for the P-wave reflectivity RP given by equation (18), an expression for the S-wave reflectivity RS\n\n $R_{S}={\\frac {1}{2}}\\left({\\frac {\\Delta \\beta }{\\beta }}+{\\frac {\\Delta \\rho }{\\rho }}\\right)$", null, "(29)\n\ncan be explicitly inserted back into equation (28) to get\n\n $\\displaystyle R(\\theta)=R_P+\\left(R_P-8\\frac{\\beta^2}{\\alpha^2}R_S\\right)\\sin^2\\theta + \\left(2\\frac{\\beta^2}{\\alpha^2}-\\frac{1}{2}\\right)\\frac{\\Delta\\rho}{\\rho}\\sin^2\\theta.$ (30)\n\nSet β/α = 0.5 to make the last term on the right-hand side vanish and obtain \n\n $\\displaystyle R(\\theta)=R_P+(R_P-2\\,R_S)\\sin^2\\theta.$ (31)\n\nThis equation is of the form given by equation (24) where\n\n $\\displaystyle G=R_P-2\\,R_S,$ (32)\n\nwhich can be rewritten explicitly in terms of the shear-wave reflectivity RS\n\n $R_{S}={\\frac {1}{2}}(R_{P}-G).$", null, "(33)\n\nThis is the AVO attribute equation for estimating the shear-wave reflectivity. Given the AVO intercept RP and AVO gradient G attributes, simply take half of the difference between the two attributes to derive the shear-wave reflectivity RS as described by equation (33).\n\nFigure 11.2-13 shows the reflection amplitudes as a function of angle as predicted by equation (31) for three combinations of RP and RS. Note that equation (31) is a good approximation to the P-to-P reflection amplitudes as predicted by the exact Zoeppritz equation up to nearly 30 degrees of angles of incidence.\n\nReturn to the Aki-Richards equation (15) and consider the case of N-fold CMP data represented in the domain of angle of incidence. Note that the reflection amplitude R(θ) is a linear combination of three elastic parameters — P-wave reflectivity Δα/α, S-wave reflectivity Δβ/β and fractional change in density Δρ/ρ.\n\nSmith and Gidlow argue in favor of solving for only two of the three parameters by making use of the empirical relation between density ρ and P-wave velocity α :\n\n $\\rho =k\\alpha ^{1/4},$", null, "(34a)\n\nwhere k is a scalar. This relation holds for most water-saturated rocks. Differentiate to get\n\n ${\\frac {\\Delta \\rho }{\\rho }}={\\frac {1}{4}}{\\frac {\\Delta \\alpha }{\\alpha }}.$", null, "(34b)\n\nNow substitute equation (34b) into the original Aki-Richards equation (15) and combine the terms with Δα/α\n\n $R(\\theta )=\\left[{\\frac {1}{2}}\\left(1+\\tan ^{2}\\theta \\right)+{\\frac {1}{8}}\\left(1-4{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta \\right)\\right]{\\frac {\\Delta \\alpha }{\\alpha }}-\\left[4{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta \\right]{\\frac {\\Delta \\beta }{\\beta }}.$", null, "(35)\n\nSimplify the algebra to obtain the desired two-parameter model equation for prestack amplitude inversion (Section L.6)\n\n $R(\\theta )=\\left[{\\frac {5}{8}}-{\\frac {1}{2}}{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta +{\\frac {1}{2}}\\tan ^{2}\\theta \\right]{\\frac {\\Delta \\alpha }{\\alpha }}-\\left[4{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta \\right]{\\frac {\\Delta \\beta }{\\beta }}.$", null, "(36)\n\nRedefine the coefficients ai and bi and write the discrete form of equation (36)\n\n $R_{i}=a_{i}{\\frac {\\Delta \\alpha }{\\alpha }}+b_{i}{\\frac {\\Delta \\beta }{\\beta }},$", null, "(37)\n\nwhere\n\n $\\displaystyle a_i=\\frac{5}{8}-\\frac{1}{2}\\frac{\\beta^2}{\\alpha^2}\\sin^2\\theta_i+\\frac{1}{2}\\tan^2\\theta_i$ (38a)\n\nand\n\n $\\displaystyle b_i=-4\\frac{\\beta^2}{\\alpha^2}\\sin^2\\theta_i.$ (38b)\n\nConsider the case of N-fold CMP data represented in the domain of angle of incidence. We have, for each CMP location and for a specific reflection event associated with a layer boundary, N equations of the form as equation (37) and two unknowns — Δα/α and Δβ/β. We have more equations than unknowns; hence, we encounter yet another example of a generalized linear inversion (GLI) problem (Section J.1). The objective is to determine the two parameters such that the difference between the modeled reflection amplitudes Ri represented by equation (37) and the observed reflection amplitudes Xi is minimum in the least-squares sense .\n\nThe GLI solution in matrix form is given by (Section L.6)\n\n ${\\begin{pmatrix}\\sum \\nolimits _{i}^{N}\\,a_{i}^{2}&\\sum \\nolimits _{i}^{N}\\,a_{i}b_{i}\\\\\\sum \\nolimits _{i}^{N}\\,a_{i}b_{i}&\\sum \\nolimits _{i}^{N}\\,b_{i}^{2}\\end{pmatrix}}{\\begin{pmatrix}{\\frac {\\Delta \\alpha }{\\alpha }}\\\\{\\frac {\\Delta \\beta }{\\beta }}\\end{pmatrix}}={\\begin{pmatrix}\\sum \\nolimits _{i}^{N}\\,a_{i}X_{i}\\\\\\sum \\nolimits _{i}^{N}\\,b_{i}X_{i}\\end{pmatrix}}.$", null, "(39)\n\nThis matrix equation is solved for the two parameters — P-wave reflectivity Δα/α and S-wave reflectivity Δβ/β. Note from the definitions of the coefficients ai and bi given by equations (38a,38b) that you have to choose a value for the ratio β/α to compute the two reflectivities.\n\nShown in Figure 11.2-14 are the P- and S-wave reflectivity sections that were derived from prestack amplitude inversion applied to the CRP gathers associated with the data shown in Figure 11.2-10a. Note the AVO anomalies along the flanks of the structural closure. It is apparent that some of the AVO anomalies in the P-wave reflectivity section stand out more distinctively as compared with those in the S-wave reflectivity section. This may be related to the fact that changing from brine to gas causes a small change in S-wave reflectivity, while it causes a significant change in P-wave reflectivity. Such inference is supported by the laboratory measurements of P- and S-wave reflectivities at a gas-brine interface in sandstones . Figure 11.2-15 shows P-wave reflectivities for a group of reservoir sandstones in which the pore fluid changes from brine to gas. For rocks with low induration (weak rocks), there is a large change in P-wave reflectivity, while for rocks with high induration the change becomes less significant (Figure 11.2-15a). The change in S-wave reflectivity is negligible for rocks with low and high induration (Figure 11.2-15b). A demonstrative field data example of P- and S-wave reflectivity contrasts that arise from a change in lithology and fluid saturation is shown in Figure 11.2-16.\n\nRefer to equation (17b) and note that the difference between the P-wave and S-wave reflectivities is related to change in Poisson’s ratio Δσ — a direct hydrocarbon indicator. In fact, Smith and Gidlow have coined the term pseudo-Poisson reflectivity to describe the difference between the P-wave and S-wave reflectivities\n\n ${\\frac {\\Delta {\\tilde {\\sigma }}}{\\tilde {\\sigma }}}={\\frac {\\Delta \\alpha }{\\alpha }}-{\\frac {\\Delta \\beta }{\\beta }}.$", null, "(40)\n\nNote from equation (17b) that the pseudo-Poisson reflectivity ${\\Delta {\\tilde {\\sigma }}}/{\\tilde {\\sigma }}$", null, "is not exactly the same as what may be referred to as the proper Poisson reflectivity Δσ/σ. If we define the ratio\n\n ${\\tilde {\\sigma }}={\\frac {\\alpha }{\\beta }}$", null, "(41a)\n\nby differentiation, we can derive the difference relation given by equation (40) and thus show that\n\n ${\\frac {\\Delta {\\tilde {\\sigma }}}{\\tilde {\\sigma }}}={\\frac {\\Delta (\\alpha /\\beta )}{\\alpha /\\beta }}.$", null, "(41b)\n\nCastagna defined a straight line in the plane of S-wave velocity versus P-wave velocity as shown in Figure 11.2-17. This is called the mudrock line and is represented by the equation\n\n $\\alpha =c_{0}+c_{1}\\beta ,$", null, "(42)\n\nwhere the scalar coefficients c0 and c1 are empirically determined for various types of rocks. Suggested values for these scalars are c0 = 1360 and c1 = 1.16 for water-saturated clastics . Gas-bearing sandstones lie above the mudrock line, and carbonates lie below the mudrock line as shown on a crossplot of P- and S-wave velocities sketched in Figure 11.2-17. The crossplot shown in Figure 11.2-18 is based on log measurements at a gas-producing well . Note the separation of gas-sandstone cluster from the water-sandstone and shale clusters in the manner as sketched in Figure 11.2-17.\n\nA way to quantify the prospectivity of the reservoir rock of interest is by defining a fluid factor attribute that indicates the position of the rock property with respect to the mudrock line. First, apply differentiation to both sides of equation (42) and note that\n\n ${\\frac {\\Delta \\alpha }{\\alpha }}=c_{1}{\\frac {\\beta }{\\alpha }}{\\frac {\\Delta \\beta }{\\beta }}.$", null, "(43)\n\nThen, define the fluid factor ΔF\n\n $\\Delta F={\\frac {\\Delta \\alpha }{\\alpha }}-c_{1}{\\frac {\\beta }{\\alpha }}{\\frac {\\Delta \\beta }{\\beta }}.$", null, "(44)\n\nIf ΔF is close to zero, it means that you have water-saturated rock. If you have a gas-saturated sandstone, ΔF will be negative at the top and positive at the base of the reservoir unit .\n\nFigure 11.2-19 shows the pseudo-Poisson and fluid-factor sections that were derived from prestack amplitude inversion applied to the CRP gathers associated with the data shown in Figure 11.2-10a. Note the distinctive AVO anomalies along the flanks of the structural closure.\n\nThe two parameters Δα/α and Δβ/β, estimated by using the least-squares solution given by equation (39), represent fractional changes in P- and S-wave velocities. As such, they are related to P- and S-wave reflectivities, ΔIP/IP and ΔIS/IS, respectively, where IP and IS are the P- and S-wave impedances given by\n\n $I_{P}=\\alpha \\rho$", null, "(45a)\n\nand\n\n $I_{S}=\\beta \\rho .$", null, "(45b)\n\nFrom Section L.6, the P- and S-wave reflectivities are given by\n\n ${\\frac {\\Delta I_{P}}{I_{P}}}={\\frac {\\Delta \\alpha }{\\alpha }}+{\\frac {\\Delta \\rho }{\\rho }}$", null, "(46a)\n\nand\n\n ${\\frac {\\Delta I_{S}}{I_{S}}}={\\frac {\\Delta \\beta }{\\beta }}+{\\frac {\\Delta \\rho }{\\rho }}.$", null, "(46b)\n\nAssuming that the density obeys Gardner’s relation given by equation (34a), the P-wave reflectivity ΔIP/IP is simply the fractional change of the P-wave velocity Δα/α scaled by a constant, whereas the S-wave reflectivity ΔIS/IS is a linear combination of the fractional changes of the P- and S-wave velocities, Δα/α and Δβ/β, respectively.\n\nA direct estimation of the P- and S-wave reflectivities given by equations (L-46a,L-46b) can be made by using an alternative formulation of prestack amplitude inversion which is based on transforming the Aki-Richards equation (15) to the new variables ΔIP/IP and ΔIS/IS . Solve equation (46a) for Δα/α and equation (46b) for Δβ/β, and substitute into the Aki-Richards equation (15). Following the algebraic simplification, we obtain (Section L.6)\n\n $R(\\theta )=\\left[{\\frac {1}{2}}\\left(1+\\tan ^{2}\\theta \\right)\\right]{\\frac {\\Delta I_{P}}{I_{P}}}-\\left[4{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta \\right]{\\frac {\\Delta I_{S}}{I_{S}}}-\\left[{\\frac {1}{2}}\\tan ^{2}\\theta -2{\\frac {\\beta ^{2}}{\\alpha ^{2}}}\\sin ^{2}\\theta \\right]{\\frac {\\Delta \\rho }{\\rho }}.$", null, "(47)\n\nGoodway have implemented a specific form of equation (47) to derive the AVO attributes ΔIP/IP and ΔIS/IS. For a specific value of α/β = 2 and small angles of incidence for which tan θ ≈ sin θ, the third term in equation (47) vanishes. Compare equations (18) and (46a), and equations (29) and (46b), and note that equation (47) with the remaining terms takes the form\n\n $R(\\theta )=(1+\\tan ^{2}\\theta )R_{P}-(2\\sin ^{2}\\theta )R_{S}.$", null, "(48)\n\nThe resulting equation then is solved for the P- and S-wave reflectivities, ΔIP/IP = 2RP and ΔIS/IS = 2RS, respectively. Again, consider the case of N-fold CMP data represented in the domain of angle of incidence. In discrete form, equation (48) can be rewritten as\n\n $R_{i}=a_{i}R_{P}+b_{i}R_{S},$", null, "(49)\n\nwhere i is the trace index and the coefficients ai and bi are given by\n\n $a_{i}={\\frac {1}{2}}{\\big (}1+\\tan ^{2}\\theta _{i}{\\big )}$", null, "(50a)\n\nand\n\n $b_{i}=-2\\sin ^{2}\\theta _{i}.$", null, "(50b)\n\nThe reflection amplitude Ri in equation (49) is a linear combination of the two parameters, RP and RS. As for the Smith-Gidlow equation (37), the two parameters, RP and RS, can be estimated for a specific event from CMP data using the least-squares solution given by\n\n $\\displaystyle \\begin{pmatrix} \\sum\\nolimits_i^N\\,a^2_i&\\sum\\nolimits_i^N\\,a_ib_i\\\\ \\sum\\nolimits_i^N\\,a_ib_i&\\sum\\nolimits_i^N\\,b^2_i \\end{pmatrix} \\begin{pmatrix} R_P\\\\ R_S \\end{pmatrix}= \\begin{pmatrix} \\sum\\nolimits_i^N\\,a_iX_i\\\\ \\sum\\nolimits_i^N\\,b_iX_i \\end{pmatrix}.$ (51)\n\nFollowing the estimation of the P-wave reflectivity RP and the S-wave reflectivity RS using the least-squares solution given by equation (51), the P-wave impedance IP and the S-wave impedance IS can be computed by integration.\n\nBy using the impedance attributes IP and IS, Goodway compute two additional AVO attributes in terms of Lamé’s constants scaled by density — λρ and μρ. Substitute equation (3b) into (45a) to get the relation\n\n $(\\lambda +2\\mu )\\rho =I_{P}^{2},$", null, "(52a)\n\nand substitute equation (17c) into equation (45b) to get the relation\n\n $\\displaystyle \\mu\\rho=I^2_S.$ (52b)\n\nNote from equations (52a,52b) that\n\n $\\lambda \\rho =I_{P}^{2}-2\\,I_{S}^{2}.$", null, "(52c)\n\nFigure 11.2-20 shows the μρ and λρ AVO attribute sections which were derived from prestack amplitude inversion applied to the CRP gathers associated with the data shown in Figure 11.2-10a. As in the case of the pseudo-Poisson and fluid-factor AVO attribute sections shown in Figure 11.2-19, note the distinctive AVO anomalies along the flanks of the structural closure. Goodway convincingly demonstrates that separation of gas-bearing sands from tight sands and carbonates is much better with the crossplot of the Lamé attributes (μρ, λρ) in contrast with the crossplot of the P- and S-wave reflectivities or impedances (Figure 11.2-21).\n\nFigure 11.2-22 outlines a summary of the AVO equations that are described in this section based on the various approximations to the Aki-Richards equation (15). Start with Shuey’s arrangement of the terms in the Aki-Richards equation, which itself is an approximation to the exact expression for the P-to-P reflection amplitudes given by the Zoeppritz equations. Then, apply a transformation from S-wave velocity to Poisson’s ratio, and drop the third term to get a simple expression for the P-to-P reflection amplitude that is a linear function of sin2 θ. This linear approximation yields the AVO intercept and gradient attributes.\n\nAlternatively, you may drop the third term in the original Shuey arrangement given by equation (16) and apply Wiggins’ rearrangement of the terms. Then, assume the specific case of the P-wave velocity to be twice the S-wave velocity to obtain the equation that yields, once again, the AVO intercept and gradient attributes. The Wiggins AVO intercept and gradient attributes, unlike the Shuey counterparts, directly lead to deriving the P-wave and S-wave reflectivity attributes, albeit only under the assumption that the P-wave velocity is twice the S-wave velocity.\n\nReturning to the three-term Aki-Richards equation (15), you may reduce it to the two-term Smith-Gidlow equation (36) by using Gardner’s relation of density and P-wave velocity. Then, for a specified ratio of P- to S-wave velocity, perform inversion of prestack amplitudes associated with target events on CMP or CRP gathers to obtain the P- and S-wave reflectivity attributes. In addition, using these attributes to derive two more AVO attributes — psuedo-Poisson and fluid factor.\n\nFinally, you may recast the Aki-Richards equation (15) in terms of P- and S-wave reflectivities (equations 46a,46b) and assume that α/β = 2 to obtain the two-term Goodway et al. equation (48). Again, perform inversion of prestack amplitudes associated with target events on CMP or CRP gathers to obtain the P- and S-wave impedance attributes. Subsequently, by using the relations between impedances and Lamé’s constants, you can compute two additional AVO attributes — λρ and μρ.\n\nThe AVO equations derived in this section are all expressed in terms of angle of incidence (equations 24, 31, and 36). In practice, the mapping of amplitudes associated with a reflection event on a CMP gather from offset to angle of incidence needs to be performed. Assume that the CMP gather is associated with a horizontally layered earth model so that the event moveout on the CMP gather is given by the hyperbolic equation\n\n $t^{2}=t_{0}^{2}+{\\frac {x^{2}}{v_{rms}^{2}}},$", null, "(53)\n\nwhere t is the two-way traveltime from the source to the flat reflecting interface back to the receiver, t0 is the two-way zero-offset time, x is the offset, and vrms is the rms velocity down to the reflector. The ray parameter p is given by the stepout dt/dx measured along the hyperbolic moveout trajectory (the slant-stack transform). Apply differentiation to equation (53) to get\n\n ${\\frac {dt}{dx}}={\\frac {1}{v_{rms}^{2}}}{\\frac {x}{t}}.$", null, "(54)\n\nSince the ray parameter p is also expressed as the ratio of sin θ/vint, where vint is the interval velocity above the reflecting interface, it follows that\n\n $\\sin \\theta ={\\frac {v_{int}}{v_{rms}^{2}}}{\\frac {x}{t}}.$", null, "(55)\n\nBy using equation (55), reflection amplitudes on a CMP gather can be transformed from offset to angle domain, and subsequently used in the AVO equations (24), (31), (36), and (48)." ]
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https://math.stackexchange.com/questions/3447578/clarification-of-expectation-and-independence-three-variables
[ "# Clarification of Expectation and independence, Three Variables.\n\nI have a particular confusion on how to deal with an expectation of three variables where two are independent and the third is independent to one, but perhaps not (clearly defined) to be independent of the second.\n\nSignal $$X$$ and noise $$Z$$ are independent random variables, where $$X=\\begin{cases}+1\\quad\\text{with probability}\\,\\frac12\\\\-1\\quad\\text{with probability}\\,\\frac12\\end{cases}$$ and $$Z\\sim U[-1,1]$$. We observe $$Y=gX+Z$$, where $$g$$ itself is a random variable independent of both $$X$$ and $$Y$$. $$g=\\begin{cases}+1\\quad\\text{with probability}\\,p\\\\0\\quad\\text{with probability}\\,1-p\\end{cases}$$\n\n(a) Find the best linear MMSE estimate of $$X$$ after observing $$Y$$, your answer should be in terms of $$p$$.\n\n(b) Find the best (nonlinear) MMSE estimate of $$X$$ after observing $$Y$$, your answer should be in terms of $$p$$.\n\nThe formula for MMSE is $$\\hat x= \\frac{\\operatorname{cov}(X, Y)}{\\operatorname{var}(Y)}\\cdot(Y-\\Bbb E[Y])+\\Bbb E[X].$$\n\nWhat I've found so far is that $$\\Bbb E[X] = 0,\\quad\\Bbb E[Y] = 0,\\quad\\Bbb E[XY] = p,$$ but then the part I got stuck on is $$\\Bbb E[Y^2]$$ as $$\\Bbb E[Y^2] = \\Bbb E[(gX+Z)^2] = \\Bbb E[g^2X^2 + 2gXZ + Z^2].$$\n\nMy Problem: Even if my math is incorrect (please let me know if it is), how do we deal with $$2gXZ$$ if $$g$$ is not independent to $$Z$$? Is there a property I am forgetting?\n\nMy Attempt: Otherwise, by brute force, I would simply follow through with calculating the three summations, correct? By definition, this should be $$2\\sum_x\\sum_z\\sum_g gzxP_gP_zP_x.$$\n\nHow would one go about solving this? Wouldn't this result end up being \"independent\" anyways because each summation and random variable are independent of the indices? Also, I feel like we can only use this method because we were given that the distribution of $$g$$ is not a function of $$X$$ or $$Z$$ or $$Y$$?\n\nOther thoughts\n\nNote: That if $$g$$ is in fact independent to $$Z$$, does the logic here follow from the same logic as this post? Thus, we would say that since $$Y$$ is a function of $$g$$, $$X$$ and $$Z$$ and that $$g$$ is independent to $$Y$$, therefore $$g$$ is also independent to $$X$$ and $$Z$$? So it was redundant to say that $$g$$ was independent to $$X$$ in the first place?\n\nNote: However, I feel that this problem has a slightly different flavor and I can't exactly pinpoint the intuition or reasoning to fully understand this problem.\n\nNote that $$X\\perp g,Z$$ so $$\\Bbb E[2gXZ]=2\\Bbb E[X]\\Bbb E[gZ]=0$$ since $$\\Bbb E[X]=0$$.\n• It is possible. In the continuous case, $\\Bbb E[AB]=\\iint abf_{A,B}(a,b)\\,da\\,db$. An analogous definition exists for the discrete case. – TheSimpliFire Nov 23 '19 at 10:59" ]
[ null ]
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http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blob;f=topics/week2_encodings.mdwn;h=ac92202e696a20e38663d8813b921e8c79b47f44;hb=ac92202e696a20e38663d8813b921e8c79b47f44
[ "ac92202e696a20e38663d8813b921e8c79b47f44\n1 # Encoding Booleans, Tuples, Lists, and Numbers #\n3 The Lambda Calculus can represent any computable function?\n5 We need to do some work to show how to represent some of the functions\n6 we've become acquainted with.\n9 ## Booleans ##\n11 We'll start with the `if ... then ... else ...` construction we saw last week:\n13     if M then N else L\n15 For a boolean-valued expression `M`, the displayed expression should evaluate to whatever `N` does\n16 if `M` evaluates to `'true`, and to whatever `L` does if `M` evaluates to `'false`.\n17 In order to encode or simulate such an `if` clause in the Lambda Calculus, we\n18 need to settle on a way to represent `'true` and `'false`.\n20 We could simply add the constants `'true` and `'false` to the\n21 language, since it does make sense to extend the Lambda Calculus by adding constants.\n22 However, that would also require complicating the\n23 interpretation of the language; at the very least, we would need more\n24 than just beta-reduction as our engine of computation.  In the spirit\n25 of computational minimalism, let's see how far we can get with the\n26 \"pure\" lambda calculus, without any special constants.\n28 Let's get rid of the parts of the `if` statement that are\n29 just syntactic window-dressing.  That is, let's get rid of the\n30 `if`, the `then`, and the `else`:\n32     M  N  L\n34 Recall that our convention is that values associate left to right, so\n35 this series of terms would be evaluated as:\n37     ((M N) L)\n39 If this expression is supposed to have the meaning of `if M then N\n40 else L`, then we need to find a value for `'true` such that when it is\n41 substituted in place of `M`, the expression evaluates to `N`.  The\n42 function we're looking for should take two arguments: first `N`, then `L`,\n43 and it should throw away `L` and return `N`.\n45 We've already seen such a function.  We called it **K**: `(\\x y. x)`.\n46 Let's test:\n48     ((K N) L) == (((\\x y. x) N) L) ~~> ((\\y. N) L) ~~> N\n50 Sucess! In the same spirit, `'false` could be **K I**, which reduces to `(\\y x. x)` (also written as `(\\y. (\\x x))`):\n52     (((K I) N) L) == ((((\\x y. x) (\\x x)) N) L)\n53                      ~~> (((\\y. (\\x x)) N) L)\n54                      ~~> ((\\x x) L)\n55                      ~~> L\n57 So we have seen our first major encoding in the Lambda Calculus:\n58 \"true\" is represented by **K**, and \"false\" is represented by **K I**.\n59 We'll be building up a lot of representations in the weeks to come,\n60 and they will all maintain the discipline that if a expression is\n61 meant to be interpreted as a truth value (i.e. as a Boolean), it will\n62 be equivalent to (convertible with) **K** or **K I**.\n64 In class, we explained how \"and\" could be thought of as the function, here written\n65 in Kapulet syntax:\n67     lambda p q. if p then q else false\n69 or:\n71     lambda p q. if p then q else p\n73 Given that we know how to express `if ... then ...` in terms of our encoded Booleans,\n74 we can represent this easily in the Lambda Calculus as either:\n76     \\p q. p q (\\y x. x)\n78 or:\n80     \\p q. p q p\n82 Typically there will be more than one way to encode a given function into the Lambda Calculus, even holding fixed\n83 all your other decisions about how to encode other functions. In this case, we can use either representation\n84 because we're assuming that the `p` only gets bound to arguments that are either `\\x y. x` or `\\y x. x`. We don't make any\n85 promises about what will happen if our encodings are abused, that is, supplied with arguments they weren't designed to accept.\n86 If `p` is bound to `\\x y. x`, then the result of both of the above displayed expressions will be whatever `q` is bound to.\n87 If on the other hand, `p` is bound to `\\y x. x`, then the two displayed expressions will return the same result, namely that function.\n89 Despite this, the two displayed expressions are two different lambda terms, and\n90 are not convertible. It's only within the frame of our assumptions about the\n91 restricted arguments we're thinking of supplying them that they behave exactly\n92 alike.\n94 You can try out these expressions in the [[lambda evaluator|code/lambda evaluator]]:\n96     let true = \\x y. x in\n97     let false = \\y x. x in\n98     let and = \\p q. p q p in\n99     and true false\n101 will reduce or \"normalize\" to `\\y x. x`, or false, just as you'd predict. The `let true =` stuff isn't officially part of the Lambda Calculus language. It's just a convenient shorthand that lets you use the lambda evaluator more easily. Behind the scenes, the displayed expression above gets translated to:\n103     (\\true.\n104       (\\false.\n105         (\\and. and true false)))\n106         (\\x y. x) ; this gets bound to variable \"true\"\n107         (\\y x. x) ; this gets bound to variable \"false\"\n108         (\\p q. p q p) ; this gets bound to variable \"and\"\n110 We expect you'll agree that the first is easier to write and to read.\n112 In Scheme (Racket), all of these notions can be defined like this:\n114     (define true  (lambda (x) (lambda (y) x)))\n115     (define false (lambda (y) (lambda (x) x)))\n116     (define lambda-and (lambda (p) (lambda (q) ((p q) p))))\n118 and then used like this:\n120     ((lambda-and true) false)\n122 which will evaluate to a function, that happens to be the same function `false` is bound to. Most Scheme interpreters like Racket will helpfully display the function with the name, if any, that was first defined to be bound to it. So we'll see the result as:\n124     #<procedure:false>\n126 The funny calling pattern, where we write `((lambda-and true) false)` instead of just `(lambda-and true false)`, is because that's how you have to write curried functions in Scheme. Similarly for why we have `(lambda (x) (lambda (y) x))` instead of just `(lambda (x y) x)`.\n128 It's possible to do the next few weeks of assignment without using a Scheme interpreter, however\n129 we do recommend you [get Scheme installed on your\n130 computer](/how_to_get_the_programming_languages_running_on_your_computer), and\n131 [get started learning Scheme](/learning_scheme). It will help you understand the ideas better to experiment with it.\n133 There's also a (slow, bare-bones, but perfectly adequate) version of Scheme available for online use at <http://tryscheme.sourceforge.net/>. (Unfortunately, though, that Scheme implementation will only display the result of `((lambda-and true) false)` as `#<procedure lambda>`. You won't be able to see if it's the function assigned to `true` or the function assigned to `false`. You'd have to feed that result some more arguments to see how it behaved.)\n135 You should also be experimenting with this site's [[lambda evaluator|code/lambda evaluator]].\n138 ## Tuples ##\n140 In class, we also showed you how to encode a tuple in the Lambda Calculus. We did it with an ordered triple, but the strategy generalizes in a straightforward way. (Some authors just use this strategy to define *pairs*, then define triples as pairs whose second member is another pair, and so on. Yech. If you keep a firm grip on your wits, that can also be made to work, but it's extremely likely that people who code in that way are going to lose their grip at some point and get themselves in a corner where they'll regret having made that decision about how to encode triples. And they will be forced to add further complexities at later points, that they're probably not anticipating now. The strategy presented here is as elegant as it first looks, and will help you program more hygienically even when your attention lapses.)\n142 Our proposal was to define the triple `(a, b, c)` as:\n144     \\f. f a b c\n146 To extract the first element of this, you'd write:\n148     (\\f. f a b c) fst_of_three\n150 where `fst_of_three` is the function `\\x y z. x`:\n152     (\\f. f a b c) (\\x y z. x) ~~>\n153     (\\x y z. x) a b c ~~>\n154     (\\y z. a) b c ~~>\n155     (\\z. a) c ~~>\n156     a\n158 Here are the corresponding definitions in Scheme (Racket):\n160     (define make-triple (lambda (a) (lambda (b) (lambda (c)\n161                           (lambda (f) (((f a) b) c))))))\n163     (define fst_of_three (lambda (x) (lambda (y) (lambda (z) x))))\n164     (define snd_of_three (lambda (x) (lambda (y) (lambda (z) y))))\n165     (define trd_of_three (lambda (x) (lambda (y) (lambda (z) z))))\n167 Then:\n169     (define p (((make-triple 10) 20) 30))\n170     (p fst_of_three)  ; will evaluate to 10\n171     (p snd_of_three)  ; will evaluate to 20\n173 If you're puzzled by having the triple to the left and the function that \"uses\" or \"consumes\" or operates on it to the right, think about why it's being done this way: the triple is a package that will be used in coordination with some function for operating on its elements. We don't know in advance what that function will be. And it's not obvious how to make the triple be some structure that the function can \"look inside\" and extract the elements from. We're still trying to *figure out* how to define such structures! But what we can do is make *the triple take the function as an argument*, and return *the result of* operating on its elements with that function. In other words, the triple is a higher-order function: a function that expects another function as an argument.\n175 (Consider the similarities between this definition of a triple and a generalized quantifier. This is in fact our first taste of \"continuations\" in the course, which are a systematic pattern for inverting the naive order of who-is-the-argument? and who-is-the-operator?)\n177 If you really want to, you can disguise what's going on like this:\n179     (define lifted-fst_of_three (lambda (p) (p fst_of_three)))\n181 Then you could say:\n183     (lifted-fst_of_three p)\n187     (p fst_of_three)\n189 Of course, the last is still what's happening under the hood.\n191 (Remark: `(lifted-f (((make-triple 10) 20) 30))` stands to `((((make-triple 10) 20) 30) f)` as\n192 `((((make-triple 10) 20) 30) f)` stands to `(((f 10) 20) 30)`.)\n194 ## Lists ##\n196 There are multiple ways to encode lists, and also multiple ways to encode numbers. We are going to start with what we think are the most natural and elegant encodings. Historically these were the first encodings of numbers but not of lists.\n198 In seminar we discussed two further functions for working with lists or sequences. Reverting to Kapulet syntax, these functions work like this:\n200     fold_right (f, z) [10, 20, 30]\n202 That will evaluate to whatever this does:\n204     f (10, f (20, f (30, z)))\n206 For example, if we let `f` be `(+)` and `z` be `0`, then it will be `10 + (20 + (30 + 0))` or `60`. Another example, if we let `f` be `(&)` and `z` be `[]`, then `fold_right ((&), []) [10, 20, 30]` will be `10 & (20 & (30 & []))` or `[10, 20, 30]`, the same sequence we began with.\n208 The other function works like this:\n210     fold_left (f, z) [10, 20, 30]\n212 That will evaluate to whatever this does:\n214     f (f (f (z, 10), 20), 30)\n216 With a commutative operator like `(+)`, it makes no difference whether you say `fold_right ((+), z) xs` or `fold_left ((+), z) xs`. But with other operators it will make a difference. We can't say `fold_left ((&), []) [10, 20, 30]`, since that would start by trying to evaluate `[] & 10`, which would crash. But we could do this:\n218     let\n219       flipped_cons match lambda (xs, x). x & xs  # also expressible as `uncurried_flip (&)`\n220     in fold_left (flipped_cons, []) [10, 20, 30]\n222 and that would evaluate to `flipped_cons (flipped_cons (flipped_cons ([], 10), 20), 30)`, in other words, to `30 & (20 & (10 & []))`, or `[30, 20, 10]`. So this reverses the sequence we began with.\n224 In class we considered how to express other list operations in terms of these. For example, we saw that we could define `length xs` as:\n226     fold_right ((lambda (_, z). 1 + z), 0) xs\n228 And we could define `map g xs` as:\n230     fold_right ((lambda (x, zs). g x & zs), []) xs\n232 Here is [a nice website](http://stevekrouse.github.io/hs.js) we found that lets you evaluate these things step by step. Just click on the subexpressions to evaluate them.\n234 We also saw in seminar how to define `fold_right`. We could do this in Kapulet like this:\n236     letrec\n237       fold_right (f, z) xs = case xs of\n238                                [] then z;\n239                                y & ys then f (y, fold_right (f, z) ys)\n240                              end\n241     in fold_right\n243 (In some presentations you may see this expecting `f` to be a curried function `lambda y z. ...` rather than the uncurried `lambda (y, z). ...` that I'm expecting here. We will be shifting to the curried form ourselves momentarily.)\n245 We suggested in class that these functions were very powerful, and could be deployed to do most everything you might want to do with a list. Given how our strategy for encoding booleans turned out, this ought to suggest to you the idea that *folding is what we fundamentally do* with lists, just as *conditional branching is what we fundamentally do* with booleans. So we can try to encode lists in terms of lambda expressions that will let us perform folds on them. We could try to do this with either right-folds or left-folds. Either is viable. Some things are more natural if you use right-folds, though, so let's do that.\n247 What should the encoding look like? We don't know *what* function and *what* starting value someone might want to fold over our list!\n249 Wait, does that remind you of anything?\n251 Good. I knew it would.\n253 Indeed, we'll make our encoded lists consist of higher-order *functions* that take the `f` and the starting value `z` to be folded *as arguments*. So the list `[a, b, c]` should look something like this:\n255     \\f z. SOMETHING\n257 Now, what should the `SOMETHING` be? Well, when we supply an `f` and a `z` we should get back the right-fold of those over `[a, b, c]`, so the answer should evidently be:\n259     \\f z. f a (f b (f c z))\n261 Here we work with curried functions, because that's how the Lambda Calculus does things. You wouldn't want to build up a tuple using the mechanisms described above, and then supply `f` as an argument to that tuple, and so on. That would be a lot of red tape for no benefit. In the Lambda Calculus, it's simpler to just work with curried functions as our natural idiom.\n263 So if `[a, b, c]` should be the displayed higher-order function above, what should `[c]` be? Evidently:\n265     \\f z. f c z\n267 Now what should the empty list `[]` be? Think about it...\n269 Did you arrive at an answer?\n271 I hope it was this one: `\\f z. z`. Because when we fold a function `f` and a starting value `z` over the empty list, we just get back whatever the starting value `z` was.\n273 We saw before what a `make-triple` function would look like. What about a `make-list` function, or as we've been calling it, \"cons\" (`&` in Kapulet)? Well, we've already seen what the representation of `[]` and `[c]` are. In that simplest case, the `cons` function should take us from the encoding of `[]`, namely `\\f z. z` to the encoding of `[c]`, namely `\\f z. f c z`, as a result. Here is how we can define this:\n275     let cons = \\d ds. \\f z. f d (ds f z)\n276     in ...\n278 Let's walk through this. We supply this function with our `c` and `[]` as arguments. So its `d` gets bound to our `c`, and its `ds` gets bound to our `[]`, namely `\\f z. z`. Then our result is a higher order function of the form `\\f z. f c SOMETHING`. That looks good, what we're after is just this, except the `SOMETHING` should end up as `z`. If we just simply *substituted* `z` for `SOMETHING`, then our `cons` function would *always* end up giving us back a singleton list of the form `\\f z. f X z` for some `X`. That is the form we want in the present case, computing `cons c []`, but not in the general case. What we'd like instead is to *do something to* the second argument we fed to `cons`, here `[]` or `\\f z. z`, and have *it* reduce to `z`, with the hope that the same operation would make *more complex* second arguments reduce to *other* appropriate values. Well, `\\f z. z` expects an `f` and a `z` as arguments, and hey we happen to have an `f` and a `z` handy, since we're inside something of the form `\\f z. f c SOMETHING`. The `f` and `z` will be supplied by the consumer or user of the sequence `[c]` that we're building. So let's just give *those* `f` and `z` to `\\f z. z` as *its* arguments, and we end up with simply `z`. In other words, where `ds` is the second argument we fed to `cons`, we make `SOMETHING` in `\\f z. f c SOMETHING` be `ds f z`. That is why we make `cons` be:\n280     \\d ds. \\f z. f d (ds f z)\n282 Let's step through it formally. Given our definitions:\n284     cons c []\n286 is:\n288     (\\d ds. \\f z. f d (ds f z)) c (\\f z. z) ~~>\n289     (\\ds. \\f z. f c (ds f z)) (\\f z. z) ~~>\n290     \\f z. f c ((\\f z. z) f z) ~~>\n291     \\f z. f c ((\\z. z) z) ~~>\n292     \\f z. f c z\n294 which is just the representation of `[c]` we were after.\n296 Will this work when more complex values are supplied as the second argument to `cons`? Let's see:\n298     cons b [c]\n300 is:\n302     (\\d ds. \\f z. f d (ds f z)) b (\\f z. f c z) ~~>\n303     (\\ds. \\f z. f b (ds f z)) (\\f z. f c z) ~~>\n304     \\f z. f b ((\\f z. f c z) f z) ~~>\n305     \\f z. f b ((\\z. f c z) z) ~~>\n306     \\f z. f b (f c z)\n308 which looks right. Persuade yourself that the `cons` we've defined here, together with the representation `\\f z. z` for the empty list, always give us the correct encoding for complex lists, in terms of a function that takes an `f` and a `z` as arguments, and then returns the result of right-folding those arguments over the list elements in the appropriate order.\n310 You may notice that the encoding we're proposing for `[]` is the same encoding we proposed above for `false`. There's nothing deep to this. If we had adopted other conventions, we could easily have made it instead be `true` and `[]` that had the same encoding.\n312 Now we saw above how to define `map` in terms of `fold_right`. In Kapulet syntax, `map g xs` was:\n314     fold_right ((lambda (x, zs). g x & zs), []) xs\n316 In our Lambda Calculus encoding, `fold_right (f, z) xs` gets translated to `xs f z`. That is, the list itself is the operator, just as we saw triples being. So we just need to know how to represent `lambda (x, zs). g x & zs`, on the one hand, and `[]` on the other, into the Lambda Calculus, and then we can also express `map`. Well, in the Lambda Calculus we're working with curried functions, and there's no infix syntax, so we'll replace the first by `lambda x zs. cons (g x) zs`. But we just defined `cons`, and the lambda is straightforward. And we also just defined `[]`. So we already have all the pieces to do this. Namely:\n318     map g xs\n320 in Kapulet syntax, turns into this in our lambda evaluator:\n322     let empty = \\f z. z in\n323     let cons = \\d ds. \\f z. f d (ds f z) in\n324     xs (\\x zs. cons (g x) zs) empty\n326 Try out this:\n328     let empty = \\f z. z in\n329     let cons = \\d ds. \\f z. f d (ds f z) in\n330     let map = \\g xs. xs (\\x zs. cons (g x) zs) empty in\n331     let abc = \\f z. f a (f b (f c z)) in\n332     map g abc\n334 That will evaluate to:\n336     \\f z. f (g a) (f (g b) (f (g c) z))\n338 which looks like what we want, a higher-order function that will take an `f` and a `z` as arguments and then return the right fold of those arguments over `[g a, g b, g c]`, which is `map g [a, b, c]`.\n341 ## Numbers ##\n343 Armed with the encoding we developed for lists above, Church's method for encoding numbers in the Lambda Calculus is very natural. But this is not the order that these ideas were historically developed.\n345 It's noteworthy that when he was developing the Lambda Calculus, Church had not predicted it would be possible to encode the numbers. It came as a welcome surprise.\n347 The idea here is that a number is something like a list, only without any slot for an interesting, possibly varying head element at each level. Whereas in a list like:\n349     [a, b, c]\n351 we have:\n355 with the number `3` we instead only have:\n359 where `()` is the zero-length tuple, the one and only member of its type. That is, the head here is a type of thing that cannot interestingly vary. Or we could just eliminate the head, and have:\n361     subnumber=(subnumber=(subnumber=zero))\n363 probably more familiar to you as:\n365     succ (succ (succ zero))\n367 In other words, where a list is inductively built up out of some interesting new datum and its \"sublist\" or tail, a number is inductively built up out of no interesting new datum and its \"subnumber\" or predecessor. In this light, a number can be seen as a kind of stunted or undernourished list.\n369 Now, we had a strategy for encoding the list `[a, b, c]` as:\n371     \\f z. f a (f b (f c z))\n373 So perhaps we can apply the same kind of idea to the number `3`, and encode it as:\n375     \\f z. f   (f   (f   z))\n377 In fact, there's a way of looking at this that makes it look incredibly natural. You may have encountered the idea of a composition of two functions `f` and `g`, written as <code>f &cir; g</code>, or in Kapulet as `f comp g`. This is defined to be:\n379     \\x. f (g x)\n381 The composition of a function `f` with itself, namely:\n383     \\x. f (f x)\n385 is sometimes abbreviated as <code>f<sup>2</sup></code>. Similarly, <code>f &cir; f &cir; f</code> or `\\x. f (f (f x))` is sometimes abbreviated as <code>f<sup>3</sup></code>. <code>f<sup>1</sup></code> is understood to be just `f` itself, and <code>f<sup>0</sup></code> is understood to be the identity function.\n387 So in proposing to encode the number `3` as:\n389     \\f z. f   (f   (f   z))\n391 we are proposing to encode it as:\n393 <code>\\f z. f<sup>3</sup> z</code>\n395 (The <code>f<sup><em>n</em></sup></code> isn't some bit of new Lambda Calculus syntax. It's just our metalanguage abbreviation for the same expressions we had before. It does help focus our attention on what we're essentially doing here.)\n397 And indeed this is the Church encoding of the numbers:\n399 <code>0 &equiv; \\f z. I z &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;  or \\f z. f<sup>0</sup> z</code>\n400 <code>1 &equiv; \\f z. f z &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;  or \\f z. f<sup>1</sup> z</code>\n401 <code>2 &equiv; \\f z. f (f z) &nbsp;&nbsp;&nbsp;&nbsp;;  or \\f z. f<sup>2</sup> z</code>\n402 <code>3 &equiv; \\f z. f (f (f z)) ;  or \\f z. f<sup>3</sup> z</code>\n403 <code>...</code>\n405 The encoding for `0` is equivalent to `\\f z. z`, which we've also proposed as the encoding for `[]` and for `false`. Don't read too much into this.\n407 Given the above, can you figure out how to define the `succ` function? We already worked through the definition of `cons`, and this is just a simplification of that, so you should be able to do it. We'll make it a homework.\n409 We saw that using the `cons` operation (Kapulet's `&`) and `[]` as arguments to `fold_right` over a list give us back that very same list. In the Lambda Calculus, that comes to the following:\n411     [a, b, c] cons []\n413 with the appropriate lambda terms substituted throughout, just reduces to the same lambda term we used to encode `[a, b, c]`.\n415 In the same spirit, what do you expect this will reduce to:\n417     3 succ 0\n419 Since `3` is `\\f z. f (f (f z))`, it should reduce to whatever:\n421     succ (succ (succ 0))\n423 does. And if we define `succ` properly, we should expect that to give us the same lambda term that we used to encode `3` in the first place.\n426 We'll look at other encodings of lists and numbers later." ]
[ null ]
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https://dam.ukdataservice.ac.uk/dataskills/glossary.html
[ "95% confidence interval\nSurveys: What are survey data?\nThis is a measure of the range within which we can be 95% sure that the population figure lies, based on a sample statistic. For a sample percentage, it is calculated as the sample percentage minus 1.96 times the standard error, to the sample percentage plus 1.96 times the standard error.\nBias\nSurveys: What are survey data?\nA problem that results in incorrect estimates being produced from a sample. Results will be too high or too low. This may arise where the sample is not representative of the population.\nCase\nSurveys: What are survey data?\nA case is a unit for which values are captured. When data are collected from a survey the case is usually a respondent. Most statistics packages show each case in a single row of data.\nCategorical variable\nSurveys: Exploring data\nA variable that holds values which represent discrete classes of reponses. For example a marital status contains the classes (or categories) of single (never married), married, civil partnership, divorced, widowed etc.\nClustering\nSurveys: What are survey data?\nThe process of dividing a population into groups and selecting the sample from only some of them. Geographical clustering is common in surveys conducted face to face. The population is split into geographical units and the sample is selected from only some of them. This is undertaken to reduce the amount of travel the interviewer needs to do.\nCodebook\nSurveys: Exploring data\nA codebook describes the contents, structure, and layout of a data collection. Codebooks begin with basic front matter, including the study title, name of the principal investigator(s), table of contents, and an introduction describing the purpose and format of the codebook. Some codebooks also include methodological details, such as how weights were computed, and data collection instruments, while others, especially with larger or more complex data collections, leave those details for a separate user guide and/or data collection instrument.\nSurveys: What are survey data?\nA control variable is a variable that is included in an analysis in order to account for it's effect and therefore distinguish any affect that is has from the effect of another variable which may be of more interest. For example if we were looking at the the impact of having a degree on health amongst adults over 40 we might need to consider the impact of age at the same time. Older people tend to be less likely to have a degree and to have poorer health. If we control for age we can see whether graduate health is generally better than non-graduate health once age has been accounted for.\nSurveys: What are survey data?\nCross-sectional data is collected at a single point in time. It has been likened to taking a snapshot.\nSurveys: What are survey data?\nA variable that is created after data collection following some sort of calculation or other processing.\nSurveys: What are survey data?\nA statistic which simply describes a characteristic of variable for a group of cases this generally does not have any explanatory power.\nEstimate\nSurveys: What are survey data?\nA statistic, produced using a sample of cases, which is designed to produce information about the characteristics of the population.\nSurveys: What are survey data?\nData that contains information about the same units (usually respondents) over time is called longitudinal data. It can be contrasted with cross-sectional data which collects data at a single time.\nMicrodata\nSurveys: What are survey data?\nData stored as cases, and variables,, usually with one case per respondent,.\nMissing value\nSurveys: What are survey data?\nA value that is differentiated from a 'valid' response, such as 'did not answer' or 'not applicable'. Missing values are excluded from most procedures.\nSurveys: What are survey data?\nThese are methods that use data from more than two variables at a time, often several variables are included as controls. Statistical modelling is a particularly common form of multivariate method.\nNonimal variable\nSurveys: Exploring data\nThis a categorical variable that contains values which represent categories which do not have a natural order. For example there is no natural order to a set of categories describing religion followed. The values assigned to each class is wholly arbitrary.\nOrdinal variable\nSurveys: Exploring data\nThis a categorical variable that contains values which represent categories which have a natural order. For example a highest level of qualification might respect an ordering such as; higher degree, first degree, further education below degree, GCSE or equivalent, no qualification. The values assigned to the classes should respect the natural order.\nPopulation\nSurveys: What are survey data?\nThe population is a defined set of units, for example all 'residents in England and Wales in 2011'. The population is the group that we seek to describe.\nPrecision\nSurveys: What are survey data?\nPrecision is the accuracy with which a sample statistic is able to estimate a population statistic. A precise sample is characterised by a low standard error and a narrow 95% confidence interval.\nProbability sample\nSurveys: What are survey data?\nA sample based on random selection of elements. It should be possible for the sample designer to calculate the probability with which an element in the population is selected for inclusion in the sample.\nPSPP\nSurveys: Exploring data\nPSPP is an open source statistics package which has a similar design and basic functionality of SPSS. Visit the website for more information.\nRaw variable\nSurveys: What are survey data?\nA variable that stores responses given to a question in the survey in their original form.\nRepresentative sample\nSurveys: What are survey data?\nA representative sample is one that replicates the characteristics of the population.\nRespondent\nSurveys: What are survey data?\nA person, or other entity, who responds to a survey.\nSample\nSurveys: What are survey data?\nA sample is a subset of a population.\nSPSS\nSurveys: What are survey data?\nSPSS is a commercial statistics package. Visit the website for more information.\nStandard error\nSurveys: What are survey data?\nThe standard error for a statistic is a measure of the amount that a sample statistic (such as a percentage) varies from the true population statistic. The standard error for a percentage can be calculated by se(pct) = sqrt((pct * (100-pct)/n) In other words; multiply the sample percentage by 100 minus the sample percentage. Divide the product by the number of cases used to calculate the percentage. Finally square root the answer to get the standard error.\nSurveys: What are survey data?\nA statistical model is a theoretical construction of the relationship of a set of explanatory variables to another variable of interest which depends in order to better understand the relationships. The model is expressed as function. For example, a researcher may use a function such as;\ny =b1x1 + b2x2 + ... + bmxm\nto express the relationship between variable y and the m variables it depends on x1 to xm where the impact of a change in 1 unit of each explanatory variable is given by the factor b1 to bm respectively if (s)he believes this function is an appropriate mathematical description of the relationships in the data.\nStandard models have well known methods to determine the b values and the strength of evidence that each variable has an effect on y.\nStatistically modelling is a major topic and outsidethe scope of the module. Readers who want to know more will find extensive accounts of statistical models including linear regression and logistic regression in statistical texts and online.\nStructured interview\nA survey undertaken by an interviewer usually face to face or over the phone that is constructed from standard questions.\nSurvey non-response\nSurveys: Exploring data\nSample members may not be contactable, or may refuse to participate in the survey. Sample members who do not take part in the survey are known as 'non-respondents'.\nUnit of analysis\nSurveys: What are survey data?\nThe unit which is being analysed. This is synonymous to the case.\nValue\nSurveys: What are survey data?\nA representation of a characteristic for one case, for one value. In many packages the value is represented by a number.\nValue label\nSurveys: What are survey data?\nA label associated with a value to enable humans to understand what it means.\nVariable\nA variable is anything which can vary. In surveys, this is usually a characteristic that varies between cases.\nWeighting\nSurveys: Exploring data\nA means by which the relative importance of cases can be changed. By default all cases count as one unit. Weighting changes this so that a case with high weight counts more and a case with low weight counts less. The process is usually undertaken in order to fix problems of unrepresentativeness in a sample." ]
[ null ]
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https://www.centerspace.net/examples/nmath/visual-basic/core/vector-range-example.php
[ "# VB Vector Range Example\n\n← All NMath Code Examples\n\n```Imports System\n\nImports CenterSpace.NMath.Core\nImports Range = CenterSpace.NMath.Core.Range\n\nNamespace CenterSpace.NMath.Examples.VisualBasic\n\n' A .NET example in Visual Basic showing how to use the indexing class Range with the vector classes.\nModule VectorRangeExample\n\nSub Main()\n\nDim length As Integer = 10\n\nConsole.WriteLine()\n\nDim u As New DoubleVector(length, 0, 1)\nConsole.WriteLine(\"u = \" & u.ToString()) ' u = [0 1 2 3 4 5 6 7 8 9]\n\n' Last five elements of the vector u:\nDim uLast5 As DoubleVector = u(New Range(5, length - 1))\nConsole.WriteLine(\"uLast5 = \" & uLast5.ToString()) ' uLast5 = [5 6 7 8 9]\n\n' Could also get this by specifying all elements from the 6th to the end using\n' the End value from the Position enum\nuLast5 = u(New Range(5, Position.End))\nConsole.WriteLine(\"uLast5 = \" & uLast5.ToString()) ' uLast5 = [5 6 7 8 9]\n\n' You can use negative strides too. Here is the vector u, reversed.\nDim uRev As DoubleVector = u(New Range(length - 1, Position.Start, -1))\nConsole.WriteLine(\"uRev = \" & uRev.ToString()) ' uRev = [9 8 7 6 5 4 3 2 1 0]\n\n' Notice that when you create a new DoubleVector using the Range or Slice class,\n' you are creating a different \"view\" of the vectors data. That is, the\n' DoubleVector instance returned by the indexing operator taking a Range object,\n' and the DoubleVector instance being indexed share the same data:\nuRev(0) = 0\nConsole.WriteLine(\"uRev = \" & uRev.ToString()) ' uRev = [0 8 7 6 5 4 3 2 1 0]\nConsole.WriteLine(\"u = \" & u.ToString()) ' u = [0 1 2 3 4 5 6 7 8 0]\n\n' Finally, we use the DoubleVector method Set(Range) to change the contents of u\n' to alternate values 0 and 1\nDim evenElts As New Range(0, Position.End, 2)\nDim oddElts As New Range(1, Position.End, 2)\nu.Set(evenElts, 0)\nu.Set(oddElts, 1)\nConsole.WriteLine(\"u = \" & u.ToString()) ' u = [0 1 0 1 0 1 0 1 0 1]\n\nConsole.WriteLine()\nConsole.WriteLine(\"Press Enter Key\")" ]
[ null ]
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https://socratic.org/questions/circle-a-has-a-radius-of-5-and-a-center-of-2-7-circle-b-has-a-radius-of-1-and-a--1#557074
[ "# Circle A has a radius of 5 and a center of (2 ,7 ). Circle B has a radius of 1 and a center of (3 ,1 ). If circle B is translated by <1 ,3 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?\n\nFeb 23, 2018\n\nThey do not overlap and the minimum distance between the two circles is >1.\n\n#### Explanation:\n\nTo figure this out, the simplest thing to do is to graph it out. From all the information given, we can find the equations for both circles and graph them. A circle's equation is:\n\n${x}^{2} + {y}^{2} = {r}^{2}$\n\n$r$ in this case equals the $r a \\mathrm{di} u s$ of the circle.\n\nAlso, the problem gives us the center point at which the circle sits. This will also help with forming the equations.\n\nCircle A is ${\\left(x - 2\\right)}^{2} + {\\left(y - 7\\right)}^{2} = 25$\nCircle B is ${\\left(x - 3\\right)}^{2} + {\\left(y - 1\\right)}^{2} = 1$\n\nNow that we have our equations, we can graph them. graph{(x-2)^2+(y-7)^2=25 [-13.39, 14.7, 0.26, 14.31]}\n\ngraph{(x-3)^2+(y-1)^2=1 [-11.13, 13.84, -1.94, 10.55]}\n\nNow, let's visualize Circle B translated to the right one, and up three. This will make Circle B's new equation look like:\n\n${\\left(x - 4\\right)}^{2} + {\\left(y - 10\\right)}^{2} = 1$\ngraph{(x-4)^2+(y-10)^2=1 [-6.25, 13.48, 3.71, 13.58]}\n\nIf we now compare the graph of Circle A with the translated graph of Circle B, we can see that they still do not overlap and the minimum distance between the two circles is >1.\n\nFeb 23, 2018\n\n$\\text{circle B is inside circle A}$\n\n#### Explanation:\n\n$\\text{What we have to do here is \"color(blue)\"compare\"\" the distance}$\n$\\text{(d) between the centres to the \"color(blue)\"sum/difference of the}$\n$\\textcolor{b l u e}{\\text{radii}}$\n\n• \" if sum of radii\">d \" then circles overlap\"\n\n• \" if sum of radii\"< d\" then no overlap\"\n\n• \" if difference of radii\">d\" then 1 circle inside other\"\n\n$\\text{Before calculating d we require to find the centre of B}$\n$\\text{under the given translation}$\n\n$\\text{under a translation } < 1 , 3 >$\n\n$\\left(3 , 1\\right) \\to \\left(3 + 1 , 1 + 3\\right) \\to \\left(4 , 4\\right) \\leftarrow \\textcolor{red}{\\text{new centre of B}}$\n\n$\\text{to calculate d use the \"color(blue)\"distance formula}$\n\n•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2\n\n$\\text{let \"(x_1,y_1)=2,7)\" and } \\left({x}_{2} , {y}_{2}\\right) = \\left(4 , 4\\right)$\n\n$d = \\sqrt{{\\left(4 - 2\\right)}^{2} + {\\left(4 - 7\\right)}^{2}} = \\sqrt{4 + 9} = \\sqrt{13} \\approx 3.61$\n\n$\\text{sum of radii } = 5 + 1 = 6$\n\n$\\text{difference of radii } = 5 - 1 = 4$\n\n$\\text{Since diff. of radii\">d\" then 1 circle inside other}$\ngraph{((x-2)^2+(y-7)^2-25)((x-4)^2+(y-4)^2-1)=0 [-40, 40, -20, 20]}" ]
[ null ]
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https://studylib.net/doc/10947644/
[ "# Document 10947644", null, "```Hindawi Publishing Corporation\nMathematical Problems in Engineering\nVolume 2009, Article ID 249162, 18 pages\ndoi:10.1155/2009/249162\nResearch Article\nA MATLAB-Linked Solver to Find Fuel Depletion\nin a PWR, a Suggested VVER-1000 Type\nF. Faghihi and M. Saidi Nezhad\nDepartment of Nuclear Engineering, School of Mechanical Engineering, Shiraz University,\nShiraz 71348-51154, Iran\nCorrespondence should be addressed to F. Faghihi, [email protected]\nReceived 11 September 2009; Accepted 30 November 2009\nRecommended by Shijun Liao\nCoupled first-order IVPs are frequently used in many parts of engineering and sciences. We present\na “solver” including three computer programs which were joint with the MATLAB software to\nsolve and plot solutions of the first-order coupled stiff or nonstiff IVPs. Some applications related\nto IVPs are given here using our MATLAB-linked solver. Muon catalyzed fusion in a D-T mixture\nis considered as a first dynamical example of the coupled IVPs. Then, we have focused on the\nfuel depletion in a suggested PWR including poisons burnups xenon-135 and samarium-149,\nplutonium isotopes production, and uranium depletion.\nreproduction in any medium, provided the original work is properly cited.\n1. Introduction\nCoupled first-order IVPs are frequently used in many parts of engineering and sciences\n1–3, and we presented a package seems to be useful for researchers to solve IVPs 4. It is\npossible to describe many dynamical problems using IVPs; MATLAB is the best software for\nengineers and applied scientists to solve the problems numerically, specially solving IVPs.\nIn our early studies, we have utilized a numerical “MATLAB-linked solver” to calculate\nstiff or nonstiff first-order coupled IVPs using MATLAB software 4, and reader can find\nthese programs in the appendix. The well-known numerical methods such as Runge-Kutta,\nRosenbrock, Classical method, Taylor series, Adams-Bashforth are used to solve IVPs using\nThe main aim of the present research is to give a MATLAB-linked solver to solve firstorder coupled differential equation which is used in many subjects of the nuclear engineering.\nTherefore, in the present study, some dynamical problems which mathematically are\ncoupled first-order IVPs are studied as examples of the present solver ability. First we explain\nMuon Catalyzed Fusion μCF and find the fusion cycling rate. Then, we focus on the poisons,\n2\nMathematical Problems in Engineering\nincluding xenon135 and samarium-149, burnups in a suggested 1000 MWe PWR as well as its\nplutonium isotopes build up. Their solutions are given using our “MATLAB-linked solver.”\nBasically, consider a first-order coupled IVPs such as\ndx1 t\nx1 p11 tx1 &middot; &middot; &middot; p1n txn ,\ndt\ndx2 t\nx2 p21 tx1 &middot; &middot; &middot; p2n txn\ndt\n...\n1.1\n..\n.\ndxn t\nxn pn1 tx1 &middot; &middot; &middot; pnn txn ,\ndt\nwhere initial values of the dependent variables are:\nxi t0 αi ,\nαi const., i 1, 2, . . . , n.\n1.2\nHere, t is used for the independent variable and may refer to time in a dynamical problems,\nand xi t stands for dependent variables.\nCoupled IVPs with constant coefficients. First, we consider the IVPs with constant\ncoefficients, or in other words constant pij , and we illustrate our package procedures to solve\nand plot the calculated dependent variables. Three programs were written and connected to\nthe MATLAB, software where these programs will be run in the MATLAB’s editorial page,\nby running DEPLET.m M-file. Some questionnaires should be answered by the user such as\nthe following:\ni Entering the number of differential equations unknowns.\nii Inserting initial values of xi dependent variables.\niii Inserting start and end points of the computations, or in another words\nindependent variables interval.\niv The type of coupled differential equation should be specified. The answer includes\n“Stiff” or “Nonstiff” cases.\nv The next question is the method in which user wants for executing. Answers\nincludes “ode45 method”, “ode23 method”, “ode113 method” for the nonstiff case,\nand also “ode15s method”, “ode23s method”, “ode23t method”, “ode23tb method”\nto the MATLAB help 5. By clicking on each solvers, a short review on the\nspecified numerical method will be given. Finally, user should insert pij s and\nexecution would be begun. After execution, dependent variables xi ts will be\ncomputed according to the desired numerical method, and user can plot xi ts in\nthe computational interval. For plotting x1 t as an example, user should write\n“1” and then a new window will be opened and x1 t will be plotted versus the\ncomputed interval.\nMathematical Problems in Engineering\n3\nCoupled IVPs with variable coefficients. The so-called package called DEPLET m-file can\nbe extended to the IVPs with variable coefficients or in another words pij t. In this case, the\ncomputational interval ab should be divided into many step-size intervals so that variations\nof pij s are ignored in each step-size each step-size is equal to h b − a/N, where N is a\ndesired grid interval and therefore tk a hk, where k 0, 1, 2, . . . , N, and therefore we can\nassume average of pij s in eachstep-size:\npij tk pij ,\nwhere pij pij tk pij tk1 .\n2\n1.3\nIn this case again we return into the coupled differential equations with constant coefficients\nwhich can be solved by the DEPLET.m. Calculated xtk , in each interval, will be used as an\ninitial conditions for the next step, and therefore by combining given solutions the full-solutions\nwould be obtained.\n2. Some Dynamical Problems Related to Coupled IVPs\n2.1. Muon Catalyzed Fusion System\nThe basic process of the muon catalyzed fusion in a D-T mixture as depicted in the upper\npart of Figure 1, can be summarized as follows 6. After high-energy μ injection and\nthen stopping and decreasing its energy in a D-T mixture, either dμ or a tμ atom is\nformed, with a probability more or less, proportional to the relative concentration of D\ncd and T ct . Because of the difference between dμ and tμ in the binding energies\nof their atomic states, μ− in dμ undergoes a transfer reaction to tritium yielding tμ\nduring a collision with the surrounding tritium in either D-T or T2 molecules. Thus the\nformed tμ reacts with D2 , DT , or T2 to form a muonic-molecule dtμ at a rate of λdtμ\nfollowed by a fusion reaction occurring from a molecular state of the dtμ. The fusion\ntakes place and a 14-Mev neutron and a 3.6-Mev α-particle are emitted. After the fusion\nreaction inside the dtμ molecule, most of the μ− are liberated to participate in a second\nμCF cycle. There is however some small fraction of the μ− which are captured by the\nrecoiling positively charged α. The probability of forming an αμ ion is called the\ninitial sticking probability ωs0 . Once the αμ is formed, the μ− can be stripped from the\nαμ ion where it is stuck and liberated again. This process is called regeneration, with a\ncorresponding fraction R. Thus, μ− in the form of either a nonstuck μ− or one regenerated\nfrom αμ can participate in a second μCF cycle, leading to an effective sticking parameter\nωs 1 − Rωs0 .\nNow, consider a homogeneous media in which the μCF is carried out 7–9. The ion\ndensity of the media ρ, in another words tritium and deuterium concentrations, atomic\nf\nand molecular formation rates λa , and λdtμ , and fusion decay rates λdtμ are known\nas the constants due to a fixed temperature of the media and therefore are assumed to be\nindependent of time. Therefore, according to the physical model and also Figure 1, the firstorder linear coupled dynamical equations for the Muon Catalyzed Fusion system μCF\n4\nMathematical Problems in Engineering\nare given by\ndNμ t\n−λ0 Nμ t − λa cd φm Nμ t − λa ct φm Nμ t 1 − ωs λμdt Ndtμ t,\ndt\ndNμd t\n1\n− λ0 Nμd t λa cd φm Nμ t − λdt ct φm Nμd t,\ndt\nτ\ndNμt t\n1\n− λ0 Nμt t λa ct φm Nμ t λdt ct φm Nμd t − λdtμ cd φm Nμt t,\ndt\nτ\n2.1\ndNdtμ t\nf\nλdtμ cd φm Nμt t − λdtμ Ndtμ t − λ0 Ndtμ t,\ndt\ndNn t\nf\nλdtμ Ndtμ t,\ndt\nwhere cp and ct are the relative concentration of deuterium and tritium, respectively. The\nmuonic-atoms formation rates are given by λi i μd, μt, and the muonic-molecule\nf\nformation rate of dtμ is given by λdtμ . The dtμ fusion rate is shown by λdtμ . The possible\nleakage rate of muonic-atoms is proportional to Nμd /τ and Nμt /τ, and also λ0 is the muon\ndecay constant. In 2.1, φm is the dimensionless ion density of the media and is proportional\nto liquid hydrogen density close to 0.07. As said before, ωs is the muon effective sticking\ncoefficient. Table 1 gives values of the constants for solving 2.1.\nWe have solved these coupled dynamics equations in time range of 0 to 2.2 &times; 10−6 sec,\nthe muon life-time, using our MATLAB-linked solver with the following initial conditions:\nNμ t 0 1,\nNk t 0 0,\nk μd, μt, dtμ, n.\n2.2\nAccording to the coupled dynamical equation 2.1 and also Figure 1, the calculated neutrons,\nNn t 2.2 &times; 10−6 s for each one inserted muon, corresponds to the muon cycling rate of the\nexplained cold fusion μCF, or which are proportional to the number of fusion i.e., each\nneutron corresponds to one fusion: d t α n.\nAt the end of running, neutron concentration is plotted in our calculated time interval\nand is given in Figure 2. According to Figure 2, Nn t 2.2 μs 110 is the muon cycling\nrate of the mentioned Muon Catalyzed Fusion system. Each fusion gives 17.6Me 5 energy\nso that total obtained energy is about 110 &times; 17.6 1.94 GeV. For producing one muon, due\nto an accelerator, we must expense about 4 GeV energy so that the above cold fusion is not\ncommercial. Increasing temperature as well as more ion density concentration together with\ndecreasing muon sticking coefficient ωs has been some ideas for obtaining commercial cold\nfusion which is under research. Another comments are taken into account which are beyond\nthe scope of present research.\n2.2. Plutonium Build Up in a Nuclear Pressurized Water Reactor\nConsider a PWR which has been operating in a suggested time interval. In a PWR reactors,\nnuclear fuel is UO2 pellets, and uranium consist of 235 U and 238 U isotopes neglecting 234 U\nisotope. The most important isotopes of interest that have been produced as a result of\nMathematical Problems in Engineering\n5\ntμ\ndμ\nμ\nFree μ−\nR ∼ 0.35\nreactivation\n3.5 MeV\nμ\nαμ\ninitial\nsticking\nμ−\nα\nμαKα\n4000\n3000\nKβ\nKα ,Kβ\nX-rays\n14 MeV\nneutron\n7000\n2000\n4\n6\n8\n10\n12\nX-ray energy keV\nY Kα γKα ωso\n0.35\n14\nTiming ns\n6000\n1000\n0\nα\nn\nThermalized\nαμ\neffective sticking:\nωs 1 − Rωs0\nD-T liquid 80 – 2080 ns\n5000\ndtμ\nωs versus Y Kα 5000\n4000\n3000\nn\nγ\n0.3\n−150\n0.25\n−50\n50\n150\nNγ-TDC ch\n0.2\nλn ,Yn\n0.15\n0.3\n0.4\n0.5\n0.6\n0.7\nEffective sticking ωs ωs0 1 − R\nThis exp.\nSolid\nLiquid\nTheory φ 1.2\nCohen 88\nMerkushin 88\nCohen 98\nW 1 − λ0 /λn /Yn\nωs W − Wdd − Wtt &middot; &middot; &middot;\nFigure 1: Reaction cycle of the Muon Catalyzed Fusion, μCF.\nuranium fuel depletion, are two isotopes of plutonium element, that is, Pu-239 and Pu-241.\nBecause they can also be employed as fuel, like as U-235 atom. The process at which U238 fresh fuel is converted into plutonium isotopes is shown in Figure 3. The appropriate\nmagnitude of each neutron capture cross-section for corresponded nuclear n,γ reaction\nis given on each arrow in terms of barns 10. According to the foregoing chain, a set\nof coupled first-order ordinary differential equation can be established to give the timedependent concentration of some of interesting isotopes. This is done via the conservation of\nmass principle, that is, production rate minus consumption rate equals the net rate of change\nof isotope concentration. The 238 U concentration is represented by N 28 , and 239 Pu by N 49 .\n6\nMathematical Problems in Engineering\nThe other plutonium isotopes such as 240 Pu, 241 Pu, and 242 Pu are denoted by N 40 , N 41 , N 42 ,\nrespectively. All interested materials and isotopes are balanced as follows.\n235\nU depletion Absorption of thermal neutrons in the 235 U cause fission.\nU depletion Absorption of thermal neutrons in 238 U and absorption of\nresonance neutron in the 238 U to produce 239 Pu, and absorption of fast neutrons\nin 238 U to cause fission.\n238\nPu production Absorption of thermal neutrons in the 238 U Absorption of\nresonance neutrons from 235 U fission in 238 UAbsorption of resonance neutrons\nfrom 239 Pu fission in 238 U Absorption of resonance neutrons from 241 Pu fission\nin 238 U-Absorption of thermal neutrons in 239 Pu Absorption of fast neutrons from\n235\nU,238 U, and 239 Pu fissions in 238 U.\n239\nPu production Neutron absorption in the 239 Pu to produce 240 Pu minus neutron\nabsorption in the 240 Pu to produce 241 Pu.\n240\nPu production Neutron absorption in the 240 Pu to produce 241 Pu minus neutron\nabsorption in the 241 Pu to produce 242 Pu.\n241\nFission fragments production Fission yields of\nFission yields of 239 Pu Fission yields of 241 Pu.\n235\nU Fission yields of\n238\nU\nTherefore, according to our defined parameters, the coupled first-order differential\nequations which describes plutonium and uranium isotopes concentrations are given as:\ndN 25 t\n−σa25 φN 25 t,\ndt\ndN 28 t\n−σa28 φN 28 t − σa28 P1 φN 28 t − σa28 φN 28 t,\ndt\ndN 49 t\nσa28 φN 28 t η25 P1 1 − p σa25 φN 25 t η49 P1 1 − p σa49 φN 49 t\ndt\nη41 P1 1 − p σa41 φN 41 t − σa49 φN 49 t,\n2.3\nα28 − 1 25 25 25\nη σa N t η49 σa49 N 49 t η41 σa41 N 41 t φ,\n28\n28\n1α η −1\ndN 40 t α49 σa49\nφN 49 t − σa40 φtN 40 t,\ndt\n1 α49\ndN 41 t\nσa40 φN 40 t − σa41 φN 41 t,\ndt\nwhere φt is the average thermal neutron flux of the core we have considered φt is\nαβ\nindependent of time and equal to a constant, and σa α 2, 4 and β 0, 5, 8, 9 are the\nnuclear thermal microscopic absorption cross section which refer to the desired isotopes.\nAlso, other parameters are described in Table 3. As it is seen, the set of 2.3 are IVP, so it is\napparent that we must know the values of atom densities at the initiation of fuel irradiation.\nMathematical Problems in Engineering\n7\n&times;107\n6\n4\nNn\n2\n2.2\n0\nTime μs\nFigure 2: : dNn t/dt is plotted versus time using MATLAB-linked solver. In our real physical conditions\nand our suggested model here Nn t 2.2 μs 110, is the muon cycling rate of the mentioned μCF.\n238\n92 U\n2.7b\nn, γ\n239\n92 U\nβ− 23.5 m\nFission\n742.5b\n239\n39 Np\nβ\n−\nFission\n1009b\n2.35 d\n239\n94 Pu\n268.8b\nn, γ\n240\n94 Pu\n289.5b\nn, γ\n241\n94 Pu\n368b\nn, γ\nβ− 13.2 y\n241\n95 Am\n242\n94 Pu\n18.5b\nn, γ\n243\n94 Pu\nβ− 4.98 h\n243\n95 Am\nFigure 3: U-238 is converted to plutonium isotopes through the above chains.\nBut, it was stated that the core is initially loaded with fresh UO2 fuel and there are, in fact, no\nplutonium isotopes at starting time. Thus the only ones should be determined are N 28 and\nN 25 at the time of reactor startup. On the other hand uranium element is composed of two\nisotopes of U-235 and U-238, in which in a typical PWR type the fuel is enriched to about\naveraged value of 3.5 percent where the initial values are given in Table 2.\nTo solve the set of above IVP, 2.3, we make some simplifying assumptions in the first\niteration such as the following.\ni Effective cross sections remain constant throughout the core and during fuel\nii Average neutron flux within the core is constant and is considered to be equal to\n3.5 &times; 1013 neutrons/cm2 &middot; s.\niii The time duration at which reactor fuel has to be replaced with the fresh fuel, due\nto neutronic and/or thermal hydraulic reasons, is about 7300 hours.\n8\nMathematical Problems in Engineering\nTable 1: Constant values for solving 2.1 in 500◦ C temperature and media with one liquid hydrogen\ndensity. Also, it is supposed that there are equal concentrations of deuterium and tritium in the media.\nProcess\nRelative concentration of deuterium\nRelative concentration of tritium\nMuon decay constant\nMuonic-atom formation rate\nMedia ion density\nSticking coefficient\nFusion rate of dtμ molecule\nFormation rate of dtμ molecule\nTime of leakage\nMuon exchange rate between dμ and tμ atoms\nParameter\ncd\nct\nμ0\nλa\nφm\nωs\nf\nλμdt\nValue\n0.5\n0.5\n0.455 &times; 106 s−1\n1 &times; 1010 s−1\nLiquid hydrogen density\n0.008\n1.1 &times; 1012 s−1\nλμdt\nτ\nλdt\n2.8 &times; 108 s−1\n7.08 &times; 10−7 s\n1 &times; 1010 s−1\nTable 2: Masses and atom densities of each fuel isotopes at the time of reactor startup.\nMaterial\nUO2\n235\nU\n238\nU\nMass, kg\n93246\n3058.043\n84314.620\nConcentration, N&times;1024 , atoms/cm3\n0.0217391\n0.0007700\n0.0209645\nUsing data given in Table 3, the set of 2.3 are solved using our presented MATLABlinked solver. The solver was run and gave our desired results. Beginning of cycle BOC\nmasses of U-235, U-238, important plutonium isotopes, fission fragments burnup/or buildup\nand also End of Cycle EOC masses are illustrated in Table 4.\n2.3. Samarium-149 Build Up in a Nuclear Pressurized Water Reactor\nThe fission fragments are highly radioactive which undergo β and γ emissions. Some of\nthe fission fragments are highly neutron absorber materials and strongly affect neutronic\nbalance within the core as if they act as a neutron poison. They tend to capture a neutron\nand form a nucleus which contains a neutron more. So as will be seen, as time goes on, fission\nfragments would be converted to some other atoms and it is necessary to make an estimation\nof about their atom density number of atoms per unit volume within the fuel, with respect\nto irradiation time. According to the foregoing discussion, it is expected to have a completely\ndifferent fuel at the end of fuel life with that originally loaded within the core. In most cases\nof interest, such as study of fission products poisoning, involved isotopes form a radioactive\nand neutron reacting chain in which its members are linked together via β decay and n, γ\nreactions. Also some members of the chain are produced directly from U-235 fission; that\nis, they have a finite yield from fission. Consider, for example, that U-235 fission rate is\nNf σf φt, in which Nf is U-235 atom density, σf is the effective U-235 microscopic fission\ncross section, and φt is the time dependent neutron flux within the core. So as a result, this\namount of U-235 atoms are undergoing fission per unit volume of the fuel per unit time. We\ndefine here fission yield of i-th species, yi , as the ratio of i-th atoms produced to U-235 atoms\nundergoing fission. Consequently, constant formation rate of the i-th nuclide per unit volume\ncould be written as Pi yi Nf σf φt.\nMathematical Problems in Engineering\n9\nAs shown in Figure 4, some members of the chain will have two different probable\nmodes of disappearance, depending on whether the β decay or neutron capture is more\nprobable, they tend to make two completely different nuclei. This state of affair is taken\ninto account in writing the rate equations for some nuclei. Using the so-called chain, we can\ndevelop appropriate ”rate equation” for individual nuclide per unit volume. Before this, we\nshow some characteristics of the involved isotopes of the Sm-149 chain in Table 5.\nAccording to Figure 4, a set of 12 coupled ordinary first-order differential equations\nthat describe the rate of change of each of the 11 nuclei in the Sm-149 fission-product chain as\nwell as U-235 are written as follows:\ndN1\ny1 Nf σf φ − σ1 φ λ1 N1 ,\ndt\n2.4\ndN2\ny2 Nf σf φ λ1 N1 − σ2 φ λ2 N2 ,\ndt\n2.5\ndN3\ny3 Nf σf φ λ2 N2 − σ3 φ N3 ,\ndt\n2.6\n147\n60 Nd\n147\n61 Pm\n:\n147\n62 Sm\n:\n:\n148m\n61 Pm\n:\ndN4\nσ24 φN2 − σ4 φ λ4 N4 ,\ndt\n2.7\ndN5\nλ45 N4 σ25 φN2 − σ5 φ λ5 N5 ,\ndt\n2.8\ndN6\ny6 Nf σf φ σ4 φN4 σ5 φN5 − σ6 φ λ6 N6 ,\ndt\n2.9\ndN7\ny7 Nf σf φ λ6 N6 − σ7 φN7 ,\ndt\n2.10\n:\ndN8\nσ6 φN6 − σ8 φ λ8 N8 ,\ndt\n2.11\n:\ndN9\nσ7 φN7 λ8 N8 − σ9 φN9 ,\ndt\n2.12\ndN10\ny10 Nf σf φ σ9 φN9 − σ10 φ λ10 N10 ,\ndt\n2.13\ndN11\ny11 Nf σf φ σ10 φN10 − σ11 φN11 ,\ndt\n2.14\ndNf\n−σf φNf ,\ndt\n2.15\n148\n61 Pm\n149\n61 Pm\n:\n:\n149\n62 Sm\n:\n150\n61 Pm\n150\n62 Sm\n151\n62 Sm\n:\n152\n62 Sm\n:\n235\n92 U\n:\nwhere in 2.7, σ24 is radiative capture cross section for 147 Pmn, γ148m Pm reaction and in a\nsimilar manner, in 2.8 σ25 is for 147 Pmn, γ148 Pm reaction. Also in 2.8 λ45 is a radioactive\ndecay constant that 148m Pm, as a result of a β decay, disintegrates to 148 Pm. Moreover, yi\nindicates direct fission yield for i-th species from U-235 thermal fission, and finally, 2.15 is a\nrate equation for U-235 atom density in which σf is U-235 effective fission cross section. This\nequation implies that U-235 atom density decreases as an exponential function as time goes\non. Nf is time-dependent U-235 atom density.\n10\nMathematical Problems in Engineering\ny\n147\n60 Nd\n148\n61 Pm\ny\ny\n147\n61 Pm\n148\n61 Pm\ny\n147\n62 Sm\n149\n61 Pm\n150\n61 Pm\n149\n62 Sm\n150\n62 Sm\ny\n148\n62 Sm\ny\n151\n62 Sm\ny\n152\n62 Sm\ny Direct yield from fission\nFigure 4: The fission-product chain leading to Sm-149.\nTable 3: Effective properties of nuclide for thermal neutron in 1000 MWe PWR 3000 MW thermal power.\nNuclide\n235\nU\n238\nU\n239\nPu\n240\nPu\n241\nPu\nis fast fission factor 1.0476.\np is resonance scape probability 0.7725.\nP1 is fast to 238 U resonance probability 0.9889.\nη is neutrons produced per neutrons absorbed.\nα is ratio of capture to fission cross section.\nSubscript\n25\n28\n49\n40\n41\nσa barn\n556\n2.2342\n1618.2\n2616.8\n1567.3\nη\n1.96\n2.3432\n1.86\nα\n0.2398\n0.1907\n0.5430\n2.223\n0.3765\nTable 4: Fuel composition in a PWR after 1 year irradiation. All values are in terms of kg.\nMaterial\n235\nU\n238\nU\nPu\nFission fragments\nBOC\n3058\n84314\n0\n0\nEOC\n2632\n83604\n210\n926\nThe set of equations of 2.4 through 2.15 should be solved simultaneously to give\ndesired result and when the matrix of coefficient is established and further investigated, it\nturns out that this set of equations is a nonstiff one and here, is then solved using the RungeKuta method 11. Using our MATLAB-linked solver as well as data given in Table 5, our\ncalculated results are shown in Figure 5.\n2.4. Xenon135 Build Up in a Nuclear Pressurized Water Reactor\nAnother poison of our interest, as the greatest fission product in a nuclear reactor, is xenon135\nisotope. It is the most important neutron absorber poison in a typical PWR type such that it\nMathematical Problems in Engineering\n11\n&times;1016\n2\n1.8\n7.5\nAtom density #/cc\nAtom density #/cc\n&times;1020\n8\n7\n6.5\n6\n5.5\n1.6\n1.4\n1.2\n1\n0.8\n0.6\n0.4\n0.2\n5\n0\n0.5\n1\n1.5\n2\n2.5\n0\n3\n&times;107\n0\n0.5\n1\n1.5\n2\nU-235\n2.5\n3\n&times;107\nSm-149\na\nb\n&times;10\n12\n17\nAtom density #/cc\n10\n8\n6\n4\n2\n0\n0\n0.5\n1\n1.5\n2\n2.5\nPm-148\nPm-147\nSm-151\n3 7\n&times;10\nSm-152\nSm-150\nc\nFigure 5: a Uranium-235 depletion. b Samarium-149 atom density variation as a function of irradiation\ntime. c Atom density variation of other important members of the samarium chain.\nis produced directly from U-235 nucleus fission and indirectly from decay of Te-135 chain. Its\ndecay chain is in the form\n135\n135\n135\n135\nFission 135\n52 Te 53 I 54 Xe 55 Cs 56 Ba.\n2.16\n54 Xe is a great neutron absorber and under the neutron flux within the reactor\nwill be changed into 136\n54 Xe. Similar to the previous samarium poisoning subsection and\naccording to the so-called neutron absorbing and radioactive decay chain, we develop a set\n12\nMathematical Problems in Engineering\nTable 5: Nuclear properties for Sm decay chain.\nNuclide\nNuclide\nindication\nHalf-life\n147\nNd\nN1\n11.1 d\n147\nPm\nN2\n2.62 y\n147\nSm\nN3\n∞\n42 d 7% to 148 Pm,\n93% to 148 Sm 5.4 d\n53.1 h\n∞\n2.7 h\n∞\n87 y\n∞\n147m\n148\nPm\nPm\nPm\n149\nSm\n150\nPm\n150\nSm\n151\nSm\n152\nSm\n149\nN4\nN5\nN6\nN7\nN8\nN9\nN10\nN11\nAbsorption cross\nsection b\nDirect yield from\nU-235\n0\n845.72 to 148m Pm,\n448.23 to 148 Pm\n274.2\n0.0236\n31964\n0\n13858\n1105.6\n73635\n0\n158.38\n9734.5\n813.01\n0\n0.0113\n0\n0\n0\n0.0044\n0.00281\n0\n0\nof six coupled first-order differential equations that describe the rate of change of each of the\nfive nuclei in the fission-product chain as well as again U-235 atom. They are as follows:\n135\n135\n135\nXe :\n135\ndT\nyT Nf σf φ − λT T\ndt\nTe :\nI:\ndI\nλT T − λI I\ndt\n2.17\n2.18\ndX\nyX Nf σf φ λI I − σX Xφ − λX X\ndt\n2.19\ndC\nλX X − σC Cφ − λC C\ndt\n2.20\ndB\nλC C\ndt\n2.21\ndU\n−σa Nf φ\ndt\n2.22\nCs :\n135\n235\nBa :\nU:\nin which yT and yX stand for fission yields of 135 Te and 135 Xe, respectively. Also, λ\nare associated radioactive decay constants; σ are associated absorption cross-section, and\nexplicitly σf and σa are fission and absorption cross-sections for U-235 nucleus, respectively.\nConstant values that were appeared in the set of equations of 2.17 through 2.22 are given\nin Table 6. Equations 2.17 through 2.22 are again coupled IVPs and are stiff case 12, 13.\nThese equations are solved simultaneously to give desired results; which we have focused\non the Xe-135 concentration in the case of reactor power variation and results are given in\nFigure 6. In the first period, reactor operates at full power and xenon concentration increases\ntoward to a constant value after about 40 hours. In the second period, reactor is shut down\nand therefore, xenon peaks after about 11 hours and then decreases. In the third period,\nreactor operates at full power and a same manner as like as period 1 for xenon behavior\nMathematical Problems in Engineering\n13\nXenon-135 concentration\nReactor power profile\n100%\n50%\n0%\nPeriod I\nAt full power for 1000 hrs\nPeriod II\n0% for 48 hrs\nPeriod III\nPeriod IV\nAt full power for 500 hrs At 50% of full power\nFigure 6: Xenon135 atom density as well as power variations in the four-time interval is given.\nTable 6: Nuclear properties of fission products of mass 135.\nNuclide\n135\nTe\nI\n135\nXe\n135\nCs\n135\nBa\n135\nNuclide\nindication\nHalf life\ndecay\nconstant s−1\nAbsorption\ncross-section\nb\nDirect yield\nfrom U-235\nT\nI\nX\nC\nB\n29 s\n6.7 h\n9.2 h\n3 &times; 106 yr\nstable\n0.0239\n2.87 &times; 10−5\n2.09 &times; 10−5\n7.3 &times; 10−15\n0\n0\n0\n2.64 &times; 106\n17.2\n0\n0.0609\n0\n0.0032\n0\n0\nare obtained. In the fourth period, reactor operates at half of nominal power 50% and\ntherefore a xenon peak occurs after 11 hours, but xenon steady-state concentration is more\nthan previous period as we expected.\n3. Conclusion\nWe have presented a computer package to solve first-order IVPs with constant and variable\ncoefficients using MATLAB software, in which the solution of a given stiff or nonstiff coupled\ndifferential equations with known initial values were found and plotted. In the present paper,\nsome well-known nuclear engineering dynamical problems, related to the IVPs, were given.\nA major application of IVPs to a real problem is the fuel depletion in a suggested PWR,\nwhere it is computed by the present MATLAB-linked “solver”. We used matrices form such\nas d/dtXj P ij Xj with known initial values in each case. But we have focused on\nthe constant P ij matrix, where its elements are multiplication of neutronic flux and material\ncross sections. Our results are good compared with the well-known texts 10, 14. Obviously,\nour approach should be extended to a variable P ij or coupled IVPs with variable coefficients\nfor more accuracy, for instance, cross section is not fixed during fuel depletion 15, 16.\nOur aim here is to bring out a MATLAB-linked solver for researchers to solve coupled\nIVPs numerically where it is appeared frequently in many cases of nuclear engineering\nproblems. Reader may refer to the appendix to find our written MATLAB-linked solver\nprogram.\n14\nMathematical Problems in Engineering\nAppendix\nThree programs which are named COUPLED, COEFFICIENT, and DEPLET must be written\nas an M-file and then saved in the work directory of the MATLAB software. The first program\nis\nfunction dy = coupled(t,y) format(’long’,’e’) global Di\ndy = zeros(Di,1); % a column vector\n%disired variable\nload moham if O==1 run coefficient\nend\ndy=H∗y\nO=O+1;\nsave moham O\nThe second program is\nfunction coeficent\ndisp(’∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗’)\ndisp(’Coupled Differential Equations is computed in the form of\nDy=H∗y.’) disp(’ You should ENTER the H(n,m) array.’)\ndisp(’∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗’) load Di\nfor n=1:Di\nfor m=1:Di\ndisp(’In the following, you can find desired (n,m) to RUN:’)\ndisp([n m])\nH(n,m)=input(’Please ENTER value of H(n,m) for the above given\n(n,m):’);\nend end save H H\nThe 3rd program is:\nThis program compute and plot set of Coupled Differential\nEquations and Inintial Values(IVP) Using MATLAB commands. To\nstart computation one must enetr number of unknowns and equations,\nconstants and choose desired numerical method. function deplet\ndisp(’∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗’)\nDi=input(’∗∗Please ENTER the Number of Differential\nEquations(Unknowns): ’) save Di Di O=1; save moham O\n%----------------------------------------------% xi’s are initial conditions for unknowns.\nB=zeros(1,Di); for w=1:Di;\ndisp(’Insert initial values of Yi where i is:’);\ndisp([w])\nB(1,w)=input(’Enter Yi: ’);\nend\n%-------------------------------------------% t0 and t1 are the start and end points of time interval\nMathematical Problems in Engineering\n15\ndisp(’∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗∗’)\nT0=input(’Insert Start-point of the computations: ’);\ndisp(’∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗∗’)\nT1=input(’Insert End-point of the computations: ’);\ndisp(’∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗∗’)\n’,’NonStiff Equations’,’Stiff Equation’);\nif P==1;\nA=menu(’Which method you want for executing?’,\n’ode45 method’,’ode23 method’,’ ode113 method’);\nif A==1;\ndisp(’This methos is Based on an explicit Runge-Kutta (4,5)\nformula, the Dormand-Prince pair...’)\ndisp(’It is a one-step solver - in computing, it needs only ’)\ndisp(’the solution at the immediately preceding time point,.’)\ndisp(’In general, ode45 is the best function to\napply as &quot;first try&quot; for most problems.’)\ndisp(’###############################’)\ndisp(’∗∗press any key to continue computations∗∗’)\ndisp(’###############################’)\npause\n[t,y]=ode45(@coupled,[T0:1:T1],B);\nJ=input(’Which variables you want for plotting? ’);\nplot(t,y(:,J))\n%-----------------------------------------------------elseif A==2\ndisp(’This method is Based on an explicit Runge-Kutta (2,3) pair ’)\ndisp(’of Bogacki and Shampine. It may be more efficient’)\ndisp(’than ode45 at crude tolerances and in the ’)\ndisp(’presence of mild stiffness.’)\ndisp(’Like ode45, ode23 is a one-step solver.’)\ndisp(’###############################’)\ndisp(’∗∗press any key to continue computations∗∗’)\ndisp(’###############################’)\npause\n[t,y]=ode23(@coupled,[T0 T1],B)\nJ=input(’Which variables you want for plotting? ’);\nplot(t,y(:,J))\nelseif A==3\ndisp(’Software will use variable order Adams-Bashforth-Moulton PECE\nsolver.’)\ndisp(’It may be more efficient than ode45 at stringent’)\ndisp(’tolerances and when the ODE function is particularly ’)\ndisp(’expensive to evaluate. ode113 is a multistep’)\ndisp(’solver - it normally needs the solutions’)\ndisp(’at several preceding time points ’)\n16\nMathematical Problems in Engineering\ndisp(’###############################’)\ndisp(’∗∗press any key to continue computations∗∗’)\ndisp(’###############################’)\npause\n[t,y]=ode113(@coupled,[T0 T1],B)\nJ=input(’which variables you want for plotting? ’);\nplot(t,y(:,J))\nend\nelseif P==2\nG=menu(’Which method you want for executing’,\n’ode15s method’,’ode23s’,’ode23t’,’ode23tb’)\nif G==1\ndisp(’Software will use Variable-order solver based on the ’)\ndisp(’numerical differentiation formulas (NDFs).’)\ndisp(’Optionally it uses the backward differentiation formulas’)\ndisp(’BDFs, (also known as Gear method).’)\ndisp(’Like ode113, ode15s is a multistep solver.’)\ndisp(’If you suspect that a problem is stiff ’)\ndisp(’or if ode45 failed or was very inefficient, try ode15s’)\ndisp(’###############################’)\ndisp(’∗∗press any key to continue computations∗∗’)\ndisp(’###############################’)\npause\n[t,y]=ode15s(@coupled,[T0 T1],B)\nJ=input(’Which variables you want for plotting? ’);\nplot(t,y(:,J))\nelseif G==2\ndisp(’This method is Based on a modified Rosenbrock formula of\norder 2.’)\ndisp(’Because it is a one-step solver, ’)\ndisp(’it may be more efficient than ode15s ’)\ndisp(’at crude tolerances. It can solve some’)\ndisp(’kinds of stiff problems for which ode15s is not effective.’)\ndisp(’###############################’)\ndisp(’∗∗press any key to continue computations∗∗’)\ndisp(’###############################’)\npause\n[t,y]=ode23s(@coupled,[T0 T1],B)\nJ=input(’Which variables you want for plotting? ’);\nplot(t,y(:,J))\nelseif G==3\ndisp(’software wil use an implementation of the trapezoidal rule ’)\ndisp(’using a &quot;free&quot; interpolant.’)\ndisp(’Use this solver if the problem’)\ndisp(’is only moderately stiff and you’)\nMathematical Problems in Engineering\n17\ndisp(’need a solution without numerical damping.’)\ndisp(’###############################’)\ndisp(’∗∗press any key to continue computations∗∗’)\ndisp(’###############################’)\npause\n[t,y]=ode23t(@coupled,[T0 T1],B)\nJ=input(’Which variables you want for plotting? ’);\nplot(t,y(:,J))\nelseif G==4\ndisp(’software will use an implementation of TR-BDF2,’)\ndisp(’an implicit Runge-Kutta formula with ’)\ndisp(’a first stage that is a trapezoidal ’)\ndisp(’rule step and a second stage that is a’)\ndisp(’backward differentiation formula of ’)\ndisp(’order 2. Like ode23s, this solver may ’)\ndisp(’be more efficient than ode15s at crude tolerances.’)\ndisp(’###############################’)\ndisp(’∗∗press any key to continue computations∗∗’)\ndisp(’###############################’)\npause\n[t,y]=ode23tb(@coupled,[T0 T1],B)\nJ=input(’Which variables you want for plotting? ’);\nplot(t,y(:,J)) end disp(’If you want to RUN this code again, you\nmust rewrite (re-Enter) options.’) disp(’TO start again, RUN\ndeplet.m’) end\nAcknowledgments\nThis work is supported under academic Grant no. 88-GR-ENG-6. The corresponding author\nwishes to acknowledge the Research Council of the Shiraz University for their financial\nsupport.\nReferences\n1 F. Faghihi and K. Hadad, “Numerical solutions of coupled differential equations and initial values\nusing Maple software,” Applied Mathematics and Computation, vol. 155, no. 2, pp. 563–572, 2004.\n2 F. Faghihi, “Coupled differential equations and initial values using softwares; an applied program,”\nin Proceedings of the International Conference on Applied Mathematics and Numerical Analysis (ICNAAM\n’05), Rhodes, Greece, September 2005.\n3 F. Faghihi, “Numerical minimization procedures of the adiabatic approximation wavefunction,”\nApplied Mathematics and Computation, vol. 162, no. 3, pp. 1013–1021, 2005.\n4 F. Faghihi and M. R. Nematollahi, “Nuclear fuel depletion analysis using MATLAB software,”\nInternational Journal of Modern Physics C, vol. 17, no. 6, pp. 805–815, 2006.\n5 MATLAB Software Help, Version 7.0.0.19920R14, License No. 205273, Release 2004.\n6 K. Nagamine, T. Matsuzaki, K. Ishida, S. N. Nakamura, and N. Kawamura, “Implications of the recent\nD-T μCF experiments at RIKEN-RAL and near-future directions,” Hyperfine Interactions, vol. 119, no.\n1–4, pp. 273–280, 1999.\n7 F. Faghihi and M. R. Eskandari, “Nuclear fusion rate study of A muonic molecule via nuclear\nthreshold resonances,” International Journal of Modern Physics E, vol. 14, no. 8, pp. 1213–1221, 2005.\n18\nMathematical Problems in Engineering\n8 M. R. Eskandari and F. Faghihi, “Forced fusion in the excited state of dtμ muonic-molecule and its\npossible drivers,” International Journal of Modern Physics C, vol. 14, no. 10, pp. 1281–1293, 2003.\n9 M. R. Eskandari, F. Faghihi, and R. Gheisari, “μCF study of D/T and H/D/T mixtures in\nhomogeneous and inhomogeneous medium, and comparison of their fusion yields,” International\nJournal of Modern Physics C, vol. 13, no. 5, pp. 689–705, 2002.\n10 M. Benedict, T. H. Pigford, and H. W. Levi, Nuclear Chemical Engineering, McGraw-Hill, New York,\nNY, USA, 1981.\n11 M. Venkatesulu and P. D. N. Srinivas, “Solutions of nonstandard initial value problems for a first\norder ordinary differential equation,” Journal of Applied Mathematics and Simulation, vol. 2, no. 4, pp.\n225–237, 1989.\n12 S. Sekar, “Analysis of linear and nonlinear stiff problems using the RK-Butcher algorithm,”\nMathematical Problems in Engineering, vol. 2006, Article ID 39246, 15 pages, 2006.\n13 I. P. Gavrilyuk, M. Hermann, M. V. Kutniv, and V. L. Makarov, “Difference schemes for nonlinear\nBVPs using Runge-Kutta IVP-solvers,” Advances in Difference Equations, vol. 2006, Article ID 12167, 29\npages, 2006.\n14 J. R. Lamarsh, Introduction to Nuclear Engineering, Prentice Hall, Upper Saddle River, NJ, USA, 2001.\n15 M. Legua, I. Morales, and L. M. Sánchez Ruiz, “Resolution of first- and second-order linear differential\nequations with periodic inputs by a computer algebra system,” Mathematical Problems in Engineering,\nvol. 2008, Article ID 654820, 7 pages, 2008.\n16 A. J. Arenas, G. González-Parra, L. Jódar, and R.-J. Villanueva, “Piecewise finite series solution of\nnonlinear initial value differential problem,” Applied Mathematics and Computation, vol. 212, no. 1, pp.\n209–215, 2009.\n```" ]
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{"ft_lang_label":"__label__en","ft_lang_prob":0.8061764,"math_prob":0.9087273,"size":36908,"snap":"2019-51-2020-05","text_gpt3_token_len":11084,"char_repetition_ratio":0.1412313,"word_repetition_ratio":0.0669145,"special_character_ratio":0.30421588,"punctuation_ratio":0.13187818,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9830766,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-11T21:16:20Z\",\"WARC-Record-ID\":\"<urn:uuid:67fdc3af-75b7-4c49-9059-9d1852eb0a06>\",\"Content-Length\":\"135823\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2b7bb8b2-e1af-4f50-b99e-bcc89402a13f>\",\"WARC-Concurrent-To\":\"<urn:uuid:cfe96ed3-24ea-40a8-8d2b-66b33a39233a>\",\"WARC-IP-Address\":\"104.24.125.188\",\"WARC-Target-URI\":\"https://studylib.net/doc/10947644/\",\"WARC-Payload-Digest\":\"sha1:ZCOPDF4MWEUKWUFZ2U4TMZADQIAHV3ZC\",\"WARC-Block-Digest\":\"sha1:KEL6ACBQUUOV3VIMTJO76WZSZNWAHZQ4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540532624.3_warc_CC-MAIN-20191211184309-20191211212309-00491.warc.gz\"}"}
https://dsp.stackexchange.com/questions/73315/applying-superposition-property-x2n-vs-xn2
[ "# Applying Superposition Property : $x^{2}[n]$ vs $x[n^{2}]$\n\nIf we consider the mapping $$\\mathcal{H} : x[n]\\mapsto y[n]$$ and define the following output signal $$y_{1}[n]:=\\mathcal{H}\\{x[n]\\}:=x^{2}[n]$$, then one can easily verify that such system is non-linear for it rejects the superposition property. But I am having a hard time applying the superposition property to $$y_{2}[n]:=\\mathcal{H}\\{x[n]\\}:=x[n^{2}]$$ because its confuses with me with $$y_{1}[n]$$. I hope someone can offer any assitance I would be very much grateful.\n\n• Showing whether $\\mathcal{H}\\{x[n^2]\\}$ is linear (or not) follows the exact same steps of showing that $\\mathcal{H}\\{x^2[n]\\}$ is non-linear...? On which step did you have the trouble? Feb 19, 2021 at 20:45\n• The first step, how do I substitute $a_{1}x_{1}+a_{2}x_{2}$ in place of $x[n^{2}]$ because its supposedly not same as replacing it in place of $x^{2}[n]$. @Fat32 Feb 19, 2021 at 22:06\n• but it's not the first step. You shall first define y1 and y2 from x1 and x2. Feb 19, 2021 at 22:15\n• Indeed, we define $x_{1}[n]\\mapsto y_{1}[n]$ and $x_{2}[n]\\mapsto y_{2}[n]$ by the means of the system $\\mathcal{H}$ for we shall prove that $\\mathcal{H}\\{a_{1}x_{1}+a_{2}x_{2}\\}=a_{1}\\mathcal{H}\\{x_{1}\\}+a_{2}\\mathcal{H}\\{x_{2}\\}$. @Fat32 Feb 19, 2021 at 22:19\n\nGiven the system I/O definition:\n\n$$y[n] = \\mathcal{H}\\{x[n]\\} = x[n^2] \\tag{1}$$\n\nyou can easily show that it's a linear (but time-varying) system.\n\nFollowing the standard procedure\n\nlet $$y_1[n] = \\mathcal{H}\\{x_1[n]\\} = x_1[n^2] \\tag{2.1}$$ and $$y_2[n] = \\mathcal{H}\\{x_2[n]\\} = x_2[n^2] \\tag{2.2}$$\n\nthen define\n\n$$x_3[n] = a x_1[n] + b x_2[n] \\tag{3}$$\n\nand\n\n\\begin{align} y_3[n] &= \\mathcal{H}\\{x_3[n]\\} \\tag{4}\\\\\\\\ &= x_3[n^2] \\tag{5}\\\\\\\\ &= a x_1[n^2] + b x_2[n^2]\\tag{6}\\\\\\\\ &= a y_1[n] + b y_2[n]\\tag{7}\\\\ \\end{align}\n\nwhere Eqs(4)-(5) follow Eq.(1), Eq.(6) follows Eq.(3), and Eq.(7) follows Eq.(2).\n\nEquation (7) indicates that the system is linear." ]
[ null ]
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https://passion4maths.com/resources/new-a-level-coming-soon/ocr/pure-and-statistics/
[ "For OCR\nStats revision notes\nTake a look at the latest Sample Paper\nPure Topics see separate page\nStatistics Topics\nSampling; a basic understanding\nSingle Variable Data; line charts, dot plots, stem & leaf, box & whisker, cumulative frequency, histogram.\nBivariate Data; Scatter graphs, regression lines.\nProbability; probability trees, sample spaces, Venn diagrams New\nDiscrete Probability Distributions; In a table, Binomial.\nNormal Distribution New (previously S2)\nHypothesis Testing; proportion in Binomial, mean of a Normal\nPearson’s Correlation coefficient New\nModelling using a Data Set  New\nYes, a knowledge of the Geography of England & Wales will help!", null, "No longer in the Maths A level but included in Further Maths\nArrangements & Selections\nGeometric Distribution\nEquation of a regression Lines\nSpearman’s Rank" ]
[ null, "https://passion4maths.com/wp-content/uploads/2017/03/English_regions_2009-214x300.jpg", null ]
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https://daxos.org/what-fraction-is-bigger-3-4-or-1-2/
[ "## What fraction is bigger 3 4 or 1 2?\n\n0.75 is greater than 0.5. Therefore, 3/4 is greater than 1/2 and the solution to the question “Is 3/4 greater than 1/2?” is sure. Note: When evaluating fractions equivalent to 3/4 and 1/2, you should additionally convert the fractions (if necessary) so they have the same denominator after which evaluate which numerator is larger.\n\n### What is greater 7/8 or 5 10 or lesser?\n\nNo, it equals to half of, which is 1/2. 7/8 is larger than 1/2. 5/10 equals to half of. 7/8 is higher than 5/10.\n\n(*2*)\n\n#### What is better 3/5 or 1/4 or much less?\n\n0.6 is greater than 0.25. Therefore, 3/5 is more than 1/4 and the solution to the query “Is 3/5 greater than 1/4?” is sure. Note: When comparing fractions such as 3/Five and 1/4, it’s worthwhile to also convert the fractions (if essential) so they have got the same denominator and then compare which numerator is higher.\n\nWhich is the biggest fraction?\n\nTo examine fractions with like numerators, have a look at the denominators. The fraction with the smaller denominator is the larger fraction. Let’s take a look at some examples. Since one-half has the smaller denominator, it is the larger fraction.\n\nWhat fraction is bigger 2/3 or 3 4?\n\nFor 34 , we are multiplying 3 to the bottom (denominator) so we need to multiply 3 to the highest (numerator). For 23 we’re multiplying 4 to the ground so we have to multiply 4 to the top.\n\n## What is the most important fraction?\n\nFor higher fraction, the numerator should be higher (denominators are same) and/or denominator should be smaller (numerators are similar). So comparing 1/24, 1/Forty five and 1/72, we forget about 1/Forty five and 1/72. Since 1/4.29 has the smallest denominator, the most important fraction might be 7/30.\n\n### Which fraction is bigger 2 3 or 2 6?\n\n2/3 is more than 2/6. Denominator is greater, this means that 2/6 should be smaller.\n\n#### What is bigger 5/8ths or 1 2?\n\nThese are all the identical questions with one resolution. 0.625 is more than 0.5. Therefore, 5/8 is more than 1/2 and the answer to the query “Is 5/8 greater than 1/2?” is yes.\n\nWhat is the least to greatest in fractions?\n\nNow that they all have the similar denominator, the fractions are simple to check. Use their top number, or numerator, to rank them from least to biggest. Ranking the fractions we discovered above, we get: 6/18, 12/18, 15/18.\n\n(*1*)\n\n(*3*)\n\nin" ]
[ null ]
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https://www.markedbyteachers.com/international-baccalaureate/maths/this-essay-will-examine-theoretical-and-experimental-probability-in-relation-to-the-korean-card-game-called-sut-da-first-a-definition-of-probability-and-how-it-is-used-in-general-life-will-be-examined-each-hand-of.html
[ "• Join over 1.2 million students every month\n• Accelerate your learning by 29%\n• Unlimited access from just £6.99 per month\n\n# This essay will examine theoretical and experimental probability in relation to the Korean card game called Sut-Da. First, a definition of probability and how it is used in general life will be examined. Each hand of Sut-Da provides the theore\n\nExtracts from this document...\n\nIntroduction\n\nABSTRACT\n\nThis essay will examine theoretical and experimental probability in relation to the Korean card game called ‘Sut-Da’. First, a definition of probability and how it is used in general life will be examined. Each hand of ‘Sut-Da’ provides the theoretical probability for a player to win the game. It is clear however, that the theoretical value of winning in ‘Sut-Da’ does not always apply in real life games. Secondly, the experimental probability of winning for each hand is examined. To find out the probability of winning with each hand, I am using permutation & combination, theoretical probability and experimental probability. Experimental probability data was gained from my friend and I playing the game. Finally, within my evaluation, I looked at experimental probability using excel spread sheets and also using calculations that were compared with the experimental probability data gained from actually playing the game. The theory of probability has been covered in a number of textbooks and I used these textbooks to help me get used to the formula. I have then worked out all the possibilities of hands and their probabilities for winning, performing all the calculations myself and using my own numbers in presenting my data for the experimental probability data.\n\nIntroduction\n\nIt all began when I started to watch a Korean drama called “Ta-JJa”. I decided to watch this drama as one of my favourite actor was the main character in the drama. This drama was about this man getting into the world of gambling in order to be successful in his life. This drama was only based on the tricks that could have been used while playing the game “Sut-Da”.\n\nMiddle\n\nProbability of winning with April (Ddaeng-4) is split into eight different                         possibilities\n\nGraph 7. Tree Diagram of Ddang-4", null, "", null, "", null, "= 4.9545604 x 10-3\n\nProbability of winning with March (Ddaeng-3) is split into nine different                         possibilities.\n\nGraph 8. Tree Diagram of Ddang-3", null, "For Ddaeng-3, it is slightly different than other hands. This is because Ddaeng-3         includes a card that has 光. As this hand requires光card to complete the hand,         3-8 Guang-Ddaeng and 1-3 Guang-Ddaeng cannot be created. Hence these two         hands were eliminated from the probability of opponent winning.", null, "", null, "= 4.9879601 x 10-3\n\nProbability of winning with February (Ddaeng-2) is split into ten different                         possibilities.\n\nGraph 9. Tree Diagram of Ddang-2", null, "", null, "", null, "= 4.8847609 x 10-3\n\nProbability of winning with January (Ddaeng-1) is split into eleven different                 possibilities.\n\nGraph 10. Tree Diagram of Ddang-1", null, "For this hand, it is similar with Ddaeng-3. Because this hand requires 光card, 1-3         Guang-Ddaeng and 1-8 Guang-Ddaeng cannot be created. Hence these two         hands were eliminated from the probability of opponent winning.", null, "", null, "= 4.9191606 x 10-3\n\nAli\n\nProbability for player 1 to get Ali is 2/20C2. Ali could be formed using one January                 and one February card; hence there are four combinations and 20C2 represents         getting two cards from a deck of 20 cards. However, this needs to be split into         two different ways where the January card may be 光card or not. Hence, the         probability for player 1 to win with Ali is (1/2) x (2/20C2) x (1 – (10/18C2) – (12/18C2).         (10/18C2) is the sum of probabilities where player 2 will win when player 1 has Ali         with January 光card. (12/18C2) is the sum of probabilities where player 2 will win         then player 1 has Ali with normal January card.\n\nHence, by subtracting from 1, 2nd bracket represents the sum of probabilities of         player 2 receiving a lower hand than player 1.\n\nP(player 1 win with Ali)        =", null, "", null, "= 9.76952185 x 10-3\n\nDok-Sa\n\nProbability for player 1 to get Dok-Sa is 2/20C2.\n\nConclusion\n\nHowever, considering that the game is limited, a game where the player has limited information, there are not many situations in different parts of the world that undergoes similar concepts. However, this could be seen similarly in combats between two groups. For example, when there is a debate between two parties, then both sides are going through the same concept compared to ‘Sut-Da’. Since they lack in information, they are handicapped in preparing for the discussion, however, they do have choice in what they will do in order to win the discussion.\n\nTo conclude, it was obtained by the calculations that the percentage difference between the theoretical probability and the experimental probability is similar for some hands but also have huge difference in other hands. To fix this problem, when the number of trials were increased, then the probability would be more spread out than by just having 1000 trials. Also, this concept of ‘Sut-Da’ could be seen in the combat between two groups such as debating.\n\nAppendices\n\nAppendix 1. Photos of My Friend and I Playing ‘Sut-Da’", null, "", null, "", null, "", null, "## Bibliography\n\nChaudhri, Vivek. \"Game Theory and Business Applications.\" Economic Record (2005): 88+.\n\n\"Game Theory.\" The Wilson Quarterly (2005): 92+.\n\nGendenko, B. V. and B. D. Seckler. The Theory of Probability. New York: Chelsea Publishing Company, 1962.\n\nHanafuda The Japanese Flowercard Game. 2010. 10 October 2009 <http://www.hanafuda.com/>.\n\nHenry E. Kyburg, Jr. Probability Theory. Englewood Cliffs: Prentice-Hall, 1969.\n\nKneale, William. Probability and Induction. Oxford: Clarendon Press, 1949.\n\nLeonard, Graham. Sutda. 26 04 2004. 12 December 2009 <http://hanafubuki.org/sutda.html>.\n\nUrban, Paul, et al. Mathematics for the international students Mathematics HL (Core). Adelaide: Haese & Harris, 2008.\n\nWilson, Matthew C. \"Uncertainty and Probability in Institutional Economics.\" Journal of Economic Issues (2007): 1087+.\n\n| Page\n\nThis student written piece of work is one of many that can be found in our International Baccalaureate Maths section.\n\n## Found what you're looking for?\n\n• Start learning 29% faster today\n• 150,000+ documents available\n• Just £6.99 a month\n\nNot the one? Search for your essay title...\n• Join over 1.2 million students every month\n• Accelerate your learning by 29%\n• Unlimited access from just £6.99 per month\n\n# Related International Baccalaureate Maths essays\n\n1.", null, "## Extended Essay- Math\n\n�&\\$h���(Ú]C a���\\$Hn��du�{C3/4 ��g�}6�Rd���\\$Û·oO���\"'c�ÌE��(KL��L�g��'�m0J�f...j# �Y�\"w�o~�H'f��h6i�d�3/4} �+l��Nj��M���(c)-BÖ¬Y��;�i�&o,'�ST �L\"�~�qI�&'R\"u�m�z+�:N�6������,-8�� \"��=.ImT�mä·L�3/4�\\$�gÙ²e��QdoÅ9���V0P4�;�%�\"�()u;���c�=��G�d�P...-\"0oh���(c)�Ñ�-\\$��1/2�Gy�h�[5!���_}���A?�x�U\"Vï¿½Ô ï¿½e-�LDǸ\\$�' J�L�1/41/2��=x�`�E� �×8I�\"�;y�ƿO�)�h�-�L� v���+yC�\"��� ص(c)�-�´@A�d�vB��u�Kâ·¡V �*(c)����-wM��]1/4dbIXD�,3/4(tm)�k)�Ѩ� -\\$,[�UW]m�z+?�-' ���H6R �n��{����N�k��pI�\\!E�Q?N#��[\\$A?� ��'�K�6-�Hã°1/2��'\"W��ӧO\"� �G{�����(`�7q'H:�d\"�Ó<�7�x�U\"V�7o�-j�U(c)M �E����v-.]�,(c)�0'{/L{?Ú21��DM7dI�m�3/4H[is��(�x�C�H�!� Wx(r)�''���'hFR�#P7'�w ,��c�(c)uOq(c)� d-�e?�i�P�. QU-1/4-��.A?�^{-,2�g�G�-B�=�o��WG&� /1/4P|G� \"�-�P �� -s�S -mX\\$��EX~�f�pv/X� �\"�3/4�ƭ�Zig\"��0�-Z��Q����\" M�,,���)�m�\"�ÍϪ@�h��' 8m�\"�Q��`'x��d'�C�RG~��(c):� ��1/2��l�'\"I^z饱/[:��a'�/�`�,Y8\"i�%��-���O9pj%��\\'\"ï¿½× V���cP/P� �\"^=�nâ°ï¿½x Z���ڴiS�] #`5-��dU\" �_Þ\"E'�M�x�Rd:�9T,�{\\��Źç C,���K&(c)���ÙN�p\\�1/2��ͣ'�Q�m1/4y\\$7w�����M�?�\"�1/2{�b�j%�-�[email protected]�ٳ',2.E\"%�cZ�l�k�.��}1/2>��#�� O\\{eI�m~b'�i�qK�^1/2z%�\"� ��1/4���@y-���^��'��#F������Y�� � � 3/4bX�.��S,�\\$�OK�\\$\\$ä� V�GN#�N��M1/2Ȥ7�]��K/9 W��c�\"�;\\$V4�\"KR���m\"-��^�\"E�h�}��\\$\\'1/[email protected]�...0�� ���-\"�dxB��%�\\�(9jԨ��PK�@�3/4�'K.\\��4�(tm)c-�8�,(tm)(c)9-�...�\\'�5\\��NbY�:q�A?��\\$<����v�<Y�:K�F-3/4 �h]�}��Q�kZ��\"�69�x�a[)�\"w�Þ��� (tm)\n\n2.", null, "## In this essay, I am going to investigate the maximum number of pieces obtained ...\n\ndifferences 11 7 4 2 (Two-dimensional) differences 4 3 2 (One-dimensional) differences 1 1 As we found that all the dimensional objects separated into 2 parts when n=1, therefore when n=1, Q1=2. Use the difference array again to find out the results of the four-dimensional.\n\n1.", null, "## THE DICE GAME - calculating probabilities\n\n32/216 Bob rolls 1 - Ann wins 35/36 of the time... 35/216 Ann wins a total of 57.8% of the time Second: In case when Ann is rolling for the second time is only happened when both Ann and Bob didnt win the first roll.\n\n2.", null, "## Stellar Numbers. After establishing the general formula for the triangular numbers, stellar (star) shapes ...\n\nThe first step is to substitute the established values into the three quadratic equations, as shown below: Un = an2 + bn + c Therefore: quadratic When n = 1, Un = 1 1 = a(1)2 + b(1) + c 1 = 1a + 1b + c 1 = a\n\n1.", null, "## Math IA type 2. In this task I will be investigating Probabilities and investigating ...\n\nTherefore although it can be used relatively accurately to predict the most probable outcome, still it is not set in stone. Also unless, the total numbers of points played are multiples of three, the last 2 points or any 2 points will have to be distributed such that for example\n\n2.", null, "## While the general population may be 15% left handed, MENSA membership is populated to ...\n\nThe poll will specify that only IB junior and senior students should answer. After collecting sufficient data, I will process it through a variety of charts; I plan to visually display my data in the form of a pi chart, comparing the percentage distribution of left and right-handed people's GPA\n\n1.", null, "## The purpose of this investigation is to create and model a dice-based casino game ...\n\nTherefore the probability that players A and B both roll the same number is , or . Because the probability that both players roll the same number is , it stands to reason that the probability in which both players roll different numbers is . Let the ordered pair (m,n)\n\n2.", null, "## Modelling Probabilities on games of tennis\n\nTherefore here I will add all the above fractions: = = 1 As the fractions sum up to 1, the values are true. From the above values, a histogram is created using Microsoft Excel and then exported to Microsoft Word: According to the histogram above, the modal value is 7 due to its highest probability.", null, "• Over 160,000 pieces\nof student written work\n• Annotated by\nexperienced teachers\n• Ideas and feedback to", null, "" ]
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https://origin.geeksforgeeks.org/unordered_map-reserve-in-c-stl/
[ "# unordered_map reserve() in C++ STL\n\n• Difficulty Level : Hard\n• Last Updated : 31 Dec, 2018\n\nAs we know a Bucket is a slot in the container’s internal hash table to which all the element are assigned based on the hash value of their key . Buckets are numbered from 0 to bucket_count. Now as a Bucket hold variable number of the item . This number is based on the term Load Factor .When the Load Factor(load_factor) reaches a certain threshold, the container increases the number of buckets and rehashes the map.But when we call rehash(n) then it directly sets the number of buckets to n and triggers a rebuild of the entire hash table.But when we call reserve(n) then it create enough Buckets to hold at least n items.If then we add > n items to the map, a rehash may be triggered depending on the load factor. By calling reserve with the size we expected for the unordered_map container we avoided the multiple rehashes that the increases in container size could have produced and optimized the size of the hash table. The C++ function std::unordered_map::reserve() sets the number of buckets in the container (bucket_count) to the most appropriate to contain at least n elements.\n\nSyntax:\n\n`unordered_map_name.reserve(N)`\n\nParameters: The function accepts a single mandatory parameter N which specifies the number of elements requested as the minimum capacity.\n\nReturn Value: The function does not return anything.\n\nBelow programs illustrates the above function:\n\nProgram 1:\n\n `// C++ program to illustrate the ` `// unordered_map::reserve() ` `#include ` `using` `namespace` `std; ` ` `  `int` `main() ` `{ ` ` `  `    ``// declaration ` `    ``unordered_map<``int``, ``int``> sample1, sample2; ` ` `  `    ``// the sample1 size is reserved for ` `    ``// the bucket to contain a minimum of ` `    ``// one elements ` `    ``sample1.reserve(1); ` ` `  `    ``// inserts key and element ` `    ``// in sample1 ` `    ``sample1.insert({ 10, 100 }); ` `    ``sample1.insert({ 50, 500 }); ` ` `  `    ``// inserts key and element ` `    ``// in sample1 ` ` `  `    ``// the sample1 size is reserved for ` `    ``// the bucket to contain a minimum of ` `    ``// three elements ` `    ``sample2.reserve(3); ` ` `  `    ``sample2.insert({ 20, 200 }); ` `    ``sample2.insert({ 30, 300 }); ` `    ``sample2.insert({ 30, 150 }); ` ` `  `    ``cout << ``\"The size of Sample1 is: \"` `<< sample1.size(); ` ` `  `    ``cout << ``\"\\nKey and Elements of Sample1 are:\"``; ` `    ``for` `(``auto` `it = sample1.begin(); it != sample1.end(); it++) { ` `        ``cout << ``\"{\"` `<< it->first << ``\", \"` `<< it->second << ``\"} \"``; ` `    ``} ` ` `  `    ``cout << ``\"\\n\\nThe size of Sample2 is: \"` `<< sample2.size(); ` ` `  `    ``cout << ``\"\\nKey and Elements of Sample2 are:\"``; ` `    ``for` `(``auto` `it = sample2.begin(); it != sample2.end(); it++) { ` `        ``cout << ``\"{\"` `<< it->first << ``\", \"` `<< it->second << ``\"} \"``; ` `    ``} ` ` `  `    ``return` `0; ` `} `\n\nOutput:\n\n```The size of Sample1 is: 2\nKey and Elements of Sample1 are:{50, 500} {10, 100}\n\nThe size of Sample2 is: 2\nKey and Elements of Sample2 are:{30, 300} {20, 200}\n```\n\nProgram 2:\n\n `// C++ program to illustrate the ` `// unordered_map::reserve() ` `#include ` `using` `namespace` `std; ` ` `  `int` `main() ` `{ ` ` `  `    ``// declaration ` `    ``unordered_map<``char``, ``char``> sample1, sample2; ` ` `  `    ``// the sample1 size is reserved for ` `    ``// the bucket to contain a minimum of ` `    ``// one elements ` `    ``sample1.reserve(1); ` ` `  `    ``// inserts key and element ` `    ``// in sample1 ` `    ``sample1.insert({ ``'a'``, ``'A'` `}); ` `    ``sample1.insert({ ``'g'``, ``'G'` `}); ` ` `  `    ``// inserts key and element ` `    ``// in sample1 ` ` `  `    ``// the sample1 size is reserved for ` `    ``// the bucket to contain a minimum of ` `    ``// three elements ` `    ``sample2.reserve(3); ` ` `  `    ``sample2.insert({ ``'b'``, ``'B'` `}); ` `    ``sample2.insert({ ``'c'``, ``'C'` `}); ` `    ``sample2.insert({ ``'d'``, ``'D'` `}); ` ` `  `    ``cout << ``\"The size of Sample1 is: \"` `<< sample1.size(); ` ` `  `    ``cout << ``\"\\nKey and Elements of Sample1 are:\"``; ` `    ``for` `(``auto` `it = sample1.begin(); it != sample1.end(); it++) { ` `        ``cout << ``\"{\"` `<< it->first << ``\", \"` `<< it->second << ``\"} \"``; ` `    ``} ` ` `  `    ``cout << ``\"\\n\\nThe size of Sample2 is: \"` `<< sample2.size(); ` ` `  `    ``cout << ``\"\\nKey and Elements of Sample2 are:\"``; ` `    ``for` `(``auto` `it = sample2.begin(); it != sample2.end(); it++) { ` `        ``cout << ``\"{\"` `<< it->first << ``\", \"` `<< it->second << ``\"} \"``; ` `    ``} ` ` `  `    ``return` `0; ` `} `\n\nOutput:\n\n```The size of Sample1 is: 2\nKey and Elements of Sample1 are:{g, G} {a, A}\n\nThe size of Sample2 is: 3\nKey and Elements of Sample2 are:{d, D} {c, C} {b, B}\n```\n\nMy Personal Notes arrow_drop_up\nRecommended Articles\nPage :" ]
[ null ]
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https://learnesy.com/excel-functions/stdev/
[ "# STDEV\n\nSee more Excel functions\n\nIn this lesson we are going to quickly show how to calculate standard deviation in Excel using the STDEV function.\nIt consists of only one argument: the cells for which we want to calculate a standard deviation.\nWe’ll write Equals, STDEV, and then select the cells.\nFor this particular example, we have a standard deviation of about 2.78.\nNote that any Text, or Logical Values are ignored when using this version of standard deviation calculation.\nThis lesson has gone through the STDEV function, which returns the standard deviation of a range of cells." ]
[ null ]
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https://winmundo.com/error-in-python-script-expected-2d-array-got-1d-array-instead/
[ "# Error in Python script Expected 2D array, got 1D array instead:?\n\n## Error in Python script Expected 2D array, got 1D array instead:?\n\nYou are just supposed to provide the `predict` method with the same 2D array, but with one value that you want to process (or more). In short, you can just replace\n\n``````[0.58,0.76]\n``````\n\nWith\n\n``````[[0.58,0.76]]\n``````\n\nAnd it should work.\n\nEDIT: This answer became popular so I thought Id add a little more explanation about ML. The short version: we can only use `predict` on data that is of the same dimensionality as the training data (`X`) was.\n\nIn the example in question, we give the computer a bunch of rows in `X` (with 2 values each) and we show it the correct responses in `y`. When we want to `predict` using new values, our program expects the same – a bunch of rows. Even if we want to do it to just one row (with two values), that row has to be part of another array.\n\nThe problem is occurring when you run prediction on the array `[0.58,0.76]`. Fix the problem by reshaping it before you call `predict()`:\n\n``````import numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib import style\n\nstyle.use(ggplot)\nfrom sklearn import svm\n\nx = [1, 5, 1.5, 8, 1, 9]\ny = [2, 8, 1.8, 8, 0.6, 11]\n\nplt.scatter(x,y)\nplt.show()\n\nX = np.array([[1,2],\n[5,8],\n[1.5,1.8],\n[8,8],\n[1,0.6],\n[9,11]])\n\ny = [0,1,0,1,0,1]\n\nclf = svm.SVC(kernel=linear, C = 1.0)\nclf.fit(X,y)\n\ntest = np.array([0.58, 0.76])\nprint test # Produces: [ 0.58 0.76]\nprint test.shape # Produces: (2,) meaning 2 rows, 1 col\n\ntest = test.reshape(1, -1)\nprint test # Produces: [[ 0.58 0.76]]\nprint test.shape # Produces (1, 2) meaning 1 row, 2 cols\n\nprint(clf.predict(test)) # Produces , as expected\n``````\n\n#### Error in Python script Expected 2D array, got 1D array instead:?\n\nI use the below approach.\n\n``````reg = linear_model.LinearRegression()\nreg.fit(df[[year]],df.income)\n\nreg.predict([])\n``````" ]
[ null ]
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https://answers.everydaycalculation.com/divide-fractions/4-2-divided-by-3-7
[ "Solutions by everydaycalculation.com\n\n## Divide 4/2 with 3/7\n\n1st number: 2 0/2, 2nd number: 3/7\n\n4/2 ÷ 3/7 is 14/3.\n\n#### Steps for dividing fractions\n\n1. Find the reciprocal of the divisor\nReciprocal of 3/7: 7/3\n2. Now, multiply it with the dividend\nSo, 4/2 ÷ 3/7 = 4/2 × 7/3\n3. = 4 × 7/2 × 3 = 28/6\n4. After reducing the fraction, the answer is 14/3\n5. In mixed form: 42/3\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://www.jpost.com/international/j-street-not-promoting-goldstone-tour
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[ null ]
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https://www.arxiv-vanity.com/papers/astro-ph/9906073/
[ "# Perturbations in a coupled scalar field cosmology\n\nLuca Amendola Osservatorio Astronomico di Roma,\nViale Parco Mellini 84,\n00136 Roma, Italy\nJuly 2, 2022\n###### Abstract\n\nI analyze the density perturbations in a cosmological model with a scalar field coupled to ordinary matter, such as one obtains in string theory and in conformally transformed scalar-tensor theories. The spectrum of multipoles on the last scattering surface and the power spectrum at the present are compared with observations to derive bounds on the coupling constant and on the exponential potential slope. It is found that the acoustic peaks and the power spectrum are strongly sensitive to the model parameters. The models that best fit the galaxy spectrum and satisfy the cluster abundance normalization have field energy density and a scale factor expansion law ,\n\n## I Introduction\n\nPerhaps the most important concept in modern cosmology is that fundamental physics, along with gravity, shapes the distribution of matter on very large scales. Fundamental physics enters in at least two distinct ways: through the potential of the inflationary field, which sets the initial conditions of the fluctuation field, and through the properties of the dark matter, which govern the evolution of the fluctuations up to the present. As a consequence, the imprint of the density fluctuations on the microwave background and on the galaxy distribution allows tests of basic laws of physics that, in many cases, could not be realized with any other mean.\n\nAn impressive array of different proposals have been formulated for as concerns the inflationary side of the story, that is, the initial conditions. So far, there is not an overwhelming reason to modify the simplest inflationary prescription of a flat spectrum, although several variations on the theme, like a small tilting (Lucchin & Matarrese 1985, Cen et al. 1992) or some break in the scale invariance (Gottloeber et al. 1994, Amendola et al. 1995) or the contribute of primordial voids (Amendola et al. 1996) cannot be excluded either.\n\nSimilarly, many theories have been proposed for as concerns the evolution of the fluctuations, trying to elucidate the nature and properties of the dark matter component. A partial list of the dark matter recipes includes the standard CDM and variations such as CDM plus a hot component (MDM), or plus a cosmological constant (CDM), or plus a scalar field ( CDM). The latter class of models, in particular, has been explored greatly in recent times, to various purposes. First, a light scalar field is predicted by many fundamental theories (string theory, pseudo-Nambu-Goldstone model, Brans-Dicke theory etc), so that it is natural to look at its cosmological consequences (Wetterich 1995, Frieman et al. 1995, Ferreira & Joyce 1998). Second, a scalar field may produce an effective cosmological constant, with the benefit that its dynamics can be linked to some underlying theory, or can help escape the strong constraints on a true cosmological constant (Coble, Dodelson & Frieman 1997, Waga & Miceli 1999). In turn, this effective cosmological constant can be tuned to explain the observation of an accelerated expansion (Perlmutter et al. 1998, Riess et al. 1998) and to fix the standard CDM spectrum as well (Zlatev et al. 1998, Caldwell et al. 1998, Perrotta & Baccigalupi 1999, Viana & Liddle 1998). Finally, even a small amount of scalar field density may give a detectable contribution to the standard CDM scenario, similar to what one has in the MDM model (Ferreira & Joyce 1998, hereinafter FJ).\n\nIn this paper we pursue the investigation of the effects of a scalar field in cosmology by adding a coupling between the field and ordinary matter. Such a coupling has been proposed and studied several times in the past (e.g. Ellis et al. 1989, Wetterich 1995) but, as far as we know, its consequences on the microwave background and on the power spectrum have not been determined. Scope of this paper is to solve the fluctuation equations for a coupled scalar field theory, and to compare with the already available data in the microwave sky and in galaxy surveys. We refer to this model as coupled CDM. Up to a conformal transformation, the model we study is equivalent to a non-minimal coupling theory in which the scalar field couples to gravity like in a Brans-Dicke Lagrangian; the perturbations in such models have been investigated by Chen & Kamionkowsky (1999) and Baccigalupi et al. (1999) in a background in which the scalar field acts like a dynamical cosmological constant (see also Uzan 1999). The model we present here is in fact more general, since a wide class of non-minimal coupling models can be recast in the form we study below (Amendola et al. 1993, Wetterich 1995, Amendola 1999).\n\nThere are several models of cosmological scalar field in the literature, essentially characterized by the scalar field potential and by the initial conditions. We can divide the models in two broad class: in the first one, the field potential energy dominates at the present, so that it resembles a cosmological constant. In the second one, the field kinetic energy is not negligible, and the field adds to the ordinary matter as an additional component, like in MDM models. To this second class belongs the model of FJ. They adopt an exponential potential for the scalar field, able to drive an attractor scaling solution which self-adjusts to the dominant matter component. In such a model, the density fraction of the field does not depends on the initial conditions, but is determined by the potential parameters. Therefore, the coincidence that the energy density in the field and in the matter components are comparable can be explained by the underlying physics (the field potential) rather than by the initial conditions. Although the coupling we will introduce can be applied to any scalar field model, we focus our attention in this paper on the exponential potential model of FJ. Beside being particularly simple, because of its attractor properties (Wetterich 1988, Ratra & Peebles 1988), such a model is also easily falsifiable, because the effect of the scalar field is important at all times (not just at the present as when the field acts as a cosmological constant), and therefore induces a strong effect on the cosmological sky. As a consequence, the constraints we derive on the model parameters are rather strong.\n\nThe same exponential potential also allows solutions which belong to the first class mentioned above, in which the field acts much like a cosmological constant, and drives at the present an accelerated expansion. These solutions, and their linear perturbations, have been studied by Viana & Liddle (1998) and Caldwell et al. (1998). The effect of adding a coupling to these models will be analyzed in a subsequent work.\n\n## Ii Coupled scalar field model\n\nConsider two components, a scalar field and ordinary matter (e.g., baryons plus CDM) described by the energy-momentum tensors and . General covariance requires the conservation of their sum, so that it is possible to consider a coupling such that, for instance,\n\n Tμν(ϕ);μ = CT(m)ϕ;μ, Tμν(m);μ = −CT(m)ϕ;μ. (1)\n\nSuch a coupling arises for instance in string theory, or after a conformal transformation of Brans-Dicke theory (Wetterich 1995, Amendola 1999). It has also been proposed to explain ’fifth-force’ experiments, since it corresponds to a new interaction that can compete with gravity and be material-dependent. The coupling arises from Lagrangian terms of the form (Wetterich 1995)\n\n −m2ψexp(−Cκϕ)ψ,μψ,μ, (2)\n\nwhere and is the ordinary matter field of mass , e.g., the nucleon field.\n\nThe specific coupling (1) is only one of the possible form. Non-linear couplings as or more complicate functions are also possible. Also, one can think of different coupling to different matter species, for instance coupling the scalar field only to dark matter and not to baryons. Such a species-dependent coupling has been proposed by Damour, Gibbons & Gundlach (1990),  and shown to be observationally viable. Notice that the coupling to radiation (subscript ) vanishes, since Here we restrict ourselves to the simplest possibility (1), which is also the same investigated earlier by Wetterich (1995) and is the kind of coupling that arises from Brans-Dicke models. For instance, a field with coupling to gravity in the Lagrangian acquires, after conformal transformation, a coupling to matter of the form (1) with\n\n C=κ(6+1/ξ)1/2; (3)\n\nin the limit of small positive coupling this becomes\n\n C=κ√ξ. (4)\n\nThere are several constraints on the coupling constant along with constraints on the mass of the scalar field particles, reviewed by Ellis et al. (1989). The constraints arise from a variety of observations, ranging from Cavendish-type experiments, to primordial nucleosynthesis bounds, to stellar structure, etc etc. Most of them, however, apply only if the scalar couples to baryons, which is not necessarily the case, and/or involve the mass of the scalar field particles, which is unknown. The most stringent bound, quoted by Wetterich (1995) amounts to\n\n |C|<0.1M−1P (5)\n\nbut again holds only for a coupling to baryons. Moreover, these constraints are local both in space and time, and could be easily escaped by a time-dependent coupling constant. In the following we leave therefore as a free parameter.\n\nThe constraints from nucleosynthesis refer to the energy density in the scalar component. This has to be small enough not to perturb element production, so that at the epoch of nucleosynthesis (Wetterich 1995, Sarkar 1996, FJ)\n\n Ωϕ<0.1−0.2 (6)\n\nWe will see that this bound is satisfied by all the interesting models.\n\nThere is an immediate consequence of the coupling for as concerns cosmology. The coupling modifies the conservation equation for the ordinary matter, leading to a different effective equation of state for the matter. This alters the scale factor expansion law in matter dominated era (MDE) from to , . In turn, this has three effects. First, the sound horizon at decoupling (when decoupling occurs in MDE) is modified with respect to the uncoupled case, being larger for and smaller in the opposite case, as we will show. This modifies the peak structure of the microwave background multipoles. Second, the epoch of matter/radiation equivalence moves to a later epoch if and to an earlier epoch in the opposite case. This shifts the range of scales for which there is the growth suppression of the sub-horizon modes in radiation dominated era (RDE), leading to a turnaround of the power spectrum on larger scales if (smaller if ). Finally, the different scale factor law modifies the fluctuation growth for sub-horizon modes in the MDE, generally reducing the growth for all values of . Similar effects have been observed by Chen & Kamionkowsky (1999) and Baccigalupi et al. (1999) in Brans-Dicke models. The next sections investigate these effects in detail.\n\n## Iii Background\n\nHere we derive the background equations in the conformal FRW metric\n\n ds2=a2(−dτ2+δijdxidxj). (7)\n\nThe scalar field equation is\n\n ¨ϕ+2H˙ϕ+a2U,ϕ=Cρma2, (8)\n\nwhere , and we adopt the exponential potential\n\n U(ϕ)=Aesϕ. (9)\n\nThe matter (subscript ) and the radiation (subscript ) equations are\n\n ˙ρm+3Hρm = −Cρm˙ϕ (10) ˙ργ+4Hργ = 0. (11)\n\nDenoting with the conformal time today, let us put\n\n a(τ0)=1,ρm(τ0)=3H208πΩm=ρm0,ργ(τ0)=ργ0,ϕ(τ0)=ϕ0. (12)\n\nWithout loss of generality, the scalar field can be rescaled by a constant quantity, by a suitable redefinition of the potential constant . We put then . This gives\n\n ρm = ρm0a−3e−Cϕ, ργ = ργ0a−4. (13)\n\nThe (0,0) Einstein equation can be written\n\n H2=κ23(ρm0ae−Cϕ+ργ0a2+12˙ϕ2+Ua2). (14)\n\nThe dynamics of the model is very simple to study in the regime in which either matter or radiation dominates. Assume that the dominant component has equation of state\n\n p=(w−1)ρ. (15)\n\nThen, following Copeland et al. (1997) we define\n\n x=κ˙ϕ√6H,y=κ√U√3H, (16)\n\nand introduce the independent variable . Notice that and give the fraction of total energy density carried by the scalar field kinetic and potential energy, respectively . Then, we can rewrite the equations as (Amendola 1999)\n\n x′ = −3x+3x[x2+12w(1−x2−y2)]−μy2+β(1−x2−y2), y′ = μxy+3y[x2+12w(1−x2−y2)]. (17)\n\nwhere the prime denotes here and where we introduce the adimensional constants\n\n β=√32Cκ,μ=√32sκ, (18)\n\n(in Amendola 1999 we defined one half of the definition above). Notice that in this simplified system with a single component, plus the scalar field, the constant is the coupling constant for the dominant component only, so that we are implicitly assuming during RDE. The system is invariant under the change of sign of and of . Since it is also limited by the condition to the circle , we limit the analysis only to the unitary semicircle of positive . The critical points, i.e. the points that verify , are scaling solutions, on which the scalar field equation of state is\n\n wϕ=2x2x2+y2=const, (19)\n\nthe scalar field total energy density is , and the scale factor is\n\n a∼τp1−p=tp,p=23[1w+Ωϕ(wϕ−w)] (20)\n\n( being the time defined by ).\n\nThe system (17) with an exponential potential has up to five critical points, that can be classified according to the dominant energy density: one dominated by the scalar field total energy density, one in which the fractions of energy density in the matter and in the field are both non-zero, one in which the matter field and the field kinetic energy are both non-zero, while the field potential energy vanishes, and finally two dominated by the kinetic energy of the scalar field (at ) . The critical points are listed in Tab. I, where we put For any value of the parameters there is one and only one stable critical point (attractor). More details on the phase space dynamics in Amendola (1999) and, for , in Copeland et al. (1997).\n\n x y Ωϕ p wϕ a −μ/3 (1−x2a)1/2 1 3/μ2 2μ2/9 b −3w2(μ+β) −xb(g9w2−1)1/2 g4(β+μ)2 23w(1+βμ) 18w2g c 23β2−w 0 49(β2−w)2 6(2−w)4β2+9(2−w)w 2 d −1 0 1 1/3 2 e +1 0 1 1/3 2 Tab. I\n\nThe perturbations on solutions converging toward the attractor have been studied in Viana & Liddle (1998) and in Caldwell et al. (1999) for zero coupling. In this case the scalar field is starting to dominate today, and mimics a cosmological constant. The case of interest here is instead the solution in Tab. I, since this is the only critical point which allow a partition of the energy between the scalar field and the matter and (contrary to ) is stable also in the RDE, when . The solution is compatible with a larger or smaller than . It exists and is stable (that is, is an attractor) in the region delimited by and and the two branches of the curve\n\n μ0=−14β(4β2+18w−9w2). (21)\n\nThe scale factor slope on the attractor is (Wetterich 1995)\n\n p=23w(1+βμ). (22)\n\nand, if , is inflationary for\n\n 2β>μ. (23)\n\nThe parametric space region in which the attractor exists is shown in Fig. 1. For any value of the parameters there is a pair of observables . When radiation dominates, , and the scale factor is the usual RDE one, . The mapping from to is shown in the same Fig. 1: as one can see, to get a large a large is also needed. In Fig. 2 we show the phase space of the system for assuming matter domination. Notice that only for there is the possibility to get an inflationary attractor with , as some observations suggest. It can be easily demonstrated that the coupled exponential potential with is the only model that allows inflationary attractors with a non-vanishing matter component. Although such a possibility is intriguing, it is hardly realistic, since an inflationary expansion that lasted for most of the MDE would not allow any fluctuation growth via gravitational instability.\n\nWhen both radiation and matter are present, the system goes rapidly from the radiation attractor, for which\n\n Ωϕ(R)=6/μ2,pR=1/2, (24)\n\nto the matter attractor\n\n Ωϕ=g4(β+μ)2,p=23(1+βμ). (25)\n\nIt is convenient to note that is a measure of the deviation from the uncoupled law in MDE:\n\n βμ=Cs=3p2−1=pp0−1=δρp. (26)\n\nWe give also the relation between the parameters and the observables\n\n g = 18pΩϕp0−p(1−Ωϕ), β = (g−18)2(Ωϕg)1/2,μ=12[(gΩϕ)1/2−2β]. (27)\n\nFor small we have\n\n C≃κ√3Ω−1/2ϕδρp. (28)\n\nSince the slope and the matter content in the MDE depend on the model parameters, the equivalence epoch (subscript ) also depends on them. It is easy to see that the following relation holds\n\n a4−3p0/pe=ργ0ρm0. (29)\n\nClearly, the equivalence occurs earlier with respect to the uncoupled case if (that is, ), later if (that is, ).\n\nWe will make often use of the fact that on the attractor in the RDE (subscript R) and in the MDE (subscript M) we have\n\n ϕ=αM,Rloga, (30)\n\nwhere\n\n αR=−4s,αM=−3s+C. (31)\n\nFinally, it is useful to note that\n\n CαM=−3Cs+C≃−3δpp (32)\n\n(the latter is valid for ).\n\n## Iv Perturbations\n\nWe now proceed to study the evolution of the perturbations in the coupled CDM theory. This involves the following tasks: 1) calculate the linear perturbation equations (we choose the synchronous gauge for the perturbed metric) for the coupled system of baryons (subscript ), CDM (), radiation (), scalar field (), massless neutrinos (); 2) establish initial conditions (we adopt adiabatic initial conditions); 3) evolve the equations from deep into the radiation era and outside the horizon down to the present; 4) calculate the radiation fluctuations on the microwave background and the matter power spectrum at the present; 5) compare with observations.\n\nLet us identify the effects of adding a scalar field to standard CDM. The field component clearly induces two main consequences for as concerns the perturbation equations: delays the epoch of equivalence, because the matter density at the present is smaller than without scalar field, and changes the perturbation equations. The first effect induces a turn-over of the power spectrum at larger scales, just as in the case of an open universe, or a model with a large cosmological constant, so that the power spectrum normalized to COBE has less power on small scales, as observed. The modification to the perturbation equations goes in the same direction: the evolution in the MDE for sub-horizon modes is suppressed with respect to standard CDM, as we will see below. The evolution equations in the other cases (super-horizon modes, RDE) give the same behavior as for the pure CDM . The net result is that FJ find that gives a good fit to observations, comparable or superior to MDM or CDM\n\nWhen we insert the coupling, the two effects above mentioned are again the dominant ones. But now, the consequences of the coupling can be in either directions, that is, the equivalence epoch can be delayed or anticipated, and the perturbations can be either suppressed or enhanced with respect to the uncoupled case, although not by a large factor. To understand this effects we first discuss analytically the perturbation equations. Following the discussion in FJ, we simplify the problem by reducing the system to three components, CDM, scalar field, and radiation. The notation is\n\n δ=δρ/ρ,φ=δϕ,vi=δui,ikivi=θ. (33)\n\nwhere is the comoving velocity. The perturbation equations in synchronous gauge are:\n\nScalar field equation:\n\n ¨φ+2H˙φ+k2φ+a2U,ϕϕφ+12˙h˙ϕ=Ca2ρmΩcδc, (34)\n\nCDM:\n\n ˙δc = −θc−12˙h−C˙φ, (35) ˙θc = −Hθc+C(k2φ+˙ϕθc). (36)\n\n ˙δγ = −43θγ−23˙h, (37) ˙θγ = k24δγ. (38)\n\nEnergy-momentum tensor:\n\n a2δT00 = (39) a2k2ikiδT0i = a2k2wγθγργ+˙ϕφ (40) a2δTii = −a2δγργ−3(˙ϕ˙φ−a2U,φ). (41)\n\nMetric:\n\n H˙h = 2k2η+8πa2δT00 (42) ˙η = 4πa2k2ikiδT0i (43) ¨h = −H˙h−8πa2(δT00−δTii). (44)\n\nDeriving Eq. (35) and inserting equation (44) we get\n\n ¨δc+H˙δc−32H2(Ωcδc+2Ωγδγ)−8π(2˙ϕ˙φ−sa2Uφ)+C(H˙φ+k2φ+¨φ−4H2Ωγφ)=0. (45)\n\nThe equation for the scalar field becomes (putting )\n\n ¨φ+2H˙φ+k2φ+s2a2Uφ−˙δc˙ϕ=C(3H28πΩcδc+˙ϕ˙φ). (46)\n\n ¨δγ+k23δγ−43(¨δc+˙θc+C¨φ)=0. (47)\n\nThe adiabatic initial condition gives now, putting for the initial value of the scalar field ( is determined below),\n\n δγ=43δc(1+Cχ). (48)\n\nIn the large scale limit, , and in RDE, where and and assuming the adiabatic condition, the system reduces to\n\n ¨δc+τ−1˙δc−4τ−2δcΩγ−8π(2˙ϕ˙φ−sa2Uφ)+C(τ−1˙φ+¨φ−4τ−2Ωγφ) = 0, ¨φ+2τ−1˙φ+s2a2Uφ−˙δc˙ϕ−C˙ϕ˙φ = 0. (49)\n\nInserting the RDE attractor solution for , we obtain that the growing mode both for and goes as Therefore, the super-horizon perturbations in RDE grow similarly in CDM, in CDM and in coupled CDM. Moreover, we have that, initially,\n\n φ=−45sδc(1+4C5s)−1≡χδc. (50)\n\nTherefore, the initial condition for the CDM density fluctuations on the attractor in the RDE is\n\n δc=−12h1+Cχ. (51)\n\nNow we consider the super-horizon modes in MDE. The equations are now\n\n ¨δc+H˙δc−32H2Ωcδc−8π(2˙ϕ˙φ−sa2Uφ)+C(H˙φ+¨φ) = 0, ¨φ+2H˙φ+s2a2Uφ−˙δc˙ϕ−C(3H28πΩcδc+˙ϕ˙φ) = 0. (52)\n\nThe growing mode is again , that is, there is no difference with respect to the standard case.\n\nIn the sub-horizon regime, neglecting the gravitational feed-back, we have in RDE\n\n ¨δc+H˙δc−4H2Ωγδγ−8π(2˙ϕ˙φ−sa2Uφ)+C(H˙φ+k2φ+¨φ−4H2Ωγφ) = 0 (53) ¨φ+H(2−Cα)˙φ+k2φ = 0 (54) ¨δγ+k23δγ = 0 (55)\n\nThe oscillating behavior of and of gives a negligible influence on , so that\n\n ¨δc+H˙δc=0. (56)\n\nwhich gives , once again with no difference with respect to standard CDM.\n\nWe finally come to the regime where the new physics makes the difference. In the sub-horizon MDE regime, neglecting again the gravitational feed-back, we have\n\n ¨δc+H˙δc−32H2Ωcδc−8π(2˙ϕ˙φ−sa2Uφ)+C[−H˙φ+C(3H28πΩcδc+˙ϕ˙φ)] = 0 (57) ¨φ+2H˙φ+k2φ−C(3H28πΩcδc+˙ϕ˙φ) = 0 (58)\n\nNeglecting the oscillating behavior of we obtain\n\n ¨δc+H(1+CαM)˙δc−32H2Ωcδc(1−C24π)=0. (59)\n\nInserting the trial solution we obtain two solutions for :\n\n m±=1−p2p{−1±[1+F(Ωϕ,p)]1/2}, (60)\n\nwhere\n\n F(Ωϕ,p)=6p(1−Ωϕ)[−8+26p+3(Ωϕ−7)p2](p−1)2[2+3p(Ωϕ−1)]. (61)\n\nFor  this reduces to the form found in FJ\n\n m±=14(−1±√25−24Ωϕ). (62)\n\nIn Fig. 3 we show the contour plot of . This figure is crucial for the understanding of the perturbation evolution, so we discuss it at some length. First, we observe that for all values of there is suppression with respect to CDM: the slope is in fact always less than 1 and, for , the slope is smaller for larger . Second, we notice the unexpected fact that the value is close to the maximum for all values of , and closest for small . For , for instance, the maximum is at , while for it is at . This implies immediately that the coupling does not enhance much the fluctuation growth with respect to the uncoupled case, while it can sensibly reduce it further as long as is far from Third, there is only a finite range of , almost centered around , for which real values of exist. Beyond that range, the power-law solutions of Eq. (59) are replaced by oscillating solutions , in which the restoring force is the coupling interaction.\n\nLet us then summarize the asymptotic evolution of the fluctuations in the coupled model. There are two relevant cases. If , the equivalence epoch occurs later than in the uncoupled case. Then, smaller wavenumbers reenter during the RDE than in the uncoupled case, and therefore there is extra suppression at these scales. Then, in the subsequent MDE regime, the modes are further suppressed with respect to the uncoupled case, unless is close to . The transfer function will be then more steeply declining with respect to the uncoupled case. If , on the other hand, the equivalence occurs earlier, and the scales smaller than are less suppressed. At the same time, the MDE regime induces again a slower fluctuation growth, so that there is an intermediate region of wavenumbers with a depleted transfer function, and a large wavenumber region with an enhanced transfer function. Fig. 4 displays some of these features.\n\nThe only important difference that arises when the baryons are added is in the tight coupling approximation. Referring to the notation used in Ma & Bertschinger (1995), we have the two equations\n\n ˙θγ = k2(14δγ−σγ)+1τc(θb−θγ) (63) ˙θb = −Hθb+c2sk2δb−Rτc(θb−θγ)+C(k2φ+˙ϕθb). (64)\n\nThe slip equation in the tight coupling approximation can be derived exactly as in Ma & Bertschinger (1995), taking into account that now (here is the electron density and the Thomson cross section)\n\n τc = (aneσT)−1∼a−2eCϕ,˙τc=(2H+C˙ϕ)τc R = 4ργ3ρb,˙R=(H−C˙ϕ)R. (65)\n\nTo second order in we obtain that the slip between baryons and photons is\n\n ˙θb−˙θγ = 2(H−C˙ϕ)R1+R(θb−θγ) (66) +τc1+R[−¨aaθb−12(H+12C˙ϕ)k2δγ+k2(c2s˙δb−14˙δγ)+ C(Hk2φ+H˙ϕθb+k2˙φ+¨ϕθb)].\n\nThe equation for the photons is\n\n ˙θγ=−R−1[˙θb+Hθb−k2c2sδb−C(k2φ+˙ϕθb)]+k2(14δγ−σγ). (67)\n\nThis concludes the analysis of the asymptotic regimes in the coupled CDM model. The results that will be presented in the next Sections make use of the full machinery of the Boltzmann code, as implemented in the CMBFAST code of Seljak and Zaldarriaga (1996), opportunely modified to take into account the coupled scalar field (including the transient from the RDE attractor to the MDE one). The equations are essentially the same as in FJ, with the new terms due to the coupling as detailed above. We tested the code with the results of FJ when , and we also checked our results with the asymptotics found above.\n\n## V Comparison with observations: cosmic microwave background\n\nThe main effect of the coupling on the cosmic microwave background is on the location and amplitude of the acoustic peaks. The location of the peak is related to the size of the sound horizon at decoupling (subscript ). Since the photon-baryon fluid has sound velocity\n\n c2spb=13r,r≡Rw′c+R, (68)\n\nwhere , the sound horizon is\n\nThis expression can be simplified as follows. First, we put ourselves in the case and neglect the RDE stage altogether. In MDE we have\n\n H2a2≃H20ae−Cϕ. (70)\n\nThen we can write, remembering that on the attractor and defining the standard sound horizon\n\nWe can further simplify, for , i.e. (which is true at decoupling)\n\n rs=rs0aCα/2d1+Cα, (72)\n\nand the corresponding peak multipole is, for\n\n ℓpeak≃2πrsH0=ℓ0(1+Cα)a−Cα/2d=ℓ0(1−3δpp)a1.5δp/pd, (73)\n\nwhere the standard peak multipole is\n\n ℓ0=2πrs0H0≃200. (74)\n\nThe qualitative behavior is clear: for there is a larger than in the uncoupled model, for a smaller For instance, for we expect in agreement with the numerical results.\n\nWe calculated the spectrum for several coupled CDM models, parametrized by the two observables . The range of values we explore, in this and in the next Section, is\n\n Ωϕ=0.05−0.2,p=0.65−0.70. (75)\n\nThe values of the other relevant parameters are fixed as follows\n\n h=0.7,Ωb=0.04,ΩΛ=0,n=1. (76)\n\nIn Fig. 5 we display the multipole spectra. As anticipated, the acoustic peaks move to larger multipoles as decreases.\n\nThere are two other effects worth discussing: the amplitude of the acoustic peaks and the slope of the multipole spectrum at small . The amplitude of the peak is depressed as increases, save for values close to 2/3, since the matter fluctuations that drive the radiation peaks are suppressed, as shown above. The small region is dominated by the Sachs-Wolfe (SW) effect. As well known, the integrated SW (ISW) effect in flat space vanishes only if the fluctuations grow as , which is not the case here. The ISW then adds at small multipoles and tilts the spectrum. Moreover, the overall normalization now takes into account the ISW power, and as a consequence the normalization for the perturbation at decoupling time is reduced. This effect shows also in the final amplitude of the power spectrum.\n\nDeriving precise constraints from the whole set of observations on the CMB requires considerable detail in the statistical procedure, beyond the scope of this paper. Here we content ourselves to derive rough limits on the parameters. It is probably safe to state that current observations rule out values or , although the present level of errors does not permit to attach a strong significance to such bounds. Future precision observations around the first peaks are likely to constrain to two decimal digits. As already found by FJ, on the other hand, the microwave sky does not impose strong constraints on , since this parameter influences mainly the fluctuation growth, and thus the absolute normalization. To constrain it, we have to evaluate the present power spectrum of the fluctuations.\n\n## Vi Comparison with observations: power spectrum\n\nThe analytical expression (61) for the fluctuation growth exponent found in Section 3 is a clear guide to the results of this Section. As anticipated, the coupling introduces an extra suppression for the scales that enter the horizon in the MDE. The suppression is larger for models with high and high . A small suppression factor, as well known, helps to bring the standard CDM model into agreement with observations. FJ found that the best uncoupled models have ; here we see that the coupling allows also models with smaller , but to meet the observations. This can be helpful to reduce the constraints from nucleosynthesis, which, in some restrictive analysis, require .\n\nIn Fig. 6 we report the power spectra normalized to COBE, compared to the data as compiled and corrected for redshift and non-linear distortions by Peacock & Dodds (1994). For a quantitative comparison, we plot in Fig. 7 the contour plot of , the number density variance in 8 /h spheres. The models with a value of larger than 0.5, as required by cluster abundance (White, Efstathiou & Frenk 1993, Viana & Liddle 1996, Girardi et al. 1998), have and at most a small deviations from . The suppression of with respect to COBE-normalized standard CDM is due both to the growth suppression in MDE and to the fact that now the COBE normalization includes the ISW effect.\n\nFor as concerns the shape of the spectrum, the comparison with the galaxy data is uncertain due to biasing. Assuming a scale-independent bias between matter and galaxies, we can quantify the agreement with the data by evaluating the of the ratio between the theoretical and the galaxy spectrum, that is by evaluating\n\n χ2=∑i[Ri−^R]2/σ2(ki), (77)\n\nwhere are the average and variance of , neglecting cosmic variance. The contour plots of are in Fig. 8. They show, as anticipated, that the models with follow better the real data because are more bent at small scales. The best models among those studied here have for 15 degrees of freedom (16 real data, minus the average estimated from the data themselves). For instance the model with gives a very good fit, and has as required. Notice that we performed the fits without varying all the other cosmological parameters, which, at least in principle, can be determined by other observations.\n\nIn Fig. 9 we summarize the constraints obtained in this Section, considering the models which have and . The cluster abundance normalization usually quoted for is , but this is calculated for standard models, so that conservatively a larger region has been adopted. Only a stripe around and appears to be viable, if the bias is indeed scale-independent. From Eq. (28) we deduce a limit\n\n 0\n\nwhich, although still far from the limit 0.1 quoted in Wetterich (1995) from local measures, is global and applies even if the scalar field is not coupled to baryons, as proposed in Damour, Gibbons & Gundlach (1990). Future data will certainly tighten the constraint even further.\n\n## Vii Conclusion\n\nIn this paper we discussed the perturbations of a coupled scalar field with exponential potential on the CMB and on the present large scale structure along an attractor solution. For as concerns the CMB, we found that the coupling induces a strong effect on the location and amplitude of the acoustic peaks, due to the variation of the scale factor expansion law. Future precision measures in the region have the potential of constraining the coupling to two orders of magnitudes better than at the present (see for instance the discussion in Chen & Kamionkowsky 1999).\n\nWe found that subhorizon perturbations are always more suppressed in MDE with respect to standard CDM, no matter what the parameters and are. Moreover, the suppression increases for far from the standard value. The amplitude at the present is between 0.5 and 1 only for , being smaller for larger , as already found in the uncoupled case by FJ. Adding the request to fit the galaxy power spectrum shape, the parametric space is reduced as in Fig. 9. A positive coupling has the advantage to warp the spectrum to a closer agreement with the data.\n\nThe background solution we adopted here is only one of the possible solutions. An equally interesting one is to consider a solution heading toward the inflationary attractor , but still short of it. This would provide closure density to a universe, and an acceleration as recently claimed, although at the price of sensibility to the initial conditions. Such a model will be investigated in a future work.\n\n## Acknowledgments\n\nI am indebted to Carlo Baccigalupi, Francesca Perrotta and Michael Joyce for useful discussions on the topic.\n\n## References", null, "Figure 1: Parameter space for the attractors. In the dark-shaded region the solution b is an attractor; in the other regions the attractors are the solutions a,c or d, as labelled. In all the paper we focus on the attractor b. The continuous curves mark values of Ωϕ equal to 0.05,0.1, 0.2, 0.3,…,0.9, top to bottom. The dotted lines are values of p equal to 0.6, 0.65, 2/3, 0.7, 0.8, 1, 1.3, left to right. There exists also a completely equivalent symmetric region with β→−β and μ→−μ.", null, "Figure 2: Phase space corresponding to Ωϕ=0.1,p=0.7, in MDE.", null, "Figure 3: Contour plot of the exponent m+ of the fluctuation growth law δc∼am versus Ωϕ,p. The contour levels are for m=0.9 (enclosing the white region), down to 0 in steps of 0.1. In the black region m is complex. Notice that for any given Ωϕ the maximum of m is close to p=2/3, especially for small Ωϕ.", null, "Figure 4: Growth of the dark matter fluctuations for various values of the coupling and Ωϕ=0.1. In the top panel the trend of the horizon length and of two comoving scale (the horizontal lines) show the horizon crossing and the radiation and matter eras. Thick lines: wavelength ≃900Mpc/h. Thin lines: wavelength ≃100Mpc/h.", null, "Figure 5: Cℓ spectrum for various models (actually we plot [ℓ(ℓ+1)Cℓ/2π]1/2, as customary). Notice the shift of the peak location for the different values of p, in agreement with the approximation given in the text. The amplitude decreases for p≠2/3 (except for values slightly larger than 2/3) and, for a given p, decreases for smaller Ωϕ , as expected.  The data points are from Tegmark’s home page (http:// www.sns.ias.edu/~max).", null, "Figure 6: Dark matter power spectra Δ2(k) for the same models as above. Notice again that the power is suppressed as long as p deviates from the uncoupled law 2/3 (except for values slightly larger than 2/3). Also notice that models with higher p are more flattened at small scales." ]
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http://www.kjm-math.org/article_16711.html
[ "# Periodicity and Stability in Nonlinear Neutral Dynamic Equations with Infinite Delay on a Time Scale\n\nDocument Type: Original Article\n\nAuthors\n\n1 Department of Mathematics and Informatics, University of Souk Ahras, P.O.Box 1553, Souk Ahras, 41000, Algeria.\n\n2 Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria.\n\nAbstract\n\nLet $\\mathbb{T}$ be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay $x^{\\Delta}(t)=-a(t)x^{\\sigma}(t)+\\left( Q(t,x(t-g(t))))\\right) ^{\\Delta }+\\int_{-\\infty}^{t}D\\left( t,u\\right) f\\left( x(u)\\right) \\Delta u,\\ t\\in\\mathbb{T},$ has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid of the contraction mapping principle we study the asymptotic stability of the zero solution provided that $Q(t,0)=f(0)=0$. The results obtained here extend the work of Althubiti, Makhzoum and Raffoul .\n\nKeywords\n\nMain Subjects" ]
[ null ]
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https://e-eduanswers.com/mathematics/question13568164
[ " Tyler said that the composition of an even number of opposite isometries is a direct isometry and thay the composition of an odd number", null, "", null, ", 18.10.2019 07:00, maustin5323\n\n# Tyler said that the composition of an even number of opposite isometries is a direct isometry and thay the composition of an odd number if opposite isometries is an opposite isometry. do u agree with tyler? justify your answer.​", null, "### Other questions on the subject: Mathematics", null, "Mathematics, 21.06.2019 16:10, vannah94\nIn the rectangle below ac=30 units what is de", null, "Mathematics, 21.06.2019 17:40, Gattuso\nIs the relationship shown by the data linear", null, "Mathematics, 21.06.2019 22:30, magics\nFactor the polynomial, if possible. if the polynomial cannot be factored, write prime. 9n^3 + 27n^2 – 25n – 75", null, "Mathematics, 21.06.2019 23:00, spaigenicole\nSomeone answer this asap for the first five terms of a sequence are shown. 5, 11, 23, 47, 95, . . which recursive function defines the nth term in the sequence for n > 1? a. f(n) = f(n - 1) + 6 b) f(n) = f(n - 1) + 48 c) f(n) = 3 • f(n - 1) + 1 d) f(n) = 3 • f(n - 1) - 4\nDo you know the correct answer?\nTyler said that the composition of an even number of opposite isometries is a direct isometry and th...\n\n### Questions in other subjects:", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Total solved problems on the site: 7529928" ]
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https://www.slideshare.net/HarshaKrishnaBhatP1/sampling-of-attributes-hypothesis-test-of-hypothesis-one-tailed-two-tailed-type1-type2-errors
[ "Successfully reported this slideshow.\n\n# Sampling of Attributes Hypothesis Test of Hypothesis One tailed Two tailed Type1 & Type2 Errors\n\n12\n\nShare", null, "", null, "", null, "×\n1 of 18\n1 of 18\n\n# Sampling of Attributes Hypothesis Test of Hypothesis One tailed Two tailed Type1 & Type2 Errors\n\n12\n\nShare\n\nHYPOTHESIS\nA hypothesis is an idea or explanation that you then test through study and experimentation. Outside of science, theory or guess can also be called a hypothesis. A hypothesis is something more than a wild guess but less than a well-established theory.\n.\n.\n.\nTypes\n1)one-tailed\n2)Two-tailed\n.\n.\nOne-tailed test alludes to the significance test in which the region of rejection appears on one end of the sampling distribution. It represents that the estimated test parameter is greater or less than the critical value. When the sample tested falls in the region of rejection, i.e. either left or right side, as the case may be, it leads to the acceptance of the alternative hypothesis rather than the null hypothesis.\n..\n.\n.\nexamples...\n\nHYPOTHESIS\nA hypothesis is an idea or explanation that you then test through study and experimentation. Outside of science, theory or guess can also be called a hypothesis. A hypothesis is something more than a wild guess but less than a well-established theory.\n.\n.\n.\nTypes\n1)one-tailed\n2)Two-tailed\n.\n.\nOne-tailed test alludes to the significance test in which the region of rejection appears on one end of the sampling distribution. It represents that the estimated test parameter is greater or less than the critical value. When the sample tested falls in the region of rejection, i.e. either left or right side, as the case may be, it leads to the acceptance of the alternative hypothesis rather than the null hypothesis.\n..\n.\n.\nexamples...\n\n## More Related Content\n\n### Related Books\n\nFree with a 14 day trial from Scribd\n\nSee all\n\n### Related Audiobooks\n\nFree with a 14 day trial from Scribd\n\nSee all\n\n### Sampling of Attributes Hypothesis Test of Hypothesis One tailed Two tailed Type1 & Type2 Errors\n\n1. 1. Sampling of attributes\n2. 2. HYPOTHESIS Hypothesis is an idea or explanation that you then test through study and experimentation. Outside science, a theory or guess can also be called a hypothesis. A hypothesis is something more than a wild guess but less than a well-established theory.\n3. 3. Testing of HYPOTHESIS It deals with the verification of validity of presumptions regarding the parameters of the population using samples drawn from population.\n4. 4. Types 1)one tailed 2)Two tailed\n5. 5. Definition of One-tailed Test One-tailed test alludes to the significance test in which the region of rejection appears on one end of the sampling distribution. It represents that the estimated test parameter is greater or less than the critical value. When the sample tested falls in the region of rejection, i.e. either left or right side, as the case may be, it leads to the acceptance of alternative hypothesis rather than the null hypothesis.\n6. 6. • In this statistical hypothesis test, all the critical region, related to α, is placed in any one of the two tails. One-tailed test can be: • Left-tailed test: When the population parameter is believed to be lower than the assumed one, the hypothesis test carried out is the left-tailed test. • Right-tailed test: When the population parameter is supposed to be greater than the assumed one, the statistical test conducted is a right-tailed test.\n7. 7. Definition of Two-tailed Test The two-tailed test is described as a hypothesis test, in which the critical area is on both the ends. It determines whether the sample tested falls within or outside a certain range of values. Therefore, an alternative hypothesis is accepted in place of the null hypothesis, if the calculated value falls in either of the two tails of the probability distribution.\n8. 8. In this test, α is bi-furcated into two equal parts, placing half on each side, i.e. it considers the possibility of both positive and negative effects. It is performed to see, whether the estimated parameter is either above or below the assumed parameter, so the extreme values, work as evidence against the null hypothesis.\n9. 9. ERROR • Type1 error • Type2 error\n10. 10. Actual fact Decision based on the samples Decision Error 1 Ho is true Accept Ho Correct decision ---- 2 Ho is true Reject Ho wrong decision Type 1 3 Ho is not true Accept Ho wrong decision Type 2 4 Ho is not true Reject Ho Correct decision ----\n11. 11. Type 1 Error of the first kind is taking a wrong decision to reject the null hypothesis when it is actually true. Type I error is a false positive\n12. 12. Type 2 Error of the second kind is taking a wrong decision to accept the null hypothesis when it is actually not true. Type II error is a false negative." ]
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https://nbviewer.jupyter.org/github/SHTOOLS/SHTOOLS/blob/v4.6.2/examples/notebooks/Introduction-2.ipynb
[ "# Localization Windows and Spectral Analysis¶\n\nNow that we know how to work with the spherical harmonic coefficient and grid classes, let's move on to the other major feature of pyshtools: localization windows and localized spectral analysis. pyshtools allows for localized spectral analyses using either spherical-cap localization windows or localization windows constructed from an arbitrary mask. The windows are constructed to solve the same optimization problem as the Slepian windows that are used in Cartesian multitaper spectral analysis problems. A single class, SHWindow, bundles the relevant shtools functions. In this notebook, we will demonstrate how to construct optimal localization windows, and how to obtain localized spectral estimates for arbitrary regions on the sphere.\n\nIn :\nimport matplotlib.pyplot as plt\nimport numpy as np\nimport pyshtools as pysh\n\npysh.utils.figstyle(rel_width=0.75)\n%config InlineBackend.figure_format = 'retina' # if you are not using a retina display, comment this line\n\n\n## Spherical Cap Localization Windows¶\n\nTo demonstrate the localized spectral analysis routines, we will make use of a pathological data set. In particular, we will construct a function on the sphere whose power spectrum is different in the northern and southern hemispheres. We first create two grids using random coefficients that have power spectra following power laws with exponents of -2 and -3, up to and including degree 300:\n\nIn :\nldata = 300\ndegrees = np.arange(ldata+1, dtype=float)\ndegrees = np.inf\n\npower_north = degrees**(-2)\npower_south = degrees**(-3)\n\nclm_north = pysh.SHCoeffs.from_random(power_north, seed=12345)\ngrid_north = clm_north.expand()\n\nclm_south = pysh.SHCoeffs.from_random(power_south, seed=54321)\ngrid_south = clm_south.expand()\n\n\nNext, create a new grid that contains data from the northern hemisphere of one grid and the southern hemisphere of the other. The SHGrid method from_array() returns a copy of the data, so you don't need to worry about modifying the original data set:\n\nIn :\ngrid = pysh.SHGrid.from_array(grid_north.data)\n\nnlat = grid_north.nlat\ngrid.data[nlat//2:nlat+1,:] = grid_south.data[nlat//2:nlat+1,:].copy()\ngrid.plot(show=False)\n\nclm = grid.expand()", null, "Here, we made use of the grid attribute nlat, which is the number of rows of the gridded data, and we modified the raw gridded data for grid that is stored in the data class attribute.\n\nNext, let's construct some spherical-cap localization windows. This is done using the constructor from_cap() that is associated with the SHWindow class. The other option, as we will demonstrate later, is from_mask() and takes as input a user defined mask. For spherical-cap windows, we need to specify both the angular radius of the cap and its spherical harmonic bandwidth, and for this example we will use an angular radius of 30 degrees and a bandwidth of 29.\n\nIn :\nlwin = 29\ncapwin = pysh.SHWindow.from_cap(theta=30.,\nlwin=lwin)\n\n\nThis command calculates the spherical harmonic coefficients of the spherical cap windows along with their associated angular orders and concentration factors. If you ever need to access these directly, they are stored in the class attributes tapers, orders and eigenvalues. By default, theta should be provided in degrees, but this can be input in radians by specifying the optional parameter theta_degrees=False. If you are curious to see what these windows look like, you can plot them using the built in method plot_windows(). Let's plot the first 12 of them:\n\nIn :\nfig, axes = capwin.plot_windows(12, loss=True, show=False)", null, "As is seen, the windows are centered oven the north pole, 1 minus the concentration factor is noted above the window as the loss factor, and all of these windows are very well localized. To instead provide the concentration factor in the title, just set loss=False. If you want to know how many windows have concentration factors greater than a specified value, you can use the method number_concentrated():\n\nIn :\ncapwin.number_concentrated(0.99)\n\nOut:\n34\n\nYou can return an SHGrid class instance of an individual window using the method to_shgrid(), you can return the spherical harmonic coefficients of individual windows using to_array() and to_shcoeffs(), and you can also return as a numpy array the power spectra of one or more windows using the method spectra(). If you want to plot the power spectra of the windows, this can be done using the built in method plot_spectra():\n\nIn :\nfig, axes = capwin.plot_spectra(12, loss=True, show=False)", null, "In general, we will not perform localized spectral analyses at the north pole, so let's rotate the windows so that they are centered at 45 degrees north and 90 degrees east. This is easily accomplished using the rotate() method. To speed things up, we will rotate only the first 50 best-localized windows, and not all 900 of them:\n\nIn :\ncapwin.rotate(clat=45.,\nclon=90.,\nnwinrot=50)\n\nfig, axes = capwin.plot_windows(12, loss=True, show=False)", null, "In rotating the windows, the spherical harmonic coefficients of the initial tapers centered at the north pole are not modified, but a second set of rotated coefficients are created and stored in the attribute coeffs. If you ever forget how you constructed your windows, you can always use the info() method to print out all the metadata:\n\nIn :\ncapwin.info()\n\nkind = 'cap'\ntheta = 30.000000 degrees\nlwin = 29\nnwin = 900\nnwinrot = 50\nshannon = 60.288568\narea (radians) = 8.417872e-01\nclat = 45.000000 degrees\nclon = 90.000000 degrees\ndj_matrix is stored\nTaper weights are not set\n\n\nNext, let's calculate the localized power spectrum at two different locations, one in the northern hemisphere and the other in the southern hemisphere. We will use all 34 windows that have concentration factors greater than 0.99:\n\nIn :\nk = capwin.number_concentrated(0.99)\n\nmtse_north, sd_north = capwin.multitaper_spectrum(clm, k)\nmtse_south, sd_south = capwin.multitaper_spectrum(clm, k, clat=-55., clon=90.)\n\n\nIf you don't provide the central latitude and longitude of the analysis with the parameters clat and clon, the coefficients that were created previously using the rotate() method will be employed. If these coefficients are not available, the analysis will be performed at the north pole.\n\nmultitaper_spectrum returns a power spectrum whose maximum degree is ldata - lwin. This is because localized degrees beyond this limit depend upon coefficients of the global data beyond ldata, and these are not known. If the global function was truly zero beyond ldata, you could simply construct the spherical harmonic coefficients of clm to have zeros beyond that degree.\n\nWhen a function is multiplied by a window, the power spectrum of the localized function is modified. For the case of stationary and random data, the expectation of this biasing effect can be estimated using two methods. First, we could calculate the \"coupling matrix\" using the method coupling_matrix(). The expectation of the output windowed power spectrum is then simply the multiplication of this matrix by the input global spectrum. If you are interested, you can plot the coupling matrix using the built in method plot_coupling_matrix():\n\nIn :\nfig, ax = capwin.plot_coupling_matrix(ldata, k=k, show=False)" ]
[ null, 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 ", null, 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qH1fWafbomSz0Cd32dEGqHKNsHM7k3oZbWK8KPoKe5+Y/e9KqU2QW1CL2oTxoBu0snIMrPVZuaEQU8XAg8yM0+2zRDGY5jdZmanR7vHN8D271LGBOlFro4L2KK4+Bzpl0TrW+In3P1jhJmJ3ki4+baYMNHEL8zsle0ZeegyfwTh5t4vk80nA18AzhvA1Op3Jo+7dUuU3MBbm/y5d5mCkqnkzye8vrcTbmCt7ZB0FenNw9e7u+VcLk3qelKXNGeUqXvO43sA4UvjboQbs6e4+zWDKk+kifpsE5qq1SY4+b6zdWwTkv/YvJ3wn4szCTfyVwAvAX5jZk9vz8jdv0FoQ15J+I/eBPBk4AdmVmSQ7kq4+zbSgcuNuaFIefbf6u7vdPfHufs+7r7U3Q9z91cRwqyekiT9rbtfn6yPQpvQ+j6zwsy6/SdvD9LzSf8hk7FXdZtgZvcifNc6INn/We7+84EexM7UJqT1UZvQmdqEMaCbdDLKWuOirUv+vod0TINO2zZH+14crZ/SpYzjSX/ZuKJLuqrEF8k8swHFs9Re1/6ku9+cNMKHEKYqv5wwmOl7zOyIDuk3ufvH3P04wrF/I3nqGcCLWunM7OdmtqbEEn+Zac2Edf9uPfXMbDnQGlfvsl4vSIf9TyL8SraCMJ7FyZ49TttawhcvmPvaNlbSg+4iwi+kGwg3IH/ZfS+RsdRPm9BUrTZhAnhgjvSt69Y24Jb2J939Wnd/PaFXyd8l+e8CnGNme3VIf5e7f4AQ6vQ44H+Tp15jZo9vpSvZHqwxs8/nexlmXUkISQI4vOC+3byadKzSs6Pto9Am5P0+8/hovY7vMyLDVlmbYGb7E75rHUEIiXyWu391MNXuSm3CXGoTdqY2YQzoJp2MLHc/3t33J4y3BmGG0/2ztrn756LdryLtAv68LjeJnhqtf6myymf7drT+zG4Jk8bzscmfv+3W3d7dpzxMxNA6nkngpG75Jz3rnkL44gLwmOjpfejexTtribtefyt53J+5DUW7uJ6XdqtzOzN7QlLOMsJNzBPc/fKs9O6+gzAbE8BjzKx9yvVGSUKXfwTci9Az8WR3//FwayUyHH22CU1VpE14IPDg1n7J9ayjpAfBfxPGJYLwI8bDu6R3d/8e8ATCf1BhbptQpj24N2moTV57kva+ruQ/FWZ2PGFICAg/BH209dyItAkXkP4n9Xld0rXa/+2kP8CJjK2q2gQzO4hwg+4BhBk9T3X3ojeTqqI2YS61CTtTmzAGdJNOxsH9k8drO2zrGPLn7k6YPALCL1Eva09jZvsRflWC0LjV8SvDpYSLK8AzzOyvOyVKQk8/TOiqDGlj0sv6aH1LZqrUFOlMSnE3+QMLdPGOlwOjvD9OGvL6DjNb2eE4lxAGboVwk+3T0XP3NbNfm9k6M9upETKzpxDGqlhCuCF7QpcedLEPJY97Ax8ZQJhvJZKxN35IOAduJsyO23GWKZF5pnCb0GBfIx136DVmdlynRMm18hzSMJz/yJl/0TZhM+EL/Zz0JdsDc/eTomOYTI6jo+THtHdEmy5se/4YM7vGzG42s8fQgwXPJfyQs4Awjs9zPcyeHmt0m5CEfP2/5M8nmNmT2tOY2dFAa/vH3H19exqRMVa6TTCzw4AfE2aHvQd4vLt/q9s+A6Y2IX1ebUIHahPGhDdg9gotWvpZgC8TxmbYv8O2/brstwD4RZJumvDr0QLCuAYPJ9zYcUKjXGimU0rO7po8dz/CAKatMTPeTRgo1ghd0E+I6u1JXtaWxwcIvxIeCixMtt2HdMaf7cDBUfoXJfs8DFiabFsBvC0q57kDeO9Oi/K/jDC1/PLkfXgY8Kvo+Se27fsf0XO3tj334uQ9dcKNrN0L1GkC+GKU968JPf1WJs8bYUyKRxMG2l1S0WtxRtY50SHtKYQvRg78jnIzix1IBbNWatHStKVsm5CR17lVfE56fbbJmMkvee646PO+lTAGz/7JtWgFYQbseJa6Mzrk8RnC7H0HE3pSG+EHqtbseHcBy6P0byTM3nc0sDjZtifhP32tcv684vftrwht3xnAo4BVyfblyWvwjajsn9A2Ozfwuej5n3cp596EsYu+GaW/A/izjPSj0CbsSvghy5Nz5dSkXkYISbs5eW4NsHfZ81SLllFcyrYJyXWnNUPnDcBRFdZJbULv10htwtxy1SbMo2XoFdCipd+FcHNnKzDRtm0zPaZVJ4QJ/ja60G4l3JRr/b2WEEJYtE6rKXmTLnn+UMLNF4+WDaQ3npzQy+1tHRql5YRfs1rpthN+GWv9PQ38bds+P24r6862vz/W67Xs4/17LumXjdZxxX9vBV7YYb8zozS3Rdtf1lb32+g+Rfoa2m5yEXrffbQtn9brsr1t24kVvQ5n5GkMCb98TbXVqdfxPaJDPgeim3RaxnChjzahQ17nVvE56fXZpst/yJLnjydMABRfe+5u+3szYWbu9h9t7teWbguhPWn9vQ14XJTeCP8hjduMdW15/OsA3rd3dbjm3tX29zThP4UrO+z/2SjdL9qe2zM57qkO+X2KHjdvm9wmROkPbTtHNiVL6+/VwJH9nKdatIziUqZNIPxQHH9+1tP7u9YzCtRJbULv10htwtwy1SbMoyWeWlhk5FiYffUQ4E/uPtO27Y+eXGGyuPttZvZw4OWEm0WHEhqjy4GvAO9399sGeAhZ9brKzB5MmLDhGYSefXsSxoe7ErgE+Ki7X9th982EX59eABxLmIXKCDcjLwHe5e5Xtu3zEuBvCb9UHQCsJIzbdxUhLPgHvV7Lstz902Z2IfAK4C8JN48WAH8kjL1xlrtf12HXDxLG5DuQMMBrS3vX/zwzws7pqu7uW4EXmdmHCb0MTyT0RFxOGIj4FkLj9j1KTGbRp4cwt755xsNYPKC6iDRKv21CU7n7z5Owq78hjBV6DLA78CfCODy/ILQJOw0MTvjP1amEsWmOIFzjtxPag58S2oT2md2eBpxOuJ4eQOjF/QfC9e497v6rKo8v8c+E2cSfT2iLDyb0cFhNCEm7EviwZw898XbC+EvLgX/p8LwR/mN5O6G3yI+BH3qX8VxbGt4mtOp4lZkdRWgPn054/bYRenl8Afigu28YRt1EhqWPNuEIwuyvLSuTpZulPZ6vjNoEtQk56qg2YYTZiH5fFWk0M1tNaMQOcvfVw62NyM7M7EBCV/jrfe5YgSJSMTMLP0m7Z85kLTJsOk9F6qHPmowCnafDo4kjREREREREREREhkw36UQG6+dmtiZZzhl2ZWR+M7NzWucjoWu/iNQoag/WmNlbhl0fmd/M7C3xOTns+ojMN2oTpEnUJjSHxqQTGax7ReurhlYLkWAVYTwPERmO+PPXa3wjkUFbidoEkWFSmyBNojahITQmnYiIiIiIiIiIyJAp3FVERERERERERGTIdJNORERERERERERkyHSTTkREREREREREZMh0k05ERERERERERGTIdJNORERERERERERkyHSTTkREREREREREZMh0k05ERERERERERGTIdJNORERERERERERkyHSTTkREREREREREZMh0k05ERERERERERGTIdJNORERERERERERkyHSTTkREREREREREZMh0k05ERERERERERGTIdJNORERERERERERkyHSTbsSZ2QYz2zDsegyKjm+06fhGm45v9IzjMcV0fKNNxzfadHyjZxyPKabjG206vtGm4xsc3aQTEREREREREREZMt2kExERERERERERGbJ5c5POzP7KzL5jZmvNbKuZXWVm/25mu3fZ52gz+5SZ3ZLsc7WZnWlmu2WkP83MLjGzjWZ2sZmdMrgjEhERERERERGRcTH2N+nMbBcz+0/g68DjgC3ALcADgNcBvzOzB3TY79nAxcBzgV2AK4GDgH8GfmNm92lL/2Tgy8AhwFXA4cDXzOzkAR2aiIiIiIiIiIiMibG/SQe8HfgHYC3wKOC+wMHAEcB1wP7AJ8zMWjuY2UOBTwALgf8L7O3uxwAPJNzgOwD4opnFr98bgZuBg9z9IcChwCbg1QM9OhERERERERERGXljfZPOzI4BXpn8+Ux3/7GnLgceC0wDxwFPjHY9C1gAnO3u73H37QDufjVwWpLmYcCp0T6HA+e7+7ok7Y3ABYTedyIiIiIiIiIiIpnG+iYdIVR1ArjE3X/Y/qS7Xwt8K/nz5QBmdgTwZ8m293TY55fAL6P8W24ATmyNV2dmBwDHA1f0fxgiIiIiIiIiIjLOxv0m3THJ46Vd0nw3eTw0eXxS8niJu1+Tsc/XksdHRtveTRJCa2a/IoxhtztwZqEai4iIiIiIiIjIvLNg2BUYsH2Tx41d0tycPB5gZguAByd/X9xln98nj/cys4XuvgP4b8CAVxHGrvs18AZ375ZPX8xsMikTMzsMWAf4oMobktbx7TXsigyIjm+06fhGlzH3+nm1u08Pt0r9UZswFnR8o03HN7rUJoymcT4nQcc36nR8o2uobcK436S7ktC77cguaVq9CRcAewEHJn/f1mWfO6N99wFudHcHzkmWvpnZhjzJgGXJ+riH1d4+7AoMmI5vtOn4RtsVwCYz6/qfF3dfUVN9dqI2YSfjfk7q+Eabjm+0qU0YPeN+Tur4RpuOb7TV3iaMe7jrj5LHx5rZce1Pmtky4PXRpvXArsl6npt0APv1VUMREREREREREZn3xr0n3f8DXkYIP/2Wmf0TYQy67cCjgH8jHYtug7tvMbOp5O/JLvnGr9umaqsc5LkTm3S9HPdfxkRE6vBQd79y2JXIojZBRKRWahNERKSl1jZhrG/Suft2M3sKcB5hEomPtyW5Evgo4UZe60VfQwiRvVeXrFdF6zdVU9tS1sV/HM/jWMTiYdVFRGRkbGcbP5+dNwhou56OqDnHsN8bXsvksmVZaas1bqMcdWLDrsAAzIf3bb4Yx/OzRtObNnHzO98Vb1Kb0A9dW0aTriMiwPDbhLG+SQfg7leZ2fHAs4GHAYcQ4qa/R7h5d0GS9FvJ45rkce8u2e6ZPG4lhMgOy5wmcBGLWWS6SSci0tPO/4EYh/9SzDmGyWXLmFy+fAglj6lx/M/LfHjf5otxPD+Haxw+HWoTpBhdR0Sy1HpVG/ubdADuvg04N1lmmdmhwCOSP7+UPN6YPD68S5bHJo83JBNGiIiIjJf51Lpl/cfEM9Z77TcqitR/FM+HUX9/eul1fo6TcX8vR8G4n2OxsufbqL9GReo/ip/JUX9/JDWK518B4z5xRCYzW0zoSWfAF9z9t8lTFyWPDzKz+2fs/qTk8bsZz4uIiIiIiIiIiOQ2L2/SmdkKQq+6Ywgztf5z9PRFwOpk/dUd9j0JOCr589wBVVFEREREREREROaReRHu2mJmewGPBd4OHAjcDTzF3a9rpXH3aTN7HfBZ4KVmdiXwYXffkcyS9Lkk6Wfc/ZJaD0BERGQQ6g4BGZcwhSaGzgzqtc0TElyHUTx36niNBvm6NOE8L1qHUTxPmkSf63KaeByDei+z8q37NWjC9amoJp4nRTThNR/zNmHse9KZ2UPN7Hdmdi1hwohPE27QfRl4oLv/uH0fd/8c8B/Jn2cBt5nZpcBlwF7AT4G/r6H6IiIiIiIiIiIyD8yHnnTLCTO63gNcmCzfA/6326QP7v46M/tf4FWEiSLuD/wW+ARJz7rBVltEREREREREROaLsb9J5+4XAktL7ns+cH6lFRIRERln4xp2NyohPL32G5WQj7rq2YSwnaar472o+n0Yx9mYR9W4tgl1K/s69tpvVF7Duuqp60RvahMGbuzDXUVERERERERERJpON+lERERERERERESGbOzDXUVERGTA+gkZKBvS0G+YQh2hFEVZxnqVZcdpmxLqMah6jPsMlZ6xXoeqj7WOkLymzEY5H6hNqOa8KvsZL1J2nLYpoa+DqseoDFsxitQmVEo96URERERERERERIZMPelERESknEH19sqTb9N+oa6610SRMrK298pvmL3q6ni9ymrAr+iNV3dvp0FeE7yPfWUutQmpqntXFymjbA+hYfaqq+P1Kqtp51YTqU2olHrSiYiIiIiIiIiIDJlu0omIiIiIiIiIiAyZwl1FRETmu1bYwDAmU+gUsjBfQ0vKhjb1CoNtyiQZZcNamhwGFRvmeTsqAzoZ3vIAACAASURBVKIX3a/sAPhly5NgzNsEKzIUQKGMeyfxKkOCiw510Npe9yD/WYY1SUg/ZRcxn4ZOUJtQKfWkExERERERERERGTLdpBMRERERERERERkyhbvK+LCM/q+2871omyjX/9hnMvrI+kyHbSPSn1ZExlNrdqqmhLX0yqPucKYMPUORmhKy6RnrVdSvynNGYVDjqa73tVP6suFO8/19nSdtgmVdG6OLu83snCZzv4y8O7YVlvF8vN76b0mcWdZ+vWRdt6s47wf12dFwCeNJbUKl1JNORERERERERERkyHSTTkREREREREREZMgU7iqjJw5rjUJZbXIyWo/uPyfb4+eJ13uFvsYhrtPTs6serc/dPrPz83E4rMJgRaROVYcx9sqvitCFHGYjhbLCmXKELs0+HTUZFu0Yb/dOIUp5fuqssJ5zFAnZyJN2mCGuoxj+1MkwZ1it+6tF2WPNs1/ZmTfLhqrPt69lY9QmdLp+2kznsFaLvpbbVJpmYqq1LX1+IkpLnEencNeoHZiJ/nvh0f+yZxbE20MmPpnWIW5rmCgZBlvkfc2TdpghrqM4TEIn8+naojahUupJJyIiIiIiIiIiMmS6SSciIiIiIiIiIjJkCneVZusQ2jonrHVhegrbooVp2sWLo+2LAPAli9Lno/18wZw4p3Q9CUu1qaif+460L/zE1u1p0u3pum3blmzbkT4f7acwWBFprEHOelUy76xw0NmQpjgUKSu0aWbn8NI4dKgVfgQwsyAOQYoKnPSd0rIgLrBzPZmtZ1SHjGaADvXcKb9OssquMoSn6vOhbGjvoMqouuwqVP0aDSt8rehrWDZksuysf5Yz3Xw0Sm3CtCWP6bbJ7VFY67Zoe7S+YIsnj/HzacYTU+l63Ma0QlTjNmN6cbo+tQvR+s5pZtL/qjC9KG5rojZoMio7TVE+9LXK93CYswTP19m/q37N1SZklzfkNkE96URERERERERERIZMN+lERERERERERESGrLJwVzNbChxCuPF3mbtP9dhFpLcOs7fGYa22y5J0ffmy2fWZ5Utn16dWhjQ7VqT7TS1N852KuqbPmeEv6dK+IOryvmBz2s994YY0nHXy7q2z6xMbN4eVjZvSzLakz5NGxuLx7FFz/hARGYBBhUIOUqcQV9KQpon0UszEtvT5yXh7tN4Kj/VoFr6ZRVGI0tIo9DUaRcEXhx0nl6WZLVyYXrcnJ9P2YSaq59SOyTmPAL4tKjyaZTCeXdCzQl+brEgIVr959ZN3P+UMog51Gdax5kk7qFn4RvGaV6cRf306zeQah7hORl+/F26M1jekB77k7nAdX7Q+vQAv2JDGw05sjr64T0Xf1ReE6/jM0nQ4nakVaQzr9t3S/2ZvXZle83esCPXbMefcjcNh40avc+jryCgyVEO/efWTdz/lDKIOdVGb0Fh99aSz4K/N7BfABuDXwCXAwRlpH2Rm6r0nIiIiIiIiIiISKd2Tzsz2BL4GPLy1KXnc6f6lmU0C1wP7AicCPylbrswD0a9GNhGtJ5M9zOk9t2L57Pr0Hun6tr3SnnSb9wr7bd0zzWvbbmlxU8vS3g8efSJaPRoWbEp//Vq8Pl1fsjZNvPSOtLvF4jtCmknLuD0fTxARjRjuc0YxH8Ffy0SkWVoD32ZdTnr9mlh2sOkKBqmeOzD4zj0lIO0dN7klfX5h1IF54caoF/SWnQcB92hw7u0r0vWt0QHsWJ7u1+pBt9fuG2a33Wtp2jVj0WTaC2PrdNomrN8aRg+/a3M6iviWybS3xfTmaCKjuAPFnPcnqVPZpmGQ+1XZey5PfmXzbkKvijzKHn8dr0XZPMoO8J2nnCLXmxHpQTEwI9wmzJE5mVDyGHV2m4g6wU1G7cDie9LGZMkdIdGCO9JrO3feNbs6c/c9aXFT6XXeFoRr98TKXWe3LVq1e1r2jhXpfpZe82eSCeumox7cca/tTpNThD+i9X7P37L7VzFBzSB7SY/K5BNF1NEGqU1oXJtQqlebmRnwReA4wiFdC3woK727TwM/TtL+VZkyRURERERERERExlXZ0NNnACcQ7j++HXigu7+ixz4XJI9HlixzJJjZaWZ2iZltNLOLzeyUYddJRERERERERESarWy463OTx++4+5ty7nNz8rhfyTIrZWb7EcbQ2xvA58Qazqb5EvCULtlscvflUfonA18G7gGuAg4HvmZmj3b3CzLykG7iIQxbE0csTPuEzyxLw4e2r0rXN+6bntqb9g9v7Zb908G+d9sn7dJ+n93Wz64vX5AOFLtxKnRNv3F9Ghu7/ta06/qONVE9FqTl2Uyox+JtaX/7ia1pvj4Z9b2fM0SjJo4QkQHI0/W/tb1sGMoAwwTmhH3G4a7J4OALtqTbFt2dJl66Ng1LWnRXet2d2BK2++J0+IKte6bDKEwvSq/nW/ZO816xLIxAfvSqm2e3HbksXV8xmVZk3VQ6/MI1SSZXTaaZ3RoNdr4lmjjCp+MxFxi8QYU8VR3iOiphrQ0Ll8lU97GWHeA7K01Wfp22lw3tHGcj3iaUFo8qE3399gXJEwvSNiH+v4YtSieGmDOhXWsYniitR3nM5ttWXiNfm5ZBDY1QdYjrqIS1jsroRWoTGtcmlL1JdxThUD5WYJ9bkseh36Qzs4XAeSQ36LpoTYBxEZ3f0i1tf7+RcDPyKHdfZ2b3Aa4AXk3ak1BERERERERERGSOsjfp9k0ery2wT+tn6j1KllmltxPCdb8NPKFTgmTcvYOBde5+Ys58Dwc+7u7rANz9RjO7ADio/yqLiIiIiIiIiMi4KnuT7h5gFcVuuB2WPK7vmmrAkpDU1xJ69r2ejJt0hONbAfyyQPY3ACea2W7uvt7MDgCOBy4sX2NpsdbsdlFoaRyuNLU07Uu+fbdopr59QhjpfgfcObvtcfteObv+58uvml3fazKdGvCO6WUA/GS3Q2e3fXfxYbPrt0ztNbu+cGNUj7tCPRZFdYvrbNGsr6PSC1pE5rkqZufLCiUokF8c+tqaAS+evW/RpjQedtG69ImFN69Li2vN1Lc4nW1vl6m0Y/2WPdNhDWK7LQ2d5x+y4vrZbSfscs3s+oqJtOw1U+nwCxNJRddtT2cdj2d63TqRhlKVbhOqDtNowmxyVcws20/eVZbXyzBDbYc582/ZkKcis/7lDe3UF7JihtkmZIWtJl+7ZxamGUwviWbr9jj8NN1xapfQFixclV6LJ7esnF2f2JFe2zvNvDqzMM1repd0fcdS67g+tcySuqV5xXX26L8PpcNkq55Rt47wvypCXOu+tg/qujHMcEu1CY1oE8pOHLE6eTy6wD6tm2F/Kllm38zsYOAThJf9hcDdXZK3Ql2v6ZKm3buBI4DrzOxXwJXA7sCZxWsrIiIiIiIiIiLzRdmbdN8k3Id8kZkt6pXYzB4FPJVwc+wHJcvsi5ktAT4PrATe6O7f6rFLmZt0/w28CLgJeCBhYoq/cPeLC1ZXRERERERERETmkbLhrh8lhIweBnzAzP6Pu091SmhmTySdYGIGOKdkmf06C3gw8EXgnTnSt27S/V8zex0wBdwK/BT4JPADd5/TETL5+xwqOEYz29A7VRPmHhkwT/uVt15um4n6ms+075Ckjbu/LwyJdl+SzvNxyJLbZtePWnTP7Prek8tm12+fDttvjdL+askBs+s3L4zqNhH1Te9Ut5mdjyP8kXEAIlK368ysa+d2d+8cB1mDytqEXt38y4ZNZu1XQchNPPd61vpscXNmf02/lvjGdCiD6fWhE71FwxBMrEzf2slt6cyssRWLwizd912YDp1wcDSr32JL13f4xnS/iTAr7ALrfL3vMLl88kTnzYUUmQWtlypCjerKI29eZfOtorymGGSYV9n3ssiMfFlpyoY5pdQmtG9rYJtgE2kmM0nmno5kMCeMdCr9ig97xvklGU6kGc9MRv+RiMqYU3ZrczRb98R0VMZMh7Qhl/Bv/H+VjPWssksr+9nqpIrwxrryyJtX2XyrKK8p1CZkqbVNKNWTzt3XAG8mHNqLgZ+b2d9HSR5vZm80s68BXwfuRTj0D7j7dX3WuTAzez7wEuAPwOntN9cy7ANcD1wOXJ1sux/wAuB7wGeSWWJFRERERERERET6UrYnHe7+HjPbE3gdcCzwX6T3IM+KkrbuUX4jSVsrMzsCOJswYcVp7tHP2124+yuAV0T5GGEMvrcBpwDPJIS1vqbqOifl97wTa2Z7AbcPonwRkXnmIHe/Y9iVyKI2QUSkVmoTRESkpdY2ofRNOgB3f4OZ/ZgQPnpURrINhIkTznT36Yw0A2FmK4AvAEuAv3b3IuPLzZH0vvttMjvsV4AnAS83s3e4+53d95ZCoo6OPpOu244dYdv2HbPbJrams/ctiGbLW7gx3W/ynhCKevM9u85u+8PKe8+u7zWZhrvusyCNHrh1areQdnOaNs6jlW97eQs2z+xUt7jO7EjX4+MjVwdPEZGcWrNT5QkfKBLmVPWsfp2ejkOK4uiCKBzJk28wM9HIuFPRTH7Tu6Sd3SeXp3FOE5s2JxvjGbij9YzXayap1FZP890wk17nt1oaXnvbdNoerZ0K/5devz3dtm1HNEv5VBTUEEfEzont7VynXnUupGxobFNCXOsIbW3aTH6esV5H2VW8J2Vn5MuTR2t72evfOBrhNiFzt7jsySSMNPrfrU9G/6dYFP2fYpf0er3L8jCUwV4r0mER9l++fnb9XovT/yfsMpl+h98yHdqC27al/zdYs3G32fU7NqTtzpaNaQyubwkVtO1p5W26wPU+j0GFao5SiGsdoa1NnvG7LLUJjWgT+rpJB+Du3wS+aWYPBk4C7gvsAqwFLgG+5+55xk0YhDcTxs3bApxpZu2zrM5+tTez3ySrZ7v72VkZurub2VsJN+kWE3oRfr/SWouIiIiIiIiIyLzS9026Fne/FLi0qvwqslfyuAvwoB5pW8/vkyPfP0brnUeYlmrEE0dMh3Xbtm12m21MJ4NYtC79lWrpsrRXxNTSsL5+4e6z276yI+34+btVaU+5XRdunV2/Z8cSAK67c4/ZbVvWpNEFK25Kez8svT3tJLpo3dad6uZRnVvH0X58IiIDkWfg79b2or8edtqvaG+LXmXHHQziTmdJr4ipXdIE23ZN1xfsnbYJNpNexxcsiUYVT+xYlfZ42LFL54qu3xp6wl2+JW0zFlrHObO4aut+s+u/3xDS37YxbT+2bom6/21PDyruTdF9eGKyX+ciPeIG1etl1HvPNa1XxSAN8lgHNdh3VhllJz6wHOWMkzFqEzptn9N7Lpo4wpam1+sVu6bf0e+3x1oAHrrbDbPbHrns6tn1QxemPelWTqTX7ruTntRX7Uh70v1s+f1n1y9ect/Z9Wsn05kqNlhoSzz+b3gUcJOrV12v63yv97joa9vLuPeea1rv60FSm9CINqHUxBGjwt1Pd3fLWoCTo7St7WfkyPrwaP3iqustIiIiIiIiIiLzy1jfpBuEZAKJ1gQYVxEmjxARERERERERESmtY7irmZ0KnFpRGZaUs4Qwhttid398RXkPhJkdDfwt8BHgKvcQk2hm+wHvBk4jdEx+XjKhhAxKPInEdAgpnYlCRyc2poO8Tk6m95yXWRQyNBO6lS/YnIbAbrlj5ez6lSvTbupzusXvCHksujvNa/c70ueX3Zp2m196c9ptfnJt6BbvUd1m5oS7RvOn6PQRkTr16uafFSZQJNSgSHlxmoyyOw0MDulEDlNLo+v2nMRpmzC9KJpYaI8Q7mrRxD3bV6Ttw44VnSty16aQx8Xr0xCmm7elg4TviGJxb9uStis3bQjtzV33LE3rvjn9+mVTBQYPL/o+VBm6NMhwpSpDlIoecx0hT/2Wm8egJg/pJ22Vg33nyaNImFOe/OaDJrYJnVT8Hk1E4wm01hdOpN/rl1gaf7piIr1eL43CXWeSmX7itHEencqoTNlw5CqHOBjksAZVXpfLhmznUeXb2sTrkNqEockak+4Y4HQG8xViFO5KPAf4p2TZbGZXE8aeO5hwDLcDL3d3hbqKiIiIiIiIiEjfek0cUeXvcvd0TdUs7wRuAE4BDgQOIdT/h8D/Au9x9/WZe4uIiIiIiIiIiBSQdZPuXODCHvvuBvwnsB9wJfBh4HpgO+Hm3u7AcYQeeSuAzwKvcPftfda5Mu5+IR1uRLr73YTj+XDddZIuZkKYqEczIM1s3jy7PhHNlDoZzaC6bEvYYfH6NNxp+80LZ9d3LEtDlGbSiCcmppPu75uimVvvSQtfcGca4jpx98bZdd+wIeS1JZ0p1ndEMwDOROGuIiKD0pqdKk/IQL9hTr1CCvLm3UOn0NeZRenGHVFmPpFun45mbJ3cGtYtmlx7enGUR8ac7Vs2hjDZqyf2mt22ZlEa7jo9k+axZVsaErVtS2hvZrZEIa7RjK7kmcmvlypCUpoW4lp1iJJm8uut6jCvsmFJvfIoMjtpr7xa20f9vcujaW1C1a95K7/oWmzxCDPRdXdTNMP2LZvC8AS/X5DO3B27aeqO2fUVE+l3/w0zYb8/bU/bhNZs3nG+7eW16jFneIOZCtqBLFWGnA4zxLXqoQw043dvahOGpuNNOne/nnDDrSMzmyD0KtsX+DRwurt3uvPwGTN7G/AN4MWEw31Zv5UWEREREREREREZJ2Vnd30G8CjgarJv0AHg7muBxwPrgL83s0eULFNERERERERERGQs9RqTLsvzCL3iPtDtBl2Lu683s/cA7wBeSBjXTaScKFx0TujrTNoF3aLwUtsSti/akM6st3Bx1O18URr6ymTUFzYJd7XtaSG2LY3W9k1pqO2c0NYk/ZxZXBXiKiLDUiTsqGw4Sbxf0dkAO81Sl6POs5OpRrPmzUQze+9YkG6Pw1knWrOpRuGuHg11MLO4c4GehKtunEmHTtg0uSTaMS3Doxlb2ZGENhWZxXWnwls7dtjWrkhIR5Wzv1ZVXt0hSsMKba16NtYqQnOqmG2zVz2Knhu9ZrEskl/JMPuxU3ebkFV2p/2y8igwK2w8keqc/6VG4a47NqX/D7g9CVvdHA1TcNOmdCiD3Ren3/cXTaQZbk/GyLlrW/r/i3Wb0vWNm9L2YSoa7mC2HlHdCk/+Oqg2YVBDLvQzi2vdQxkMK7S1idcktQlDU7Yn3ZHJ428L7NO6MfdnJcsUEREREREREREZS2Vv0u2TPC7smmqu1v3J/UuWKSIiIiIiIiIiMpbKhruuA+4FPJTes8C2PCR5nOqaSqSIOPQ1mt01DjW1qXDK2eYoHHZBNMveZDylazzTUnJfOcprZio9feMy5sze2qqHN6zfrIjML63ZqfKEonbaNsj9iswG2KPsTjO+QhQOy9xw1tbk35nZZvx8aTuSPabT9sOjGCWLKhLPHNsKg7Ws48/S6TUoGhZS5ex8de9XdR5F8xt0vk1UxbGWnSW4yMyiefIuEnY5X76u1dkmdKtD3vzytAM9zjeLZ03dEa1H1+upZCiC9dvShmLDxnRYgxsn09DXiYloeIUk75npdL/peObuaN2mou1TDWsT8qhy9u+6QlybcJ0f9WuL2oShKduT7neEQ3memS3qlTiZDfavkz//VLJMERERERERERGRsVT2Jt2XksejgPflSP+vhLHoHPh6yTJFRERERERERETGUtlw13OB1wEHAi81s2OB1wI/c09j/MzsSODtwCnJpk3Ah8pWVqSrOLw0ms7Jt4e4I7f4nvS22TWb6N5v2Wcy+rx6PDVgA/rFioh0UlcIay+9Ql/zlFEk9HXOepQ4iUzKvGxnNAmtGVnjS79FiTNn56siFKxIGGmVs/ONeojrIMOSmjaTX9WzxZZNW2VYUp48yl7H2vMY9VDlIqpuE8ixvUw9eg2RkKdOcehrnDYOfZ1O/n+wI/1/wvQWj57uMQR73CbE4bVZ25vcJhQ5B/Lk0e9+w8gjb1795F1FeXVQmzA0pW7Suft2M3s6cBGwC3Bcsr7dzK4GtgD3B1YmuxjhJXmJu9/Rd61FRERERERERETGSNmedLj7pWZ2MvBF0hlbFwNHJOvx/cftwEvd/TNlyxMprdVdIupdN+fpmY6bRUTmj16DUFfR46FTeXH6sr07cvTs8yK/5GZJ8s7sMVcir53qMaieEkX3q7I3QtH9+i17mJNMlC2jKap438v2eOiVR9nrStE8JOjVJmQp0jO6035x+l69r9vT5H2+LU2rlzQZvaQ7th9xEYPsRd2UNqGXsp+nOnpMD3OSibJlNIXahKEpOyYdAO7+K+AwQujr75PNcQfBu4CPAUe4+7n9lCUiIiIiIiIiIjKuSveka3H3zcC7gHeZ2Z7AvYGlwFrgT+4Z3ZdEREREREREREQEqOAmXczd1xJuzomIiMgwtfq1FwkTqjssKd6eZ78iYbKxYYYeVhGiVOVA3IMMcR3lAcNHcZDwrM9MWb3qVDY0reg5V+UEBkVD+MdZv21Ct3zb8ysbvhlvz7NfkfYoVuBaVckQB73KGZU2oYrrZB0hrlXkUfR97/c60sQhEtQmDE1f4a4iIiIiIiIiIiLSv0p70mUxswXAEsLEEovd/eY6yhURERERERERERkFpW7SmVk/48x52XJFRESkoLKhqIMMS+pUTtn9OtWnm7L7dZKnbnWEnNa9X688BhmeWneI0nyaya+KELMi50PR2fk67Vf2utKeXxNDzQalSJtQNiyt6PAFsSIhs53261Sfbsrulzev9vzGsU0oOwttnrx75VH3UAZVnxtNpjZhaMreLBvFrx4iIiIiIiIiIiKNVPYm3Q30vr+4CNg3WXfgPOA64J6SZYqIiIiIiIiIiIylUjfp3P3APOnMbDfgxcBbgROAM9z96jJlioiISJ96hTlVPbNW1SGzRfbLUmUIQxWzyQ4yHGsUw46GORtg3rzK5lu2jDyqni22yPNFZgDME+bUK+9BXlfmm7KvSdnhEsrOwljFflmqjA+br21CllEcUqFMXmXzLVtGXdQmDM1AZ3d19/Xu/i7gqcB+wPlmtniQZYqIiIiIiIiIiIyagd6ka3H3bwKfAg4DnltHmSIiIiIiIiIiIqOizllWPwe8AHge8LEayxUREZl/WrNTFQlhLTqzVpWhr1XMAJilaEhspzrVEcIyiuGio1jnInkUza9Mvk1RNjysbFhSkbyHEYo/bnq1CZ0UDUurMvS1ipnCs1RxbS9r3NuEfvPNyruuENemDY0wTGoThqaWnnSJO5LHQ2oss29mdoKZfcXMbjezLWZ2mZn9i5kt6ZDWzOzvkzQbzOzHZvaIYdRbRERERERERERGR5096Y5JHlfVWGZfzOy1wJmEe6u3AdcARwJvB55mZie7+93RLv8H+ACwNkl7HPAjMzvK3a+qtfIiIiJQ/0Ddecru9St5nl9hi/zSXsWvolX+Ct6UHgFN6z2XZ986es+NyiDhVfcGKjLYd1Y9em2vuvdDFXlYlzzHUZ5zpcoJfWJFescV6VGdJ48823vJcx72m2+WUWwTquhp1u/1usmTTJQtoy5qE4amlp50ZrYceFny53V1lNkvMzsV+A/C2/cc4N7ufhRwPLAJOBb4aJTegDcBlwL3dfdjk7QLCTfvREREREREREREOhr4TTozexzwHUJPOge+O+gy+2VmC4Gzkj//xd0/4+7TAO7+C+D05LmnmdmDk/VVwF7Aee6+JUl7KXAZcFBddRcRERERERERkdFTKtzVzH7YI8kk4YbVvYHl0fa7gbeVKbNmjwMOBLYCH+7w/JcI4a/3IvSyuxS4i9DD7vFm9kF332pmxwIPAL5dR6VFRES6qnuA7yrKzsqj035VTxRQ1jAnIxhU6M8gy25CuNIwJ5koqtfnoOw5XvY1KhLyNMgQpU55lL0ejbMq3q9hhqJl5dFpv6onCqgjlHHc24Q872sThjUY5iQTRVUZrltkP7UJA1N2TLqTKH7qbgCe6e7rSpZZpyclj99w9w3tT7r7jJl9HXgh8Mhk27SZvZcQ8nq9ma0BjgY2Ax+sp9oiIiIiIiIiIjKK+gl3tRwLwO+AdwL3d/fv9VFenVohrBd3SfP75PHe0ba3Am8g9Bi8P3ABcIK731B5DUVEREREREREZGyU7UmXZ4y1TcBdrbHcRsyByeNtXdLcmTzuZ2YT7j7j7lPAvydLX8xspx58nZL1W46IiABwnZl17SHu7ivqqky7Um1C6+eyqsNPi4ScVlF21n69yqhiVr8qZ88s2mJXGR7VxDDTJpddpB5NnMlvUHUq+1krOvNjp+vJoMPod35u/NqEIqnLhr52Slt1OFvWfr3KqGIG0irN1zahaH5F8q16dtoy9Sh7Pg3yf/VqEzpva3CbUOomnbtfX1UFGmrX5DHPTboFhPH3uqUVERERERERERHJVLYn3bibAhYTJsDIEr92m6quQJ47sWa2F3B71WWLiMxDB7n7HcOuRBa1CSIitVKbICIiLbW2CWVnd31zsvqhvBNBmNm+wHHAOne/qEy5NVoDHEqYvTXLquTxHnffOPgqiYiIlFAk/LTqmbXyhJb0Cp/ttb3qEKZeYSFVh6Q0Jdynyjz6CTMdVLhS1SFKw5zVr1O4TxUz05V9basMX8/Kr+i1pGyY03xQx0yIRYZLaE/f73W+iqEO8pTdb75lyyta9ii2CUWuZ4MK3R1mOHJRgzpH52ubYFT/HhVUtifdGYRDOQ/IO1vrscCXgF8DDylZbl1aN+n27pJmz+Tx5sFXR0RERERERERExlk/s7sWdUvymGfSiWG7MXl8eJc0xyaPmrlVRERERERERET6UueYdK2bWotqLLOsi4DTgSeY2Qp3nzODkpktAJ6Y/PndmusmIiLSW2t2qiIzr1Y9C98wZ/LLk1+RtHXP4ln3DKSDyqPJIa5V5ZE3r7L5FlX1OVdH+GHVofj9hvCPo04zflc1E2KdeWTt16uMPPn1mzYPtQn9a+Ks4WXyKptvUWoTeu/XMLluY9QpZAAAIABJREFU0pnZ3sCSDk/tZ2Zbu+w6CewOnEgaInt5wToOw/nA+4EVwD8AZ7Y9/zzCcW0jhPyKiIiIiIiIiIiUlrcn3VuAv2/bZsAPCpTV+u3mCwX2GQp3v8vM3ka4OfcOM/sT8EV3nzGzPwf+K0n6Xne/aWgVFRERERERERGRsZD3Jt13gZd02F60w+DngHcV3GdY3k0I0X0Wod63mtla4Mjk+S8Cb87YV0REpBmKzLxadLbIfmcAzFOPXtvzfBOpIlR1UKEogwyHGdTsdsMMpWpyGFc/+fVbXtnXK0/aKsMP6w6jz7vfiIRAVaLIzKtFhkuIt1cRzpa1X6/tec75Joc4q02oNu+6QlzrDm2tYwiOcW8TsrSGixmivDfpfkAYp61V3ROT9YuBzV32mwFuJUzE8AV3v7hkPWuX9Jp7DvB94KXA4YSQ358C/x/wCXdv8iVeRERERERERERGRK6bdO5+D3BS628zm0lWn+/ufxxAvRohuQl3TrKIiIiMtrIDfPf6NTXPL6h1/CKbRx09ZuroOVWkvKb0JCibRx1lN3mSiX5UUacqB/6uuwdF0d7B803Z17rXNTrP9b6K63zZyYTy5F0ltQmDy6Ns3k05vrx5VWW+twlZGtb1amLYFRAREREREREREZnv8oa7tjs5ebyhqoqIiIiIiIiIiIjMV6Vu0rn7j6quiIiIiFSoNRh62UkdRmWQ8F55lUlTpuwi6qrDqIT7DCvEtYo8qp5kokg5ZcPJi5SRlXfdE8tUfR2bj6GvrcHQ6w4zLptH1n55tvcqo2iaQVOb0DuPPNe4JgxrMMgQ3qLl9Fv2OLUJVUyMUyOFu4qIiIiIiIiIiAxZ1550ZvZs4L3ANPAad/9ssv1jfZTp7v7CPvYXEREREREREREZK73CXT8I7E7oAPgh4LPJ9tPpryOgbtKJiIjUoY6w1X5m1up3Jr8iz+cpo6yq8xvUsTQ93GdYZVcdotSUWf2qDAcsGnJYdvbnfsPvi+bhNCK8qTbDDDPOyiNr327buuWR9/k8ZZSlNiH//t3y6Pd1LHt8VQ9l0JTZv+dTm9BLt9mrhxwG3yvcdTVpFde0PWclFxEREREREREREYn06kl3KvCPwB3Ap6PtJ3dOLiIiIiIiIiIiIkV1vUnn7jcBr++wXbO7ioiIjJqqw1arCFWteya/ImnzzJ5ZRtm4gqJ1qDK8ZpAhUaNc9iDfkyLlVB0OWEXIYdkw+qbMPD0f1B1mnLVfr+1Fh1HoVUa/aaumNqGa/ao4vn7Pqapn3K2qnLzljXqbkKWKmWVrpNldRUREREREREREhqxXuGtHZvaoZPWX7r61wH67AZPufmeZckVERERERERERMZRqZt0wIXADHA48Mc8O5jZU4HPARehMe1EREQGqzVjYd0zto7KTH5ZqpxBth9NmDWuieFMVefRhLIHGWZXNnSrbMhh2WtJlrpmnm5AeNPAtY6z7hlbi4YmDmvG7yyDus4UpTahXNlVzwKapcrQ60GeU+PYJpT9ftntWIc8DEI/4a5FX9LVyT6H91GmiIiIiIiIiIjI2Cnbk66MfZPHlTWWKSIiMr9V0SOu6l8ps8rplm+37UXK66Vsj40qyuhlkIOLN6UXQB2Ddhc55+ooO48qP6N5nq9jYhnLWK+77Pmmih5xVZ83WeV0y7fb9iLl9VLHuaI2of569Dov63qN6po0JG95TW8TyvYSreL7ao36nTgi1+GY2bHAfyR/XttnmSIiIiIiIiIiImMlV086M3sfcGqHp35oZju67DoJ7A4sS/524EeFaigiIiIiIiIiIjLm8oa7/g54JTt3Gtwvx75xR8LrgDfkLFNERETK6jRI+CAG183av9v2shNA1D2pQ57XblDqCIGpI1RnlPIos1/VIa6DPIeLlFFl+GnR176Osudj6GunyYQGFdpWxQRCeZ6vYzKhplCbUG0eZdVdt6rP4VFsE3qp+vtqA64beW/SfS95bD+sPKfpLcCNwOeB/3L3zfmrJyIiIiIiIiIiMv5y3aRz9zVE49eZ2QzhBtwD3f2PA6qbiIiIiIiIiIjIvFDn7K4iIiJStzrCAIqGMJWdSW2YYYP9qiOMsaqy+w3xbEo4U9k86ii7rvekys9r2dDRrOtHHWGrea9/DQhvqk3dr3vWfr22l50JNkvT3mO1Cc3Jo+z5nCfvvHn0MyxAEU1uE/LUqcrvq93yGPJ3yLI36d6SPK6tqiIiIiIiIiIiIiLzVambdO7+lt6pREREREREREREJA+Fu4qIiMwXVc7OlbVfnu2DCicpmzaPukMfytZ/UOFfdYT7VJHHMGf9G+YstEXKG2SIUllVh0fVXf9RNaiwtCpm/K76s9y0IRCKUptQLo+y51HWuV/1OVf10Ai9NKFNKPpds4rvq2XzGJK+b9KZ2TLgNOBg4N7Aog7JFgK7AiuBXd39wf2W21RmdhrwJuBQ4ErgDHf/+nBrJSIiIiIiIiIiTVb6Jp2ZLQLeBryYcAMu12404LcrM9sP+DWwN4C7d7x3amZfAp7SJatN7r48Sv9k4MvAPcBVwOHA18zs0e5+QUXVFxERERERERGRMdNPT7ovAU8kf0dOA7YAa/oos29mthA4j+QGXQ8HJ48X0fnm4pa2v98I3Awc5e7rzOw+wBXAqwHdpBMRkfq0ZiysIwygaMjDfJzJrynht00MZ6pCk8NkBzWrX9GZUjs9XzbMKYvCVpurNWNhHa970fNnPs74rTZhsAbVJmSd271mPM2Td6d88+g3v6rbhLJh7WMYtlpWqZt0ZvYM4C8JL8ktwEeAO4APJdseB0wBS4AnAC8HVgOPcvdb+651f94OnAB8m1C3jszMCDfp1rn7iTnzPhz4uLuvA3D3G83sAuCg/qosIiIiIiIiIiLjrGxPuucnj7cCx7n7GjNbTrhJB3Cxu9+drH/HzH4EfBH4gpmd4O5D+d0rCUd9LeHG4uvpcpMOWAWsAH5ZoIgbgBPNbDd3X29mBwDHAxeWq7GIiIiIiIiIiMwHEyX3exChx9wH3H0NgLtvBLYmz88Zo87dzwc+BzwCeGbJMvtiZgcDnyDU+4XA3d33mA11vaZAMe8GjgCuM7NfESaO2B04s1htRUREKuLRkqUVBpUnj175WcZSpJ5FysuSVY8iS9H6VVX3PPXPo0g9ipRR5BwoWs8q8qtSr7L7eY+rrEesjjoVOU+Gocj5Pt9U8d4VuS6VvSYWvUb30u81vOqlKLUJ5fOrUhXfa6pQJL9Bll0k32Fec/s9h2tW9iZdazy3S9u235Y8Htphn88RXprTS5ZZmpktAT5PmF32je7+rRy7lblJ99/Ai4CbgAcSJqf4C3e/uEAeIiIiIiIiIiIyz5QNd10L7Ausb9t+K3BfQojn99ueW508HlmyzH6cBTyYEHL7zpz7tG7S/V8zex1hjL1bgZ8CnwR+0B62m/x9TrL0xcw25EnWbzkiIgKEHtBdfz9z9xV1VaZdZW1CfIT9DgyelSbPwL958yqTJm95dau6PmV/7R3k4OJF8u6VX10DlA+zp1cvVZwzVX/mq1RksPJBDijeuYfF/GgTqh6QvVOaXu9tkbzKpMlbXt3UJhTLb5zahF6fk249CPPmMcjXa1CvUd7rdbc6VNHmde5RV2ubULYn3XXJ4/3atv+UcOjPNLP2G4D7J4+7lSyzFDN7PvAS4A/A6QXGw9sHuB64HLg62XY/4AXA94DPJDPFioiIiIiIiIiI9KVsT7prgUcCRwPnRdu/CryaMMvpG4B/AzCzpYSJGgCuKFlmYWZ2BHA2ocffacm4ebm4+yuAV0R5GeF43wacQhhb7ybgNVXWOSq/551YM9sLuH0Q5YuIzDMHufsdw65EFrUJIiK1UpsgIiIttbYJZXvSfYJkfLm4N5m7X0QYhw3gDDP7mZmdR5hA4RGEjoO/6KO+c5jZMWZ2YcZyAvAFYAnwLHcvMrbcTjz4LfBk4GvJ5peb2ar+jkJERGQIigzMXMdAyU0cJLxo/aqqe57651H34OJF8u2VX9k86hpQvMrXpemacKxVnIsNGxi8cYq8flVc23speo0uW49hLUWpTSiXx3xqE+o61n7fkyrrMArnRgmletK5+w/N7A/ACsIkEZdFT78I+BmwCDguWVrWAW8tV9WOdgNOzHjuvcBhwBbgTDNrn2F1UWvFzH6TrJ7t7md3K9Dd3czeCjwJWAwcy87j74mIiIiIiIiIiORWNtwV4DHA7R0mT/i1mT2W0NvuwOipK4G/cffKul27+4Vk3Ps0s3OBhwK7AA/qkVXr+X1yFv3HaH15zn1EREREREREREQ6Kn2Tzt1v6/LcT8zsEMIsr/sTJpr4jbvvKFteifqdDpye9byZnQRckKQt2snx8Gj94oL7ioiIDF6rC3+ecINWmjytYac0RcrIk1+RsvMYZnjbsGaKy6OO2QCrngGwClXMANivuIw8s9Rl7Vvm+TxlVKnIjH3t6Qel6CyI46AV9lXkOl/22l62LclbZpm0ecqug9qEavOrwri3CUXe1yYea1PqVKN+etJ15e4zhLBXAMzsVDP7m/CUP3VQ5Q5aMoHE65I/ryJMHiEiIiIiIiIiIlJa2YkjyjgEOC1ZGs3Mjjaz95nZA81sItq+H/BpwjHsAJ7XHu4rIiIiIiIiIiJS1MB60o245wD/lCybzexqwthzBxM6Q94OvNzdFeoqIiLNViSkqOrwun7CYPOWnUcVoT/D/Emu39egrpCwQYXUNDE8qpcioTpFw2zKhhcWKaNs3nUoEj6b9/WcTz+5F7nOl7229zO8QZWhe4PMY5jUJlSbXx3qbhOKGOT7Woci4bN5r0FDPn90k66zdwI3AKcQJr84BLgH+CHwv8B73H390GonIiIiIiIiIiJjZd7epOs2M6y73w18OFlEREREREREREQGat7epBMREZnXioRTDCMMtkzaovWoQ9NmqctSx2yATZt1tB9lZ7+s4zNTxX7j8l41bMa+RqvjPB3mLN956lEHtQnlymj653dU2oSmva91G5GZveucOEJEREREREREREQ6UE86ERGRcdQaDL3IQN1Ff5ktO4B93b+ej3pvvCp7ENTdC6Upv1Q3pRdGkcGrY53SVz2xSVPeK/V+G4zWYOhFevpUfZ72Kq9sGUU15VwvS21C/5pybanys1a1pr1G0JzzZ8DUk05ERERERERERGTIdJNORERERERERERkyLqGu5rZmyss65EV5iUiIiJ51D1AcZ6082mQ8LrLrjIUpO6BqYuWOaiwl7KfmWF+TvIY1rkxyPCkOt6rcVPHpEFF086nyYTUJgyuTLUJxQwrbHqQn4Gy17eGhdH2GpPuDOZ3MyYiIiIiIiIiIjJweSaOaNh9RRERERERERERkfHS6ybd39ZSCxERERm8sl37qwiDLbJfU8L8qp49s191hQ2WVcXrPChVhCDVES5edr8mnhvjeD6Mm6pD88q+5732q/o9Gpf3vImf+9g4XgNGpU0YpLrf17pnsm1AF7WuN+nc/eN1VURERERERERERGS+0uyuIiIiIiL/P3v3HTbJUd57/3c/YfNKq7AKq5xQBgkEAmOC7JdkE6Tjc8AE2xgMBotjDA7CfsEWNtiIZBkMxhiwkM0hmCAfkWWSBCZJAoQQEkor7WoVVlpt3n3iff6onql6Zid1T098vp/r6mt6eqqrqid0zdTU3QUAANBn7VyTDgAAjJp6YQd5h/h3K0SpVzN/DXMZeZT9fA77jLtFlR0u3qqMbhn2z1fZTMNZ77LVew7yvle6dSmDQQ/rbGXQ3l+0CeUYlTZh2D9fZXP1vd6MpAMAAAAAAAD6jE46AAAAAAAAoM8IdwUAAEGvZ+xrp+yyDfLsYnkMYwhMP2cLbJRHmSHZZdctTx16HZoziO+NAZudbySM6ozF/Sin22gTysljmNuEfhrEEOohnsWbkXQAAAAAAABAn9FJBwAAAAAAAPQZ4a4AAIyiyoyFZYeRNSqrU70K6Rj22TPL1IvnvOznouyQxkoevfictGMxzT48iOFRo6wyY2EvzteD8nlqxzCeB7tlGJ8L2oTODcr7cxDDqfuEkXQAAAAAAABAnzGSDgCAUVb2hb/LyKufI16G5cL8RfXzuR2W56iedp63QR6FOYijyIb5/TDKyp4gqIy8+vleGfX3KW1CMcPeJgyiQWynBhQj6QAAAAAAAIA+o5MOAAAAAAAA6DPCXQEAWIzqhR30Kqxi0MI3ioZgLNbQjUF5/cq+YHgr3SqDUL/iFutnsBvqvRd69fwO2us4SmHnvTAo5xHahM4N+3t4UN6LHVo0I+nM7NfN7Ctm9qCZ7TWzW8zsbWZ2QIv9Hmlm/25m92b73Wpml5jZmgbpzzez68xsp5lda2bP7s4RAQAAAAAAYFSMfCedmS03s/dJ+rykp0vaI+leSY+QdJGkG8zsEQ32faGkayW9WNJySTdLOk7Sn0n6sZkdVZP+uZI+J+lESbdIOk3SlWZ2XhcODQAAAAAAACNi5DvpJL1V0h9IelDSkyUdLel4SadLulPSkZIuN7MFgzvN7BxJl0ualPQnkg5x97MknarQyXeMpM+YWfocvlHSJknHuftjJJ0saZek13ft6AAAKIvlXEaFN1hSo3z8UuPnoNXzMiiGpZ715P3c1Xv/5Xn9Ruk5QneN6vuplTI+k8Nu2F/3YalnPUXff2Usw2KY3osFjHQnnZmdJem12d0XuPs1Ht0k6WmS5iSdK+lZNbtfqnDNvg+4+7vcfVqS3P1WSednaR4r6XnJPqdJusLdt2RpN0j6hsLoOwAAAAAAAKCuke6kUwhTHZN0nbt/vfZBd79d0peyuxdWtpvZ6ZKemN19V539fiDpB0kZFXdLekrlenVmdoykx0v6eWeHAQAAAAAAgFE26rO7npXdXt8kzVclPVshNLXiOdntde5+W4P9rpT0OEm/lGx7p6QPS7rTzG6TdIZCuOwlOesNAMDgG6bQiCK8wTqGw6C8ZsP+ORn2+qN3BuUzB9QzKO/PYT+nDsrzOMJGfSTd4dntziZpNmW3x5hZpdPy0dnttU32+2l2e6iZTWbr/yrp9yTdo3Dtuh9J+lV3b5YPAAAAAAAAFrlRH0l3s8IEEWc0SVPpqJyQtFZhUohjs233N9nvoWT/wyRtcHdXGEn34YL1zWtBP/y0pujZBoA2TGuqdtOw/68p1RzD3K5d/arH6KBNRRm6dXbp1ftzFM6OLdQ5X47CUdMmAINo2M8ui+C7Ub/bBAv9SqPJzP63pPdkdx/v7t+veXylpKsVR86tcPc9ZnazQvjrhe7+/gZ5nyrppkZ5l1D3He0kk7SyzHIBYJHapRZfO9x9dY/qsg/aBADoKdoEAEBFT9uEUQ93/WfFSRu+ZGa/bWaHmdmBZna+pO9JOjN7fIe778nWZ7Pb8SZ5p6MQ+WsKAAAAAAAAhQ11uKuZnSXp0gYP/5G7/9jMLpD0CYVJJD5ak+ZmSR+S9OpsvWKjQpjsoU2KPyhZvydPvdvRTk+smZ0iZo4FgDKc4+43t07WH7QJANBTtAkAgIqetglD3UknaY2kpzR5TO5+i5k9XtILJT1W0omSHpB0lULn3Tey9F9K9t2Y3R7SpOyDs9u9krbmrnk5blUcxXeOpC0avSjxO7Pb4/pai+7h+IYbxze8TNId2fo5CufTYUebMPw4vuHG8Q0v2oThNMrvSYnjG3Yc3/Dqa5sw1J107v5NtXERP3efknRZtlSZ2cmSnpDd/Wzy0Ibs9nFNsj07u73b+3RhP3efMzPP1gf2375OJMe3ud916QaOb7hxfMNt1M6ftAnDj+MbbhzfcBu18ydtwvDj+IYbxzfc+nn+HPVr0jVkZksVRtKZpE+7+0+Sh6/Obh9lZic1yOI52e1Xu1RFAAAAAAAALBKLspPOzFYrjKo7S9JDkv6sJsnVktZn6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", null ]
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https://najeebk.com/category/statistics/
[ "## Statistical Testing – Why, What, and How?\n\nStatistical testing or hypothesis testing is a popular statistical technique to make data-driven decisions. This article briefly describes why we need statistical testing, what could be accomplished with statistical tests, and the basic mechanism of how statistical tests work. Why do we need statistical testing? To answer this, let’s first state a few statistical preliminaries. …" ]
[ null ]
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https://mathoverflow.net/questions/419465/does-the-category-of-commutative-and-cocommutative-hopf-algebras-have-enough-inj/422248
[ "# Does the category of commutative and cocommutative Hopf algebras have enough injectives?\n\nIt is well-known that the category of commutative and cocommutative Hopf algebras is abelian (see https://arxiv.org/abs/1502.04001v2 and its references). But does it have enough injectives? What about projectives?\n\n• As far as i can understand, the category of finite dimensional, commutative and cocommutative Hopf algebras over an algebraically closed field of char 0, is equivalent to the category of finite abelian groups (as a consequence of applying the Cartier-Konstant-Milnor-Moore classification theorem of cocommutative hopf algebras in the fin dim case). Does this answer your question ? Apr 3 at 22:07\n• @KonstantinosKanakoglou Unfortunately, I need to allow infinite-dimensional Hopf algebras too. Apr 4 at 14:45\n\nOver a field $$k$$, the answer is yes for injectives; I'm not sure about projectives. Over $$\\mathbb Z$$ or other commutative rings, I really don't know -- the use of the fundamental theorem of coalgebra below seems pretty essential (and the fundamental theorem of coalgebra fails over $$\\mathbb Z$$).\n\nOver a field, in fact more is true:\n\nClaim: Let $$k$$ be a field. Then the following categories are locally finitely presentable:\n\n1. The category of coalgebras over $$k$$;\n\n2. The category of cocommutative coalgebras over $$k$$;\n\n3. The category of algebra objects in either (1) or (2);\n\n4. The category of commutative algebra objects in (1) or (2);\n\n5. As in (3) or (4), but with restricting to objects with antipodes.\n\nMoreover, the natural tensor product on each of these categories is a symmetric monoidal structure preserving filtered colimits, with compact unit.\n\nCorollary: The category of commutative, cocommutative Hopf algebras over a field $$k$$ is a Grothendieck abelian category (and in particular has enough injectives).\n\nProof: Every locally finitely presentable abelian category is Grothendieck.\n\nProof of Claim: The conclusion for (1) and (2) follows from the fundamental theorem of coalgebra. Then (3) and (4) follow: in general if you have a locally finitely-presentable category with a monoidal structure with compact unit and which preserves filtered colimits, its category of monoids will be locally finitely-presentable, and similarly for commutative monoids. Finally, (5) follows because Hopf algebras are closed among bialgebras under filtered colimits (when the monoidal product has compact unit and preserves filtered colimits).\n\n• It occurs to me that from what you said in your question and from the introduction to the paper you linked, it's unclear in what generality the category of commutative and cocommutative Hopf algebras over $k$ is abelian. Of course, any restrictions on $k$ required for that to be true should be applied also in the above Corollary. May 11 at 3:04\n• Do you have a more down-to-earth reference for what a locally finitely-presentable category is? I'm finding it really hard to read the nLab article you referenced. May 23 at 15:12" ]
[ null ]
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https://www.acmicpc.net/problem/8314
[ "시간 제한메모리 제한제출정답맞힌 사람정답 비율\n2 초 512 MB31151548.387%\n\n## 문제\n\nByteman is studying directed graphs. He especially likes graphs which do not contain cycles, since this is a class of graphs in which many problems can be solved easily and effectively. Now he is trying to find a method of representing any directed graph as a sum of acyclic graphs.\n\nFor a given directed graph he is trying to find a way to divide the set of its edges into a minimal number of subsets in such a way that the graphs constructed using the respective subsets of edges do not contain cycles. Could you write a program which solves Byteman's problem?\n\n## 입력\n\nThe first line of the standard input contains two integers n and m (1 ≤ n, m ≤ 100,000), denoting the number of vertices and the number of edges in the graph, respectively. The vertices are numbered from 1 to n. Each of the following m lines contains a description of one edge of the graph as a pair of integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi). Such a pair denotes a directed edge of the graph from the vertex ai to the vertex bi. You may assume that the graph does not contain multiple edges.\n\n## 출력\n\nThe first line of the standard output should contain a single integer k - the minimal number of acyclic graphs in any decomposition of the graph. Each of the following k lines should contain a description of one element of the decomposition, starting with an integer li denoting the number of edges in the ith element. It should be followed by an increasing sequence of li numbers of edges belonging to the ith element of the decomposition. The edges are numbered from 1 to m in the order in which they appear in the input. Each edge should be present in exactly one element of the decomposition.\n\nIf there are multiple correct solutions, your program should output any one of them.\n\n## 예제 입력 1\n\n6 5\n1 2\n2 3\n3 1\n4 5\n5 4\n\n\n## 예제 출력 1\n\n2\n2 3 5\n3 1 2 4\n\n\n## 힌트", null, "Illustration of the example from the task statement. The circles represent the vertices, while the lines and arcs (continuous and dashed) represent the edges of the graph. The numbers next to the circles are the numbers of the vertices, and the numbers next to the lines/arcs are the numbers of edges. This graph can be decomposed into two acyclic graphs: the edges of the first one are denoted by continuous lines/arcs and the edges of the second one - by dashed lines/arcs." ]
[ null, "https://onlinejudgeimages.s3-ap-northeast-1.amazonaws.com/problem/8314/1.gif", null ]
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https://turbomachinery.asmedigitalcollection.asme.org/vibrationacoustics/article-abstract/141/4/041007/727743/Reduction-of-Hybrid-FE-SEA-Model-for-the-Mid?searchresult=1
[ "In this paper, an improved hybrid finite element (FE)-statistical energy analysis (SEA) method is proposed for the mid-frequency vibration of vibro-acoustic systems. Within the framework of the hybrid FE-SEA method, the present method reduces the size of the total dynamic matrix of a vibro-acoustic system by employing dynamic condensation to reduce the order of the dynamic matrix of the acoustic cavity. A fast algorithm is introduced to obtain the dynamic flexibility matrix of the slave degrees-of-freedom (DOFs) of the acoustic cavity FE model, thereby avoiding the direct inverse computation of a large dynamic stiffness matrix at each frequency point of interest. The first numerical example illustrates the validity and efficiency of the present method, while the convergence and accuracy analysis of the proposed method is investigated numerically by the second example.\n\n## References\n\n1.\nIhlenburg\n,\nF.\n,\nCioranescu\n,\nD.\n, and\nLloyd\n,\nG.\n,\n1998\n,\nFinite Element Analysis of Acoustic Scattering\n,\nSpringer-Verlag\n,\nNew York\n.\n2.\nHarari\n,\nI.\n,\n2006\n, “\nA Survey of Finite Element Methods for Time-Harmonic Acoustics\n,”\nComp. Methods Appl. Mech. Eng.\n,\n195\n(\n13–16\n), pp.\n1594\n1607\n.\n3.\nLi\n,\nE.\n,\nHe\n,\nZ. C.\n,\nXu\n,\nX.\n, and\nLiu\n,\nG. R.\n,\n2015\n, “\nHybrid Smoothed Finite Element Method for Acoustic Problems\n,”\nComp. Methods Appl. Mech. Eng.\n,\n283\n, pp.\n664\n688\n.\n4.\nLi\n,\nE.\n,\nHe\n,\nZ. C.\n,\nJiang\n,\nY.\n, and\nLi\n,\nB.\n,\n2016\n, “\n3D Mass-Redistributed Finite Element Method in Structural–Acoustic Interaction Problems\n,”\nActa Mech.\n,\n227\n(\n3\n), pp.\n857\n879\n.\n5.\nHe\n,\nZ. C.\n,\nLi\n,\nE.\n,\nLiu\n,\nG. R.\n,\nLi\n,\nG. Y.\n, and\nCheng\n,\nA. G.\n,\n2016\n, “\nA Mass-Redistributed Finite Element Method (MR-FEM) for Acoustic Problems Using Triangular Mesh\n,”\nJ. Comput. Phys.\n,\n323\n, pp.\n149\n170\n.\n6.\nDesmet\n,\nW.\n,\n2002\n, “\nMid-Frequency Vibro-Acoustic Modelling: Challenges and Potential Solutions\n,”\nProceedings of 2002 International Conference on Noise and Vibration Engineering\n,\nISMA, Leuven, Belgium\n, pp.\n835\n862\n.\n7.\n,\nP.\n,\nBarbarulo\n,\nA.\n,\nRiou\n,\nH.\n, and\nKovalevsky\n,\nL.\n,\n2012\n,\nMid-Frequency - CAE Methodologies for Mid-Frequency Analysis in Vibration and Acoustics\n,\nLeuven University Press\n,\nLeuven\n.\n8.\nHe\n,\nZ. C.\n,\nLi\n,\nG. Y.\n,\nZhong\n,\nZ. H.\n,\nCheng\n,\nA. G.\n,\nZhang\n,\nG. Y.\n,\nLi\n,\nE.\n, and\nLiu\n,\nG. R.\n,\n2012\n, “\nAn ES-FEM for Accurate Analysis of 3D Mid-Frequency Acoustics Using Tetrahedron Mesh\n,”\nComput. Struct.\n,\n106–107\n, pp.\n125\n134\n.\n9.\nHe\n,\nZ. C.\n,\nLi\n,\nG. Y.\n,\nLi\n,\nE.\n,\nZhong\n,\nZ. H.\n, and\nLiu\n,\nG. R.\n,\n2014\n, “\nMid-Frequency Acoustic Analysis Using Edge-Based Smoothed Tetrahedron Radial point Interpolation Methods\n,”\nInt. J. Comput. Methods\n,\n11\n(\n5\n), 1350103.\n10.\nWu\n,\nF.\n,\nHe\n,\nZ. C.\n,\nLiu\n,\nG. R.\n,\nLi\n,\nG. Y.\n, and\nCheng\n,\nA. G.\n,\n2016\n, “\nA Novel Hybrid ES-FE-SEA for Mid-Frequency Prediction of Transmission Losses in Complex Acoustic Systems\n,”\nAppl. Acoust.\n,\n111\n, pp.\n198\n204\n.\n11.\nShorter\n,\nP. J.\n, and\nLangley\n,\nR. S.\n,\n2005\n, “\nVibro-Acoustic Analysis of Complex Systems\n,”\nJ. Sound Vib.\n,\n288\n(\n3\n), pp.\n669\n699\n.\n12.\nLangley\n,\nR. S.\n, and\nCordioli\n,\nJ. A.\n2009\n, “\nHybrid Deterministic-Statistical Analysis of Vibro-Acoustic Systems With Domain Couplings on Statistical Components\n,”\nJ. Sound Vib.\n,\n321\n(\n3–5\n), pp.\n893\n912\n.\n13.\nBathe\n,\nK. J.\n,\n1996\n,\nFinite Element Procedures\n,\nPrentice Hall\n,\n.\n14.\nLyon\n,\nR. H.\n, and\nDeJong\n,\nR. G.\n,\n1995\n,\nTheory and Application of Statistical Energy Analysis\n,\nButterworth-Heinemann\n,\nBoston\n.\n15.\nShorter\n,\nP. J.\n, and\nLangley\n,\nR. S.\n,\n2005\n, “\n,”\nJ. Acoust. Soc. Am.\n,\n117\n(\n1\n), pp.\n85\n95\n.\n16.\nLeung\n,\nA. Y. T.\n,\n1993\n,\nDynamic Stiffness and Substructures\n,\nSpringer\n,\nLondon\n.\n17.\nVergote\n,\nK.\n,\nVan Genechten\n,\nB.\n,\nVandepitte\n,\nD.\n, and\nDesmet\n,\nW.\n,\n2011\n, “\nOn the Analysis of Vibro-Acoustic Systems in the Mid-Frequency Range Using a Hybrid Deterministic-Statistical Approach\n,”\nComput. Struct.\n,\n89\n(\n11–12\n), pp.\n868\n877\n.\n18.\nDesmet\n,\nW.\n,\n1998\n, “\nA Wave Based Prediction Technique for Coupled Vibro-Acoustic Analysis\n,”\nPh.D. Thesis\n,\nK. U. Leuven\n,\nLeuven\n.\n19.\nPluymers\n,\nB.\n,\nVan Hal\n,\nB.\n,\nVandepitte\n,\nD.\n, and\nDesmet\n,\nW.\n,\n2007\n, “\nTrefftz-Based Methods for Time-Harmonic Acoustics\n,”\nArch. Comput. Methods Eng.\n,\n14\n(\n4\n), pp.\n343\n381\n.\n20.\nGao\n,\nR.\n,\nZhang\n,\nY.\n, and\nKennedy\n,\nD.\n,\n2018\n, “\nA Hybrid Boundary Element-Statistical Energy Analysis for the Mid-Frequency Vibration of Vibro-Acoustic Systems\n,”\nComput. Struct.\n,\n203\n, pp.\n34\n42\n.\n21.\nWu\n,\nT. W.\n,\n2000\n,\nBoundary Element Acoustics: Fundamentals and Computer Codes\n,\nWIT\n,\nSouthampton\n.\n22.\nKuhar\n,\nE. J.\n, and\nStahle\n,\nC. V.\n,\n1974\n, “\nDynamic Transformation Method for Modal Synthesis\n,”\nAIAA J.\n12\n(\n5\n), pp.\n672\n678\n.\n23.\nAtalla\n,\nN.\n, and\nSgard\n,\nF.\n,\n2015\n,\nFinite Element and Boundary Methods in Structural Acoustics and Vibration\n,\nCRC Press\n,\nBoca Raton, FL\n.\n24.\nThe Julia Programming Language\n,” accessed Mar. 18, 2018, https://julialang.org\n25.\nCremer\n,\nL.\n,\nHeckl\n,\nM.\n, and" ]
[ null ]
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https://www.ilfc.com/millimeters/954mm-to-inches-convert-954mm-to-inches.html/
[ "Millimeters\n\n# 954mm to inches-convert 954mm to inches\n\nConvert 954mm to inches, 954mm to inches conversion, 954mm to inches calculator, 954mm to inches converter, easy way to convert 954mm to inches, 954mm equals how many inches, you can use our calculator to convert 954mm to inches fast\n\nThe Millimeter is the SI (metric) unit of length, the current International System of Units (SI) definition of the Millimeter officially recognized by the International Committee for weights and Measures is (D1)”. The inch is the international unit of length of exactly 25.4 Millimeter. It is the unit of length in imperial,\n\nU.S.\n\nThe answer is: 954mm= 37.5591 inches\n\n## Mm to inches formula:\n\nIt is easy to use and write metric units correctly if you know how the system works. It is simple and logical and consists of units and prefixes.\n\nExample:  you want to convert 10mm to inches\n\nAccording to formula —> 10mm= 0.393701Inches\n\n## Inches to Millimeter Formula:\n\n1 inches (in) = 25.4 Millimeters (mm)\n\nExample: you want to convert 20 inches to Millimeters\n\nAccording to the formula—>\n\n20×25.4 = 1000\n\n### Mm to Inches (in) Converter and Calculations:\n\nYou can use our converter to convert 954mm to inches\n\nConversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding. The following sections are intended as a guide through this multi-step process.\n\n### Benefits of our calculator:\n\nThe activities of everyday life have always been affected either directly or indirectly by measures and conversions:\n\n1- Convert mm to inches\n\n2- Easy and simple way\n\n3- You can figure out length\n\n4- You can determine length manually\n\n5- Check out length by yourself at home\n\n6- Calculate and find out the result without calculator\n\n### SI system has many benefits:\n\n1- Only one unit for each quantity\n\n2- No need to memorize numbers\n\n3- Can measure any physical quaintly\n\n4- Has unique symbols\n\n### Now you can have an answer to all of your questions:\n\n1- Convert 954mm to inches\n\n2- How many inches are in 954mm?\n\n3- How to convert 954mm to inches?\n\n4- How much is 954mm in inches\n\n5- 954mm converted to inches\n\n6- 954mm conversion to inches\n\n7- How many is 954mm in inches\n\n8- 954mm is equal to how many inches\n\n9- What is 954mm in inches?" ]
[ null ]
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https://kr.mathworks.com/matlabcentral/cody/problems/44835
[ "Cody\n\n# Problem 44835. Calculate the square of a number (Super Easy)\n\nThe goal is to calculate the square (y) of a number (x). Good way to start MatLab for beginners.\n\n### Solution Stats\n\n88.0% Correct | 12.0% Incorrect\nLast Solution submitted on May 08, 2020" ]
[ null ]
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https://dokumen.tips/business/jee-normalization.html
[ "# Jee normalization\n\n• View\n1.198\n\n2\n\nEmbed Size (px)\n\nDESCRIPTION\n\nThis presentation gives you an idea about how the normalization process is being done in JEE by using board percentile as the basis.\n\nTranscript\n\n• 1. Presented by Anchit Das 13810010 Ashish Pandey 13810020 Gaurav kumar Gupta 13810030 Kartik Khamesra 13810040 Mohit Chaudhary 13810050 Pawan Arora 13810060 Shashi Kiran Lugun 13810070 Vaibhav Agarwal 13810080\n• 2. Adjusting values measured on different scales to notionally common scales. In Indian JEE context: Process for ensuring students are neither advantaged nor disadvantaged by the difficulty of their respective board exams\n• 3. Percentile Score: No. of candidates in the group with aggregate marks less than the candidates Total number of Candidate in that group For example, the 20th Percentile is the value (or score) below which 20 Percent of the observations may be found. 100 *\n• 4. i) Note down the aggregate marks (A0) obtained by each student in JEE- Main. ii) Compute the percentile (P) of each student on the basis of aggregate marks in his/her own board (B0) computed from the list of five subjects specified (each marked out of 100). The percentile is to be computed among all students of the board whose subject combinations meet the eligibility criteria of JEE-Main. iii) Determine the JEE- Main aggregate marks corresponding to percentile (P) at the All- India level. Regard this as B1. iv) Also, determine the JEE- Main aggregate marks corresponding to percentile (P) among the set of aggregate scores obtained in the JEE- Main by the students of that board. Regard this as B2. The normalized board score of the candidate will be computed as: Bfinal = 0.5 * (B1 + B2)\n• 5. Step 1: Calculate Percentile (Pi) of the Candidate with reference to the group of Candidates of Board ABCD who also satisfy the eligibility criteria of JEE (Main).\n• 6. Step 2. Arrange JEE (Main) score of all 11.5 lakhs Candidates in ascending order and find out Percentile for each score.\n• 7. Step 3. Arrange JEE (Main) score of Candidates from Board ABCD only, in ascending order and find out the Percentile for each score.\n• 8. Step 4. 4.i Use Percentile (Pi), 50.07, calculated from step 1 and find out the same Percentile in the Percentile calculated in step 2.\n• 9. 4.ii Now, to find B1, find out JEE (Main) score, corresponding to the matched Percentile in 4.i above. This is B1. Here, B1 = 48.\n• 10. Step 5. 5.i Use Percentile (Pi), 50.07, calculated from step 1 (Table 2) and find out the same Percentile in the Percentile calculated in step 3 (Table 4).\n• 11. 5. ii Now, to find B2, find out JEE (Main) score, corresponding to the matched Percentile in 5.i. above. This is B2. Here B2 = 80. Board Percentage (B0)\n• 12. Step 6. Normalised Board mark of the Candidate from Board ABCD who has scored 60% will be Bfinal = 0.5 * (B1 + B2) => Bfinal = 0.5 * (48+80) => Bfinal = 0.5 * (128) => Bfinal = 64\n• 13. For the purpose of admission to CFTIs where it has been decided to use the JEE Mains performance and the Normalized Board performance in the 60:40 ratio, the composite score for drawing the merit list will be computed as: C = 0.6 * AO + 0.4 * Bfinal\n• 14. Example to support the argument that boards are playing the role of deciding factors whereas the JEE (main) has become almost redundant: Student Name: Karthik Board: CBSE Marks in JEE (main): 99 Board Percentage: 94.6 AIR: 34000 (approximately.) Student Name: Ashish Board: CBSE Marks in JEE (main): 135 Board Percentage: 90 AIR: 60000 (approximately.)\n• 15. Example to support the argument that different boards differ radically in terms of their competition levels. Student Name= Gaurav Board= CBSE Board Percentage= 90.2% Marks in JEE (main) = 267 Rank= Beyond 5000 Student Name= Anchit Board= Rajasthan Board Board Percentage= 90% Marks in JEE (main) = 195 Rank= 4400\n• 16. Example to explain how major the role played by the boards was Student Name: Vaibhav Board: CBSE Marks in JEE (main): 201 Board Percentage: 88 AIR: 23000 (approximately.) Student Name: Mohit Board: CBSE Marks in JEE (main): 201 Board Percentage: 94 AIR: 9000 (approximately.)" ]
[ null ]
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http://www.math.utah.edu/~yplee/teaching/2270f14/
[ "## Honors Linear Algebra, Math 2270-3, Fall 2014\n\nSyllabus\n\nAny comments and suggestions about this class are much appreciated! You may either talk to me, or email me at", null, "If you prefer to stay anonymous, please use the following anonymous feedback form.\nAnnouncements:\n• (12/1) The last midterm exam will take place on Friday, 5 Dec, covering Chapters 8-11.\n• (11/24) Comments on HW8: graded 6 of them at 6 points each and the remaining 14 at 1 point each. The 6 problems to receive 6 points each were 8.1.4, 8.2.12, 8.4.3, 8.4.5, 8.4.21, and 8.5.1. Again, the main reason that students lost points was that they did not finish the problems for a particular chapter and section; they would do the first few and leave off the last few problems for a section.\n• (11/19) A computational strategy for the Jordan normal form by Tabrizian.\n• (10/27) Third midterm will be Friday, 7th Nov. It will cover Chapters VI and VII. HW7 is due on Wednesday, 29th Oct instead of the usual Monday.\n• (10/20) Comments on HW6: graded problems 5.3.6, 5.4.1, 5.4.2, 5.5.2, 5.6.5, and 5.6.6 at 5 points each, then 2 points each for the other 10 problems. It is graded somewhat more strictly than prior homeworks. For instance, if the student indicated that it would be trivial to prove some point, but does not actually prove the point, then the student lost some points. Also on problems 5.4.1 and 5.4.2, many students took short cuts in their proofs such as \"\\sum_{i=1}^n \\sum_{j=1}^m Y_i a_{i,j} X_{j} = \\sum_{i=1}^n \\sum_{j=1}^m X_i a_{i,j} Y_{j}\" means that \"a_{i,j} = a_{j,i}\". What I was looking for was more detailed steps in the proof which would show why that statement is true in this case. That is one of the more telling issues on the last few homeworks, the students do not take the time to prove all points, instead they just make (possibly correct) assumptions without any proof to back the statement up. Another issue which lost a lot of points comes from questions with two parts, such as problem 5.4.1 which had a second part which was \"show that this is a scalar product\" - many students did not include that part of the answer.\n• (10/5) Comments on HW5: scored 4.3.2, 5.1.2, 5.1.3, 5.2.6, and 5.2.9 at 8 points each and the other problems all at 1 point each.\n• The last problem, 5.2.9, was difficult to grade. What I was looking for was for the student to show why their new vector \"'w\" was equal to \"v\". Many just skipped over showing why that is true and just stated it without proof. This makes their proofs just a lot of assumptions. On problem 5.2.8, many students had issues trying to find the magnitude of vectors which had complex components. On problem 5.1.3, many students failed to do the second part of the problem which was to provide a matrix \"M\" which was positive definite for this operation (in their partial defense, the way the book defines positive definite and the way that this problem is stated do not make use of the term in the same manner).\n• (9/29) Some comments on HW4: Scored problems: 3.3.4, 3.3.9, 3.3.10, and 3.4.7 at 8 points each and the remainder at 2 points each for a total of 50 points. The biggest problems that students seemed to have was that they leave out entire problems or leave out part (b) of a problem. Other than that, the solutions for linear operators on the space of infinitely differentiable functions caused some issues for a few students because they would set up that the kernel is the set of functions such that an ODE (some function of the derivative, etc...) is equal to zero, but they did not solve for the kernel any further.\n• (9/28) Comments on HW3: Most everyone did well. The biggest problems were that a few students did not do all of the problems, they may have run out of time at the end. A mistake that keeps coming up is that students attack a proof in the wrong way. For instance, to prove that if A has an inverse and B has an inverse, then AB has an inverse, some students started with the statement that the inverse of AB is the inverse of B times the inverse of A. But that assumes existence, which is something that needs to be proven here.\n• (9/28) Comments on HW2: The issue on 1.4.3 was that the one student who lost points was that the student used \"A - cB = 0\" to show that A, and B form a basis, for the student who lost points on 1.4.4 simply mis-stated the formation of the basis formed by U and W.\n• (9/28) Comments on HW1: For one problem, 1.2.8, a re-occurring issue was that students could not get the derivative of sin t to be +cos t. Other errors came from having to solve a 3 x 3 set of equations to prove linear dependence, there were many arithmetic errors there. So a mostly easy problem got included in my set of 5 point problems. Some of the proofs involved in the 1 point problems were difficult for some of the students. The most common error was that they would start with the line to be proven such as \"c O = O\" and then prove something given that fact. Some students use a proof of the contra-positive to complete some of the proofs required here and that type of proof works very well.\n• (9/26) HW for V.3 is moved to the next. On the other hand, I add #6 to V.2.\n• (9/8) The scanned pdf of Gaussian elimination.\n• (9/8) If you are interested in mathematics, you might consider going to undergraduate colloquia on Wednesdays 12:55-13:45. Free pizzas after each talk. For more details, consult the link above.\n• (7/31) This is an honors, PhD-track class and requires permission code, which can be requested easily at mathematics department homepage.\n• (7/27) Please email me or see me in my office if you have any question about the class.\n\nHW:\n• Always read the textbook and lecture notes!\n• (Due 9/3) Sect 1.1: 1-5, 9-13. Sect 1.2: 1(a,c,e,g), 3-4, 5(a,c,e,g,i), 7-10.\n• (Due 9/8) Sect 1.4: 1-4. (Review Chapter 1. Midterm is a week away!)\n• (Due 9/15) Sect 2.1: (matrices) 2, 4, 5, 8, 10; (dimensions) 1-2. Sect 2.2: 1-2 + additional 2 problems #15, 16 in the scanned PDF. Sect 2.3: 1, 3(c), 4, 8, 11, 17-19, 21, 35.\n• (Due 9/22) Sect 3.2: 1(a-d), 2, 4. Sect 3.3: 3-10. Sect 3.4: 2, 7.\n• (Due 9/29) Sect 4.2: 1, 2(a,b,c), 6. Sect 4.3: 1, 2. Sect 5.1: 2, 3. Sect 5.2: 0-6, 9.\n• (Due 10/8) Sect 5.3: 1(a,c,e,g), 2, 4(b,d), 5(b,d), 6. Sect 5.4: 1-4. Sect 5.5: 1(a), 2. Sect 5.6: 2-6.\n• (Due 10/29) Sect 6.2: 1, 2. Sect 6.3: 2(a,i), 3, 5. Sect 6.4: 1(a,c). Sect 6.8: 1(a,c,e), 2-4. Sect 6.7: 1-3. Sect 6.9: 1, 3, 5.\n• (Due 11/3) Sect 7.1: 1, 2, 6, 7. Sect 7.2: 2, 5, 9. Sect 7.3: 1, 2, 3(b), 4(c), 6, 7.\n• (Due 11/17) Sect 8.1: 1-4, 7. Sect 8.2: 2, 4(a,c), 8 (d,f), 9-13. Sect 8.4: 1, 3, 5, 6, 9(a,c,e), 21. Sect 8.5: 1.\n• (Due 11/24) Sect 10.1: 1, 2, 4, 6. Sect 10.3: 1, 2. Sect 11.1: 1(a,b), 2, 3. Sect 11.2: 1, 3, 4.\n• (Due 12/5) Sect 11.3: 1, 2, 4, 5, 6, 15. Sect 11.4: 1, 2, 3. Sect 11.5: 1, 2, 5. Sect 11.6: 1-4.\n\nCoordinating Page" ]
[ null, "http://www.math.utah.edu/~yplee/email.GIF", null ]
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https://www.frontiersin.org/articles/10.3389/fenrg.2021.773805/full
[ "## ORIGINAL RESEARCH article\n\nFront. Energy Res., 10 November 2021\nSec. Process and Energy Systems Engineering\nVolume 9 - 2021 | https://doi.org/10.3389/fenrg.2021.773805\n\n# Electricity Theft Detection in Power Consumption Data Based on Adaptive Tuning Recurrent Neural Network", null, "Guoying Lin1,2,", null, "Haoyang Feng1,", null, "Xiaofeng Feng1,", null, "Hongwu Wen3,", null, "Yuanzheng Li4,", null, "Shaoyong Hong5* and", null, "Zhixian Ni4\n• 1Metrology Center of Guangdong Power Grid Corporation, Guangzhou, China\n• 2College of Electrical Engineering, Zhejiang University, Hangzhou, China\n• 3Zhanjiang Power Supply Bureau of Guangdong Power Grid Co. Ltd., Zhanjiang, China\n• 4China-EU Institute for Clean and Renewable Energy, Huazhong University of Science and Technology, Wuhan, China\n• 5School of Data Science, Guangzhou Huashang College, Guangzhou, China\n\nElectricity theft behavior has serious influence on the normal operation of power grid and the economic benefits of power enterprises. Intelligent anti-power-theft algorithm is required for monitoring the power consumption data to recognize electricity power theft. In this paper, an adaptive time-series recurrent neural network (TSRNN) architecture was built up to detect the abnormal users (i.e., the electricity theft users) in time-series data of the power consumption. In fusion with the synthetic minority oversampling technique (SMOTE) algorithm, a batch of virtual abnormal observations were generated as the implementation for training the TSRNN model. The power consumption record was characterized with the sharp data (ARP), the peak data (PEA), and the shoulder data (SHO). In the TSRNN architectural framework, a basic network unit was formed with three input nodes linked to one hidden neuron for extracting data features from the three characteristic variables. For time-series analysis, the TSRNN structure was re-formed by circulating the basic unit. Each hidden node was designed receiving data from both the current input neurons and the time-former neuron, thus to form a combination of network linking weights for adaptive tuning. The optimization of the TSRNN model is to automatically search for the most suitable values of these linking weights driven by the collected and simulated data. The TSRNN model was trained and optimized with a high discriminant accuracy of 95.1%, and evaluated to have 89.3% accuracy. Finally, the optimized TSRNN model was used to predict the 47 real abnormal samples, resulting in having only three samples false predicted. These experimental results indicated that the proposed adaptive TSRNN architecture combined with SMOTE is feasible to identify the abnormal electricity theft behavior. It is prospective to be applied to online monitoring of distributed analysis of large-scale electricity power consumption data.\n\n## Introduction\n\nWith the increasing scale of the power grid, the power consumption is becoming larger year by year. People are concerning on the economic operation of power network, saving of electric resources, reduction of grid line loss, and structural optimization on power consumption (Dileep, 2020). However, the customer’s behavior of stealing electricity comes in non-stopping emergence. This infraction phenomenon has seriously affected the normal operation of power grid and the economic benefits of power enterprises (Li et al., 2019; Zhang et al., 2020). The electricity theft rate in developing countries is as high as 30%, and the social power supply and consumption has also been greatly influenced. According to rough statistics, China’s power enterprises lose as much as 20 billion CNY every year due to power theft. Therefore, power enterprises must carry out efficient anti-electricity-theft work, in order to guarantee the reasonable power supply and rational use of electricity, thus to reduce economic losses as much as possible (Aryanezhad, 2019).\n\nThe traditional detection methods of power theft mainly rely on the scheduled operations of technicians who work in power supply enterprises. The operation goes with reading the electricity meter and then recording, counting, and performing manual analysis and calculation. In the hardware aspect, there are multifaceted operations that can prevent energy theft, such as to install the specialized watt-hour metering box, to implement a kind of conductor that closes the low-voltage outlet to the metering device, to add anti-thief function to the watt-hour meter, and to improve the application rate of electrical acquisition system (Jokar et al., 2016). However, most of these traditional anti-theft detection methods focus on the improvement of power devices. There is a lack of sufficient anti-power-stealing algorithms to analyze massive historical power consumption data, so it is difficult to find the power consumption characteristics of power-stealing users and detect the power-stealing behavior realized by advanced attack means (Ahmad et al., 2015). Therefore, the development of power industry needs to strengthen the development of new artificial intelligence and information and automation technology. With the continuous improvement of dynamic monitoring and acquisition technology of power consumption data of power grid users, it is of great engineering significance to study the intelligent anti-power-theft algorithm based on the big data of the power consumption to identify the power theft behavior (Ren et al., 2020; Zhang et al., 2021).\n\nAt present, the most popular scheme is to lay out the smart grid detection architecture and framework, then to collect the power consumption data, and upload them to the centralized data processing center through the terminal smart meter, and successively, the centralized data can be further analyzed by intelligent algorithms to detect electricity theft. The prevalent anti-power-stealing data mining algorithms include clustering, BP neural network, and local outlier detection algorithm (Al-Dahidi et al., 2019; Li Y. et al., 2021). Many practical experiments have been studied in previous research works. A typical load curve is extracted from the power consumption data by applying the adaptive K-means clustering algorithm to realize load forecasting and load control (Zhu et al., 2016). The situation of abnormal point detection method was proposed based on a fuzzy neural network to deal with various data, which provides a new idea for mining abnormal data from the power consumption records (Mozaffar et al., 2018). The flying anomaly factor detection and analysis method was investigated to detect an electric energy meter flying anomaly (Li et al., 2016). A novel detection method of power theft was constructed based on the one-class SVM algorithm. A calibration model was established by analyzing a large number of historical data. If the current data are inconsistent with the model, it is considered that there is a possibility of power theft (Dou et al., 2018). Also, the RBF neural network was proposed to detect the electricity-stealing behavior, which used the data characteristics of voltage, current, and power factor to detect electricity theft, to make a positive detection on electricity stealing (Cao et al., 2018).\n\nDue to the wide layout of the power grid, the large-scale deployment of smart meters should consume a lot of resources. In order to save the energy consumption of distributed terminal nodes, and reduce the non-essential data transmission, it is necessary to study modern data mining technology, in integration with machine learning algorithms (Wang et al., 2020; Li Z. et al., 2021). The application of indirect data anomaly detection as well as some preprocessing and analyzing technologies is much necessary to achieve the online detection of power theft. However, data-driven power theft detection is a special type of anomaly detection, which has a serious class imbalance problem (Avila et al., 2018). Actually, the number of normal power consumption users is much larger than the number of abnormal users. The inherent imbalance of data will affect the performance of traditional machine learning methods. Until now, only a few studies have considered the category imbalance in power theft detection (Zhang et al., 2019). The solutions of these works are mainly performed with undersampling and oversampling methods in the aspects of data analytical algorithm. They were keen on simultaneously implementing the random oversampling and undersampling techniques, to select the best detection effect by testing different sampling ratios. Otherwise, they focus on increasing the misclassification cost of abnormal users to improve the detection rate of electricity theft, by setting penalty parameters for support vector machine misclassification of normal and abnormal users (Hu et al., 2019).\n\nGenerally, the electricity theft monitoring data are a kind of time-series data. The difficulty of data analysis lies in how to find the abnormal data from the constantly updated dynamic data flow, so as to accurately predict the theft users. The fact that the data are extremely imbalance is the first-of-all analytical difficulty. Many experiments have proved that oversampling is a solution to the category imbalance problem. In essence, the random oversampling method increases the weight in the sample set by randomly copying a few samples. It does not increase classification accuracy but is easy to cause over-fitting (He and Garcia, 2019). Synthetic minority oversampling technique (SMOTE) is an unbalanced data recall method that is improved from the linear interpolation calculation methodology. It uses the local prior distribution information of samples to improve the accuracy of minority samples, to solve the data imbalance problem (Zhu et al., 2017). Furthermore, the recurrent neural network (RNN) is an effective intelligent machine learning method that is especially effective for monitoring and analyzing time-series dynamic data flow. The RNN is derived from the conventional fully connected neural network (FCNN) model. Its core operation is to compute the result of each neuron not only from its input data (similar to the FCNN) but also from the historical variables from its former calculations (different from the FCNN). The RNN model is widely used in addressing the tasks of sequential data processing (Liu et al., 2020). The running of the RNN structure is to produce a neuron output by combined fusing of the current status data with the previous status data of the system. The RNN is able to automatically learn the time correlation of the input data without specifying any lag observations (Cossu et al., 2021). It is well known that the traditional time-series analytical methods (such as auto-correlation) need to identify the seasonality and stability from the time-series data. The effectiveness of identification may vary according to the network structure and the calculation speed, and it needs to be adjusted for each simulation (Chen et al., 2018; Farjaminezhad et al., 2021). The characteristic of the RNN is to create a closed-loop calculation in the hidden layer, which forms a circulating adaptive model to capture the internal hidden historical state features in the way of iterative update, and thus to complete the process of error level accumulation in the training stage. In effect, the RNN model is enforced to adapt the error accumulation and improve the model robustness (Ståhl et al., 2019).\n\nThis paper is aimed at designing a data-driven adaptive parameter optimization time-series RNN (TSRNN) architecture, for intelligent machine learning to solve the problem of abnormal monitoring of power consumption. The TSRNN architecture with an adaptive training strategy is constructed by monitoring, collecting, and analyzing the observed data of a stage. Then, the non-linear features of the observed data can be extracted by developing a hyperparametric optimization mode of RNN, in fusion with a SMOTE solvation of data imbalance. On this algorithmic basis, the power-stealing users with abnormal characteristics are identified in a large number of power user samples. In structural detail, grid search is designed for the parameter selection of the RNN linking weights, and also, a fault-tolerance iteration mechanism is adopted for parameter optimization in the closed-loop training stage, to control the error accumulation in model prediction, so as to enhance the model robustness. In this way, the proposed intelligent TSRNN architecture with data-driven adaptive parameter optimization is validated through data training and prediction. The optimized model is effective for accurate extraction of the data features of power-stealing behavior. The establishment of the intelligent TSRNN model is expected to overcome the costly, laborious, and time-consuming problems of the traditional methods for monitoring electricity theft. It is feasible to speed up to locate the abnormal watt-hour meter terminals and accurately identify the power-stealing users. The proposed method helps promote the development of artificial intelligence and information analysis technology in the field of power grid operation and maintenance.\n\n## Methodologies\n\nIn this section, we discuss the basic structure of the TSRNN architecture and the algorithmic progress of SMOTE balancing. The energy theft detection model is established and further optimized by fusion of TSRNN and SMOTE. And the discriminant indicators are introduced based on the confusion matrix for the quasi-qualitative recognition of the abnormal user data.\n\n### The Principle of SMOTE\n\nThe SMOTE algorithm is an oversampling method based on synthetic sampling proposed by Chawla (Chawla et al., 2002). In geometric sense, the SMOTE method firstly observes the minority samples and connects them and a batch of their surrounding samples. Then, it produces new samples by random insertion on the connecting lines. The connection and insertion operation can reduce the imbalance of sample space and simultaneously prevent the over-fitting phenomenon by suppressing too large repetition of the original minority samples (Fernández et al., 2018; Chen et al., 2021). The schematic diagram for generating new samples by the SMOTE algorithm is shown in Figure 1. Specifically, the SMOTE sample-generating procedures are described in the following steps:\n\nStep 1: Let $\\left\\{{x}_{i}|i=1,2\\dots \\right\\}$ be the minority samples and set the sampling number $r$ according to the number ratio of the majority samples over the minority samples\n\nStep 2: Search $k$ samples in the neighborhood of the minority samples, where $k>r$\n\nStep 3: Randomly select $r$ samples from the $k$ neighborhood sample, to form the neighborhood sample set $\\left\\{{y}_{1},{y}_{2}\\dots {y}_{r}\\right\\}$\n\nStep 4: To generate a set of new samples by random linear interpolation computation, the new samples are denoted as $\\left\\{{p}_{j}|j=1,2\\dots \\right\\}$, where\n\nwith $rand(0,1)$ representing a random number in the interval of $[0,1]$. Then, ${pj}$ is regarded as the algorithmic implementation of the minority samples.\n\nStep 5: The newly generated samples $\\left\\{{p}_{j}\\right\\}$ are regarded as the algorithmic implementation of the minority samples, added to the original sample set to form a brand new training sample set together with the majority samples.\n\nFIGURE 1\n\nFIGURE 1. Schematic diagram of the SMOTE algorithm.\n\nThe SMOTE algorithm makes artificial synthesis of minority samples by random interpolation. Compared with the traditional methods of random replication, SMOTE reduces redundant information of newly generated minority samples and effectively avoids the phenomenon of over-fitting in the subsequent data mining processes. In algorithm, SMOTE shows its uncertainty in part of selecting the nearest neighborhood of the original minority samples, namely, the number of neighbor samples (i.e., the number of $k$) has a great influence on the model performance. When SMOTE is embedded in fusion with the TSRNN architecture, the number of neighbor samples would be designed as one of the tunable parameters for the network model optimization.\n\n### Time-Series RNN Model\n\nThe data-driven time-series analysis problem is theoretically described as a general ordinary differential model (Li and Yang, 2021), formulated as\n\n$z^=f(z,x),(2)$\n\nwhere $z∈Rd$ is the current state of the system and $x∈Rd$ represents the instant input data. In common sense, the model function $f$ is unknown, but it can be estimated by simulation on the discrete observation of the current state $z$ and the instant input $x$. On these lines, the fully connected neural network (FCNN) is suitable to resolve the data-driven analytical models.\n\nAn FCNN module is traditionally applied as a black box to directly transform the input data to the hidden layer and then to get the output. The generated data acquired at each neuron node are described as $zt+1=g(zt,xt)$, where the activation function $g(⋅)$ is usually a kind of simple linear transformation, while the operation inside the FCNN has no physical interpretations. The black-box model may not be able to capture the detailed data transition in the time series. The TSRNN is proposed to solve this issue.\n\nThe TSRNN architecture is built up with circulation computation of the hidden layer. To unfold the circulation ring, the TSRNN structure is introduced as shown in Figure 2. As is shown in Figure 2, the TSRNN architecture is supposed to be constructed along a time variance axis. At the starting of time, the power consumption user data are input into the network and delivered to the first hidden layer (H1) while $t=1$. The data are transformed and calculated to extract the first level of neural features and then delivered to the next hidden layer when $t$ varies. At each time step, the result of each neuron computation depends not only on the current input but also on the computation results. In this way, the TSRNN captures the intercorrelation between the time longitudinal parameters and the section parameters. As such, there are two network linking weight effects: one describes the direct effect from network layer delivery and the other shows the indirect data influence from the time-series circulation of the hidden layers. Any change in the direct weights or in the indirect weights will cause a change in the output at any instant moment of time (Alkinani et al., 2021).\n\nFIGURE 2\n\nFIGURE 2. Structural design of the time-series RNN (TSRNN) architecture.\n\nFigure 2 also presents a simple TSRNN cell structure at the instant moment of time $t=t$. To be specific, a TSRNN cell is actually a single layer of hidden neurons. This hidden layer is denoted as $H(t)$, and there are many hidden neurons for functional calculation, i.e., $H(t)={hi(t)|i=1,2…m}$. Suppose the current input data are $X(t)={xi(t)|i=1,2…n}$ from the power consumption user data, regarded as the direct input. The time-lag input data are acquired from the network calculation in the hidden layer $H(t−1)$ at the time moment of $t−1$, taken as the indirect input. Then, $H(t)$ works as a $t$-time hidden layer to extract data features from the direct inputs as well as the indirect inputs. The output of $H(t)$ is influenced by both $X(t)$ and $H(t−1)$. It can be formulated as\n\n$H(t)=f(W⋅X(t)+U⋅H(t−1)),(3)$\n\nwhere the function $f(⋅)$ simply represents the sigmoid function which would strictly limit the transformed features in the standard variable range of $[−1,1]$. The parameters $W$ and $U$ represent the linking weights for data connection and for the time variance connection, respectively.\n\nSuccessively, data $H(t)$, namely, the set of feature data included in ${hi(t)}$, are further delivered to a softmax unit for discriminant calculation. Thus, the neural network output at the time-series moment of $t$ is mathematically demonstrated as\n\n$O(t)=K(V⋅H(t)),(4)$\n\nwhere $V$ represents the linking weights involving the data transform from $H(t)$ to $O(t)$ and the function $K(⋅)$ operates the k-means clustering by Mahalanobis distance\n\nThe Mahalanobis distance between any two of the $n$ samples is calculated according to Eq. 5 and then to obtain the distance matrix $KM$ at the instant time moment of $t$, namely,\n\nwhere $mahij≜mah(Oi,Oj)$.\n\nFinally, the Mahalanobis-based k-means clustering results of the TSRNN-extracted feature data are used for further calculation of the discriminant indicators, thus to help identify the abnormal users from all of the electric power consumption data.\n\n### Discriminant Indicators\n\nThe power consumption data are originally imbalanced because the normal electricity users are much larger than the electricity thieves. It is expensive to identify the abnormal users. In our algorithmic designs, SMOTE is functional to alleviate the data imbalance, and the adaptive TSRNN model extracts the feature of power consumption data for improving the model discrimination accuracy with the k-means Mahalanobis measure. The model should be evaluated with quantitative indicators. The confusion matrix is a basic tool to evaluate the model performance (see Table 1). Then, the indicators of each model are verified based on the matrix table.\n\nTABLE 1\n\nTABLE 1. Confusion matrix for evaluation of the discrimination/classification models.\n\nBy definition of the confusion matrix, the normal power consumption users are distinguished as the negative records, while the abnormal users are taken as positive. Thus, the table markers are interpreted with the following information:\n\n- TP indicates that the abnormal user (positive) is accurately predicted as abnormal (positive),\n\n- TN indicates that the normal user (negative) is accurately predicted as normal (negative),\n\n- FP indicates that the actual normal user (negative) is predicted false as abnormal (positive),\n\n- FN indicates that the actual abnormal user (positive) is predicted false as normal (negative).\n\nMultiple indicators are further calculated according to the confusion matrix, such as the classification accuracy ($ACC$), true positive rate ($TPR$), and false alarm rate ($FAR$). The calculations are presented as follows:\n\n$ACC=TP+TNTP+FN+FP+TN,(7)$\n$TPR=TPTP+FN,(8)$\n$FAR=FPFP+TN.(9)$\n\nThese indicators are used to evaluate the model performance of the adaptive parametric-scaling TSRNN architecture. It is learnt from Eqs. 79 that the higher the TP and TN are, the better the model performance is.\n\nFor fault-tolerant analysis, the model prediction results can be monitored at every moment of the dynamic changing time series. By data export, there are a series of prediction results acquired for the model classification of normal and abnormal users. Then, the frequency of identification of abnormal is counted for each user over the whole time-series axis, thus to provide an extra confirmation of the model predictions.\n\n## Analysis of Power Consumption Data\n\nA total of 929 electricity/power consumption users were monitored continuously from January 1, 2017, to March 31, 2019, with the minimum time changing unit of 1 day; thus, we recorded 820 instant moments in the long time series spanning 25 months. Their electricity use data were collected in different partitions of time periods of hours according to the total usage amount. In detail, the electricity used during the hours of 00:00–08:00 is named the off-peak data (denoted as OPE for short), during 08:00–12:00 as the peak data (PEA), during 18:00–22:00 as the sharp data (ARP), and during the rest hours as the shoulder data (SHO).\n\nIf the electricity users are taken as the analytical samples, the power consumption characteristics of the 929 samples are demonstrated by the recorded data of OPE, PEA ARP, and SHO. There are 820 digital records for each user by time variance. As the maximum record is over thirty thousand and the minimum record is zero, the dataset should be normalized before analysis, applying the min–max normalization method (Jin et al., 2015). Then, we statistically derived the sample distribution using the average electricity consumption of the 820 time nodes (see Figure 3). As is seen from Figure 3, the users do not use electricity all along time; for example, some electricity consumption appears high in the ARP time but low or even zero in SHO, and some goes high in PEA but zero in ARP or OPE. To be specific, it is seen from the sub-figure of OPE (the blue plot) that only one user out of the 929 keeps using electricity during the OPE time period. Thus, it is recognized with statistical principles that the OPE data property hardly provides data information for discriminating the abnormal users. Then, the OPE data do not participate in the following modeling processes of SMOTE balancing and TSRNN training.\n\nFIGURE 3\n\nFIGURE 3. Statistical descriptive plots of the power consumption data in different time period partitions.\n\n## Data Balancing by SMOTE\n\nPractically, we have the priori target classification index for the 929 available power consumption user samples. There are originally 882 normal samples and only 47 abnormal samples. The normal samples are the majority, and the abnormal ones are the minority. The imbalance ratio of the normal over the abnormal goes to a great extent of around 19:1. The scattering distribution of the 929 samples is a plot in the 3D axis based on the three basic variables of ARP, PEA, and SHO (see Figure 4A). To ease the heavy imbalance status, the SMOTE algorithm is applied to increase the proportion of the minority samples by linear interpolations. According to the principle of the SMOTE simulation as introduced in The Principle of SMOTE, a batch of virtual samples are generated by interpolations on the original 47 abnormal samples.\n\nFIGURE 4\n\nFIGURE 4. Distribution of the power consumption user samples (panel (A) is for the original 929 samples, and panel (B) is for the SMOTE-balanced output of the 1,151 samples).\n\nTheoretically, one virtual sample is generated from the linking edge of every two samples. The 47 available samples are able to generate 1,081 (i.e., $C472$) new samples in all, from which we randomly chose 222 samples as a supplement to data balance. By SMOTE simulation, we finally have total of 1,151 samples for modeling analysis, of which 269 are abnormal samples, while 882 are normal data from the original. The scattering distribution is shown in Figure 4B. In this case, we have the sample balance ratio at about 3:1 for the normal samples over the abnormal samples.\n\nHereafter, the 1,151 SMOTE-balancing samples were used to train the TSRNN model (defined in Time-Series RNN Model), as to build up an intelligent network architecture with adaptive grid optimization of parameters, for accurate recognition of the abnormal power users who are stealing electricity.\n\n## Discriminations Based on TSRNN Training and Testing\n\nAn applicable discrimination model for detecting electricity theft was trained using the TSRNN architecture based on the power consumption data of the 1,151 SMOTE-balanced samples. The recorded ARP, PEA, and SHO variables are taken as the network input. The data have a time-series record of 820 days.\n\nThe data samples were divided into two sets for model training and testing: 918 samples (∼80%) for training and 233 (∼20%) for testing. The training data were used to conduct the data-driven machine learning optimization of the TSRNN model. The model was constructed with three input neurons and one hidden neuron to produce the output results. There, we have three input-to-hidden linking weights ($w1$,, and $w3$) and one hidden-to-output linking weight ($v$) to adjust. There is also a linking weight ($u$) to help accept another data input from the former time moment of the circle iteration. With machine learning operations, these linking weights were adaptively identified as their most suitable values during the model training process, and then the testing data were used to examine the model discrimination effectiveness by using the data-driven decisive parameters.\n\nIn progress, the 918 training samples were introduced to the input layer at every moment of time and then delivered to compute the hidden variables. Notably, the RNN architecture is characterized with the circle of reproducing the hidden layer. The hidden variables at $t$ moment are affected by both the $t$-moment input and the hidden variables at the $t−1$ moment, where $t=1,2…820$. Thus, a series of phased discriminant results were obtained from the output layers at every time moment. Specifically, we chose to make a segmentation to the full time series from January 1, 2017, to March 31, 2019. There, we set five time markers (see Table 2), to observe five phased modeling outputs for examining the progress of model optimization.\n\nTABLE 2\n\nTABLE 2. Markers of the five special time nodes for investigation of the TSRNN model performance.\n\nBased on the 918 training samples, the TSRNN model was trained with parameters’ iteration by circle improvement of the hidden neurons. We calculated the model discriminant indicators at each phase stoppage moment of $t1,t2,t3,t4$, and $t5$ and drew the ROC curves (see Figure 5). The ROC figures show that the TSRNN model was continuously improved with the promotion of time series. Eventually, the optimal model was observed at $t=t5=820$.\n\nFIGURE 5\n\nFIGURE 5. ROC curves for the evaluation of the TSRNN training effects at the five selected time markers based on the 918 training samples.\n\nTo study the machine learning progress on parameter optimization, we further investigate the running procedures of the adaptive tuning of the TSRNN linking weights. If the linking weights are denoted as a combination of $(w1,w2,w3,v,u)$, we initialized this combination as for model optimization by network iteration of time-series circulation. When time varies, the more and more power consumption data were input to the network, and thus, the linking weights were adjusted for the improving TSRNN model. The changing values of each linking weight were recorded with a time interval of every 20 moments, and thus, we obtained the variation trends of the five linking weights for model optimization (see Figure 6). It is seen from Figure 6 that the network weights of $wi$ and $v$ were presented as an overall downward trend with cyclical recovery fluctuations, ending with optimal values close to zero. And the parameter $u$ (i.e., the weight of the iteration of time series) shows a trend of first falling and then rising. In the end, the optimal value of was recognized as after 820 iterations by time series, noting that $u=0.564$ was for the circle iterative optimization from $t=819$ to $t=820$. These observed optimal values of parameters indicated that the optimal TSRNN model was trained to have a linear formula expression with simple weight coefficients, while the circle iteration of time series pays a certain contribution to the network model.\n\nFIGURE 6\n\nFIGURE 6. Training of linking weights in the TSRNN structure.\n\nThe predictive performance of the TSRNN discriminant model with adaptive tuning of the network weights was further evaluated by the 233 test samples, which were assumed to be “unknown” because they were not involved in the training process. We have the knowledge that there were 53 abnormal samples and 180 normal samples in the test sample set. The optimal TSRNN model is evaluated with a relative high prediction accuracy upon the quantitative metrics of the model indicators. The predictive ACC, TPR, and FAR were 89.3, 92.5, and 11.7%, respectively. The corresponding confusion matrix is shown in Table 3.\n\nTABLE 3\n\nTABLE 3. Confusion matrix of the discriminating results predicted by the optimal TSRNN model for the 233 test samples.\n\nAiming to find out the electricity theft from the real power consumption users, the optimal model output its discriminant results for each sample (shown in Figure 7). The virtual use data which were produced by SMOTE balancing were not targeted for prediction. Thus, it is necessary to distinguish the real abnormal data from the virtual abnormal data. Practically, we used solid stars to mark the 10 real abnormal samples in the figure, and only two of them were predicted to be false. The results indicated that the adaptive TSRNN architecture is functional to predict the abnormal cases in the daily records of the power consumption data.\n\nFIGURE 7\n\nFIGURE 7. Discrimination for each test sample by the optimal TSRNN model.\n\nFurthermore, the well-trained TSRNN architecture was utilized to monitor the time-series data from January 1, 2017, to March 31, 2019, to recognize the power consumption users who probably have electricity theft behavior. The identification of the real abnormal users is listed in Table 4. It is learnt from Table 4 that the optimal TSRNN model successfully identified 44 of the total of 47 abnormal users. The results show that the proposed adaptive TSRNN architecture combined with SMOTE sample balancing technique is able to accurately find the abnormal samples based on the analysis of the time-series–recorded power consumption data, thus to recognize the electricity theft behaviors.\n\nTABLE 4\n\nTABLE 4. Discrimination results for the 47 real abnormal data of the electricity theft users.\n\n## Conclusion\n\nIn this paper, an adaptive TSRNN architecture was built up to detect the electricity theft based on time-series data of the power consumption. The recorded data were monitored continuously from January 1, 2017, to March 31, 2019 (820 days in total). By monitoring the ARP, PEA, and SHO data, the users who are suspicious of stealing electricity were denoted as abnormal samples, while the other common users were denoted as normal. There, we had collected the data of 882 normal samples and 47 abnormal samples. As the abnormal users appear as the minority in all of the recorded data, the SMOTE algorithm was used to ease the data imbalance by generating 222 virtual abnormal samples, to make the ratio of the normal over the abnormal at about 3:1.\n\nThe TSRNN model was established based on the total of 1,151 user samples over the 820 time-series moments. A basic network was formed with three input nodes for receiving the data in the three variables of ARP, PEA, and SHO, and with one hidden neuron for extracting data features. Then, the network output was computed as a k-means classified result to discriminate the sample as an abnormal one or a normal one. The k-means classifier calculation was on the basis of Mahalanobis distance. As for the successive analysis of the non-stopping input time-series data, the TSRNN structure was re-formed by circulating this kind of basic network. Then, each hidden node was influenced by the input data at the current time moment and the data delivery from the time-former hidden node, and thus, the output results can be optimized by adaptively tuning the network parameters in the combination of linking weights $(w1,w2,w3,v,u)$. In our empirical experiment, the most optimal values of the combination of linking weights were observed as after 820 iterations by time series. There, we obtained the discriminant model with a high prediction accuracy of ACC = 95.1%. The optimal TSRNN model was evaluated to be much effective by the 233 test samples, with the testing ACC = 89.3, TPR = 92.5, and FAR = 11.7%. Therefore, the adaptive TSRNN model was finally used to predict the 47 real abnormal samples, and the discriminating results are quite appreciating, with only three samples predicted to be false. The prediction accuracy was as high as 93.6%.\n\nThe experimental results indicated that the proposed adaptive TSRNN architecture in fusion with the SMOTE balancing technique is feasible to extract data features for monitoring the abnormal electricity theft behavior. The methodology framework is prospectively promoted to be used for online monitoring on big data analysis for a large scale of electricity power consumption.\n\n## Data Availability Statement\n\nThe original contributions presented in the study are included in the article/Supplementary Material, and further inquiries can be directed to the corresponding author.\n\n## Author Contributions\n\nYL conceptualized the idea and supervised the work. GL and SH performed the methodology. GL and HW visualized the results. HW was involved in formal analysis. SH and ZN investigated the data. ZN validated the data.GL and HF wrote the original draft. HF curated the data and ran the software. XF and SH reviewed and edited the paper. XF obtained the resources.\n\n## Funding\n\nThis research was funded by the project supported by the China Southern Power Grid Corporation (Grant No. GDKJXM20185800).\n\n## Conflict of Interest\n\nThe author HW was employed by Zhanjiang Power Supply Bureau of Guangdong Power Grid Co., Ltd.\n\nThe remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\n\n## Publisher’s Note\n\nAll claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.\n\n## References\n\nAhmad, T., Hasan, D. Q. U., and Zada, S. (2015). 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Energy Theft Detection in an Edge Data center Using Threshold-Based Abnormality Detector. Int. J. Electr. Power Energ. Syst. 121, 106162. doi:10.1016/j.ijepes.2020.106162\n\nZhu, L., Lu, C., Dong, Z. Y., and Hong, C. (2017). Imbalance Learning Machine-Based Power System Short-Term Voltage Stability Assessment. IEEE Trans. Ind. Inf. 13, 2533–2543. doi:10.1109/tii.2017.2696534\n\nZhu, W., Wang, Y., Luo, M., Lin, G., Cheng, J., and Kang, C. (2016). Distributed Clustering Algorithm for Awareness of Electricity Consumption Characteristics of Massive Consumers. Autom. Elec. Power Syst. 40 (12), 21–27. doi:10.7500/AEPS20160316007\n\nKeywords: electricity theft, TSRNN, adaptive parameter tuning, intelligent learning, SMOTE, power consumption data\n\nCitation: Lin G, Feng H, Feng X, Wen H, Li Y, Hong S and Ni Z (2021) Electricity Theft Detection in Power Consumption Data Based on Adaptive Tuning Recurrent Neural Network. Front. Energy Res. 9:773805. doi: 10.3389/fenrg.2021.773805\n\nReceived: 10 September 2021; Accepted: 04 October 2021;\nPublished: 10 November 2021.\n\nEdited by:\n\nBin Zhou, Hunan University, China\n\nReviewed by:\n\nHuazhou Chen, Guilin University of Technology, China\nXueqian Fu, China Agricultural University, China\nChao Yuan, Hunan University, China\nJun Zeng, South China University of Technology, China\n\nCopyright © 2021 Lin, Feng, Feng, Wen, Li, Hong and Ni. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.\n\n*Correspondence: Shaoyong Hong, [email protected]" ]
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https://rdrr.io/cran/ecpc/man/simDat.html
[ "simDat: Simulate data In ecpc: Flexible Co-Data Learning for High-Dimensional Prediction\n\nDescription\n\nSimulate toy data with linear or logistic response.\n\nUsage\n\n 1 2 simDat(n, p, n2 = 20, muGrp, varGrp, indT, sigma = 1, model = c(\"linear\",\"logistic\"), flag = FALSE)\n\nArguments\n\n n Number of samples for the training set. p Number of covariates. n2 Number of independent samples for the test set. muGrp Prior mean for different groups. varGrp Prior variance for different groups. indT True group index of each covariate; p-dimensional vector. sigma Variance parameter for linear model. model Type of model. flag Should linear predictors and true response be plotted?\n\nValue\n\nA list with\n\n beta Simulated regression coefficients Xctd Simulated observed data for training set Y Simulated response data for test set X2ctd Simulated observed data for test set Y2 Simulated response data for test set\n\nExamples\n\n 1 2 3 4 5 6 7 8 9 10 11 12 n<-10 p<-30 #simulate beta from two normal distributions; beta_k ~ N(mu_k,tau^2_k) muGrp <- c(0,0.1) #mean (mu_1,mu_2) varGrp <- c(0.05,0.01) #variance (tau^2_1,tau^2_2) #group number of each covariate; first half in group 1, second half in group 2 indT <- rep(c(1,2),each=15) dataLin <- simDat(n, p, n2 = 20, muGrp, varGrp, indT, sigma = 1, model = \"linear\", flag = TRUE) dataLog <- simDat(n, p, n2 = 20, muGrp, varGrp, indT, model = \"logistic\", flag = TRUE)\n\necpc documentation built on May 3, 2021, 9:08 a.m." ]
[ null ]
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http://inpatientrehab.org/download/differentiable-operators-and-nonlinear-equations-operator-theory-advances-and
[ "# Download Differentiable Operators and Nonlinear Equations (Operator by Victor Khatskevich, David Shoiykhet PDF\n\nO ° Ilw(xo,h)11 = Ilhll . 3) In this case the expression Ah is called the Frechet differential of F at Xo and is denoted by Ah = dF(xo, h). Clearly, an operator which is Frechet differentiable at Xo is continuous at this point and also Gateaux differentiable. Generally speaking, the converse is not true. 2. 2 ----+ ffi. be the operator defined by the equalities { F(xl, X2) = 1 if X2 = xI, Xl F(Xl,X2) = 0 otherwise, -I- ° 37 Derivative and differential This operator is not continuous at (0,0) and therefore is not Fhkhet differentiable.\n\n8) holds. Thus, the number IIHII is called the norm of the operator H. D). D) is a linear normed space relatively to the norm IIHII. §7. Higher order derivatives A way of defining the derivatives and differentials of higher orders is the following. 1. D be an operator and suppose that the first variation of(x, hi) exists in a neighborhood of a point x, for any element hi EX. 1) exists in the space Z), then it is called the second variation of the operator F and is denoted by 82F(x, hI, h2)' The n-th variations are defined by induction." ]
[ null ]
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https://responsivedesigntool.com/qa/what-is-the-weight-of-1-litre-of-oil.html
[ "", null, "# What Is The Weight Of 1 Litre Of Oil?\n\n## What is the weight of 1 Litre of cooking oil?\n\n1 kg1 litre = 10 cm x 10 cm x 10 cm = 1000 cm^3 .\n\n1 litre of water = 1 kg weight.\n\nDensity of oil is less than that of water that’s why oil floats in the water.\n\n1 kg oil = (1/0.9) litre = 1.1 litre ..\n\n## How heavy is a Litre of olive oil?\n\nGeneral Weight Conversions1 Pound = .454 Kilograms1 Gallon = 7.61 Pounds1 Liter = .264 Gallons1 Liter = .913 Kilograms1 Liter = 33.8 Ounces1 Kilogram = 2.2046 Pounds1 Metric Ton = 2,205 Pounds8 more rows•Apr 6, 2018\n\n## Does 1 Litre weigh 1 kg?\n\nOne litre of water has a mass of almost exactly one kilogram when measured at its maximal density, which occurs at about 4 °C. It follows, therefore, that 1000th of a litre, known as one millilitre (1 mL), of water has a mass of about 1 g; 1000 litres of water has a mass of about 1000 kg (1 tonne).\n\n## What is 2 kg in Litres?\n\nConversion Tablekilograms to literskgl11223317 more rows\n\n## What does 100ml of oil weigh?\n\n94.7 grams.100 ml of oil in gramsIngredient:gram kilogram pound ounceCalculate!Significant Figures: 2 3 4 5Results 100 milliliters of oil weighs 94.7 grams. (*) (*) or precisely 94.7 grams. All values are approximate.6 more rows\n\n## How many grams are in a liter of oil?\n\n910 gramsBecause the density of that kind of oil is 910 grams per litre.\n\n## How much does 1 ml of olive oil weigh?\n\n0.9 gramOlive oil Conversion Chart Near 1 millilitermilliliters to grams of Olive oil1 milliliter=0.9 gram1.1 milliliters=0.99 gram1.2 milliliters=1.08 grams1.3 milliliters=1.17 grams33 more rows\n\n## What does 1 tablespoon olive oil weigh?\n\n13.3 grams.1 tbsp of olive oil in gramsIngredient:gram kilogram pound ounceCalculate!Significant Figures: 2 3 4 5Results 1 US tablespoon of olive oil weighs 13.3 grams. (*) (*) or precisely 13.308088303125 grams. All values are approximate.6 more rows\n\n## How much does coconut oil weigh?\n\nAccording to Hawley’s Condensed Chemical Dictionary the density of coconut oil is 0.92, so a cup of coconut oil (8 fluid ounces) actually weighs only 7.36 ounces (8 X 0.92 =7.36).\n\n## What weighs more 1 liter of water or oil?\n\nWater has a density of 1 kg /L, that is, 1 liter of water has a mass of exactly 1 kg. … This is because the oil has a lower density than water: about 0.91 kg / L. That is, 1 liter of water and 1 liter of oil have the same volume, but 1 liter of water is heavier than 1 liter of oil.\n\n## How much does 1 Litre of coconut oil weigh?\n\nCoconut oil is lighter than water. According to Hawley’s Condensed Chemical Dictionary the density of coconut oil is 0.92, So 1 kg of coconut oil will be 1/0.92 = 1.086956522 litres.\n\n## How many kg is 4 Litres?\n\nConvert 4 Liter to Kg In case of water at sea level and 39.2 °F, D = 1, so kg = L. Under these conditions, 4 liters of water equal 4 kilograms.\n\n## What is 5kg in Litres?\n\nConvert 5 Kilograms to Liters5 Kilograms (kg)5 Liters (L)1 kg = 1 L1 L = 1 kg\n\n## How many Litres is 1 kg of milk?\n\nl to kg conversion table:0.1 liter = 0.1 kg2.1 liters = 2.1 kg7 liters = 7 kg0.8 liter = 0.8 kg2.8 liters = 2.8 kg14 liters = 14 kg0.9 liter = 0.9 kg2.9 liters = 2.9 kg15 liters = 15 kg1 liter = 1 kg3 liters = 3 kg16 liters = 16 kg1.1 liter = 1.1 kg3.1 liters = 3.1 kg17 liters = 17 kg16 more rows\n\n## What is 25kg in Litres?\n\nUnder these circumstances, 25 kilograms of water equal 25 liters.\n\n## What does 5 Litres weigh?\n\nThe density of water is 1 kilogram per liter (kg/L) at 39.2°. This means that 1 liter (L) of water weighs 1 kilogram (kg) and 1 milliliter (mL) of water weighs 1 gram (g). In common US measures, one gallon of water weighs 8.345 pounds.\n\n## How many Litres is 1 kg?\n\nkilograms to liters Weight of 1 liter (l) of pure water at temperature 4 °C = 1 kilogram (kg). A liter is defined as one cubic decimetre (1 l = 1 cubic dm)." ]
[ null, "https://mc.yandex.ru/watch/67483648", null ]
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https://pytorch.org/docs/stable/generated/torch.histogram.html
[ "Shortcuts\n\n# torch.histogram¶\n\ntorch.histogram(input, bins, *, range=None, weight=None, density=False, out=None)\n\nComputes a histogram of the values in a tensor.\n\nbins can be an integer or a 1D tensor.\n\nIf bins is an int, it specifies the number of equal-width bins. By default, the lower and upper range of the bins is determined by the minimum and maximum elements of the input tensor. The range argument can be provided to specify a range for the bins.\n\nIf bins is a 1D tensor, it specifies the sequence of bin edges including the rightmost edge. It should contain at least 2 elements and its elements should be increasing.\n\nParameters\n• input (Tensor) – the input tensor.\n\n• bins – int or 1D Tensor. If int, defines the number of equal-width bins. If tensor, defines the sequence of bin edges including the rightmost edge.\n\nKeyword Arguments\n• range (tuple of python:float) – Defines the range of the bins.\n\n• weight (Tensor) – If provided, weight should have the same shape as input. Each value in input contributes its associated weight towards its bin’s result.\n\n• density (bool) – If False, the result will contain the count (or total weight) in each bin. If True, the result is the value of the probability density function over the bins, normalized such that the integral over the range of the bins is 1.\n\n• out (Tensor, optional) – the output tensor. (tuple, optional): The result tuple of two output tensors (hist, bin_edges).\n\nReturns\n\n1D Tensor containing the values of the histogram. bin_edges(Tensor): 1D Tensor containing the edges of the histogram bins.\n\nReturn type\n\nhist (Tensor)\n\nExample:\n\n>>> torch.histogram(torch.tensor([1., 2, 1]), bins=4, range=(0., 3.), weight=torch.tensor([1., 2., 4.]))\n(tensor([ 0., 5., 2., 0.]), tensor([0., 0.75, 1.5, 2.25, 3.]))\n>>> torch.histogram(torch.tensor([1., 2, 1]), bins=4, range=(0., 3.), weight=torch.tensor([1., 2., 4.]), density=True)\n(tensor([ 0., 0.9524, 0.3810, 0.]), tensor([0., 0.75, 1.5, 2.25, 3.]))", null, "## Docs\n\nAccess comprehensive developer documentation for PyTorch\n\nView Docs\n\n## Tutorials\n\nGet in-depth tutorials for beginners and advanced developers\n\nView Tutorials\n\n## Resources\n\nFind development resources and get your questions answered\n\nView Resources" ]
[ null, "https://www.googleadservices.com/pagead/conversion/795629140/", null ]
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https://www.queryhome.com/business/2232/what-difference-between-gross-margin-contribution-margin
[ "", null, "", null, "", null, "# What is the difference between gross margin and contribution margin?\n\n+1 vote\n49 views\nWhat is the difference between gross margin and contribution margin?", null, "posted Jul 28, 2017\nShare this question\n\n## 1 Answer\n\n0 votes\n\nGross Margin is the Gross Profit as a percentage of Net Sales. The calculation of the Gross Profit is: Sales minus Cost of Goods Sold. The Cost of Goods Sold consists of the fixed and variable product costs, but it excludes all of the selling and administrative expenses.\n\nContribution Margin is Net Sales minus the variable product costs and the variable period expenses. The Contribution Margin Ratio is the Contribution Margin as a percentage of Net Sales.", null, "answer Jul 31, 2017\nSimilar Questions" ]
[ null, "https://queryhomebase.appspot.com/images/facebook-side.png", null, "https://queryhomebase.appspot.com/images/google-side.png", null, "https://queryhomebase.appspot.com/images/qh-side.png", null, "https://www.queryhome.com/business/", null, "https://www.gravatar.com/avatar/e396ebb62db2802724a6f56233115265", null ]
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https://www.litscape.com/word_analysis/moulins
[ "# Definition of moulins\n\n## \"moulins\" in the noun sense\n\n### 1. moulin, glacier mill\n\na chute through which supraglacial water enters a glacier, boring either to the bedrock or to the depth of common crevasse formation\n\n\"the icy river plunged, roaring, into the moulin's blue depths\"\n\nSource: WordNet® (An amazing lexical database of English)\n\nWordNet®. Princeton University. 2010.\n\n# moulins in Scrabble®\n\nThe word moulins is playable in Scrabble®, no blanks required.\n\nMOULINS\n(86 = 36 + 50)\nMOULINS\n(86 = 36 + 50)\n\nmoulins\n\nMOULINS\n(86 = 36 + 50)\nMOULINS\n(86 = 36 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(77 = 27 + 50)\nMOULINS\n(76 = 26 + 50)\nMOULINS\n(74 = 24 + 50)\nMOULINS\n(74 = 24 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(67 = 17 + 50)\nMOULINS\n(64 = 14 + 50)\nMOULINS\n(64 = 14 + 50)\nMOULINS\n(63 = 13 + 50)\nMOULINS\n(63 = 13 + 50)\nMOULINS\n(63 = 13 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(60 = 10 + 50)\n\nMOULINS\n(86 = 36 + 50)\nMOULINS\n(86 = 36 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(80 = 30 + 50)\nMOULINS\n(77 = 27 + 50)\nMOULINS\n(76 = 26 + 50)\nMOULINS\n(74 = 24 + 50)\nMOULINS\n(74 = 24 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(72 = 22 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(70 = 20 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(68 = 18 + 50)\nMOULINS\n(67 = 17 + 50)\nMOULINS\n(64 = 14 + 50)\nMOULINS\n(64 = 14 + 50)\nMOULINS\n(63 = 13 + 50)\nMOULINS\n(63 = 13 + 50)\nMOULINS\n(63 = 13 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(61 = 11 + 50)\nMOULINS\n(60 = 10 + 50)\nMUSLIN\n(33)\nMOULIN\n(33)\nMUONS\n(30)\nMINUS\n(30)\nMUSLIN\n(28)\nMOULIN\n(28)\nMUSLIN\n(27)\nMUSLIN\n(27)\nMOULIN\n(27)\nMUSLIN\n(27)\nMUSLIN\n(27)\nSLIM\n(27)\nMILS\n(27)\nMUON\n(27)\nSLUM\n(27)\nMUSLIN\n(27)\nMOULIN\n(27)\nMOULIN\n(27)\nMOULIN\n(27)\nMOULIN\n(27)\nMUONS\n(26)\nMINUS\n(26)\nMUSLIN\n(24)\nLIMNS\n(24)\nMUSLIN\n(24)\nMINUS\n(24)\nMUONS\n(24)\nLIMNS\n(24)\nLIMOS\n(24)\nMUONS\n(24)\nLIMOS\n(24)\nMINUS\n(24)\nLIMOS\n(24)\nLIMOS\n(24)\nMUONS\n(24)\nMINUS\n(24)\nMOULIN\n(24)\nMOULIN\n(24)\nLIMNS\n(24)\nLIMNS\n(24)\nMOULIN\n(22)\nMUSLIN\n(22)\nMUSLIN\n(22)\nMOULIN\n(22)\nMINUS\n(21)\nSUMO\n(21)\nLIMN\n(21)\nMINUS\n(21)\nMUONS\n(21)\nOMNI\n(21)\nLIMOS\n(21)\nSLUM\n(21)\nMILS\n(21)\nMINUS\n(21)\nLIMN\n(21)\nLIMO\n(21)\nLIMNS\n(21)\nMUONS\n(21)\nLIMOS\n(21)\nOMNI\n(21)\nLIMOS\n(21)\nLIMNS\n(21)\nMUONS\n(21)\nLIMO\n(21)\nSUMO\n(21)\nMUON\n(21)\nSLIM\n(21)\nLIMNS\n(21)\nMOULIN\n(20)\nMUONS\n(20)\nMUONS\n(20)\nMUSLIN\n(20)\nMOULIN\n(20)\nMOULIN\n(20)\nMUSLIN\n(20)\nMINUS\n(20)\nMINUS\n(20)\nMUSLIN\n(20)\nMUSLIN\n(18)\nLIMO\n(18)\nMUONS\n(18)\nLIONS\n(18)\nLIONS\n(18)\nLIONS\n(18)\nLIONS\n(18)\nLOINS\n(18)\nLOINS\n(18)\nSUMO\n(18)\nSUMO\n(18)\nSUMO\n(18)\nMUSLIN\n(18)\nLIMO\n(18)\nOMNI\n(18)\nLOINS\n(18)\nSUMO\n(18)\nLOINS\n(18)\nOMNI\n(18)\nMUSLIN\n(18)\nOMNI\n(18)\nMUSLIN\n(18)\nLIMOS\n(18)\nOMNI\n(18)\nLIMOS\n(18)\nMOULIN\n(18)\nLIMO\n(18)\nLIMN\n(18)\nMOULIN\n(18)\nMUON\n(18)\nMUON\n(18)\nLIMN\n(18)\nLIMN\n(18)\nSLIM\n(18)\nSLIM\n(18)\nLIMN\n(18)\nMINUS\n(18)\nSLIM\n(18)\nMUON\n(18)\nSLIM\n(18)\nSLIM\n(18)\nSLUM\n(18)\nMOULIN\n(18)\nSLUM\n(18)\nSLUM\n(18)\nMOULIN\n(18)\nSLUM\n(18)\nSLUM\n(18)\nMILS\n(18)\nMUON\n(18)\nMILS\n(18)\nMILS\n(18)\nLIMNS\n(18)\nMILS\n(18)\nLIMNS\n(18)\nMUON\n(18)\nLIMO\n(18)\nMILS\n(18)\nMUONS\n(16)\nMOULIN\n(16)\nMUSLIN\n(16)\nMUSLIN\n(16)\nMOULIN\n(16)\nMUONS\n(16)\nLIMNS\n(16)\nMOULIN\n(16)\nMOULIN\n(16)\nMOULIN\n(16)\nMUSLIN\n(16)\nMOULIN\n(16)\nLIMNS\n(16)\nLIMNS\n(16)\nMINUS\n(16)\nLIMOS\n(16)\nLIMOS\n(16)\nLIMNS\n(16)\nMUSLIN\n(16)\nMOULIN\n(16)\nLIMOS\n(16)\nMUSLIN\n(16)\n\n# moulins in Words With Friends™\n\nThe word moulins is playable in Words With Friends™, no blanks required.\n\nMOULINS\n(110 = 75 + 35)\n\nmoulins\n\nMOULINS\n(110 = 75 + 35)\nMOULINS\n(98 = 63 + 35)\nMOULINS\n(98 = 63 + 35)\nMOULINS\n(92 = 57 + 35)\nMOULINS\n(87 = 52 + 35)\nMOULINS\n(87 = 52 + 35)\nMOULINS\n(87 = 52 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(80 = 45 + 35)\nMOULINS\n(80 = 45 + 35)\nMOULINS\n(77 = 42 + 35)\nMOULINS\n(69 = 34 + 35)\nMOULINS\n(69 = 34 + 35)\nMOULINS\n(69 = 34 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(63 = 28 + 35)\nMOULINS\n(63 = 28 + 35)\nMOULINS\n(63 = 28 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(58 = 23 + 35)\nMOULINS\n(57 = 22 + 35)\nMOULINS\n(55 = 20 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(53 = 18 + 35)\nMOULINS\n(53 = 18 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(49 = 14 + 35)\nMOULINS\n(49 = 14 + 35)\nMOULINS\n(48 = 13 + 35)\n\nMOULINS\n(110 = 75 + 35)\nMOULINS\n(98 = 63 + 35)\nMOULINS\n(98 = 63 + 35)\nMOULINS\n(92 = 57 + 35)\nMOULINS\n(87 = 52 + 35)\nMOULINS\n(87 = 52 + 35)\nMOULINS\n(87 = 52 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(86 = 51 + 35)\nMOULINS\n(80 = 45 + 35)\nMOULINS\n(80 = 45 + 35)\nMOULINS\n(77 = 42 + 35)\nMOULIN\n(72)\nMOULINS\n(69 = 34 + 35)\nMOULINS\n(69 = 34 + 35)\nMOULINS\n(69 = 34 + 35)\nMUSLIN\n(66)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(65 = 30 + 35)\nMOULINS\n(63 = 28 + 35)\nMOULINS\n(63 = 28 + 35)\nMOULINS\n(63 = 28 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULINS\n(61 = 26 + 35)\nMOULIN\n(60)\nMOULIN\n(60)\nMUSLIN\n(60)\nMUSLIN\n(60)\nMOULINS\n(58 = 23 + 35)\nMOULINS\n(57 = 22 + 35)\nMOULINS\n(55 = 20 + 35)\nMOULINS\n(54 = 19 + 35)\nMINUS\n(54)\nMUONS\n(54)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(54 = 19 + 35)\nMOULINS\n(53 = 18 + 35)\nMOULINS\n(53 = 18 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(52 = 17 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(51 = 16 + 35)\nMOULINS\n(51 = 16 + 35)\nMUON\n(51)\nMOULINS\n(51 = 16 + 35)\nSLUM\n(51)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(50 = 15 + 35)\nMOULINS\n(49 = 14 + 35)\nMOULINS\n(49 = 14 + 35)\nMOULIN\n(48)\nSLIM\n(48)\nMOULIN\n(48)\nMOULIN\n(48)\nMOULIN\n(48)\nMUSLIN\n(48)\nMUSLIN\n(48)\nMOULIN\n(48)\nMUSLIN\n(48)\nMUSLIN\n(48)\nMILS\n(48)\nMUSLIN\n(48)\nMOULINS\n(48 = 13 + 35)\nLIMNS\n(42)\nMUSLIN\n(42)\nMINUS\n(42)\nLIMNS\n(42)\nMUSLIN\n(42)\nMUONS\n(42)\nMOULIN\n(42)\nMUONS\n(42)\nMOULIN\n(42)\nMUONS\n(40)\nLIMNS\n(40)\nMUSLIN\n(40)\nMINUS\n(40)\nMOULIN\n(40)\nLIMN\n(39)\nLIMN\n(39)\nMUON\n(39)\nLIMOS\n(39)\nMOULIN\n(36)\nLIMOS\n(36)\nLIMNS\n(36)\nLIMO\n(36)\nLIMNS\n(36)\nMUSLIN\n(36)\nMUSLIN\n(36)\nMUONS\n(36)\nMINUS\n(36)\nMINUS\n(36)\nMINUS\n(36)\nMUONS\n(36)\nMOULIN\n(36)\nLIMOS\n(33)\nLOINS\n(33)\nLIONS\n(33)\nLIMOS\n(33)\nLIMOS\n(33)\nLOINS\n(33)\nLIONS\n(33)\nSLUM\n(33)\nMUSLIN\n(32)\nMOULIN\n(32)\nMOULIN\n(32)\nMUSLIN\n(32)\nMUSLIN\n(32)\nLIMO\n(30)\nMINUS\n(30)\nLOIN\n(30)\nMUONS\n(30)\nOMNI\n(30)\nMUONS\n(30)\nLOIN\n(30)\nOMNI\n(30)\nMINUS\n(30)\nMILS\n(30)\nMUONS\n(30)\nSOUL\n(30)\nSUMO\n(30)\nMINUS\n(30)\nNILS\n(30)\nSLIM\n(30)\nLION\n(30)\nLIMNS\n(30)\nLIMNS\n(30)\nLIMNS\n(30)\nLION\n(30)\nSUMO\n(30)\nMOULIN\n(28)\nMINUS\n(28)\nLOINS\n(28)\nMOULIN\n(28)\nMOULIN\n(28)\nLIONS\n(28)\nMUONS\n(28)\nMOULIN\n(28)\nMUSLIN\n(28)\nLIMNS\n(28)\nMUSLIN\n(28)\nMUSLIN\n(28)\nMOULIN\n(28)\nMUSLIN\n(28)\nLIMOS\n(27)\nLIONS\n(27)\nLIMN\n(27)\nLIMN\n(27)\nLIMOS\n(27)\nMUON\n(27)\nSLUM\n(27)\nLIMN\n(27)\nMUON\n(27)\nLOINS\n(27)\nLOINS\n(27)\nMUON\n(27)\nLIONS\n(27)\nSOIL\n(27)\nMUON\n(27)\nSLUM\n(27)\nSLUM\n(27)\nSLUM\n(27)\nLIMN\n(27)\nLIMOS\n(27)\nMUSLIN\n(26)\nMUSLIN\n(26)\nLIMOS\n(26)\nMUON\n(26)\nMOULIN\n(26)\nMOULIN\n(26)\nSLUM\n(26)\nMOULIN\n(24)\nLIMNS\n(24)\nOMNI\n(24)\nMUONS\n(24)\nMINUS\n(24)\nMILS\n(24)\nMUSLIN\n(24)\nMUSLIN\n(24)\nMUONS\n(24)\nMINUS\n(24)\nSUMO\n(24)\nMILS\n(24)\nMUSLIN\n(24)\n\n# Word Growth involving moulins\n\nin ins\n\nin moulin\n\n## Longer words containing moulins\n\n(No longer words found)" ]
[ null ]
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https://rovertip.com/how-far-does-light-travel-in-microseconds/
[ "# How far does light travel in microseconds?\n\n## How many miles is a light year in words?\n\nA light year is the distance traveled by light in one year. How far is it? Multiply the number of seconds in a year by the number of miles or kilometers that light travels in a second, and there you have it: a light year. This is approximately 5.88 trillion miles (9.5 trillion km).\n\n## What is a clear day?\n\nDefinition of light day. : unit of length in astronomy equal to the distance traveled by light in a day in a vacuum, i.e. approximately 26 billion kilometres.\n\n## How long is a light hour in time?\n\nIt is defined as the distance that light travels in free space in one hour (or 3600 light seconds), and is equal to 1.079252849×1012 m. It is just over 6.7×108 miles and around 3.54×1012 feet.\n\n499.0 seconds\n\n## What is the speed of a microsecond?\n\nA microsecond is an SI unit of time equal to one millionth (0.000001 or 10−6 or ?1⁄1,000,000) of a second. Its symbol is μs, sometimes simplified for us when Unicode is not available. A microsecond is equal to 1000 nanoseconds or ?1⁄1000 of a millisecond.\n\n## How far does light travel per day?\n\nIt is defined as the distance that light travels in free space in one day (or 86,400 light-seconds) and is equal to 2.590206837 × 1013 m. It is just over 1.6×1010 miles and about 8.5×1013 feet.\n\n## How many feet does light travel in one second?\n\nIt is defined as the distance that light travels in free space in one second and is equal to exactly 299,792,458 meters (983,571,056 feet).\n\n## How many picoseconds does it take light to travel a mile?\n\nThis is what the speed of light looks like in slow motion. Light travels at 186,000 miles per second (300 million meters per second) and is believed to set the unsurpassable speed limit of the universe.\n\n## How long is a nanosecond?\n\nA nanosecond (ns) is an SI unit of time equal to one billionth of a second, or 1/1,000,000,000 of a second, or 10−9 seconds. The term combines the prefix nano- with the base unit for one sixtieth of a minute. A nanosecond is equal to 1000 picoseconds or ?1⁄1000 microsecond.\n\n## How far does 4 nanoseconds travel?\n\nLight-nanosecond. A light nanosecond is a unit of length, equal to 10−9 light seconds (0.299792458 m = 11.802853 in.\n\n## How long is a picosecond?\n\nA picosecond is an SI unit of time equal to 10−12 or 1/1,000,000,000,000 (one trillionth) of a second. It’s a trillionth, or a millionth of a millionth of a second, or 0.000000000001 seconds. A picosecond is to a second what a second is to about 31,689 years.\n\n## Is a nanosecond faster than the speed of light?\n\nA nanosecond might not seem like a lot, but “the effect is quite large,” said Parke of Fermilab, who was not part of the CERN team. The extra speed would mean that, over a distance of 621 miles (1,000 kilometers), neutrinos travel about 66 feet (20 meters) more than light travels in the same amount of time.\n\n## What is light for children?\n\nLight is a type of energy that allows us to see the world around us. We need light to see. Light comes from different sources called light sources; our main source of natural light is the sun. Other sources include fire, stars, and artificial light sources such as light bulbs and torches.\n\n## Why is the speed of light the same in air and vacuum?\n\nYou can do the same experiment with air. Light in air is 1.0003 times slower than light in a vacuum, slowing it from 299,792,458 meters per second to 299,702,547 meters per second. Outside the zone of influence of our atmosphere, you are very quickly in a vacuum.\n\n## Does light have mass?\n\nLight is made up of photons, which have no mass, so light has no mass and cannot weigh anything. Not so fast. Because photons have energy — and, as Einstein taught us, energy is equal to the mass of a body times the speed of light squared.\n\n## How do we find the speed?\n\nVelocity is a measure of how fast an object moves from one place to another. It is equal to the distance traveled divided by the time. It is possible to find any of these three values ​​using the other two.\n\n## How far can light travel in one minute in meters?\n\n1 light minute is 1.798754748 x 1010 meters (SI unit). Distance traveled by light in a vacuum in one minute.\n\n## How do we measure the speed of light?\n\nThe official definition of a meter today is: 1⁄299792458 of the distance traveled by light in a vacuum, in 1 second. A consequence of using this definition is that any attempt to measure the speed of light is cyclical; you have to use a “meter” to measure it at any given time, which is based on the speed of light." ]
[ null ]
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https://edurev.in/course/quiz/attempt/-1_MA-Mathematics-2014-GATE-Paper--Practice-Test-/8fc286ed-f839-42e5-b37a-4dffe4537b0b
[ "GATE  >  MA Mathematics - 2014 GATE Paper (Practice Test)\n\n# MA Mathematics - 2014 GATE Paper (Practice Test)\n\nTest Description\n\n## 65 Questions MCQ Test GATE Past Year Papers for Practice (All Branches) | MA Mathematics - 2014 GATE Paper (Practice Test)\n\nMA Mathematics - 2014 GATE Paper (Practice Test) for GATE 2022 is part of GATE Past Year Papers for Practice (All Branches) preparation. The MA Mathematics - 2014 GATE Paper (Practice Test) questions and answers have been prepared according to the GATE exam syllabus.The MA Mathematics - 2014 GATE Paper (Practice Test) MCQs are made for GATE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MA Mathematics - 2014 GATE Paper (Practice Test) below.\nSolutions of MA Mathematics - 2014 GATE Paper (Practice Test) questions in English are available as part of our GATE Past Year Papers for Practice (All Branches) for GATE & MA Mathematics - 2014 GATE Paper (Practice Test) solutions in Hindi for GATE Past Year Papers for Practice (All Branches) course. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free. Attempt MA Mathematics - 2014 GATE Paper (Practice Test) | 65 questions in 180 minutes | Mock test for GATE preparation | Free important questions MCQ to study GATE Past Year Papers for Practice (All Branches) for GATE Exam | Download free PDF with solutions\n 1 Crore+ students have signed up on EduRev. Have you?\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 1\n\n### Q. 1 – Q. 5 carry one mark each. Q. A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 2\n\n### Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive.\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 3\n\n### Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 4\n\nIf y = 5x2 + 3, then the tangent at x = 0, y = 3\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 5\n\nA foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q,\nwhere Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily\nproduction of 100 tonnes?\n\n(Important : you should answer only the numeric value)\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 6\n\nQ. 6 – Q. 10 carry two marks each.\n\nQ.\n\nFind the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 7\n\nAnuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building\n(the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered\nfloor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors\nbelow Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor\nimmediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the\nfollowing floor-person combinations is correct?", null, "*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 8\n\nThe smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The\nratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its\nsmallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the\nlargest angle of the quadrilateral?\n\n(Important : you should answer only the numeric value)\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 9\n\nOne percent of the people of country X are taller than 6 ft. Two percent of the people of country Y\nare taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both\ncountries together, what is the percentage of people taller than 6 ft?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 10\n\nThe monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure.\nWhich of the following are true? (k percentile is the value such that k percent of the data fall below\nthat value)", null, "(i) On average, it rains more in July than in December\n(ii) Every year, the amount of rainfall in August is more than that in January\n(iii) July rainfall can be estimated with better confidence than February rainfall\n(iv) In August, there is at least 500 mm of rainfall\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 11\n\nQ. 1 – Q. 25 carry one mark each.\n\nQ.\n\nThe function", null, "is differentiable at\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 12\n\nThe radius of convergence of the power series", null, "is _____________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 13\n\nLet   E1 and E2 be two non empty subsets of a normed linear space X and let", null, "Then which of the following statements is FALSE:\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 14\n\nLet y(x) be the solution to the initial value problem", null, "subject to y(1.2) 2. Using the Euler method with the step size h = 0.05, the approximate value of ??(1.3), correct to two\ndecimal places, is _____________________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 15\n\nLet α ∈ R. If αx is the polynomial which interpolates the function f (x) = sinπ x on [−1,1]at all the zeroes of the polynomial 4x3 − 3x , then α is ___________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 16\n\nIf u(x,t) is the D’Alembert’s solution to the wave equation", null, "with\nthe condition u(x,0) = 0", null, "is _________________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 17\n\nThe solution to the integral equation", null, "MA Mathematics - 2014 GATE Paper (Practice Test) - Question 18\n\nThe general solution to the ordinary differential equation", null, "in\nterms of Bessel’s functions, ??v(x), is\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 19\n\nThe inverse Laplace transform of", null, "MA Mathematics - 2014 GATE Paper (Practice Test) - Question 20\n\nIf  X1 , X2 is a random sample of size 2 from an (0,1) population, then", null, "follows\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 21\n\nLet", null, "be a random variable. Then the value of E[max{Z,0}] is\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 22\n\nThe number of non-isomorphic groups of order 10 is ___________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 23\n\nLet a,b,c,d be real numbers with a < c < d < b. Consider the ring C[a,b] with pointwise\naddition and multiplication. If", null, "then\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 24\n\nLet ?? be a ring. If R[x]is a principal ideal domain, then R is necessarily a\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 25\n\nConsider the group homomorphism", null, "given by φ ( A) = trace(A) . The kernel of φ\nis isomorphic to which of the following groups?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 26\n\nLet X be a set with at least two elements. Let τ and τ′ be two topologies on X such that", null, "Which of the following conditions is necessary for the identity function id :", null, "to be\ncontinuous?\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 27\n\nLet", null, "be such that det(A− I ) = 0 , where I denotes the 3×3 identity matrix. If the\ntrace(A) =13 and det(A) = 32, then the sum of squares of the eigenvalues of A is ______\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 28\n\nLet V denote the vector space", null, ". Then\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 29\n\nLet V be a real inner product space of dimension 10 . Let x, y∈V be non-zero vectors such that\n= 0 . Then the dimension of", null, "is _________________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 30\n\nConsider the following linear programming problem:\nMinimize x1 + x2\nSubject to:\n2x1 + x2 ≥ 8\n2x1 + 5x2 ≥ 10\nx1, x2 ≥ 0\nThe optimal value to this problem is _________________________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 31\n\nLet", null, "be a periodic function of period 2π. The coefficient of sin 3x in the Fourier series expansion of f(x) on the interval [−π, π] is ________________________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 32\n\nFor the sequence of functions", null, "consider the following quantities expressed in terms of Lebesgue integrals", null, "Which of the following is TRUE?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 33\n\nWhich of the following statements about the spaces", null, "is TRUE ?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 34\n\nThe maximum modulus of", null, "is\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 35\n\nLet d1, d2 and d3 be metrics on a set X with at least two elements. Which of the following is NOT\na metric on X?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 36\n\nQ. 26 – Q. 55 carry two marks each\n\nQ.\n\nLet", null, "and let ?? be a smooth curve lying in Ω with initial point −1 + 2??\nand final point 1 + 2??. The value of", null, "*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 37\n\nIf ? ? C with a <1, then the value of", null, "where Γ is the simple closed curve |??| = 1 taken with the positive orientation, is _________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 38\n\nConsider C[−1,1] equipped with the supremum norm given by", null, "Define a linear functional T on C[−1,1]by", null, "Then the value of T is _______\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 39\n\nConsider the vector space C[0,1] over R. Consider the following statements:\nP: If the set {  tf1, t2f2, t3f3} is linearly independent, then the set { f1,f2,f3} is linearly\nindependent, where f1,f2,f3  ∈C [0,1] and tn represents the polynomial function t→ tn, n ? N\n\nQ: If F: C[0,1] → R is given by", null, "then F is a linear map\n\nWhich of the above statements hold TRUE?\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 40\n\nUsing the Newton-Raphson method with the initial guess x(0) = 6, the approximate value of the\nreal root of x log10 x = 4.77 , after the second iteration, is ____________________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 41\n\nLet the following discrete data be obtained from a curve ?? = ??(??):", null, "Let S be the solid of revolution obtained by rotating the above curve about the ??-axis between x = 0 and ?? = 1 and let V denote its volume. The approximate value of V, obtained using\nSimpson’s 1/3 rule, is ______________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 42\n\nThe integral surface of the first order partial differential equation", null, "passing through the curve x2 + y2 = 2x, z = 0 is\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 43\n\nThe boundary value problem,", null, "? is converted into the\nintegral equation", null, "Then g(2/3) is\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 44\n\nIf ??1(??) = ?? is a solution to the differential equation", null, "then its\ngeneral solution is\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 45\n\nThe solution to the initial value problem", null, "is\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 46\n\nThe time to failure, in months, of light bulbs manufactured at two plants A and B obey the exponential distribution with means 6 and 2 months respectively. Plant B produces four times as many bulbs as plant A does. Bulbs from these plants are indistinguishable. They are mixed and sold together. Given that a bulb purchased at random is working after 12 months, the probability that it was manufactured at plant A is _____\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 47\n\nLet X , Y be continuous random variables with joint density function", null, "The value of E[X +Y ]is ____________________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 48\n\nLet", null, "be the subspace of R, where R is equipped with the usual topology. Which\nof the following is FALSE?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 49\n\nLet", null, "A matrix P such that P−1XP is a diagonal matrix, is\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 50\n\nUsing the Gauss-Seidel iteration method with the initial guess", null, ",the second approximation", null, "for the solution to the system of equations\n\n2x1-x2=7\n\n-x1+2x2-x3=1\n\n-x2+2x3=1\n\nis\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 51\n\nThe fourth order Runge-Kutta method given by", null, "is used to solve the initial value problem", null, "If u(1) = 1 is obtained by taking the step size h = 1, then the value of 4 K is ______________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 52\n\nA particle P of mass m moves along the cycloid x = (θ − sin θ) and ?? = (1 + cos θ),\n0 ≤ θ ≤ 2??. Let g denote the acceleration due to gravity. Neglecting the frictional force, the\nLagrangian associated with the motion of the particle P is:\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 53\n\nSuppose that ?? is a population random variable with probability density function", null, "where θ is a parameter. In order to test the null hypothesis H0: θ = 2, against the alternative\nhypothesis H1: θ = 3, the following test is used: Reject the null hypothesis if X1 ≥ 1/2 and accept otherwise, where  X1 is a random sample of size 1 drawn from the above population. Then the power of the test is _____\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 54\n\nSuppose that x1, x2,…, xn is a random sample of size n drawn from a population with probability\ndensity function", null, "where θ is a parameter such that θ > 0. The maximum likelihood estimator of θ is\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 55\n\nLet F be a vector field defined on", null, "Let", null, "be defined by ??(t) = (8 cos 2πt, 17 sin 2πt) and ??(t) = (26 cos 2πt, −10 sin 2πt).", null, "then m is _________________________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 56\n\nLet g: R3 → R3 be defined by g(x, y, z) = (3y + 4z, 2x − 3z, x + 3y) and let\n\nS = {(x, y, z) ∈ R3 : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1 }. If", null, "then α is _____________________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 57\n\nLet T1, T2 : R5 → R3 be linear transformations such that rank(T1) = 3 and nullity(T2) = 3. Let\nT3 : R3 → R3 be a linear transformation such that T3 ° T, = T2. Then rank(T3) is __________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 58\n\nLet F3 be the field of 3 elements and let F3 × F3 be the vector space over F3. The number of\ndistinct linearly dependent sets of the form {u, v}, where u, v ∈ F3 × F3 {(0,0)} and u ≠ v\nis _____________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 59\n\nLet F125 be the field of 125 elements. The number of non-zero elements α ∈ F125 such that\nα5 = α is _______________________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 60\n\nThe value of", null, "where R is the region in the first quadrant bounded by the curves\ny = x2, y + x = 2 and x = 0 is ______________\n\n*Answer can only contain numeric values\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 61\n\nConsider the heat equation", null, "with the boundary conditions u(0, t) = 0, u(π, t) = 0 for t > 0, and the initial condition", null, "is ___________________\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 62\n\nConsider the partial order in R2 given by the relation (x1, y1) < (x2, y2) EITHER if x1 < x2 OR\nif x1 = x2 and y1 < y2. Then in the order topology on R2 defined by the above order\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 63\n\nConsider the following linear programming problem:\nMinimize: x1 + x2 + 2x3\nSubject to", null, "The dual to this problem is:\nMaximize: 4y1 +5y2 + 6y3\nSubject to", null, "and further subject to:\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 64\n\nLet X = C1[0,1]. For each f ∈ X , define", null, "Which of the following statements is TRUE?\n\nMA Mathematics - 2014 GATE Paper (Practice Test) - Question 65\n\nIf the power series", null, "converges at 5i and diverges at −3i, then the power series\n\n## GATE Past Year Papers for Practice (All Branches)\n\n380 docs|127 tests\n Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code\nInformation about MA Mathematics - 2014 GATE Paper (Practice Test) Page\nIn this test you can find the Exam questions for MA Mathematics - 2014 GATE Paper (Practice Test) solved & explained in the simplest way possible. Besides giving Questions and answers for MA Mathematics - 2014 GATE Paper (Practice Test), EduRev gives you an ample number of Online tests for practice\n\n## GATE Past Year Papers for Practice (All Branches)\n\n380 docs|127 tests" ]
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https://www.jiskha.com/questions/1400518/the-area-of-a-rhombus-is-139-2cm-cm-and-its-altitude-is-9-6cm-find-the-perimeter-of-the
[ "# math\n\nThe area of a rhombus is 139.2cm.cm.and its altitude is 9.6cm.find the perimeter of the rhombus?\n\n1. 👍\n2. 👎\n3. 👁\n1. the base is 139.2/9.6 = 14.5\n\nsince all sides are the same, the perimeter is 4*14.5 = 58\n\n1. 👍\n2. 👎\n2. we know that\nperimeter of rhombus=area / altitude\n=139.2/9.6\n=14.5\nperimeter = 4a\n=4(14.5)\n=58cm\n\n1. 👍\n2. 👎\n\n## Similar Questions\n\n1. ### maths\n\nRhombus ABCD is similar to rhombus BFDE.The area of rhombus ABCD is 24 and angle BAD=60 degrees .What is the area of rhombus BFDE?\n\n2. ### Algebra-Trig help asap\n\nA rhombus has sides of 5 cm each and one diagonal is 6 cm long. Find the area of the rhombus.\n\n3. ### Math\n\nWhich of the following statements is not always true? A. In a rhombus, the diagonals bisect opposite angles. B. In a rhombus, the diagonals are perpendicular. C. In a rhombus, the diagonals are congruent. D. In a rhombus, all four\n\n4. ### math\n\nThe area of a rhombus is 60cm^2. Given that one of its diagonals is 15 cm long, calculate the perimeter of the rhombus.\n\n1. ### maths\n\nThe area of a rhombus is 84 cm2 and one diagonal is 12 cm. Find the other diagonal of the rhombus.\n\n2. ### geometry\n\nGiven: QRST is a parallelogram. Prove: QRST is a square. Complete the proof below by choosing the reason for line number 2 and line number 6. Reason Statement 1. QRST is a parallelogram. Given 2. QRST is a rectangle 3. is a right\n\n3. ### geometry\n\nlengths of diagonals of a rhombus are 12 cm and 16 cm respectively. Find the length of the side of rhombus.\n\n4. ### MATH\n\nName the quadrilaterals that have four equal angles. A. rhombus, square B. Square, rectangle C. parallelogram, rhombus D. rhombus, trapezoid My answer B\n\n1. ### geometry\n\nthe lengths of the diagonal of a rhombus are 2 in and 5 in. find the measure of the angles of the rhombus to the nearest degree. if it helps, we are learning how to use tangent right now!\n\n2. ### geometry\n\nIn the rhombus ABCD, AB=10 and AC=12. Find the area of the rhombus. I am confused about how to solve this problem.\n\n3. ### maths\n\nIn a rhombus PQRS,the diagonals intersect at O.given that angle=120 degree and OP=3 cm.what is the side of the rhombus.\n\n4. ### math\n\nDiagonal of a rhombus are in the ratio 3:4. If its perimeter is 40cm, find the length of the side and diagonals of rhombus" ]
[ null ]
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http://www.biomath.nyu.edu/biomath/oldrag/glossary/rna_glossary.html
[ "Glossary of technical terms in RNA structure and graph theory\n\nadjacency matrix: a square matrix specifying the connectivity of a graph.\n\nbridge graph: a graph with at least one edge whose deletion results in a disconnected graph.\n\nbulge: mismatched base pairs in a helical stem other than a loop or a junction.\n\nconnected graph: every pair of vertices in a connected graph has a path from one vertex to another.\n\nct file: file containing data about the base pairs in an RNA secondary structure.\n\ndiagonal matrix: a square matrix that identifies the number of connections each vertex makes along the diagonal of the matrix\n\ndigraph or directed graph: a graph each of whose edge has a specified direction.\n\ndisconnected graph: a graph with two or more subgraphs that are not connected.\n\ndual graph: a general graphical representation for RNA secondary structures.\n\nedge: an edge in a graph is a line (possibly curved) joining two vertices or points.\n\nhairpin loop: unmatched bases in single-strand turn region of a helical stem.\n\nisomorphic graphs: graphs that are structurally equivalent.\n\ninternal loop: mismatched base pairs in a helical stem.\n\nin vitro selection: an experimental method for selecting novel functional RNAs from a pool of sequences.\n\njunction: three or more helical stems converging to form a closed structure.\n\nkissing hairpins: hairpin loops in close proximity with complementary bases.\n\nlaplacian eigenvalues: eigenvalues calculated from the Laplacian matrix (second eigenvalue specifies the compactness of the graph)\n\nlaplacian matrix: a mathematical representation of the connectivity between the vertices in an RNA graph or topology.\n\nplanar tree graph: a 2D representation of a tree network.\n\npseudoknot: complex 3D motif involving intertwining of strand segments (a topology in which a stretch of nucleotides within a hairpin loop pairs with nucleotides external to that loop)\n\nRNA tree: an RNA having tree-like branching structures with no pseudoknots.\n\nstem: a motif in the secondary structure that represents more than one complementary base pair\n\nvertex: a vertex in a graph is a point or node where lines (edges) originate or end." ]
[ null ]
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https://byjus.com/maxwell-boltzmann-distribution-formula/
[ "", null, "# Maxwell Boltzmann Distribution Formula\n\nNot all the air molecules surrounding us travel at the same speed. Some air molecules travel faster, some move at a moderate speed and few others will hardly move at all. Hence, instead of asking the speed of any particular gas molecule we ask the distribution of speed in gas at a particular temperature. James Maxwell and Ludwig Boltzmann came up with a theory to show how the speeds of the molecule are distributed for an ideal gas. In the next section, we shall be discussing the Maxwell Boltzmann distribution formula in detail.\n\n## Maxwell Boltzmann Distribution Equation\n\nThe average kinetic energy of the gas molecules is given by the equation\n\n$$\\begin{array}{l}E_k=\\frac{3}{2}k_BT=\\frac{3}{2}\\frac{k}{N_A}T\\end{array}$$\n\nwhere E_k is the average kinetic energy of the gas molecules\n\nkB is the Boltzmann’s constant which is equal to\n\n$$\\begin{array}{l}1.38\\times10^{-23}\\,JK^{-1}\\end{array}$$\n\nR is the universal gas constant which is equal to 8.314 J/K/mol\n\nNA is the Avagadro’s constant which is equal to\n\n$$\\begin{array}{l}6.023\\times10^{23}\\,mol^{-1}\\end{array}$$\n\n### Solved Example\n\nExample:\n\n1. What is the average speed of hydrogen molecules on the earth?\n\nSolution:\n\nLet us consider the temperature on earth to be 300 K.\n\nThe mass of a hydrogen molecule is\n\n$$\\begin{array}{l}2\\times1.67\\times10^{-27}\\,kg\\end{array}$$\n\nThe kinetic energy of the gas molecules is given by the equation\n\n$$\\begin{array}{l}E_k=\\frac{3}{2}k_BT\\end{array}$$\n\nSubstituting the values in the equation, we get\n\n$$\\begin{array}{l}E_k=\\frac{3}{2}\\times1.38\\times10^{-23}\\times300=6.21\\times10^{-21}\\,J\\end{array}$$\n\nTo find the velocity from the average kinetic energy we use the formula\n\n$$\\begin{array}{l}E_k=\\frac{1}{2}mv^2\\end{array}$$\n\nBy re-arranging the formula, we get\n\n$$\\begin{array}{l}v^2=\\frac{2E_k}{m}\\end{array}$$\n\nV2=(2)(6.21×10-21)/(2×1.67×10-27)\n\nV   = √(12.42 × 106)/3.34\n\nV  = √3.71× 106\n\nV = 1.92× 103\n\nTherefore, the average velocity is Vrms= 1928 m/s.\n\nStay tuned with BYJU’S for more such interesting articles. Also, register to “BYJU’S – The Learning App” for loads of interactive, engaging Physics-related videos and an unlimited academic assist." ]
[ null, "https://www.facebook.com/tr", null ]
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https://directory.fedoraproject.org/docs/389ds/design/mapping_tree_assembly.html
[ "# Mapping Tree Assembly Rework\n\n## Introduction\n\nThe mapping tree, is a set of entries that is used to route the content of a query to one or more backends to satisfy the request. It allows the merging of multiple backends into a coherent view that simulates a single suffix to a client.\n\nThe mapping tree is a hierarchial structure, where suffixes are arranged in a tree to determine which satisfies a query. For example, given the following we can see which backend would service any request.\n\n`````` ┌───────┐\n│rootDSE│\n└───────┘\n│\n┌───────────────┼──────────────────┐\n│ │ │\n▼ ▼ ▼\n┌─────────┐ ┌─────────┐ ┌─────────────────┐\n│cn=schema│ │cn=config│ │dc=example,dc=com│\n└─────────┘ └─────────┘ └─────────────────┘\n│\n▼\n┌───────────────────────────┐\n│ou=people,dc=example,dc=com│\n└───────────────────────────┘\n``````\n\nHere, if we queried for “dc=example,dc=com”, then this suffix would be serviced by the exact matching backend and the child suffix for ou=people. Given a query to cn=schema, this would be serviced by the cn=schema backend.\n\n## The Problem\n\nOf course, this design doc only exists due to the existance of a problem in this system. The problem is how these entries are parsed an assembled. At startup cn=config is searched, and entries that are mapping tree items are examined. For example:\n\n``````dn: cn=dc\\3Dexample\\2Cdc\\3Dcom,cn=mapping tree,cn=config\nobjectClass: nsMappingTree\ncn: dc=example,dc=com\ncn: dc\\=example\\,dc\\=com\nnsslapd-state: backend\nnsslapd-backend: userRoot\n\ndn: cn=ou\\3Dpeople\\2Cdc\\3Dexample\\2Cdc\\3Dcom,cn=mapping tree,cn=config\nobjectClass: nsMappingTree\ncn: ou=People,dc=example,dc=com\ncn: ou\\=People\\,dc\\=example\\,dc\\=com\nnsslapd-state: backend\nnsslapd-backend: peopleRoot\nnsslapd-parent-suffix: dc=example,dc=com\n``````\n\nThis would be the config related to the example as defined above. We can see the mapping tree entries for both backends, and how they relate.\n\nInternally to 389 these are transformed into struct mt_node’s defined in ldap/servers/slapd/mapping_tree.c. These use a set of pointers indicating their child nodes, sibling nodes, and parent nodes. So for example, our rootDSE would have a childNode pointing at cn=schema, and cn=schema has a sibling of cn=config, and cn=config has a sibling of dc=example,dc=com. dc=example,dc=com has a child that is ou=People,dc=example,dc=com.\n\nTo build this tree, the rootDSE is created and the cn=config/schema/monitor nodes attached. Then the cn=config is searched for:\n\n``````(&(objectclass=nsMappingTree)(!(nsslapd-parent-suffix=*)))\n``````\n\nAfter this, each node that is found has it’s suffix searched to find their children with:\n\n``````(&(objectclass=nsMappingTree)(|(nsslapd-parent-suffix=\"<suffix>\")(nsslapd-parent-suffix=<suffix>)))\n``````\n\nIn our example, because dc=example,dc=com does not have a nsslapd-parent-suffix, it is assumed to be anchored at the rootDSE, and then the subsequent search for nsslapd-parent-suffix=dc=example,dc=com finds the ou=People,dc=example,dc=com to be attached.\n\nIn otherwords, the construction of the tree, is based upon the reverse relationship of the nsslapd-parent-suffix attribute in cn=config.\n\nThis opens a very wide door to mis-configuration, as nsslapd-parent-suffix has no constraint to related correctly or validly to the suffix that is served by the mapping tree node.\n\n## Some Examples …\n\nKnowing that the tree is constructed in reverse, we can begin to create examples that break this logic.\n\nFor example, consider this mapping tree entry:\n\n``````dn: cn=dc\\3Dexample\\2Cdc\\3Dcom,cn=mapping tree,cn=config\nobjectClass: nsMappingTree\ncn: dc=example,dc=com\nnsslapd-state: backend\nnsslapd-backend: userRoot\nnsslapd-parent-suffix: dc=com\n``````\n\nIn this example, we specify a parent-suffix that does not exist. Rather than being directly attached to the rootDSE, in this case due to the nature of the two cn=config queries, instead this entry is ignored. The backend silently is never able to be routed to. This has been seen in production from customer cases and is what initiated this investigation.\n\nAnother particularly cursed example is:\n\n``````dn: cn=dc\\3Dexample\\2Cdc\\3Dcom,cn=mapping tree,cn=config\nobjectClass: nsMappingTree\ncn: dc=example,dc=com\nnsslapd-state: backend\nnsslapd-backend: userRoot\nnsslapd-parent-suffix: ou=People,dc=example,dc=com\n\ndn: cn=ou\\3Dpeople\\2Cdc\\3Dexample\\2Cdc\\3Dcom,cn=mapping tree,cn=config\nobjectClass: nsMappingTree\ncn: ou=People,dc=example,dc=com\nnsslapd-state: backend\nnsslapd-backend: peopleRoot\n``````\n\nIn this example, we have a more general suffix below the more specific “child” suffix. The end result is that because the mapping tree assumes a valid and ordered hierarchy, that a query to dc=example,dc=com can not be routed because the rootDSE connects to ou=People, which is not a subsuffix of dc=example,dc=com.\n\nAny query to ou=People,dc=example,dc=com also fails, because the Mapping Tree after routing to ou=People attempts to see if any descendants are “more specific”. But the “more specific” check is based on is equal OR subsuffix, so the dc=example,dc=com belowe ou=People answers that it is more specific than ou=People, and it attempts to the serve the query (and yields no results, because all the ou=People entries are in the suffix above).\n\n## Suggested Resolution\n\nSince the MT today assumes that the tree must be a correct hierarchy of ordered suffixes, where each child MUST be a descendant to the parent, then we know that this ordering for existing clients must exist. There is no valid situation where a “more specific” suffix can exist above a less specific suffix, or that two equal suffixes can exist.\n\nWith this in mind, we can then identify that the issue is that the current creation of the tree is inverted to what it should be. We assemble a tree based on the parent relationship, rather than determining who are the relevant and correct child suffixes.\n\nThe proposal is that the server should ignore the nsslapd-parent-suffix, and rather should sort and determine the correct tree relationship from the cn/suffix values that exist.\n\nAt startup we would then search for any cn=config entry where objectClass=nsMappingTree. From this we can then take the first value of cn. We must escape this value, as you can see from the cn=config, that it may already be escaped.\n\nWe can then sort the suffixes based on length with the shortest first. This would give us for example:\n\n``````dc=example,dc=com\nou=People,dc=example,dc=com\n``````\n\nNext we check there are no duplicate suffixes (we don’t do this today, but they would be invalid, today we would select one or the other, we can not have a query satisfied by multiple backends).\n\nAt this point we can then repeatedly call best_matching_child(). This works because on the first insert, no parent to dc=example,dc=com, so this would return that the best match is the rootDSE. We can then add the rootDSE to the tree.\n\nWhen we call best_matching_child() next with ou=People,dc=example,dc=com, this would find the best match is dc=example,dc=com, so we would then attach this as the parent node.\n\nBecause we sorted the names of the suffixes by length, we know that parent DN’s are shorter and would be first in the set.\n\nAn important test would be around the handling of cn as the suffix given the escaping, where we have escaped, and unescaped cn’s in the test.\n\nAlso testing duplicate suffix detection, and that parent-suffix is ignored (IE we can load invalid parent suffix configs)." ]
[ null ]
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https://www.edupil.com/question/pq-ki-where-k-%E2%88%88-r-k-%E2%89%A0-0-and-i-is-the-identity-matrix-of-order-3-if-q23-k8-and-det-q-k2/
[ "# PQ = kI, where k ∈ R, k ≠ 0 and I is the identity matrix of order 3. If Q23 = – k/8 and det (Q) = k^2\n\nLet P =", null, ", Where ∝  ∈ R, Support Q = [qii] is a matrix such that PQ = kI, where k  ∈ R, k ≠ 0 and I is the identity matrix of order 3. If Q23 = – k/8 and det (Q) = k^2, then-\n\n1. ∝ = 0, k = 8\n2. 4∝ – k + 8 = 0\n3. det (Padj (Q)) = 2^9\n4.  det (Q adj (P)) = 2^13" ]
[ null, "https://www.edupil.com/wp-content/uploads/2016/05/49-1.jpg", null ]
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https://chemistry.stackexchange.com/questions/46484/calculating-equilibrium-partial-pressures-of-a-gas-given-kp
[ "# Calculating equilibrium partial pressures of a gas given Kp", null, "My work:\n\n${K_p = 28.4 = \\frac{[NOBr]^2}{[NO]^2[Br_2]}=\\frac{[NOBr]^2}{^2}} \\rightarrow$$\\ce{[NOBr]=7212 torr}. This doesn't match up with the given answer. I don't see why 262 torr is the correct answer. I correctly set up the equilibrium constant expression and everything in the reaction equation is in the gas phase so they are all included and I used only equilibrium concentrations. Another problem with the same issue:", null, "• Weird. You math is right. If the constant is based on mole fraction then I get 19.8 for the constant based on the answer of 262 torr. – MaxW Feb 18 '16 at 3:39 • It should be products over reactants, but inverted:$$ \\dfrac{(107^2) (160)}{262^2} = 26.7 $$It seems problem/answer just messed up. – MaxW Feb 18 '16 at 4:18 • @MaxW this is a consistent issue. See my edit. I found that I get the correct answer after converting all the torr values to atm and keeping Kp as is. Why is it that I must convert torr to atm? – Dissenter Feb 18 '16 at 14:26 ## 1 Answer In general k_{p} is not a dimensionless quantity. In the case of the reaction$$\\ce{2NO + Br2 <=> 2NOBr}$$the unit of measurement for k_{p} is in fact$$\\frac{pressure^2}{pressure^2 * pressure} = pressure^{-1}.$$Thus the value 28.4 of the equilibrium constant given in the assignment is incomplete. Given the correct answer, it turns out that k_p is actually given in \\mathrm{atm^{-1}}. Since$$\\mathrm{28.4~atm^{-1}} = 28.4*(\\mathrm{760~Torr})^{-1} = 0.0374~\\mathrm{Torr}^{-1}$$you should use this value for$k_p$if you prefer to do your calculation with$\\mathrm{Torr}\\$.\n\n• how do we know the units a priori – Dissenter Feb 20 '16 at 4:47\n• The unit must be given along with the numerical value. The exponent can also be derived from the stoichiometric coefficients as shown above. In the special case that the exponent is zero the unit of measurement is 1, i.e. neither Pa, nor atm, nor Torr, or any other unit of pressure measurement. – aventurin Feb 20 '16 at 16:46" ]
[ null, "https://i.stack.imgur.com/iMjWk.png", null, "https://i.stack.imgur.com/2SiBX.png", null ]
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https://eprints.uns.ac.id/4150/
[ "# APLIKASI ALGORITMA GENETIKA UNTUK OPTIMASI DESAIN RESONATOR HEMLHOLTZ GANDA MENGGUNAKAN MATLAB 7.0\n\nBramantyo , Noval (2006) APLIKASI ALGORITMA GENETIKA UNTUK OPTIMASI DESAIN RESONATOR HEMLHOLTZ GANDA MENGGUNAKAN MATLAB 7.0. Other thesis, UNIVERSITAS SEBELAS MARET.", null, "PDF - Published Version Download (1891Kb)\n\n## Abstract\n\nABSTRACT APPLICATION OF GENETIC ALGORITHM TO THE SHAPE OPTIMIZATION OF DOUBLE HEMLHOLTZ RESONATOR USE THE MATLAB 7.0 By Noval Bramantyo M0200038 Research on shape optimization of double Helmholtz resonator with the genetic algorithm method has been done by using MATLAB 7.0. Research has conducted by designing of Helmholtz resonator characteristics, then it, use as fitness function in the genetic algorithm. Genetic algorithm parameter has variation to get the best fitness and then analyzed. Result of analysis indicate that the best of parameter for the frequency of (50, 150, 250, 350, 450, 550, 650, 750, 850, 950)Hz is Grefenstette(2) (PopSize=80 , Pc=0,45 , Pm=0,01), and the best of double Helmholtz resonator design for the frequency above successively is ((V=0,01159m3 , L=0,01574m, b S=0,00032m2 , S=0,00281m2 ), (V=0,00351m3 , L=0,00414m, b S=0,00085m2 , S=0,00204m2 ), (V=0,00145m3 , L=0,00020m, b S=0,00086m2 , S=0,00162m2 ), (V=0,00044m3 , L=0,01957m, b S=0,00086m2 , S=0,00160m2 ), (V=0,00044m3 , L=0,00082m, b S=0,00087m2 , S=0,00163m2 ), (V=0,00018m3 , L=0,02137m, b S=0,00090m2 , S=0,00160m2 ), (V=0,00018m3 , L=0,00457m, b S=0,00079m2 , S=0,00163m2 ), (V=0,00013m3 , L=0,00520m, b S=0,00082m2 , S=0,00237m2 ), (V=0,00009m3 , L=0,01293m, b S=0,00090m2 , S=0,00160m2 ), (V=0,00005m3 , L=0,02457m, b S=0,00067m2 , S=0,00160m2 )).\n\nItem Type: Thesis (Other) Q Science > QA Mathematics > QA76 Computer softwareQ Science > QC Physics Fakultas Matematika dan Ilmu Pengetahuan Alam > Fisika Saputro Bagus 15 Jul 2013 02:07 15 Jul 2013 02:07 https://eprints.uns.ac.id/id/eprint/4150" ]
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http://researchonline.ljmu.ac.uk/id/eprint/15694/
[ "", null, "# Comparing the pre-SNe feedback and environmental pressures for 6000 HII regions across 19 nearby spiral galaxies\n\nBarnes, AT, Glover, SCO, Kreckel, K, Ostriker, EC, Bigiel, F, Belfiore, F, Bešlić, I, Blanc, GA, Chevance, M, Dale, DA, Egorov, O, Eibensteiner, C, Emsellem, E, Grasha, K, Groves, BA, Klessen, RS, Kruijssen, JMD, Leroy, AK, Longmore, SN, Lopez, L , McElroy, R, Meidt, SE, Murphy, EJ, Rosolowsky, E, Saito, T, Santoro, F, Schinnerer, E, Schruba, A, Sun, J, Watkins, EJ and Williams, TG (2021) Comparing the pre-SNe feedback and environmental pressures for 6000 HII regions across 19 nearby spiral galaxies. Monthly Notices of the Royal Astronomical Society, 508 (4). pp. 5362-5389. ISSN 0035-8711", null, "", null, "Preview\nText\nComparing the pre-SNe feedback and environmental pressures for 6000 HII regions across 19 nearby spiral galaxies.pdf - Published Version\n\nThe feedback from young stars (i.e. pre-supernova) is thought to play a crucial role in molecular cloud destruction. In this paper, we assess the feedback mechanisms acting within a sample of 5810 HII regions identified from the PHANGS-MUSE survey of 19 nearby ($<$ 20 Mpc) star-forming, main sequence spiral galaxies (log($M_\\star$/M$_\\odot$)= 9.4 $-$ 11). These optical spectroscopic maps are essential to constrain the physical properties of the HII regions, which we use to investigate their internal pressure terms. We estimate the photoionised gas ($P_\\mathrm{therm}$), direct radiation ($P_\\mathrm{rad}$), and mechanical wind pressure ($P_\\mathrm{wind}$), which we compare to the confining pressure of their host environment ($P_\\mathrm{de}$). The HII regions remain unresolved within our ${\\sim}50{-}100$ pc resolution observations, so we place upper ($P_\\mathrm{max}$) and lower ($P_\\mathrm{min}$) limits on each of the pressures by using a minimum (i.e. clumpy structure) and maximum (i.e. smooth structure) size, respectively. We find that the $P_\\mathrm{max}$ measurements are broadly similar, and for $P_\\mathrm{min}$ the $P_\\mathrm{therm}$ is mildly dominant. We find that the majority of HII regions are over-pressured, $P_\\mathrm{tot}/P_\\mathrm{de} = (P_\\mathrm{therm}+P_\\mathrm{wind}+P_\\mathrm{rad})/P_\\mathrm{de} > 1$, and expanding, yet there is a small sample of compact HII regions with $P_\\mathrm{tot,max}/P_\\mathrm{de} < 1$ ($\\sim$1% of the sample). These mostly reside in galaxy centres ($R_\\mathrm{gal}<1$kpc), or, specifically, environments of high gas surface density; log($\\Sigma_\\mathrm{gas}/\\mathrm{M_\\odot} \\mathrm{pc}^{-2}$)$\\sim$2.5 (measured on kpc-scales). Lastly, we compare to a sample of literature measurements for $P_\\mathrm{therm}$ and $P_\\mathrm{rad}$ to investigate how dominant pressure term transitions over around 5dex in spatial dynamic range and 10 dex in pressure.", null, "View Item" ]
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https://answers.everydaycalculation.com/divide-fractions/6-5-divided-by-9-56
[ "Solutions by everydaycalculation.com\n\n## Divide 6/5 with 9/56\n\n1st number: 1 1/5, 2nd number: 9/56\n\n6/5 ÷ 9/56 is 112/15.\n\n#### Steps for dividing fractions\n\n1. Find the reciprocal of the divisor\nReciprocal of 9/56: 56/9\n2. Now, multiply it with the dividend\nSo, 6/5 ÷ 9/56 = 6/5 × 56/9\n3. = 6 × 56/5 × 9 = 336/45\n4. After reducing the fraction, the answer is 112/15\n5. In mixed form: 77/15\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://linuxhint.com/initialize-an-array-length-in-javascript/
[ "JavaScript\n\n# How to Initialize an Array’s Length in JavaScript\n\nAt the time of array creation, the programmers need to specify the length of an array. It helps to allocate the proper amount of memory required to hold the array elements and ensures that the memory resources are effectively utilized and prevents potential overflow or memory faults.\n\nThis article will demonstrate the procedure for initializing the length of an array.\n\n## How to Initialize an Array Length in JavaScript?\n\nFor initializing the length of an array, use the “Array constructor” by passing a single argument which is the length of the array you want to create.\n\nSyntax\n\nFor using the array constructor to initialize the length of an array, follow the given syntax:\n\nnew Array(len)\n\nExample\n\nIn the given example, create an array of length “11” using the Array constructor and store it in a variable “array”:\n\nlet array = new Array(11);\n\nPrint the array on the console:\n\nconsole.log(array);\n\nIt can be observed that an empty array of length “11” has been successfully created:", null, "You can also initialize the array by passing elements in the constructor. It will create an array of a length of the specified elements:\n\nlet array = new Array(1, 3, 35, 4, 2, 27, 91, 3, 4, 5, 12);\n\nAs you can see that the created array is of the length “11” as the constructor contains 11 elements:", null, "You can also create/declare an array and initialize its specific length by calling a custom function. Here, we will first define a function named “createArrayofSize()” that takes a size of an array as an argument. Then, create an empty array and append elements in it by iterating until the specified length. Finally, return the particular length’s array to the function:\n\nfunction createArrayofSize(size) {\nvar arr = [];\nfor (var i = 0; i < size; i++) {\narr[i] = i;\n}\nreturn arr;\n}\n\nCall the function by passing the length of an array:\n\nvar array = createArrayofSize(11);\n\nPrint the specified length’s array on the console:\n\nconsole.log(array);\n\nOutput", null, "That was all about initializing the array length in JavaScript.\n\n## Conclusion\n\nTo initialize an array’s length, use the “Array constructor” as “new Array()” by passing a single argument which is the length of the array you want to create. You can also initialize the array by passing elements in the constructor such as “new Array(1, 2, 3)” or calling a custom function. In this article, we demonstrated the procedure for initializing the length of an array.", null, "" ]
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{"ft_lang_label":"__label__en","ft_lang_prob":0.7928862,"math_prob":0.93993765,"size":2164,"snap":"2023-14-2023-23","text_gpt3_token_len":453,"char_repetition_ratio":0.19629629,"word_repetition_ratio":0.14054054,"special_character_ratio":0.21534196,"punctuation_ratio":0.09268293,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95002055,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-28T01:06:18Z\",\"WARC-Record-ID\":\"<urn:uuid:d30e1908-a73b-4a8d-9c7d-46f2400c259a>\",\"Content-Length\":\"234808\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:75511e70-4bb2-4913-b2fb-f576d354343f>\",\"WARC-Concurrent-To\":\"<urn:uuid:bc9e1c9a-b6b5-43b3-83e4-5bc6954886b3>\",\"WARC-IP-Address\":\"104.18.6.55\",\"WARC-Target-URI\":\"https://linuxhint.com/initialize-an-array-length-in-javascript/\",\"WARC-Payload-Digest\":\"sha1:HIQ6VNEC3V4SH6SDPWDYCPSUPNWPO2O6\",\"WARC-Block-Digest\":\"sha1:QVMQSVNEVAMN7FNXRPI2HFMMNLDRUTAR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224643388.45_warc_CC-MAIN-20230527223515-20230528013515-00057.warc.gz\"}"}
https://www.varsitytutors.com/hotmath/hotmath_help/topics/word-problems-inverse-variation
[ "# Word Problems: Inverse Variation\n\nWhile direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship. For two quantities with inverse variation, as one quantity increases, the other quantity decreases.\n\nFor example, when you travel to a particular location, as your speed increases, the time it takes to arrive at that location decreases. When you decrease your speed, the time it takes to arrive at that location increases. So, the quantities are inversely proportional.\n\nAn inverse variation can be expressed by the equation $xy=k$ or $y=\\frac{k}{x}$ .\n\nThat is, $y$ varies inversely as $x$ if there is some nonzero constant $k$ such that, $xy$ = $k$ or $y=\\frac{k}{x}$ where $x\\ne 0$ and $y\\ne 0$ .\n\nSome word problems require the use of inverse variation. Here are the ways to solve inverse variation word problems.\n\n1. Understand the problem.\n2. Write the formula.\n3. Identify the known values and substitute in the formula.\n4. Solve for the unknown.\n\nExample 1:\n\nThe volume $V$ of a gas varies inversely as the pressure $P$ on it. If the volume is $240\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}{\\text{cm}}^{3}$ under pressure of $30\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{kg}/{\\text{cm}}^{2}$ , what pressure has to be applied to have a volume of $160\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}{\\text{cm}}^{3}$ ?\n\nThe volume $V$ varies inversely as the pressure $P$ means when the volume increases, the pressure decreases and when the volume decreases, the pressure increases.\n\nNow write the formula for inverse variation.\n\n$\\text{PV}=$ $k$\n\nSubstitute $240$ for $V$ $30$ for $P$ in the formula and find the constant\n\n$\\left(240\\right)\\left(30\\right)=k$\n\n$7200=k$\n\nNow write an equation and solve for the unknown.\n\nWe have to find the pressure when the volume is $160\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}{\\text{cm}}^{3}$ .\n\nSo,\n\n$\\left(160\\right)\\left(P\\right)=7200$ .\n\nSolve for $P$ .\n\n$\\begin{array}{l}P=\\frac{7200}{160}\\\\ \\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}=45\\end{array}$\n\nTherefore, pressure $45\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{kg}/{\\text{cm}}^{2}$ be applied to have a volume of $160\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}{\\text{cm}}^{3}$ .\n\nExample 2:\n\nThe length of a violin string varies inversely as the frequency of its vibrations. A violin string $14$ inches long vibrates at a frequency of $450$ cycles per second. Find the frequency of a $12$ -inch violin string.\n\nThe length( $l$ ) varies inversely as the frequency( $f$ ), when the length increases, the frequency decreases and when the length decreases, the frequency increases.\n\nNow write the formula for inverse variation.\n\n$lf=k$ .\n\nSubstitute $450$ for $f$ $14$ for $l$ in the formula and find the constant.\n\n$\\left(450\\right)\\left(14\\right)=k$\n\n$6300=k$\n\nNow write an equation and solve for the unknown.\n\nWe have to find the frequency of $12$ -inch violin string.\n\nSo,\n\n$\\left(12\\right)\\left(f\\right)=6300$ .\n\nSolve for $f$ .\n\n$\\begin{array}{l}f=\\frac{6300}{12}\\\\ \\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}\\text{\\hspace{0.17em}}=525\\end{array}$\n\nTherefore, $12$ -inch violin string vibrates at a frequency of $525$ cycles per second." ]
[ null ]
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https://blog.myrank.co.in/vector-product-of-two-vectors/
[ "# Vector Product of Two Vectors\n\n### Vector Product of Two Vectors\n\nThe physical quantities may be broadly classified into the vectors and the scalars. The quantities with magnitude and direction both are known as vector quantities.\n\nWhat is a vector product?\n\nThe vector product or the cross product of two vectors is a binary operation on two vectors in three dimensional spaces and the vector product is denoted by x and the product of two vectors is a vector.\n\nThe vector product or cross product of two vectors A and B is a vector C, defined as: C = A x B.\n\nWe can find the Cartesian components of C = A x B in terms of the components of A and B.\n\nCx = AyBz – AzBy\n\nCy = AzBx – AxBz\n\nCz = AxBy – AyBx\n\nAgain, consider two arbitrary vectors A and B and choose the orientation of your Cartesian coordinate system such that A point into the x – direction and B lies in the x – y plane. Then,\n\nA = (Ax, 0, 0); B = (Bx, By, 0) and Cx = 0.\n\nCy = 0\n\nCz = AxBy\n\nThen, the magnitude of C is,\n\nC = Cz = AxBy", null, "Since, Ax = A and By = B sinΦ we can write it as, C = AB sinΦ.\n\nWhere,\n\nΦ = smallest angle between the directions of the vectors A and B.\n\nC is perpendicular to both A and B.\n\ni.e., it is perpendicular to the plane that contains both A and B. the direction of C can be found by inspecting its components or by using Right – Hand rule.\n\nLet the fingers of your right hand point in the direction of A.  Orient the palm of your hand so that, as you curl your fingers, you can sweep them over to point in the direction of B.  Your thumb points in the direction of C = A X B.", null, "If A and B are parallel or anti – parallel to each other, then C = A x B = 0. Since, sinΦ = 0. If A and B are perpendicular to each other, then sinΦ = 1 and C has its maximum possible magnitude.\n\nWhen we form the scalar product of two vectors, we multiply the perpendicular component of the two vectors. The vector product is not commutative.\n\nA x B = – B x A." ]
[ null, "http://blog.myrank.co.in/wp-content/uploads/2018/05/Vector-Product-of-Two-Vectors-300x224.png", null, "http://blog.myrank.co.in/wp-content/uploads/2018/05/Vector-Product-of-Two-Vectors1.png", null ]
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https://blog.tanyakhovanova.com/2010/07/shannon-entropy-rescues-the-tuesday-child/
[ "## Shannon Entropy Rescues the Tuesday Child\n\nMy son Alexey Radul and I were discussing the Tuesday’s child puzzle:\n\nYou run into an old friend. He has two children, but you do not know their genders. He says, “I have a son born on a Tuesday.” What is the probability that his second child is also a son?\n\nHere is a letter he wrote me on the subject. I liked it because unlike many other discussions, Alexey not only asserts that different interpretations of the conditions in the puzzle form different mathematical problems, but also measures how different they are.\n\n### by Alexey Radul\n\nIf you assume that boys and girls are symmetric, and that days of the week are symmetric (and if you have no information to the contrary, assuming anything else would be sheer presumption on your part), then you can be in one of at least two states.\n\n1) You say that “at least one son born on a Tuesday” is all the information you have, in which case your distribution including this information is uniform over consistent cases, in which case your answer is 13/27 boy and your information entropy is\n\n− ∑27 (1/27) log(1/27) = − log(1/27) = 3.2958.\n\n2) You say that the information you have is “The guy might have said any true thing of the form ‘I have at least one {boy/girl} born on a {day of the week}’, and he said ‘boy’, ‘Tuesday’.” This is a different mathematical problem with a different solution. The solution: By a symmetry argument (see below [*]) we must assign uniform probability of him making any true statement in any particular situation. Then we proceed by Bayes’ Rule: the statement we heard is d, and for each possible collection of children h, the posterior is given by p(h|d) = p(h)p(d|h)/p(d). Here, p(h) = 1/142 = 1/196; p(d) = 1/14; and p(d|h) is either 1 or 1/2 according as whether his other child is or is not another boy also born on a Tuesday (or p(d|h) = 0 if neither child is a boy born on a Tuesday). There are 1 and 26 of these situations, respectively. The answer they lead to is of course 1/2; but the entropy is\n\n− ∑ p log p = − 1/14 log 1/14 − 26/28 log 1/28 = 3.2827\n\nTherefore that assumed additional structure really is more information, which is only present at best implicitly in the original problem. How much more information? The difference in entropies is 3.2958 – 3.2827 = 0.0131 nats (a nat is to a bit what the natural log is to the binary log). How much information is that? Well, the best I can do is to reproduce an argument of E.T. Jaynes’, which may or may not really apply to this situation. Suppose you have some repeatable experiment with some discrete set of possible outcomes, and suppose you assign probabilities to those outcomes. Then the number of ways those probabilities can be realized as frequencies counted over N trials is proportional to eNH, where H is the entropy of the distribution in nats. Which means that the ratio by which one distribution is easier to realize is approximately eN(H1-H2). In the case of N = 1000 and H1 – H2 = 0.0131, that’s circa 5×105. For each way to get a 1000-trial experiment to agree with version 2, there are half a million ways to get a 1000-trial experiment to agree with version 1. So that’s a nontrivial assumption.\n\n[*] The symmetry argument: We are faced with the following probability assignment problem\n\nSuppose our subject’s first child is a boy born on a Tuesday, and his second child is a girl born on a Friday. What probability must we assign to him asserting that he has at least one boy born on a Tuesday?\n\nGood question. Let’s transform our coordinates: Let Tuesday’ be Friday, Friday’ be Tuesday, boy’ be girl, girl’ be boy, first’ be second and second’ be first. Then our problem becomes\n\nSuppose our subject’s second’ child is a girl’ born on a Friday’, and his first’ child is a boy’ born on a Tuesday’. What probability must we assign to him asserting that he has at least one girl’ born on a Friday’?\n\nOur transformation necessitates p(boy Tuesday) = p(girl’ Friday’), and likewise p(girl Friday) = p(boy’ Tuesday’). But our state of complete ignorance about what’s going on with respect to the man’s attitudes about boys, girls, Tuesdays, Fridays, and first and second children has the symmetry that question and question’ are the same question, and must, by the desideratum of consistency, have the same answer. Therefore p(boy Tuesday) = p(boy’ Tuesday’) = p(girl Friday) = 1/2.\n\nShare:\n\n### 2 Comments\n\n1. #### misha:\n\nAnother popular interpretation of entropy is the average measure of surprise produced by an outcome of an experiment. Imagine some event of probability p happens. You are surprised by s(p). When another event of probability q happens, you are surprised by s(q). The total surprise is s(p)+s(q). On the other hand, if these events are independent, the probability of both of them happening is pq. We conclude that s(pq)=s(p)+s(q). It means that s(p) is proportional to log(p). Taking the average over all the possible outcomes, we get the entropy formula.\n\n2. #### Christ Schlacta:\n\nyou’re both wrong, genetics dictates that the gender and date of birth of the second child are independent from the first, therefore the probability of his second child being a girl is 50/50 regardless of what and when the first child is born and viceversa. The fact that the first child is a boy born on tuesday is simply extra information thrown in to mislead the problem-solver." ]
[ null ]
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https://tvst.arvojournals.org/article.aspx?articleid=2770797
[ "", null, "tvst\nOpen Access\nArticles  |   September 2020\nRevisiting the Drasdo Model: Implications for Structure-Function Analysis of the Macular Region\nAuthor Affiliations & Notes\n• Giovanni Montesano\nCity, University of London–Optometry and Visual Sciences, London, UK\nNIHR Biomedical Research Centre, Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK\n• Giovanni Ometto\nCity, University of London–Optometry and Visual Sciences, London, UK\nNIHR Biomedical Research Centre, Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK\n• Ruth E. Hogg\nCentre for Public Health, Queen's University Belfast, Block B, Royal Hospital, Grosvenor Road, Belfast, Northern Ireland\n• Luca M. Rossetti\nUniversity of Milan–ASST Santi Paolo e Carlo, Milan, Italy\n• David F. Garway-Heath\nNIHR Biomedical Research Centre, Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK\n• David P. Crabb\nCity, University of London–Optometry and Visual Sciences, London, UK\n• Correspondence: David P. Crabb, City, University of London, Northampton Square, London, EC1V 0HB, United Kingdom. e-mail: [email protected]\nTranslational Vision Science & Technology September 2020, Vol.9, 15. doi:https://doi.org/10.1167/tvst.9.10.15\n• Views\n• PDF\n• Share\n• Tools\n×\n###### This feature is available to authenticated users only.\n• Get Citation\n\nGiovanni Montesano, Giovanni Ometto, Ruth E. Hogg, Luca M. Rossetti, David F. Garway-Heath, David P. Crabb; Revisiting the Drasdo Model: Implications for Structure-Function Analysis of the Macular Region. Trans. Vis. Sci. Tech. 2020;9(10):15. https://doi.org/10.1167/tvst.9.10.15.\n\n© ARVO (1962-2015); The Authors (2016-present)\n\n×\n• Supplements\nAbstract\n\nPurpose: To provide a consistent implementation of a retinal ganglion cell (RGC) displacement model proposed by Drasdo et al. for macular structure-function analysis, customizable by axial length (AL).\n\nMethods: The effect of axial length on the shape of the inner retina was measured on 235 optical coherence tomography (OCT) scans from healthy eyes, to provide evidence for geometric scaling of structures with eye size. Following this assumption, we applied the Drasdo model to map perimetric stimuli on the radially displaced RGCs using two different methods: Method 1 only displaced the center of the stimuli; Method 2 applied the displacement to every point on the edge of the stimuli. We compared the accuracy of the two methods by calculating, for each stimulus, the number of expected RGC receptive fields and the number RGCs calculated from the histology map, expected to be equivalent. The same calculation was repeated on RGC density maps derived from 28 OCT scans from 28 young healthy subjects (age < 40 years) to confirm our results on clinically available measurements.\n\nResults: The size of the retinal structures significantly increased with AL (P < 0.001) and was well predicted by geometric scaling. Method 1 systematically underestimated the RGC counts by as much as 60%. No bias was observed with Method 2.\n\nConclusions: The Drasdo model can effectively account for AL assuming geometric scaling. Method 2 should be used for structure-function analyses.\n\nTranslational Relevance: We developed a free web App in Shiny R to make our results available for researchers.\n\nIntroduction\nThe health of the macula is of central importance for everyday functions, such as reading and recognizing faces.13 It is now recognized that the macula can be affected by glaucoma, even in the early stages of the disease process.4 Loss and dysfunction of retinal ganglion cells (RGCs) in glaucoma is monitored using both structural and functional measurements. Structural assessment of the macular region can be done by spectral domain optical coherence tomography (SD-OCT), which provides volumetric measurements of various retinal layers. The layers of most interest for glaucoma are the retinal nerve fiber layer (RNFL), the ganglion cell layer (GCL), and the inner plexiform layer (IPL). Together, they form the inner retina. RGC loss from glaucoma causes thinning of the RNFL (which contains RGC axons), the GCL (which contains RGC cell bodies), and the IPL (which contains the RGC dendritic arbors).\nFunctional assessment for glaucoma is typically assessed with the visual field (VF) test in the form of standard automated perimetry (SAP). For the macular region, dense testing grids, such as the standard 10-2, are used. The 10-2 spans the central 10° from fixation with a spacing of 2° between test locations. There is some evidence to suggest that these grids are more sensitive to early glaucoma damage in that region when compared to less dense testing grids, such as the 24-2 test pattern.4,5\nCombining structural and functional information should further improve the identification of glaucomatous macular damage and the detection of its progression. Moreover, studying the relationship between the two measurements offers useful insights into the kinetics and pathophysiology of RGC loss and dysfunction in glaucoma.6,7 Models seeking to match structural and functional data to histology measurements of RGC density have been used to explore this relationship.811 Recently, a method proposed by Raza and Hood12 has been used to convert the GCL thickness into RGC density to investigate the relationship between RGC number and SAP sensitivity13,14 in healthy subjects and glaucoma patients.\nThe unique features of the inner retina in the macular region need to be considered when comparing structural and functional measurements. The most significant of these is the radial displacement of RGCs from the fovea so that RGCs receiving a stimulus in the parafoveal region are displaced toward the periphery with respect to the location of their corresponding photoreceptors.1517 RGCs are connected to the corresponding photoreceptors via Henle's fibers, which have an oblique pathway in the parafoveal region. This displacement diminishes with eccentricity, becoming minor at around 10 visual degrees from the fovea.15,18 Different numerical models, based on, or verified by, histologic measurements of Henle's fibers have been proposed to account for this displacement.15,1820 The most widely used of these models is the one proposed by Drasdo et al.15 This model is valuable in the context of structure-function analyses because the displacement calculation requires equivalence between the cumulative number of RGC receptive fields (RGC-RF), estimated through psychophysical measurements, and the number of RGC bodies, estimated through histology.16 Theoretically, when applied correctly, this model would allow a one-to-one correspondence between the number of RGCs, estimated from structural maps, and psychophysical measurements, estimated from SAP sensitivity (which depends on the number of RGC-RFs stimulated during the test).\nAlthough widely used, the implementation of the model reported by Drasdo et al.15 is not straightforward. For example, Drasdo et al. only reported numerical calculations for the four principal meridians and the average displacement, in microns.15 Therefore, a method to generalize to any arbitrary meridian has not been available. A second example is that the schematic eye used by Drasdo et al.15,21 to convert visual degrees to millimeters of retina assumes a spherical shape for the retina of a certain radius. However, that radius is not the same as that assumed by Curcio and Allen16 in their published histology map of RGC density. Moreover, the radius of the sphere should be adjusted for the axial length (AL), when this is available. However, Drasdo et al.15,21 only provided average displacement values regardless of axial length. A third example is that, in many cases, a simple displacement of the stimulus centers was applied.7,13,22 However, the displacement should be applied to the perimeter of the stimulus, so that different points of the stimulus edge are independently displaced radially outward according to the model. For example, in the parafoveal region, the stimulus edge nearer the fovea is displaced further than the stimulus edge further from the fovea.14,23 This is especially important when RGC counts are involved, because small differences in the area used for calculations can result in large differences in the counts.\nThe objective of our work was to develop a revised version of the displacement model for any retinal location and with a customizable schematic eye, to account for variations in AL; determine the correct displacement model for circular perimetric stimulus (covering RGC-RFs) to corresponding RGC location. Moreover, we developed a web application to allow researchers to apply the revised model to their own structure-function data in an attempt to improve the comparability of findings from different research groups.\nMethods\nDatasets\nFor our analyses we used two datasets. The first (Dataset 1) was a collection of macular volume scans collected for the Northern Ireland Sensory Ageing (NISA) study (https://clinicaltrials.gov/ct2/show/NCT02788695), which originated from a population based aging cohort (NICOLA study https://www.qub.ac.uk/sites/NICOLA/) conducted in Belfast at Queen's University, Belfast. Scans were acquired with a Spectralis SD-OCT (Heidelberg Engineering, Heidelberg, Germany) comprised 61 horizontal B-scans centered on the fovea (ART 9, 30° × 25° with a fixed 7° rotation, counterclockwise for right eyes, clockwise for left eyes). In this dataset, 417/726 scans were classified as having a healthy outer retina by two graders. In 299 of these eyes, AL was measured using a Lenstar LS 900 Biometer (Haag-Streit AG, Switzerland). These scans were further screened by an ophthalmologist (GM) for pathologic changes of the inner retina. Seventeen scans were excluded because of poor quality that prevented a clear identification of the inner retinal layers or the Bruch's membrane within 15° from the fovea, 13 scans had local thinning that could be attributed either to glaucoma or local ischemia and four were excluded for vitreoretinal alterations. The segmentation of the retinal layers was checked and manually corrected where necessary leaving 265 scans for analysis. This dataset was used exclusively to extract metrics on the shape of the GCL profile. No thickness values were measured. The median [interquartile range] quality index (QI) was 30.6 [28.98, 32.26] dB.\nThe second dataset (Dataset 2) was a collection of SD-OCT scans acquired for a cross-sectional study on structure-function relationship in the healthy macula. The study was approved by the ethical committee Comitato Etico Milano Area 1 (code OCU_SSSF) and the data collection took place at the eye clinic at San Paolo Hospital (University of Milan) in Milan, Italy. The dataset included 28 macular scans from 28 subjects collected with a Spectralis SD-OCT and composed of 121 B-scans, centered on the fovea (ART 9, 25° × 30°, oriented vertically). AL was measured using an IOL-Master V3 A-scan (Zeiss Meditec, Dublin, CA, USA). The subjects had no known or detectable ocular disease and younger than 40 (range 23–37) years, to match the age range of the histological dataset collected by Curcio and Allen16 (see next section). Descriptive statistics for the two datasets are given in Table 1. Best corrected visual acuity in Dataset 2 was 0.00 LogMar for all subjects and was not measured further. All data collections were performed in agreement with the declaration of Helsinki after explicit written consent from the participants. All scans were of good quality and none was excluded (QI = 26.47 [25.36–27.47] dB).\nTable 1.\n\nDescriptive Statistics for Relevant Variables in the Two Datasets\nTable 1.\n\nDescriptive Statistics for Relevant Variables in the Two Datasets", null, "Histology Map\nThe original model developed by Drasdo et al.15 used the histology map provided by Curcio and Allen.16 This reports the density of ganglion cells (cells/mm2) obtained from six retinas of five healthy subjects, aged 27 to 37 years (range), for a retinal sphere with a radius of 11.459 mm. Details are reported in Appendix A\nSchematic Eye\nThe schematic eye used in this work replicated the one described by Drasdo and Fowler21 and later used by Drasdo et al.15 for their displacement model. We used numerical ray tracing through the schematic eye to calculate the correspondence between visual degrees and mm, and solid visual degrees and mm2, on the retina. The data to build the schematic eye was derived from the table reported in the original article.21 Importantly, this approach aligns with the original methodology unlike that applied in previous studies.18,19 Note the radius of the retinal sphere has been changed to match the one used for the histology map (r0 = 11.459 mm, originally 11.06 mm in Drasdo and Fowler).21 The distance between the center of the retinal sphere and the corneal vertex has also been scaled proportionally (c0 = 12.38 mm, originally 11.95 mm). Therefore the default AL (AL0) of our schematic eye was 23.84 mm (originally 23.01 mm). These changes had a small impact on the degrees-to-mm conversion, but a more important effect of the mm2/solid degree ratio (Fig. 1). The schematic eye was coded in Matlab (The MathWorks, Natick, MA, USA). Additional details are reported in Appendix B\nFigure 1.\n\nRendering of the schematic eye, with a projection of a 10-2 grid (red dots, top panel). The bottom panel shows a cross-section of the same schematic eye with additional examples of short and long axial lengths. Right panels show the distance travelled on the retina per visual degree (top) and the mm2/solid degree ratio at various retinal eccentricities (bottom). The latter represents the ratio between retinal areas in mm2 to visual degrees2. The curved relationship with eccentricity is a consequence of the nonlinear projection obtained by numerical calculations of ray tracing through the cornea, lens and vitreous, which varies with visual angle. It is important to acknowledge that the relationship between retinal mm and degrees of visual angle is also not linear. In black, the curves obtained from the original schematic eye described by Drasdo and Fowler21 (in black). In red, the results of the schematic eye used in this study.\nFigure 1.\n\nRendering of the schematic eye, with a projection of a 10-2 grid (red dots, top panel). The bottom panel shows a cross-section of the same schematic eye with additional examples of short and long axial lengths. Right panels show the distance travelled on the retina per visual degree (top) and the mm2/solid degree ratio at various retinal eccentricities (bottom). The latter represents the ratio between retinal areas in mm2 to visual degrees2. The curved relationship with eccentricity is a consequence of the nonlinear projection obtained by numerical calculations of ray tracing through the cornea, lens and vitreous, which varies with visual angle. It is important to acknowledge that the relationship between retinal mm and degrees of visual angle is also not linear. In black, the curves obtained from the original schematic eye described by Drasdo and Fowler21 (in black). In red, the results of the schematic eye used in this study.", null, "Scaling of Eye Structures and Cell Density\nA customized displacement model must account for how retinal structures scale with AL, especially the size of the displacement area (see later) and the planar density of ganglion cells derived from histology. The assumption of a spherical shape for the retina for all ALs is prone to the adoption of a global expansion model. In this model, the planar RGC density would scale inversely with the square of the retinal radius, whereas the radius of the displacement zone (rDZ = 4.034 mm in the original paper)15 would scale linearly with the retinal radius. The two scaling equations, where r is the retinal radius corresponding to a given AL, are given as:\n\\begin{equation}{r_{DZ}}\\left( {AL} \\right) = {\\rm{\\ }}4.034\\,{\\rm{*}}\\,\\left( {\\frac{r}{{{r_0}}}} \\right),\\end{equation}\n(1)\n\n\\begin{equation}RGC{\\rm{\\ }}Density\\left( {AL} \\right) = {\\rm{\\ }}RGC{\\rm{\\ }}Density\\left( {A{L_0}} \\right){\\rm{*}}{\\left( {\\frac{{{r_0}}}{r}} \\right)^2}.\\end{equation}\n(2)\n\nAn alternative model to the assumption of global expansion is “equatorial stretch,” where the posterior pole is simply moved further away from the corneal vertex with no change in the relative size of the retinal structures. Although the actual expansion process in myopia is likely to be a mixture of the two phenomena,2426 psychophysical evidence suggest that a global expansion model is a reasonable approximation for most axial lengths.2730 Global expansion is also implied in the RGC-RF model proposed by Drasdo et al.,15 which assumes a constant density of RFs per solid visual degree (see later).\nA global expansion model also implies that the amount of radial RGC displacement, when measured in mm on the retina, should increase with axial length. This is a consequence of the stretching of the retinal tissue and Henle's fibers with increasing eye size. Although direct evidence of this is not yet available, indirect confirmation can be obtained by observing how the GCL profile scales with axial length in healthy eyes. To explore this, we used the 265 macular volume scans from Dataset 1 and identified the maximum GCL thickness peak for several meridians, centered on the anatomic fovea (Fig. 3). An ellipse was then fitted through a least squares method to the locations of the peaks. We then measured the length of the major and minor axes of the ellipse. All measurements were corrected for ocular magnification using the schematic eye defined in the previous section. The relationship between the length of the ellipse axes and the axial length was explored through linear regression. The ellipse dimensions were also predicted for an exact scaling with axial length, assuming a global expansion, by multiplying the ellipse dimensions predicted from the linear regression at AL0 by the same scaling factor used for the rDZ (geometric scaling model). The goodness-of-fit of the linear regression and the geometric scaling model were compared using the mean absolute error (MAE), calculated for each model as the average of the absolute residuals.\nOCT Data Processing\nAll OCT data were exported as RAW files (.vol) using the Heidelberg Eye Explorer. The files were then imported in Matlab using a custom routine. The segmentations were then used to generate thickness maps for the whole retina and the GCL. The maps were interpolated and smoothed to match the size of the reference infrared fundus image (768 × 768 pixels, 30° × 30° field of view), padding with zeros where the OCT data were missing, i.e., outside the scanning pattern. The interpolation was performed using a thin plate spline (tpaps function in Matlab) with anisotropic smoothing parameters, so that smoothing was stronger across B-scans than within a B-scan. The fovea was automatically identified through a template matching. Correct detection was confirmed through visual inspection.\nConversion of GCL Thickness Maps into Estimated RGC Counts\nWe used the method proposed by Raza and Hood12 to convert the OCT GCL thickness maps into customized estimates of RGC density and applied this to Dataset 2. In brief, the histology map was divided point-by-point by an average healthy GCL thickness map (768 × 768 pixels), obtained as the average from all eyes in Dataset 2, after aligning the fovea and the position of the optic nerve head (ONH). This yielded a volumetric density map (RGC/mm3). The map can then be multiplied point-by-point by a GCL thickness map from a new subject to obtain a customized RGC density map (RGC/mm2). We accounted for AL by applying a magnification correction to the GCL macular volume scans and by rescaling the histology density map according to the global expansion model given by Equation (2)\nDisplacement Model\nFor the displacement model, we followed the same methodology proposed by Drasdo et al.15 in their original article. The first step was to calculate the RGC-RF density along a specific meridian obtained from a generic model based on psychophysical measurements, the derivation of which is described in detail in the original article. The final formula, where e is the eccentricity in visual degrees, Dgcrf is the density of RGC-RF (number/solid degree), Rv = 0.011785 and Ro = 0.008333 and k is a parameter that depends on eccentricity (see Appendix C), is given as follows:\n\\begin{equation}{D_{gcrf}}\\left( e \\right) = {\\rm{\\ }}\\frac{{k{\\rm{*}}\\left( {1.12 + 0.0273{\\rm{*}}e} \\right)}}{{1.155{\\rm{*}}\\left( {{{\\left( {{R_v}\\left( {1 + {\\rm{\\ }} {e {/ } {{{\\boldsymbol{E}}_{2{\\boldsymbol{v}}}}}}} \\right)} \\right)}^2} - \\ {{\\left( {{R_o}\\left( {1 + {\\rm{\\ }} {{e} {/ } {{20}}}} \\right)} \\right)}^2}} \\right)}}.\\end{equation}\n(3)\n\nThe parameter E2v in Equation (3) was used by Drasdo et al.15 to scale the RGC-RF for each principal meridian. A key objective of our new approach was to determine its value for any arbitrary meridian. Similarly to Drasdo et al.,15 we performed a numerical optimization of this parameter by simply requiring that the total counts of RGC-RF and RGC bodies are equal within the maximum displacement zone (DZ). From Drasdo et al.,15 the DZ ends at 4.034 mm from the fovea and is assumed symmetric. This value was used for AL0 and was scaled proportionally with the retinal radius for different axial lengths, as previously explained. The displacement is finally computed as the difference between the eccentricities at which the cumulative count of RGC bodies (Cgcb) and the cumulative count of RGC-RF (Cgcrf) are equal. Additional details are reported in Appendix C\nDisplacement of Perimetric Stimuli\nWe compared two methods of applying the Drasdo model to perimetric stimuli. The first commonly-applied method 13 (Method 1) consisted of a simple displacement of the center of the stimuli, without any changes to its shape (Fig. 2, left panel). In the alternative method (Method 2), the circumference of the stimulus (approximated with 72 points around the stimulus edge) is displaced according to the Drasdo model; this results in distorted stimulus shapes in the parafoveal region (Fig. 2, right panel). We tested the accuracy of each method by requiring consistency under the Drasdo model. In fact, the model calculates the displacement by equating the number of expected RGC-RF and the number of RGC bodies at any given eccentricity (in a healthy eye). Therefore the estimated number of RGC-RF within a given stimulus area should match the number of RGC bodies within the displaced stimulus on the structural map, besides some minimal discrepancy due to approximation errors in the numerical calculations. For our calculations, we used a 10-2 grid and calculated the number of RGC-RF and cellular bodies for all conventional Goldman sizes, from I to V. The RGC-RF density function can change for each meridian. Hence, we generated a dense map with the same resolution as the structural map and used binary masks to calculate the number of RGC-RFs within each stimulus size. The same methodology was applied to the displaced stimuli on the structural map. The resolution used for our calculations was 2.2 µm (0.008°) for the histology map and 0.0391° for the structural maps in Dataset 2 (the maximum resolution of the Spectralis SD-OCT). This mainly affected the precision of the binary masks, which is important for small stimulus sizes. For the first analysis, we aimed for a very precise quantification to test the theoretical validity of the two methods. For the second analysis, we used a resolution that is likely to be applied for real data as a compromise between precision and speed of calculation.\nFigure 2.\n\nRepresentations of the two candidate methods to apply the displacement to perimetric stimuli. Method 1 is the one applied by Yoshioka et al.13. Method 2 is the one proposed in this article. The color map represents the histology density at AL0 for both graphs. The vertical axes are reported both in mm and visual degrees. The black shapes represent the areas tested by a 10-2 perimetric test, displaced with the two methods. In both images we are displaying the results of the application of the two methods on Goldmann IV stimuli, assumed circular and arranged in a regular 10-2 grid.\nFigure 2.\n\nRepresentations of the two candidate methods to apply the displacement to perimetric stimuli. Method 1 is the one applied by Yoshioka et al.13. Method 2 is the one proposed in this article. The color map represents the histology density at AL0 for both graphs. The vertical axes are reported both in mm and visual degrees. The black shapes represent the areas tested by a 10-2 perimetric test, displaced with the two methods. In both images we are displaying the results of the application of the two methods on Goldmann IV stimuli, assumed circular and arranged in a regular 10-2 grid.", null, "Development of the Web App\nA web application (App) was developed using the Shiny library31 for R32 (R Foundation for Statistical Computing, Vienna, Austria). It allows the visualization of the schematic eye and the calculation for the RGC displacement. It can also import structural maps and provide calculations for different stimulus sizes. Finally, it can also be used for batch processing of a whole dataset. The App is freely available at https://relayer.online/drasdo, with detailed explanations on its use.\nThe Matlab codes for the schematic eye and the displacement model were translated in R. For faster computational execution, the displacement was pre-calculated for different ALs (from 18 to 35 mm, at 0.5 mm intervals). The planar displacement maps were calculated out to 7.5 mm from the fovea, at 0.05 mm intervals, then organized in a dense three-dimensional array. The displacement values are then obtained via linear interpolation of the array.\nResults\nScaling of Eye Structures with Axial Length\nThe calculations were performed on the eyes from Dataset 1. Both axes of the ellipses correlated negatively with AL before magnification correction (major axis MAE = 0.149 mm, P < 0.001; minor axis MAE = 0.111 mm, P < 0.001) and positively after magnification correction (major axis MAE = 0.148 mm, P < 0.001; minor axis MAE = 0.112 mm, P < 0.001). A geometric scaling model offered a very similar fit (major axis MAE = 0.175 mm; minor axis MAE = 0.131 mm). The results are presented in Figure 3\nFigure 3.\n\nScaling of ocular structures with axial lengths. Top panels show two examples of the calculation for the descriptive ellipses (in red), as described in the Methods. The black points identify the peaks in the GCL profile used for the fitting. Lower panels show the measurements of the major and minor axis of the ellipses before (left) and after (right) correction for ocular magnification.\nFigure 3.\n\nScaling of ocular structures with axial lengths. Top panels show two examples of the calculation for the descriptive ellipses (in red), as described in the Methods. The black points identify the peaks in the GCL profile used for the fitting. Lower panels show the measurements of the major and minor axis of the ellipses before (left) and after (right) correction for ocular magnification.", null, "Variability of Displacement with Axial Length\nResults of the fitting process for the parameter E2v are reported in Figure 4A. Values are very similar to those reported by Drasdo et al.15 for the principal meridians for all considered ALs. The systematic change with axial length was small (Fig. 4A). The displacement is constant for all axial lengths when measured in degrees, as a consequence of the global expansion mechanism assumed by the model. Figure 4 B shows the displacement in degrees and in mm for AL0. The values in mm are very similar to the average displacement reported by Drasdo et al.15\nFigure 4.\n\n(A) Polar plot of the results of the fitting process for the parameter E2v. N, nasal; S, superior; T, temporal; I, inferior. (B) Displacement map calculated in degrees and mm at AL0.\nFigure 4.\n\n(A) Polar plot of the results of the fitting process for the parameter E2v. N, nasal; S, superior; T, temporal; I, inferior. (B) Displacement map calculated in degrees and mm at AL0.", null, "Displacement of Perimetric Stimuli\nAverage density values (per solid degree) at different eccentricities are reported in Table 2 (calculated from the counts for the G-IV stimulus size). Method 1 yielded substantial underestimation of the RGC body counts in the parafoveal region, where the displacement is largest, and a slight overestimation at larger eccentricities (Fig. 5 and Table 2). Conversely, Method 2 provided estimates that were very consistent with the expected number of RGC-RF. The slightly larger variability with a G-I stimulus was due to numerical approximation and completely disappears for larger stimulus sizes. When converted to dB units (Fig. 5), the calculations with Method 1 yield similar results to those reported by Yoshioka et al.13 for healthy subjects. The same method was applied to the healthy macular volume SD-OCT scans in Dataset 2 (Fig. 6 and Table 2). The results were very similar to those obtained with the RGC histology map.\nTable 2.\n\nDensity Data at Different Eccentricities of the 10-2 Grid, Derived From the Counts Reported in Figure 5 and Figure 6 for a G-IV Stimulus Size\nTable 2.\n\nDensity Data at Different Eccentricities of the 10-2 Grid, Derived From the Counts Reported in Figure 5 and Figure 6 for a G-IV Stimulus Size", null, "Figure 5.\n\nComparison of the results between the two displacement methods for perimetric stimuli. Method 1 is the one used by Yoshioka et al.13. Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3)) and do not represent real subject data. The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.\nFigure 5.\n\nComparison of the results between the two displacement methods for perimetric stimuli. Method 1 is the one used by Yoshioka et al.13. Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3)) and do not represent real subject data. The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.", null, "Figure 6.\n\nComparison of the results between the two displacement methods for perimetric stimuli for real structural data. Method 1 is the one used by Yoshioka et al.13 Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3), adjusted for AL). The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.\nFigure 6.\n\nComparison of the results between the two displacement methods for perimetric stimuli for real structural data. Method 1 is the one used by Yoshioka et al.13 Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3), adjusted for AL). The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.", null, "Discussion\nIn our work we revisited the RGC displacement model proposed by Drasdo et al.15 and studied its application to perimetric data to yield consistent structure-function measurements. We also developed a web App to make our methodology easily available for other researchers, in the hope to standardize this essential aspect of structure-function analyses.\nOur implementation generalized the displacement model to any arbitrary meridian. Compared to other models 19,20 we imposed weaker constraints on the symmetry of the displacement. The model proposed by Sjostrand et al.20 used histological measurements to derive an even displacement around the fovea. Watson 19 followed an approach similar to Drasdo et al.15 but used a different equation for the RGC-RFs and extended his calculations to arbitrary meridians by assuming an elliptical symmetry around the fovea. In contrast, our approach, as in the original article, only assumes the maximum displacement to be the same for all meridians in the fitting process. However, as shown in Figure 4B, such an assumption does not prevent the displacement from adapting to the measured distributions of RGC cells provided by histology. Importantly, the effective RGC displacement region extends to smaller eccentricities in the inferior retina. A similar approach for generalization of the Drasdo model has been proposed by Turpin et al.18 Our results were in general agreement; they also showed a smaller extent of the displacement inferiorly compared to other regions. However, the displacement for the parafoveal locations was smaller in our calculations and in good agreement with the average displacement calculated by Drasdo et al.15 In addition to previous work, we implemented a numerical ray tracing model of the schematic eye used by Drasdo and Fowler21 to convert between visual degrees and distances on the retinal sphere. This allowed us to adapt the model so that the retinal sphere corresponded to the one used for the retinal histology map built by Curcio and Allen.16,33 This is crucial to obtain consistent calculations, because the Drasdo model is based on that map. The implementation of the numerical model also allowed us to customize the conversion and the RGC density map based on the axial length. In this study, we assumed a global expansion model, scaling the linear structures with the radius of the retinal sphere and the density with the squared radius; this has been shown to be a good approximation by psychophysical examinations.2730 Additionally, we confirmed this by observing how the structure of the inner retina scales with axial length using a large dataset of SD-OCT data (Fig. 3). We found that geometric scaling for axial length fitted the observed data adjusted for ocular magnification. Under this assumption, the displacement is conveniently equivalent for all axial lengths when calculated in degrees of visual angle. However, competing models have been proposed for eye growth in myopia and an elliptical growth model, combining equatorial stretching and global expansion, seems to be the most realistic from anatomic studies.2426 One advantage of our numerical implementation of the schematic eye is that it can be easily adapted to accommodate for different types of expansion models. One major limitation of our structural dataset was the lack of extreme axial lengths. Determining the optimal expansion model with a stratified data collection of structural and functional data will be the objective of future work.\nOur work was novel because it considered two different methods of applying the displacement to perimetric stimuli in structure function analyses. We showed that simply displacing the stimulus center (Method 1) does not provide estimates of RGC-RF counts within perimetric stimuli consistent with the counts expected from the Drasdo model. Instead, each point on the edge of the perimetric stimulus needs to be displaced independently (Method 2), resulting in distorted, ovoidal shapes. We were able to verify the validity of this approach by requiring that the RGC counts within a given displaced stimulus from the histology map be consistent with the expected RGC-RF counts assumed by the Drasdo model (Equation (3)). Only Method 2 yielded correct estimates (Fig. 5). We then verified that these results hold when the two methods are applied to structural data from young healthy subjects (Fig. 6). The increase in variability in this latter analysis was due both to intrasubject differences in the structural data and to the fact that the calculations were limited to the resolution of the structural maps, as explained in the Methods. Method 1 is similar to what was used by Yoshihoka et al.13 Unfortunately, those authors did not report tabulated RGC counts or estimated density. Nevertheless, the graphs reported in Figure 2 of their article13 clearly show counts that, in healthy subjects, are compatible with the results of Method 1. For example, the largest RGC counts for a G-III stimulus were approximately 25.6 dB, very similar to our results in Figures 5 and 6 for Method 1 (25.5 dB). In turn, this was crucially less than half than that derived from Method 2 (29.5 dB) and the expected RGC-RF count from Equation (3) (29.4 dB). Moreover, the RGC-RF density derived from Method 1 for the smallest eccentricity (1.41°, Table 2), when substituted into Equation (3) to derive the corresponding visual acuity (with E2v = 2), yields a value of 16.5 cycles/degree, unreasonably low for this eccentricity.15 In contrast, Method 2 yields 24.5 cycles/degree, much closer to the predicted 24.9 cycles/degree15 and compatible with the literature.34 These discrepancies might also be due to the fact that Yoshioka et al.13 provided age-corrected structural and functional measurements at 64.5 years of age. However, the boxplots in the supplementary material for the same article show minimal changes between age-corrected and raw thickness values, too low to justify such a large difference.\nOur findings are of particular importance for the interpretation of previously published results. To the extent of our knowledge, Method 2 has only been applied twice in the literature.14,23 Moreover, the actual methodology to implement the Drasdo model has been rarely reported. In many cases, the displacement appears to be symmetrical around the fovea.7,13,22,3538 This likely indicates an application of the average displacement profile presented in the graph from Figure 6 in the original paper by Drasdo et al.,15 using a fixed degrees to mm conversion. Although this might be satisfactory for some simple correlation analyses, disregarding the asymmetric nature of the displacement limits studies where a more detailed structure-function relationship is sought. For instance this is important when the development of a neural model of functional response is the main goal of the research.13 In fact, as shown by our results in Figure 6, a high degree of consistency with the calculations can be achieved, especially considering that, like the Drasdo displacement model, the method to estimate the number of RGC cell bodies from structural measurements12 is also based on the structural map produced by Curcio and Allen.16\nTo encourage translation, we have made our methodology available for researchers in a free user-friendly web App (Fig. 7, https://relayer.online/drasdo). The App allows for a straightforward and customizable application of the displacement model for different axial lengths, any perimetric grids, varied stimulus sizes and structural maps. Graphical outputs are designed to provide the researcher with tools to scrutinize the steps in the process. Batch analysis can also be done on large datasets. The App will be updated with future development of the methodology; for example, when a more comprehensive expansion model is developed.\nFigure 7.\n\nScreenshot of the second screen from the web App. It presents the results for the schematic eye at AL0, for a G-IV stimulus size and a 10-2 perimetric grid using the histological dataset by Curcio and Allen as a structural map. The Results table extends beyond what is visible on the screen and can be easily downloaded.\nFigure 7.\n\nScreenshot of the second screen from the web App. It presents the results for the schematic eye at AL0, for a G-IV stimulus size and a 10-2 perimetric grid using the histological dataset by Curcio and Allen as a structural map. The Results table extends beyond what is visible on the screen and can be easily downloaded.", null, "Acknowledgments\nThe authors thank Christine A. Curcio and Kenneth R. Sloan from the University of Alabama at Birmingham (USA) for making the histology data available for this analysis. We are grateful to all the participants of the NICOLA Study, and the whole NICOLA team, which includes nursing staff, research scientists, clerical staff, computer and laboratory technicians, managers and receptionists.\nSupported by the Atlantic Philanthropies, the Economic and Social Research Council, the UKCRC Centre of Excellence for Public Health Northern Ireland, the Centre for Ageing Research and Development in Ireland, the Office of the First Minister and Deputy First Minister, the Health and Social Care Research and Development Division of the Public Health Agency, the Wellcome Trust/Wolfson Foundation, and Queen's University Belfast. The authors alone are responsible for the interpretation of the data and any views or opinions presented are solely those of the authors and do not necessarily represent those of the NICOLA Study team. The NISA study was funded by the College of Optometrists, Macular Society, RNIB, Diabetes UK and the Thomas Pocklington Trust.\nDisclosure: G. Montesano, CenterVue (C); G. Ometto, None; R.E. Hogg, none; L.M. Rossetti, CenterVue(C); D.F. Garway-Heath, Carl Zeiss Meditec (C), CenterVue (C), Heidelberg Engineering (F), Moorfields MDT (P), ANSWERS (P), T4 (P); D.P. Crabb, CenterVue (C), ANSWERS (P), T4 (P)\nReferences\nGlen FC, Crabb DP, Smith ND, Burton R, Garway-Heath DF. Do patients with glaucoma have difficulty recognizing faces? Invest Ophthalmol Vis Sci. 2012; 53: 3629–3637.\nBurton R, Smith ND, Crabb DP. Eye movements and reading in glaucoma: observations on patients with advanced visual field loss. Graefes Arch Clin Exp Ophthalmol. 2014; 252: 1621–1630.\nGlen FC, Smith ND, Crabb DP. Saccadic eye movements and face recognition performance in patients with central glaucomatous visual field defects. Vis Res. 2013; 82: 42–51.\nDe Moraes CG, Hood DC, Thenappan A, et al. 24-2 Visual Fields miss central defects shown on 10-2 tests in glaucoma suspects, ocular hypertensives, and early glaucoma. Ophthalmology. 2017; 124: 1449–1456.\nGrillo LM, Wang DL, Ramachandran R, et al. The 24-2 Visual Field Test misses central macular damage confirmed by the 10-2 Visual Field Test and Optical Coherence Tomography. Transl Vis Sci Technol. 2016; 5: 15.\nHood DC, Kardon RH. A framework for comparing structural and functional measures of glaucomatous damage. Progr Retinal Eye Res. 2007; 26: 688–710.\nHood DC, Raza AS, de Moraes CG, Liebmann JM, Ritch R. Glaucomatous damage of the macula. Progr Retinal Eye Res. 2013; 32: 1–21.\nGarway-Heath DF, Caprioli J, Fitzke FW, Hitchings RA. Scaling the hill of vision: the physiological relationship between light sensitivity and ganglion cell numbers. Invest Ophthalmol Vis Sci. 2000; 41: 1774–1782.\nSwanson WH, Felius J, Pan F. Perimetric defects and ganglion cell damage: interpreting linear relations using a two-stage neural model. Invest Ophthalmol Vis Sci. 2004; 45: 466–472.\nHarwerth RS, Wheat JL, Fredette MJ, Anderson DR. Linking structure and function in glaucoma. Progr Retinal Eye Res. 2010; 29: 249–271.\nAnderson DR, Knighton RW. Perimetry and acuity perimetry. In: SMPIKA (ed.), Perspectives in Glaucoma. New Jersey, Thorofare, NJ: Slack, Inc.; 1988: 59–70.\nRaza AS, Hood DC. Evaluation of the structure-function relationship in glaucoma using a novel method for estimating the number of retinal ganglion cells in the human retina. Invest Ophthalmol Vis Sci. 2015; 56: 5548–5556.\nYoshioka N, Zangerl B, Phu J, et al. Consistency of structure-function correlation between spatially scaled visual field stimuli and in vivo OCT ganglion cell counts. Invest Ophthalmol Vis Sci. 2018; 59: 1693–1703.\nMontesano G, Rossetti LM, Allegrini D, Romano MR, Crabb DP. Improving visual field examination of the macula using structural information. Transl Vis Sci Technol. 2018; 7: 36.\nDrasdo N, Millican CL, Katholi CR, Curcio CA. The length of Henle fibers in the human retina and a model of ganglion receptive field density in the visual field. Vis Res. 2007; 47: 2901–2911.\nCurcio CA, Allen KA. Topography of ganglion cells in human retina. J Comp Neurol. 1990; 300: 5–25.\nLujan BJ, Roorda A, Knighton RW, Carroll J. Revealing Henle's fiber layer using spectral domain optical coherence tomography. Invest Ophthalmol Vis Sci. 2011; 52: 1486–1492.\nTurpin A, Chen S, Sepulveda JA, McKendrick AM. Customizing structure-function displacements in the macula for individual differences. Invest Ophthalmol Vis Sci. 2015; 56: 5984–5989.\nWatson AB. A formula for human retinal ganglion cell receptive field density as a function of visual field location. Journal of Vision. 2014; 14: 15.\nSjostrand J, Popovic Z, Conradi N, Marshall J. Morphometric study of the displacement of retinal ganglion cells subserving cones within the human fovea. Graefes Arch Clin Exp Ophthalmol. 1999; 237: 1014–1023.\nDrasdo N, Fowler CW. Non-linear projection of the retinal image in a wide-angle schematic eye. Br J Ophthalmol. 1974; 58: 709–714.\nMiraftabi A, Amini N, Morales E, et al. Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range. Invest Ophthalmol Vis Sci. 2016; 57: 4815–4823.\nHirasawa K, Matsuura M, Fujino Y, et al. Comparing structure-function relationships based on Drasdo's and Sjostrand's retinal ganglion cell displacement models. Invest Ophthalmol Vis Sci. 2020; 61: 10.\nAtchison DA. Optical models for human myopic eyes. Vis Res. 2006; 46: 2236–2250.\nAtchison DA, Pritchard N, Schmid KL, Scott DH, Jones CE, Pope JM. Shape of the retinal surface in emmetropia and myopia. Invest Ophthalmol Vis Sci. 2005; 46: 2698–2707.\nPope JM, Verkicharla PK, Sepehrband F, Suheimat M, Schmid KL, Atchison DA. Three-dimensional MRI study of the relationship between eye dimensions, retinal shape and myopia. Biomed Opt Express. 2017; 8: 2386–2395.\nColetta NJ, Watson T. Effect of myopia on visual acuity measured with laser interference fringes. Vis Res. 2006; 46: 636–651.\nChui TY, Song H, Burns SA. Individual variations in human cone photoreceptor packing density: variations with refractive error. Invest Ophthalmol Vis Sci. 2008; 49: 4679–4687.\nDabir S, Mangalesh S, Schouten JS, et al. Axial length and cone density as assessed with adaptive optics in myopia. Ind J Ophthalmol. 2015; 63: 423–426.\nStapley V, Anderson RS, Saunders KJ, Mulholland P. Altered spatial summation optimizes visual function in axial myopia. Sci Rep. 2020; 10: 12179.\nChang WC, Joe , Allaire JJ, Xie Y, McPherson J. Shiny: Web Application Framework for R. 2019.\nRCT. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2019.\nCurcio CA, Sloan KR, Meyers D. Computer methods for sampling, reconstruction, display and analysis of retinal whole mounts. Vis Res. 1989; 29: 529–540.\nStrasburger H, Rentschler I, Juttner M. Peripheral vision and pattern recognition: a review. J Vis. 2011; 11: 13.\nGarg A, Hood DC, Pensec N, Liebmann JM, Blumberg DM. Macular damage, as determined by structure-function staging, is associated with worse vision-related quality of life in early glaucoma. Am J Ophthalmol. 2018; 194: 88–94.\nHood DC, Tsamis E, Bommakanti NK, et al. Structure-function agreement is better than commonly thought in eyes with early glaucoma. Invest Ophthalmol Vis Sci. 2019; 60: 4241–4248.\nSato S, Hirooka K, Baba T, Tenkumo K, Nitta E, Shiraga F. Correlation between the ganglion cell-inner plexiform layer thickness measured with cirrus HD-OCT and macular visual field sensitivity measured with microperimetry. Invest Ophthalmol Vis Sci. 2013; 54: 3046–3051.\nOhkubo S, Higashide T, Udagawa S, et al. Focal relationship between structure and function within the central 10 degrees in glaucoma. Invest Ophthalmol Vis Sci. 2014; 55: 5269–5277.\nSample PA, Dannheim F, Artes PH, et al. Imaging and Perimetry Society standards and guidelines. Optom Vis Sci. 2011; 88: 4–7.\nAppendix A\nAs described in a separate article,33 the data were recorded by Curcio and Allen using spherical coordinates, reporting co-latitude (or retinal eccentricity) and longitude (or retinal meridian) in degrees. Eccentricity is calculated from the fovea, located at (0, 0). One degree of retinal eccentricity equals 2πr/360, where r is the radius of the assumed retinal sphere. From the header of the text file containing the tabulated data (https://research-materials.christineacurcio.com/), the assumed retinal sphere for the map is 11.459 mm. The map is built for a left eye, with the ONH at 20° eccentricity on the horizontal meridian (180° longitude). After conversion to mm, a continuous histology map was obtained through cubic interpolation. Figure A1 shows the correspondence between the interpolated values and the original average counts (with standard deviations) provided by Curcio and Allen (https://research-materials.christineacurcio.com/) for the four principal meridians. The map was converted into a right eye by inverting the horizontal coordinates.\nFigure A1.\n\nComparison of the cubic interpolation from the whole spherical map and the raw averages (red dots) and standard deviations (black vertical bars) reported by Curcio and Allen.16\nFigure A1.\n\nComparison of the cubic interpolation from the whole spherical map and the raw averages (red dots) and standard deviations (black vertical bars) reported by Curcio and Allen.16", null, "Appendix B\nThe data for the schematic eye are reported in Table A1. The ray tracing allows precise calculations for different ALs, which can be achieved by proportionally changing the radius and the center location of the retinal sphere (Fig. 1). The anterior part of the schematic eye is left unchanged, so that the nodal point remains the same for all ALs. The numerical estimate for the nodal point was obtained by averaging of 670 ray-tracings, with an angle of incidence between 0.1° and 67° with respect to the optic axis. The nodal point for each incident ray was derived numerically by minimizing the absolute difference between the angle of the incident and the refracted ray (after the posterior face of the lens) with respect to the optic axis. The resulting estimate was 6.93 mm, which is very close to the value of 6.95 mm reported by Drasdo and Fowler.21 The schematic eye was assumed to be radially symmetric around the optic axis. The same schematic eye was used to correct for ocular magnification in the SD-OCT macular volume scans. In their original article, Drasdo and Fowler did not clarify what point they used as a reference to calculate the visual angle. In accordance with the guidelines from the Imaging and Perimetry Society,39 we used the nodal point of the schematic eye.\nTable A1.\n\nData for the Schematic Eye Used in this Paper Along with the Original Values from Drasdo and Fowler21\nTable A1.\n\nData for the Schematic Eye Used in this Paper Along with the Original Values from Drasdo and Fowler21", null, "Appendix C\nThe value of k in formula 3 also depends on eccentricity according to\n\\begin{eqnarray}k\\left( e \\right) &=& {\\rm{\\ }}1 + \\big( 1.004 - 0.007209\\,{\\rm{*}}\\,e + 0.001694\\,{\\rm{*}}\\,{e^2} \\nonumber\\\\ &&- 0.00003765\\,{\\rm{*}}\\,{e^3} \\big)^{ - 2}\\end{eqnarray}\n(C.1)\nand accounts for the change in the relative percentage of the ON and OFF midget RGC-RF with eccentricity, as reported by Drasdo et al.15 The Dgcrf is converted into a density per mm2 with the conversion ratio derived from the schematic eye (Fig. 1), according to the axial length. The eccentricity in visual degrees is also converted into mm on the retina using the schematic eye. Then, an RGC-RF density profile from the fovea outward can be calculated and converted into cumulative counts for a circular sector centered at the fovea by\n\\begin{equation}{C_{gcrf}}\\left( r \\right) = \\mathop \\int \\limits_0^r \\left[ {2\\pi r\\,{\\rm{*}}\\,{D_{gcrf}}\\left( r \\right)} \\right]dr\\end{equation}\n(C.2)\nwhere r is the eccentricity from the fovea in mm and 2πr is a correction factor for the sector area increasing with eccentricity. The actual width of the sector considered acts only as a scaling factor and has no bearing on the results of the computation. When computed numerically, the integral is simply a cumulative summation for predefined steps in r. The same formula was used to compute the cumulative counts of RGC bodies (Cgcb). In this case, the Dgcrf is simply replaced by the density of RGC bodies (per mm2) obtained from the histology map (Dgcb) along the same meridian, after correction for the size of the retinal sphere. The displacement is finally computed as the difference between the eccentricities at which Cgcb and Cgcrf are equal (Fig. A2). For each meridian, the displacement is zero beyond the first crossing point between the two cumulative curves. Therefore the actual displacement might involve a smaller area than the DZ\nFigure A2.\n\nExample of how the displacement is computed along a specific meridian. (A) The black line indicates the meridian analyzed. The shaded area highlights the radial sector. The ticks indicate the distance in mm. The color map represents the RGC histology density map. (B) The displacement is calculated as the distance (black solid line) between the two eccentricities at which the cumulative counts of RGC-RF (blue solid line) and the RGC bodies (red solid line) are equal. The dashed vertical line indicates the eccentricity of the maximum displacement zone. The fitting process requires that the two cumulative counts are the same at this eccentricity.\nFigure A2.\n\nExample of how the displacement is computed along a specific meridian. (A) The black line indicates the meridian analyzed. The shaded area highlights the radial sector. The ticks indicate the distance in mm. The color map represents the RGC histology density map. (B) The displacement is calculated as the distance (black solid line) between the two eccentricities at which the cumulative counts of RGC-RF (blue solid line) and the RGC bodies (red solid line) are equal. The dashed vertical line indicates the eccentricity of the maximum displacement zone. The fitting process requires that the two cumulative counts are the same at this eccentricity.", null, "Figure 1.\n\nRendering of the schematic eye, with a projection of a 10-2 grid (red dots, top panel). The bottom panel shows a cross-section of the same schematic eye with additional examples of short and long axial lengths. Right panels show the distance travelled on the retina per visual degree (top) and the mm2/solid degree ratio at various retinal eccentricities (bottom). The latter represents the ratio between retinal areas in mm2 to visual degrees2. The curved relationship with eccentricity is a consequence of the nonlinear projection obtained by numerical calculations of ray tracing through the cornea, lens and vitreous, which varies with visual angle. It is important to acknowledge that the relationship between retinal mm and degrees of visual angle is also not linear. In black, the curves obtained from the original schematic eye described by Drasdo and Fowler21 (in black). In red, the results of the schematic eye used in this study.\nFigure 1.\n\nRendering of the schematic eye, with a projection of a 10-2 grid (red dots, top panel). The bottom panel shows a cross-section of the same schematic eye with additional examples of short and long axial lengths. Right panels show the distance travelled on the retina per visual degree (top) and the mm2/solid degree ratio at various retinal eccentricities (bottom). The latter represents the ratio between retinal areas in mm2 to visual degrees2. The curved relationship with eccentricity is a consequence of the nonlinear projection obtained by numerical calculations of ray tracing through the cornea, lens and vitreous, which varies with visual angle. It is important to acknowledge that the relationship between retinal mm and degrees of visual angle is also not linear. In black, the curves obtained from the original schematic eye described by Drasdo and Fowler21 (in black). In red, the results of the schematic eye used in this study.", null, "Figure 2.\n\nRepresentations of the two candidate methods to apply the displacement to perimetric stimuli. Method 1 is the one applied by Yoshioka et al.13. Method 2 is the one proposed in this article. The color map represents the histology density at AL0 for both graphs. The vertical axes are reported both in mm and visual degrees. The black shapes represent the areas tested by a 10-2 perimetric test, displaced with the two methods. In both images we are displaying the results of the application of the two methods on Goldmann IV stimuli, assumed circular and arranged in a regular 10-2 grid.\nFigure 2.\n\nRepresentations of the two candidate methods to apply the displacement to perimetric stimuli. Method 1 is the one applied by Yoshioka et al.13. Method 2 is the one proposed in this article. The color map represents the histology density at AL0 for both graphs. The vertical axes are reported both in mm and visual degrees. The black shapes represent the areas tested by a 10-2 perimetric test, displaced with the two methods. In both images we are displaying the results of the application of the two methods on Goldmann IV stimuli, assumed circular and arranged in a regular 10-2 grid.", null, "Figure 3.\n\nScaling of ocular structures with axial lengths. Top panels show two examples of the calculation for the descriptive ellipses (in red), as described in the Methods. The black points identify the peaks in the GCL profile used for the fitting. Lower panels show the measurements of the major and minor axis of the ellipses before (left) and after (right) correction for ocular magnification.\nFigure 3.\n\nScaling of ocular structures with axial lengths. Top panels show two examples of the calculation for the descriptive ellipses (in red), as described in the Methods. The black points identify the peaks in the GCL profile used for the fitting. Lower panels show the measurements of the major and minor axis of the ellipses before (left) and after (right) correction for ocular magnification.", null, "Figure 4.\n\n(A) Polar plot of the results of the fitting process for the parameter E2v. N, nasal; S, superior; T, temporal; I, inferior. (B) Displacement map calculated in degrees and mm at AL0.\nFigure 4.\n\n(A) Polar plot of the results of the fitting process for the parameter E2v. N, nasal; S, superior; T, temporal; I, inferior. (B) Displacement map calculated in degrees and mm at AL0.", null, "Figure 5.\n\nComparison of the results between the two displacement methods for perimetric stimuli. Method 1 is the one used by Yoshioka et al.13. Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3)) and do not represent real subject data. The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.\nFigure 5.\n\nComparison of the results between the two displacement methods for perimetric stimuli. Method 1 is the one used by Yoshioka et al.13. Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3)) and do not represent real subject data. The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.", null, "Figure 6.\n\nComparison of the results between the two displacement methods for perimetric stimuli for real structural data. Method 1 is the one used by Yoshioka et al.13 Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3), adjusted for AL). The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.\nFigure 6.\n\nComparison of the results between the two displacement methods for perimetric stimuli for real structural data. Method 1 is the one used by Yoshioka et al.13 Method 2 is the one proposed in this article. The horizontal axis reports the expected RGC-RF counts, calculated from the model proposed by Drasdo et al.,15 (Equation (3), adjusted for AL). The vertical axis reports the structural measurements from the RGC map both as counts (left axis) and in dB (right axis). The latter is meant for easier comparison with the results in Yoshioka et al.13. Only Method 2 yields correct estimates in the parafoveal region (higher counts). The dashed line represents the ideal line of equivalence.", null, "Figure 7.\n\nScreenshot of the second screen from the web App. It presents the results for the schematic eye at AL0, for a G-IV stimulus size and a 10-2 perimetric grid using the histological dataset by Curcio and Allen as a structural map. The Results table extends beyond what is visible on the screen and can be easily downloaded.\nFigure 7.\n\nScreenshot of the second screen from the web App. It presents the results for the schematic eye at AL0, for a G-IV stimulus size and a 10-2 perimetric grid using the histological dataset by Curcio and Allen as a structural map. The Results table extends beyond what is visible on the screen and can be easily downloaded.", null, "Figure A1.\n\nComparison of the cubic interpolation from the whole spherical map and the raw averages (red dots) and standard deviations (black vertical bars) reported by Curcio and Allen.16\nFigure A1.\n\nComparison of the cubic interpolation from the whole spherical map and the raw averages (red dots) and standard deviations (black vertical bars) reported by Curcio and Allen.16", null, "Figure A2.\n\nExample of how the displacement is computed along a specific meridian. (A) The black line indicates the meridian analyzed. The shaded area highlights the radial sector. The ticks indicate the distance in mm. The color map represents the RGC histology density map. (B) The displacement is calculated as the distance (black solid line) between the two eccentricities at which the cumulative counts of RGC-RF (blue solid line) and the RGC bodies (red solid line) are equal. The dashed vertical line indicates the eccentricity of the maximum displacement zone. The fitting process requires that the two cumulative counts are the same at this eccentricity.\nFigure A2.\n\nExample of how the displacement is computed along a specific meridian. (A) The black line indicates the meridian analyzed. The shaded area highlights the radial sector. The ticks indicate the distance in mm. The color map represents the RGC histology density map. (B) The displacement is calculated as the distance (black solid line) between the two eccentricities at which the cumulative counts of RGC-RF (blue solid line) and the RGC bodies (red solid line) are equal. The dashed vertical line indicates the eccentricity of the maximum displacement zone. The fitting process requires that the two cumulative counts are the same at this eccentricity.", null, "Table 1.\n\nDescriptive Statistics for Relevant Variables in the Two Datasets\nTable 1.\n\nDescriptive Statistics for Relevant Variables in the Two Datasets", null, "Table 2.\n\nDensity Data at Different Eccentricities of the 10-2 Grid, Derived From the Counts Reported in Figure 5 and Figure 6 for a G-IV Stimulus Size\nTable 2.\n\nDensity Data at Different Eccentricities of the 10-2 Grid, Derived From the Counts Reported in Figure 5 and Figure 6 for a G-IV Stimulus Size", null, "Table A1.\n\nData for the Schematic Eye Used in this Paper Along with the Original Values from Drasdo and Fowler21\nTable A1.\n\nData for the Schematic Eye Used in this Paper Along with the Original Values from Drasdo and Fowler21", null, "×\n\nThis PDF is available to Subscribers Only" ]
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http://git.videolan.org/?p=ffmpeg.git;a=blobdiff;f=libavcodec/dcadec.c;h=e988e944642af73cd744aee18471dff5b5c1409a;hp=e53b03e8f9dcd58bf51ac83b2827b55a7b8142d1;hb=009331303a6462d07cbe94aef9c446f1a1695519;hpb=6d97484d72e33f7dde9493a9ead1a72e2f029605;ds=sidebyside
[ "index e53b03e..e988e94 100644 (file)\n@@ -32,6 +32,7 @@\n#include \"libavutil/internal.h\"\n#include \"libavutil/mathematics.h\"\n#include \"libavutil/internal.h\"\n#include \"libavutil/mathematics.h\"\n+#include \"libavutil/opt.h\"\n#include \"libavutil/samplefmt.h\"\n#include \"avcodec.h\"\n#include \"fft.h\"\n#include \"libavutil/samplefmt.h\"\n#include \"avcodec.h\"\n#include \"fft.h\"\n@@ -40,7 +41,6 @@\n#include \"dcahuff.h\"\n#include \"dca.h\"\n#include \"dcahuff.h\"\n#include \"dca.h\"\n-#include \"dca_parser.h\"\n#include \"mathops.h\"\n#include \"synth_filter.h\"\n#include \"mathops.h\"\n#include \"synth_filter.h\"\n@@ -54,7 +54,6 @@\n//#define TRACE\n\n#define DCA_PRIM_CHANNELS_MAX  (7)\n//#define TRACE\n\n#define DCA_PRIM_CHANNELS_MAX  (7)\n-#define DCA_SUBBANDS          (32)\n#define DCA_ABITS_MAX         (32)      /* Should be 28 */\n#define DCA_SUBSUBFRAMES_MAX   (4)\n#define DCA_SUBFRAMES_MAX     (16)\n#define DCA_ABITS_MAX         (32)      /* Should be 28 */\n#define DCA_SUBSUBFRAMES_MAX   (4)\n#define DCA_SUBFRAMES_MAX     (16)\n@@ -263,6 +262,8 @@ static const int8_t dca_channel_reorder_nolfe_xch[] = {\n\n+#define DCA_NSYNCAUX        0x9A1105A0\n+\n/** Bit allocation */\ntypedef struct {\nint offset;                 ///< code values offset\n/** Bit allocation */\ntypedef struct {\nint offset;                 ///< code values offset\n@@ -284,6 +285,7 @@ static av_always_inline int get_bitalloc(GetBitContext *gb, BitAlloc *ba,\n}\n\ntypedef struct {\n}\n\ntypedef struct {\n+    AVClass *class;             ///< class for AVOptions\nAVCodecContext *avctx;\n/* Frame header */\nint frame_type;             ///< type of the current frame\nAVCodecContext *avctx;\n/* Frame header */\nint frame_type;             ///< type of the current frame\n@@ -296,7 +298,6 @@ typedef struct {\nint bit_rate;               ///< transmission bit rate\nint bit_rate_index;         ///< transmission bit rate index\n\nint bit_rate;               ///< transmission bit rate\nint bit_rate_index;         ///< transmission bit rate index\n\n-    int downmix;                ///< embedded downmix enabled\nint dynrange;               ///< embedded dynamic range flag\nint timestamp;              ///< embedded time stamp flag\nint aux_data;               ///< auxiliary data flag\nint dynrange;               ///< embedded dynamic range flag\nint timestamp;              ///< embedded time stamp flag\nint aux_data;               ///< auxiliary data flag\n@@ -335,13 +336,20 @@ typedef struct {\nint prediction_vq[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];      ///< prediction VQ coefs\nint bitalloc[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];           ///< bit allocation index\nint transition_mode[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];    ///< transition mode (transients)\nint prediction_vq[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];      ///< prediction VQ coefs\nint bitalloc[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];           ///< bit allocation index\nint transition_mode[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];    ///< transition mode (transients)\n-    int scale_factor[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];    ///< scale factors (2 if transient)\n+    int32_t scale_factor[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];///< scale factors (2 if transient)\nint joint_huff[DCA_PRIM_CHANNELS_MAX];                       ///< joint subband scale factors codebook\nint joint_scale_factor[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS]; ///< joint subband scale factors\nint joint_huff[DCA_PRIM_CHANNELS_MAX];                       ///< joint subband scale factors codebook\nint joint_scale_factor[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS]; ///< joint subband scale factors\n-    int downmix_coef[DCA_PRIM_CHANNELS_MAX];                  ///< stereo downmix coefficients\n+    float downmix_coef[DCA_PRIM_CHANNELS_MAX + 1];            ///< stereo downmix coefficients\nint dynrange_coef;                                           ///< dynamic range coefficient\n\nint dynrange_coef;                                           ///< dynamic range coefficient\n\n-    int high_freq_vq[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];       ///< VQ encoded high frequency subbands\n+    /* Core substream's embedded downmix coefficients (cf. ETSI TS 102 114 V1.4.1)\n+     * Input:  primary audio channels (incl. LFE if present)\n+     * Output: downmix audio channels (up to 4, no LFE) */\n+    uint8_t  core_downmix;                                       ///< embedded downmix coefficients available\n+    uint8_t  core_downmix_amode;                                 ///< audio channel arrangement of embedded downmix\n+    uint16_t core_downmix_codes[DCA_PRIM_CHANNELS_MAX + 1];   ///< embedded downmix coefficients (9-bit codes)\n+\n+    int32_t  high_freq_vq[DCA_PRIM_CHANNELS_MAX][DCA_SUBBANDS];  ///< VQ encoded high frequency subbands\n\nfloat lfe_data[2 * DCA_LFE_MAX * (DCA_BLOCKS_MAX + 4)];      ///< Low frequency effect data\nint lfe_scale_factor;\n\nfloat lfe_data[2 * DCA_LFE_MAX * (DCA_BLOCKS_MAX + 4)];      ///< Low frequency effect data\nint lfe_scale_factor;\n@@ -375,6 +383,7 @@ typedef struct {\n/* XCh extension information */\nint xch_present;            ///< XCh extension present and valid\nint xch_base_channel;       ///< index of first (only) channel containing XCH data\n/* XCh extension information */\nint xch_present;            ///< XCh extension present and valid\nint xch_base_channel;       ///< index of first (only) channel containing XCH data\n+    int xch_disable;            ///< whether the XCh extension should be decoded or not\n\n/* ExSS header parser */\nint static_fields;          ///< static fields present\n\n/* ExSS header parser */\nint static_fields;          ///< static fields present\n@@ -570,7 +579,7 @@ static int dca_parse_frame_header(DCAContext *s)\nif (!s->bit_rate)\nreturn AVERROR_INVALIDDATA;\n\nif (!s->bit_rate)\nreturn AVERROR_INVALIDDATA;\n\n-    s->downmix           = get_bits(&s->gb, 1);\n+    skip_bits1(&s->gb); // always 0 (reserved, cf. ETSI TS 102 114 V1.4.1)\ns->dynrange          = get_bits(&s->gb, 1);\ns->timestamp         = get_bits(&s->gb, 1);\ns->aux_data          = get_bits(&s->gb, 1);\ns->dynrange          = get_bits(&s->gb, 1);\ns->timestamp         = get_bits(&s->gb, 1);\ns->aux_data          = get_bits(&s->gb, 1);\n@@ -581,6 +590,11 @@ static int dca_parse_frame_header(DCAContext *s)\ns->lfe               = get_bits(&s->gb, 2);\ns->predictor_history = get_bits(&s->gb, 1);\n\ns->lfe               = get_bits(&s->gb, 2);\ns->predictor_history = get_bits(&s->gb, 1);\n\n+    if (s->lfe > 2) {\n+        av_log(s->avctx, AV_LOG_ERROR, \"Invalid LFE value: %d\\n\", s->lfe);\n+        return AVERROR_INVALIDDATA;\n+    }\n+\n/* TODO: check CRC */\nif (s->crc_present)\ns->header_crc    = get_bits(&s->gb, 16);\n/* TODO: check CRC */\nif (s->crc_present)\ns->header_crc    = get_bits(&s->gb, 16);\n@@ -611,7 +625,6 @@ static int dca_parse_frame_header(DCAContext *s)\ns->sample_rate);\nav_log(s->avctx, AV_LOG_DEBUG, \"bit rate: %i bits/s\\n\",\ns->bit_rate);\ns->sample_rate);\nav_log(s->avctx, AV_LOG_DEBUG, \"bit rate: %i bits/s\\n\",\ns->bit_rate);\n-    av_log(s->avctx, AV_LOG_DEBUG, \"downmix: %i\\n\", s->downmix);\nav_log(s->avctx, AV_LOG_DEBUG, \"dynrange: %i\\n\", s->dynrange);\nav_log(s->avctx, AV_LOG_DEBUG, \"timestamp: %i\\n\", s->timestamp);\nav_log(s->avctx, AV_LOG_DEBUG, \"aux_data: %i\\n\", s->aux_data);\nav_log(s->avctx, AV_LOG_DEBUG, \"dynrange: %i\\n\", s->dynrange);\nav_log(s->avctx, AV_LOG_DEBUG, \"timestamp: %i\\n\", s->timestamp);\nav_log(s->avctx, AV_LOG_DEBUG, \"aux_data: %i\\n\", s->aux_data);\n@@ -794,27 +807,6 @@ static int dca_subframe_header(DCAContext *s, int base_channel, int block_index)\n}\n}\n\n}\n}\n\n-    /* Stereo downmix coefficients */\n-    if (!base_channel && s->prim_channels > 2) {\n-        if (s->downmix) {\n-            for (j = base_channel; j < s->prim_channels; j++) {\n-                s->downmix_coef[j] = get_bits(&s->gb, 7);\n-                s->downmix_coef[j] = get_bits(&s->gb, 7);\n-            }\n-        } else {\n-            int am = s->amode & DCA_CHANNEL_MASK;\n-            if (am >= FF_ARRAY_ELEMS(dca_default_coeffs)) {\n-                av_log(s->avctx, AV_LOG_ERROR,\n-                       \"Invalid channel mode %d\\n\", am);\n-                return AVERROR_INVALIDDATA;\n-            }\n-            for (j = base_channel; j < s->prim_channels; j++) {\n-                s->downmix_coef[j] = dca_default_coeffs[am][j];\n-                s->downmix_coef[j] = dca_default_coeffs[am][j];\n-            }\n-        }\n-    }\n-\n/* Dynamic range coefficient */\nif (!base_channel && s->dynrange)\ns->dynrange_coef = get_bits(&s->gb, 8);\n/* Dynamic range coefficient */\nif (!base_channel && s->dynrange)\ns->dynrange_coef = get_bits(&s->gb, 8);\n@@ -909,16 +901,6 @@ static int dca_subframe_header(DCAContext *s, int base_channel, int block_index)\nav_log(s->avctx, AV_LOG_DEBUG, \"\\n\");\n}\n}\nav_log(s->avctx, AV_LOG_DEBUG, \"\\n\");\n}\n}\n-    if (!base_channel && s->prim_channels > 2 && s->downmix) {\n-        av_log(s->avctx, AV_LOG_DEBUG, \"Downmix coeffs:\\n\");\n-        for (j = 0; j < s->prim_channels; j++) {\n-            av_log(s->avctx, AV_LOG_DEBUG, \"Channel 0, %d = %f\\n\", j,\n-                   dca_downmix_coeffs[s->downmix_coef[j]]);\n-            av_log(s->avctx, AV_LOG_DEBUG, \"Channel 1, %d = %f\\n\", j,\n-                   dca_downmix_coeffs[s->downmix_coef[j]]);\n-        }\n-        av_log(s->avctx, AV_LOG_DEBUG, \"\\n\");\n-    }\nfor (j = base_channel; j < s->prim_channels; j++)\nfor (k = s->vq_start_subband[j]; k < s->subband_activity[j]; k++)\nav_log(s->avctx, AV_LOG_DEBUG, \"VQ index: %i\\n\", s->high_freq_vq[j][k]);\nfor (j = base_channel; j < s->prim_channels; j++)\nfor (k = s->vq_start_subband[j]; k < s->subband_activity[j]; k++)\nav_log(s->avctx, AV_LOG_DEBUG, \"VQ index: %i\\n\", s->high_freq_vq[j][k]);\n@@ -941,10 +923,8 @@ static void qmf_32_subbands(DCAContext *s, int chans,\nfloat scale)\n{\nconst float *prCoeff;\nfloat scale)\n{\nconst float *prCoeff;\n-    int i;\n\nint sb_act = s->subband_activity[chans];\n\nint sb_act = s->subband_activity[chans];\n-    int subindex;\n\nscale *= sqrt(1 / 8.0);\n\nscale *= sqrt(1 / 8.0);\n\n@@ -954,30 +934,16 @@ static void qmf_32_subbands(DCAContext *s, int chans,\nelse                        /* Perfect reconstruction */\nprCoeff = fir_32bands_perfect;\n\nelse                        /* Perfect reconstruction */\nprCoeff = fir_32bands_perfect;\n\n-    for (i = sb_act; i < 32; i++)\n-        s->raXin[i] = 0.0;\n-\n-    /* Reconstructed channel sample index */\n-    for (subindex = 0; subindex < 8; subindex++) {\n-        /* Load in one sample from each subband and clear inactive subbands */\n-        for (i = 0; i < sb_act; i++) {\n-            unsigned sign = (i - 1) & 2;\n-            uint32_t v    = AV_RN32A(&samples_in[i][subindex]) ^ sign << 30;\n-            AV_WN32A(&s->raXin[i], v);\n-        }\n-\n-        s->synth.synth_filter_float(&s->imdct,\n-                                    s->subband_fir_hist[chans],\n-                                    &s->hist_index[chans],\n-                                    s->subband_fir_noidea[chans], prCoeff,\n-                                    samples_out, s->raXin, scale);\n-        samples_out += 32;\n-    }\n+    s->dcadsp.qmf_32_subbands(samples_in, sb_act, &s->synth, &s->imdct,\n+                              s->subband_fir_hist[chans],\n+                              &s->hist_index[chans],\n+                              s->subband_fir_noidea[chans], prCoeff,\n+                              samples_out, s->raXin, scale);\n}\n\nstatic void lfe_interpolation_fir(DCAContext *s, int decimation_select,\nint num_deci_sample, float *samples_in,\n}\n\nstatic void lfe_interpolation_fir(DCAContext *s, int decimation_select,\nint num_deci_sample, float *samples_in,\n-                                  float *samples_out, float scale)\n+                                  float *samples_out)\n{\n/* samples_in: An array holding decimated samples.\n*   Samples in current subframe starts from samples_in,\n{\n/* samples_in: An array holding decimated samples.\n*   Samples in current subframe starts from samples_in,\n@@ -987,23 +953,23 @@ static void lfe_interpolation_fir(DCAContext *s, int decimation_select,\n* samples_out: An array holding interpolated samples\n*/\n\n* samples_out: An array holding interpolated samples\n*/\n\n-    int decifactor;\n+    int idx;\nconst float *prCoeff;\nint deciindex;\n\n/* Select decimation filter */\nif (decimation_select == 1) {\nconst float *prCoeff;\nint deciindex;\n\n/* Select decimation filter */\nif (decimation_select == 1) {\n-        decifactor = 64;\n+        idx = 1;\nprCoeff = lfe_fir_128;\n} else {\nprCoeff = lfe_fir_128;\n} else {\n-        decifactor = 32;\n+        idx = 0;\nprCoeff = lfe_fir_64;\n}\n/* Interpolation */\nfor (deciindex = 0; deciindex < num_deci_sample; deciindex++) {\nprCoeff = lfe_fir_64;\n}\n/* Interpolation */\nfor (deciindex = 0; deciindex < num_deci_sample; deciindex++) {\n-        s->dcadsp.lfe_fir(samples_out, samples_in, prCoeff, decifactor, scale);\n+        s->dcadsp.lfe_fir[idx](samples_out, samples_in, prCoeff);\nsamples_in++;\nsamples_in++;\n-        samples_out += 2 * decifactor;\n+        samples_out += 2 * 32 * (1 + idx);\n}\n}\n\n}\n}\n\n@@ -1029,29 +995,23 @@ static void lfe_interpolation_fir(DCAContext *s, int decimation_select,\nop2                                     \\\n}\n\nop2                                     \\\n}\n\n-static void dca_downmix(float **samples, int srcfmt,\n-                        int downmix_coef[DCA_PRIM_CHANNELS_MAX],\n+static void dca_downmix(float **samples, int srcfmt, int lfe_present,\n+                        float coef[DCA_PRIM_CHANNELS_MAX + 1],\nconst int8_t *channel_mapping)\n{\nint c, l, r, sl, sr, s;\nint i;\nfloat t, u, v;\nconst int8_t *channel_mapping)\n{\nint c, l, r, sl, sr, s;\nint i;\nfloat t, u, v;\n-    float coef[DCA_PRIM_CHANNELS_MAX];\n-\n-    for (i = 0; i < DCA_PRIM_CHANNELS_MAX; i++) {\n-        coef[i] = dca_downmix_coeffs[downmix_coef[i]];\n-        coef[i] = dca_downmix_coeffs[downmix_coef[i]];\n-    }\n\nswitch (srcfmt) {\ncase DCA_MONO:\n\nswitch (srcfmt) {\ncase DCA_MONO:\n-    case DCA_CHANNEL:\n-    case DCA_STEREO_TOTAL:\n-    case DCA_STEREO_SUMDIFF:\ncase DCA_4F2R:\nav_log(NULL, 0, \"Not implemented!\\n\");\nbreak;\ncase DCA_4F2R:\nav_log(NULL, 0, \"Not implemented!\\n\");\nbreak;\n+    case DCA_CHANNEL:\ncase DCA_STEREO:\ncase DCA_STEREO:\n+    case DCA_STEREO_TOTAL:\n+    case DCA_STEREO_SUMDIFF:\nbreak;\ncase DCA_3F:\nc = channel_mapping;\nbreak;\ncase DCA_3F:\nc = channel_mapping;\n@@ -1086,13 +1046,21 @@ static void dca_downmix(float **samples, int srcfmt,\nMIX_REAR2(samples, sl, sr, 3, coef));\nbreak;\n}\nMIX_REAR2(samples, sl, sr, 3, coef));\nbreak;\n}\n+    if (lfe_present) {\n+        int lf_buf = dca_lfe_index[srcfmt];\n+        int lf_idx = dca_channels [srcfmt];\n+        for (i = 0; i < 256; i++) {\n+            samples[i] += samples[lf_buf][i] * coef[lf_idx];\n+            samples[i] += samples[lf_buf][i] * coef[lf_idx];\n+        }\n+    }\n}\n\n#ifndef decode_blockcodes\n/* Very compact version of the block code decoder that does not use table\n* look-up but is slightly slower */\n}\n\n#ifndef decode_blockcodes\n/* Very compact version of the block code decoder that does not use table\n* look-up but is slightly slower */\n-static int decode_blockcode(int code, int levels, int *values)\n+static int decode_blockcode(int code, int levels, int32_t *values)\n{\nint i;\nint offset = (levels - 1) >> 1;\n{\nint i;\nint offset = (levels - 1) >> 1;\n@@ -1106,7 +1074,7 @@ static int decode_blockcode(int code, int levels, int *values)\nreturn code;\n}\n\nreturn code;\n}\n\n-static int decode_blockcodes(int code1, int code2, int levels, int *values)\n+static int decode_blockcodes(int code1, int code2, int levels, int32_t *values)\n{\nreturn decode_blockcode(code1, levels, values) |\ndecode_blockcode(code2, levels, values + 4);\n{\nreturn decode_blockcode(code1, levels, values) |\ndecode_blockcode(code2, levels, values + 4);\n@@ -1116,16 +1084,6 @@ static int decode_blockcodes(int code1, int code2, int levels, int *values)\nstatic const uint8_t abits_sizes  = { 7, 10, 12, 13, 15, 17, 19 };\nstatic const uint8_t abits_levels = { 3,  5,  7,  9, 13, 17, 25 };\n\nstatic const uint8_t abits_sizes  = { 7, 10, 12, 13, 15, 17, 19 };\nstatic const uint8_t abits_levels = { 3,  5,  7,  9, 13, 17, 25 };\n\n-#ifndef int8x8_fmul_int32\n-static inline void int8x8_fmul_int32(float *dst, const int8_t *src, int scale)\n-{\n-    float fscale = scale / 16.0;\n-    int i;\n-    for (i = 0; i < 8; i++)\n-        dst[i] = src[i] * fscale;\n-}\n-#endif\n-\nstatic int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\n{\nint k, l;\nstatic int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\n{\nint k, l;\n@@ -1135,7 +1093,7 @@ static int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\n\n/* FIXME */\nfloat (*subband_samples)[DCA_SUBBANDS] = s->subband_samples[block_index];\n\n/* FIXME */\nfloat (*subband_samples)[DCA_SUBBANDS] = s->subband_samples[block_index];\n-    LOCAL_ALIGNED_16(int, block, );\n+    LOCAL_ALIGNED_16(int32_t, block, [8 * DCA_SUBBANDS]);\n\n/*\n* Audio data\n\n/*\n* Audio data\n@@ -1148,6 +1106,8 @@ static int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\nquant_step_table = lossy_quant_d;\n\nfor (k = base_channel; k < s->prim_channels; k++) {\nquant_step_table = lossy_quant_d;\n\nfor (k = base_channel; k < s->prim_channels; k++) {\n+        float rscale[DCA_SUBBANDS];\n+\nif (get_bits_left(&s->gb) < 0)\nreturn AVERROR_INVALIDDATA;\n\nif (get_bits_left(&s->gb) < 0)\nreturn AVERROR_INVALIDDATA;\n\n@@ -1170,11 +1130,12 @@ static int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\n* Extract bits from the bit stream\n*/\nif (!abits) {\n* Extract bits from the bit stream\n*/\nif (!abits) {\n-                memset(subband_samples[k][l], 0, 8 * sizeof(subband_samples));\n+                rscale[l] = 0;\n+                memset(block + 8 * l, 0, 8 * sizeof(block));\n} else {\n/* Deal with transients */\nint sfi = s->transition_mode[k][l] && subsubframe >= s->transition_mode[k][l];\n} else {\n/* Deal with transients */\nint sfi = s->transition_mode[k][l] && subsubframe >= s->transition_mode[k][l];\n-                float rscale = quant_step_size * s->scale_factor[k][l][sfi] *\n+                rscale[l] = quant_step_size * s->scale_factor[k][l][sfi] *\n\nif (abits >= 11 || !dca_smpl_bitalloc[abits].vlc[sel].table) {\n\nif (abits >= 11 || !dca_smpl_bitalloc[abits].vlc[sel].table) {\n@@ -1188,7 +1149,7 @@ static int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\nblock_code1 = get_bits(&s->gb, size);\nblock_code2 = get_bits(&s->gb, size);\nerr = decode_blockcodes(block_code1, block_code2,\nblock_code1 = get_bits(&s->gb, size);\nblock_code2 = get_bits(&s->gb, size);\nerr = decode_blockcodes(block_code1, block_code2,\n-                                                levels, block);\n+                                                levels, block + 8 * l);\nif (err) {\nav_log(s->avctx, AV_LOG_ERROR,\n\"ERROR: block code look-up failed\\n\");\nif (err) {\nav_log(s->avctx, AV_LOG_ERROR,\n\"ERROR: block code look-up failed\\n\");\n@@ -1197,34 +1158,49 @@ static int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\n} else {\n/* no coding */\nfor (m = 0; m < 8; m++)\n} else {\n/* no coding */\nfor (m = 0; m < 8; m++)\n-                            block[m] = get_sbits(&s->gb, abits - 3);\n+                            block[8 * l + m] = get_sbits(&s->gb, abits - 3);\n}\n} else {\n/* Huffman coded */\nfor (m = 0; m < 8; m++)\n}\n} else {\n/* Huffman coded */\nfor (m = 0; m < 8; m++)\n-                        block[m] = get_bitalloc(&s->gb,\n+                        block[8 * l + m] = get_bitalloc(&s->gb,\n&dca_smpl_bitalloc[abits], sel);\n}\n\n&dca_smpl_bitalloc[abits], sel);\n}\n\n-                s->fmt_conv.int32_to_float_fmul_scalar(subband_samples[k][l],\n-                                                       block, rscale, 8);\n}\n}\n+        }\n+\n+        s->fmt_conv.int32_to_float_fmul_array8(&s->fmt_conv, subband_samples[k],\n+                                               block, rscale, 8 * s->vq_start_subband[k]);\n\n+        for (l = 0; l < s->vq_start_subband[k]; l++) {\n+            int m;\n/*\n* Inverse ADPCM if in prediction mode\n*/\nif (s->prediction_mode[k][l]) {\nint n;\n/*\n* Inverse ADPCM if in prediction mode\n*/\nif (s->prediction_mode[k][l]) {\nint n;\n-                for (m = 0; m < 8; m++) {\n-                    for (n = 1; n <= 4; n++)\n+                if (s->predictor_history)\n+                    subband_samples[k][l] += (adpcm_vb[s->prediction_vq[k][l]] *\n+                                                 s->subband_samples_hist[k][l] +\n+                                                 s->subband_samples_hist[k][l] +\n+                                                 s->subband_samples_hist[k][l] +\n+                                                 s->subband_samples_hist[k][l]) *\n+                                                (1.0f / 8192);\n+                for (m = 1; m < 8; m++) {\n+                    float sum = adpcm_vb[s->prediction_vq[k][l]] *\n+                                subband_samples[k][l][m - 1];\n+                    for (n = 2; n <= 4; n++)\nif (m >= n)\nif (m >= n)\n-                            subband_samples[k][l][m] +=\n-                                (adpcm_vb[s->prediction_vq[k][l]][n - 1] *\n-                                 subband_samples[k][l][m - n] / 8192);\n+                            sum += adpcm_vb[s->prediction_vq[k][l]][n - 1] *\n+                                   subband_samples[k][l][m - n];\nelse if (s->predictor_history)\nelse if (s->predictor_history)\n-                            subband_samples[k][l][m] +=\n-                                (adpcm_vb[s->prediction_vq[k][l]][n - 1] *\n-                                 s->subband_samples_hist[k][l][m - n + 4] / 8192);\n+                            sum += adpcm_vb[s->prediction_vq[k][l]][n - 1] *\n+                                   s->subband_samples_hist[k][l][m - n + 4];\n+                    subband_samples[k][l][m] += sum * 1.0f / 8192;\n}\n}\n}\n}\n}\n}\n@@ -1232,20 +1208,16 @@ static int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\n/*\n* Decode VQ encoded high frequencies\n*/\n/*\n* Decode VQ encoded high frequencies\n*/\n-        for (l = s->vq_start_subband[k]; l < s->subband_activity[k]; l++) {\n-            /* 1 vector -> 32 samples but we only need the 8 samples\n-             * for this subsubframe. */\n-            int hfvq = s->high_freq_vq[k][l];\n-\n+        if (s->subband_activity[k] > s->vq_start_subband[k]) {\nif (!s->debug_flag & 0x01) {\nav_log(s->avctx, AV_LOG_DEBUG,\n\"Stream with high frequencies VQ coding\\n\");\ns->debug_flag |= 0x01;\n}\nif (!s->debug_flag & 0x01) {\nav_log(s->avctx, AV_LOG_DEBUG,\n\"Stream with high frequencies VQ coding\\n\");\ns->debug_flag |= 0x01;\n}\n-\n-            int8x8_fmul_int32(subband_samples[k][l],\n-                              &high_freq_vq[hfvq][subsubframe * 8],\n-                              s->scale_factor[k][l]);\n+                                high_freq_vq, subsubframe * 8,\n+                                s->scale_factor[k], s->vq_start_subband[k],\n+                                s->subband_activity[k]);\n}\n}\n\n}\n}\n\n@@ -1257,15 +1229,14 @@ static int dca_subsubframe(DCAContext *s, int base_channel, int block_index)\n#endif\n} else {\nav_log(s->avctx, AV_LOG_ERROR, \"Didn't get subframe DSYNC\\n\");\n#endif\n} else {\nav_log(s->avctx, AV_LOG_ERROR, \"Didn't get subframe DSYNC\\n\");\n+            return AVERROR_INVALIDDATA;\n}\n}\n\n/* Backup predictor history for adpcm */\nfor (k = base_channel; k < s->prim_channels; k++)\nfor (l = 0; l < s->vq_start_subband[k]; l++)\n}\n}\n\n/* Backup predictor history for adpcm */\nfor (k = base_channel; k < s->prim_channels; k++)\nfor (l = 0; l < s->vq_start_subband[k]; l++)\n-            memcpy(s->subband_samples_hist[k][l],\n-                   &subband_samples[k][l],\n-                   4 * sizeof(subband_samples));\n+            AV_COPY128(s->subband_samples_hist[k][l], &subband_samples[k][l]);\n\nreturn 0;\n}\n\nreturn 0;\n}\n@@ -1285,27 +1256,29 @@ static int dca_filter_channels(DCAContext *s, int block_index)\nM_SQRT1_2 / 32768.0 /* pcm_to_double[s->source_pcm_res] */);\n}\n\nM_SQRT1_2 / 32768.0 /* pcm_to_double[s->source_pcm_res] */);\n}\n\n-    /* Down mixing */\n-    if (s->avctx->request_channels == 2 && s->prim_channels > 2) {\n-        dca_downmix(s->samples_chanptr, s->amode, s->downmix_coef, s->channel_order_tab);\n-    }\n-\n/* Generate LFE samples for this subsubframe FIXME!!! */\n/* Generate LFE samples for this subsubframe FIXME!!! */\n-    if (s->output & DCA_LFE) {\n+    if (s->lfe) {\nlfe_interpolation_fir(s, s->lfe, 2 * s->lfe,\ns->lfe_data + 2 * s->lfe * (block_index + 4),\nlfe_interpolation_fir(s, s->lfe, 2 * s->lfe,\ns->lfe_data + 2 * s->lfe * (block_index + 4),\n-                              s->samples_chanptr[dca_lfe_index[s->amode]],\n-                              1.0 / (256.0 * 32768.0));\n+                              s->samples_chanptr[dca_lfe_index[s->amode]]);\n/* Outputs 20bits pcm samples */\n}\n\n/* Outputs 20bits pcm samples */\n}\n\n+    /* Downmixing to Stereo */\n+    if (s->prim_channels + !!s->lfe > 2 &&\n+        s->avctx->request_channel_layout == AV_CH_LAYOUT_STEREO) {\n+        dca_downmix(s->samples_chanptr, s->amode, !!s->lfe, s->downmix_coef,\n+                    s->channel_order_tab);\n+    }\n+\nreturn 0;\n}\n\nstatic int dca_subframe_footer(DCAContext *s, int base_channel)\n{\nreturn 0;\n}\n\nstatic int dca_subframe_footer(DCAContext *s, int base_channel)\n{\n-    int aux_data_count = 0, i;\n+    int in, out, aux_data_count, aux_data_end, reserved;\n+    uint32_t nsyncaux;\n\n/*\n* Unpack optional information\n\n/*\n* Unpack optional information\n@@ -1316,13 +1289,89 @@ static int dca_subframe_footer(DCAContext *s, int base_channel)\nif (s->timestamp)\nskip_bits_long(&s->gb, 32);\n\nif (s->timestamp)\nskip_bits_long(&s->gb, 32);\n\n-        if (s->aux_data)\n+        if (s->aux_data) {\naux_data_count = get_bits(&s->gb, 6);\n\naux_data_count = get_bits(&s->gb, 6);\n\n-        for (i = 0; i < aux_data_count; i++)\n-            get_bits(&s->gb, 8);\n+            // align (32-bit)\n+            skip_bits_long(&s->gb, (-get_bits_count(&s->gb)) & 31);\n+\n+            aux_data_end = 8 * aux_data_count + get_bits_count(&s->gb);\n+\n+            if ((nsyncaux = get_bits_long(&s->gb, 32)) != DCA_NSYNCAUX) {\n+                av_log(s->avctx, AV_LOG_ERROR, \"nSYNCAUX mismatch %#\"PRIx32\"\\n\",\n+                       nsyncaux);\n+                return AVERROR_INVALIDDATA;\n+            }\n+\n+            if (get_bits1(&s->gb)) { // bAUXTimeStampFlag\n+                avpriv_request_sample(s->avctx,\n+                                      \"Auxiliary Decode Time Stamp Flag\");\n+                // align (4-bit)\n+                skip_bits(&s->gb, (-get_bits_count(&s->gb)) & 4);\n+                // 44 bits: nMSByte (8), nMarker (4), nLSByte (28), nMarker (4)\n+                skip_bits_long(&s->gb, 44);\n+            }\n\n-        if (s->crc_present && (s->downmix || s->dynrange))\n+            if ((s->core_downmix = get_bits1(&s->gb))) {\n+                int am = get_bits(&s->gb, 3);\n+                switch (am) {\n+                case 0:\n+                    s->core_downmix_amode = DCA_MONO;\n+                    break;\n+                case 1:\n+                    s->core_downmix_amode = DCA_STEREO;\n+                    break;\n+                case 2:\n+                    s->core_downmix_amode = DCA_STEREO_TOTAL;\n+                    break;\n+                case 3:\n+                    s->core_downmix_amode = DCA_3F;\n+                    break;\n+                case 4:\n+                    s->core_downmix_amode = DCA_2F1R;\n+                    break;\n+                case 5:\n+                    s->core_downmix_amode = DCA_2F2R;\n+                    break;\n+                case 6:\n+                    s->core_downmix_amode = DCA_3F1R;\n+                    break;\n+                default:\n+                    av_log(s->avctx, AV_LOG_ERROR,\n+                           \"Invalid mode %d for embedded downmix coefficients\\n\",\n+                           am);\n+                    return AVERROR_INVALIDDATA;\n+                }\n+                for (out = 0; out < dca_channels[s->core_downmix_amode]; out++) {\n+                    for (in = 0; in < s->prim_channels + !!s->lfe; in++) {\n+                        uint16_t tmp = get_bits(&s->gb, 9);\n+                        if ((tmp & 0xFF) > 241) {\n+                            av_log(s->avctx, AV_LOG_ERROR,\n+                                   \"Invalid downmix coefficient code %\"PRIu16\"\\n\",\n+                                   tmp);\n+                            return AVERROR_INVALIDDATA;\n+                        }\n+                        s->core_downmix_codes[in][out] = tmp;\n+                    }\n+                }\n+            }\n+\n+            align_get_bits(&s->gb); // byte align\n+            skip_bits(&s->gb, 16);  // nAUXCRC16\n+\n+            // additional data (reserved, cf. ETSI TS 102 114 V1.4.1)\n+            if ((reserved = (aux_data_end - get_bits_count(&s->gb))) < 0) {\n+                 av_log(s->avctx, AV_LOG_ERROR,\n+                        \"Overread auxiliary data by %d bits\\n\", -reserved);\n+                return AVERROR_INVALIDDATA;\n+            } else if (reserved) {\n+                avpriv_request_sample(s->avctx,\n+                                      \"Core auxiliary data reserved content\");\n+                skip_bits_long(&s->gb, reserved);\n+            }\n+        }\n+\n+        if (s->crc_present && s->dynrange)\nget_bits(&s->gb, 16);\n}\n\nget_bits(&s->gb, 16);\n}\n\n@@ -1646,6 +1695,13 @@ static void dca_exss_parse_header(DCAContext *s)\n* from the asset header */\n}\n\n* from the asset header */\n}\n\n+static float dca_dmix_code(unsigned code)\n+{\n+    int sign = (code >> 8) - 1;\n+    code &= 0xff;\n+    return ((dca_dmixtable[code] ^ sign) - sign) * (1.0 / (1U << 15));\n+}\n+\n/**\n* Main frame decoding function\n* FIXME add arguments\n/**\n* Main frame decoding function\n* FIXME add arguments\n@@ -1675,7 +1731,6 @@ static int dca_decode_frame(AVCodecContext *avctx, void *data,\nreturn AVERROR_INVALIDDATA;\n}\n\nreturn AVERROR_INVALIDDATA;\n}\n\n-    init_get_bits(&s->gb, s->dca_buffer, s->dca_buffer_size * 8);\nif ((ret = dca_parse_frame_header(s)) < 0) {\n//seems like the frame is corrupt, try with the next one\nreturn ret;\nif ((ret = dca_parse_frame_header(s)) < 0) {\n//seems like the frame is corrupt, try with the next one\nreturn ret;\n@@ -1801,8 +1856,25 @@ static int dca_decode_frame(AVCodecContext *avctx, void *data,\nif (s->amode < 16) {\navctx->channel_layout = dca_core_channel_layout[s->amode];\n\nif (s->amode < 16) {\navctx->channel_layout = dca_core_channel_layout[s->amode];\n\n-        if (s->xch_present && (!avctx->request_channels ||\n-                               avctx->request_channels > num_core_channels + !!s->lfe)) {\n+        if (s->prim_channels + !!s->lfe > 2 &&\n+            avctx->request_channel_layout == AV_CH_LAYOUT_STEREO) {\n+            /*\n+             * Neither the core's auxiliary data nor our default tables contain\n+             * downmix coefficients for the additional channel coded in the XCh\n+             * extension, so when we're doing a Stereo downmix, don't decode it.\n+             */\n+            s->xch_disable = 1;\n+        }\n+\n+#if FF_API_REQUEST_CHANNELS\n+FF_DISABLE_DEPRECATION_WARNINGS\n+        if (s->xch_present && !s->xch_disable &&\n+            (!avctx->request_channels ||\n+             avctx->request_channels > num_core_channels + !!s->lfe)) {\n+FF_ENABLE_DEPRECATION_WARNINGS\n+#else\n+        if (s->xch_present && !s->xch_disable) {\n+#endif\navctx->channel_layout |= AV_CH_BACK_CENTER;\nif (s->lfe) {\navctx->channel_layout |= AV_CH_LOW_FREQUENCY;\navctx->channel_layout |= AV_CH_BACK_CENTER;\nif (s->lfe) {\navctx->channel_layout |= AV_CH_LOW_FREQUENCY;\n@@ -1824,10 +1896,51 @@ static int dca_decode_frame(AVCodecContext *avctx, void *data,\ns->channel_order_tab[channels - 1 - !!s->lfe] < 0)\nreturn AVERROR_INVALIDDATA;\n\ns->channel_order_tab[channels - 1 - !!s->lfe] < 0)\nreturn AVERROR_INVALIDDATA;\n\n-        if (avctx->request_channels == 2 && s->prim_channels > 2) {\n+        if (num_core_channels + !!s->lfe > 2 &&\n+            avctx->request_channel_layout == AV_CH_LAYOUT_STEREO) {\nchannels = 2;\nchannels = 2;\n-            s->output = DCA_STEREO;\n+            s->output = s->prim_channels == 2 ? s->amode : DCA_STEREO;\navctx->channel_layout = AV_CH_LAYOUT_STEREO;\navctx->channel_layout = AV_CH_LAYOUT_STEREO;\n+\n+            /* Stereo downmix coefficients\n+             *\n+             * The decoder can only downmix to 2-channel, so we need to ensure\n+             * embedded downmix coefficients are actually targeting 2-channel.\n+             */\n+            if (s->core_downmix && (s->core_downmix_amode == DCA_STEREO ||\n+                                    s->core_downmix_amode == DCA_STEREO_TOTAL)) {\n+                for (i = 0; i < num_core_channels + !!s->lfe; i++) {\n+                    /* Range checked earlier */\n+                    s->downmix_coef[i] = dca_dmix_code(s->core_downmix_codes[i]);\n+                    s->downmix_coef[i] = dca_dmix_code(s->core_downmix_codes[i]);\n+                }\n+                s->output = s->core_downmix_amode;\n+            } else {\n+                int am = s->amode & DCA_CHANNEL_MASK;\n+                if (am >= FF_ARRAY_ELEMS(dca_default_coeffs)) {\n+                    av_log(s->avctx, AV_LOG_ERROR,\n+                           \"Invalid channel mode %d\\n\", am);\n+                    return AVERROR_INVALIDDATA;\n+                }\n+                if (num_core_channels + !!s->lfe >\n+                    FF_ARRAY_ELEMS(dca_default_coeffs)) {\n+                    avpriv_request_sample(s->avctx, \"Downmixing %d channels\",\n+                                          s->prim_channels + !!s->lfe);\n+                    return AVERROR_PATCHWELCOME;\n+                }\n+                for (i = 0; i < num_core_channels + !!s->lfe; i++) {\n+                    s->downmix_coef[i] = dca_default_coeffs[am][i];\n+                    s->downmix_coef[i] = dca_default_coeffs[am][i];\n+                }\n+            }\n+            av_dlog(s->avctx, \"Stereo downmix coeffs:\\n\");\n+            for (i = 0; i < num_core_channels + !!s->lfe; i++) {\n+                av_dlog(s->avctx, \"L, input channel %d = %f\\n\", i,\n+                        s->downmix_coef[i]);\n+                av_dlog(s->avctx, \"R, input channel %d = %f\\n\", i,\n+                        s->downmix_coef[i]);\n+            }\n+            av_dlog(s->avctx, \"\\n\");\n}\n} else {\nav_log(avctx, AV_LOG_ERROR, \"Non standard configuration %d !\\n\", s->amode);\n}\n} else {\nav_log(avctx, AV_LOG_ERROR, \"Non standard configuration %d !\\n\", s->amode);\n@@ -1891,6 +2004,15 @@ static int dca_decode_frame(AVCodecContext *avctx, void *data,\nfor (i = 0; i < 2 * s->lfe * 4; i++)\ns->lfe_data[i] = s->lfe_data[i + lfe_samples];\n\nfor (i = 0; i < 2 * s->lfe * 4; i++)\ns->lfe_data[i] = s->lfe_data[i + lfe_samples];\n\n+    /* AVMatrixEncoding\n+     *\n+     * DCA_STEREO_TOTAL (Lt/Rt) is equivalent to Dolby Surround */\n+    ret = ff_side_data_update_matrix_encoding(frame,\n+                                              (s->output & ~DCA_LFE) == DCA_STEREO_TOTAL ?\n+                                              AV_MATRIX_ENCODING_DOLBY : AV_MATRIX_ENCODING_NONE);\n+    if (ret < 0)\n+        return ret;\n+\n*got_frame_ptr = 1;\n\nreturn buf_size;\n*got_frame_ptr = 1;\n\nreturn buf_size;\n@@ -1920,10 +2042,15 @@ static av_cold int dca_decode_init(AVCodecContext *avctx)\navctx->sample_fmt = AV_SAMPLE_FMT_FLTP;\n\n/* allow downmixing to stereo */\navctx->sample_fmt = AV_SAMPLE_FMT_FLTP;\n\n/* allow downmixing to stereo */\n-    if (avctx->channels > 0 && avctx->request_channels < avctx->channels &&\n-        avctx->request_channels == 2) {\n-        avctx->channels = avctx->request_channels;\n-    }\n+#if FF_API_REQUEST_CHANNELS\n+FF_DISABLE_DEPRECATION_WARNINGS\n+    if (avctx->request_channels == 2)\n+        avctx->request_channel_layout = AV_CH_LAYOUT_STEREO;\n+FF_ENABLE_DEPRECATION_WARNINGS\n+#endif\n+    if (avctx->channels > 2 &&\n+        avctx->request_channel_layout == AV_CH_LAYOUT_STEREO)\n+        avctx->channels = 2;\n\nreturn 0;\n}\n\nreturn 0;\n}\n@@ -1945,17 +2072,30 @@ static const AVProfile profiles[] = {\n{ FF_PROFILE_UNKNOWN },\n};\n\n{ FF_PROFILE_UNKNOWN },\n};\n\n+static const AVOption options[] = {\n+    { \"disable_xch\", \"disable decoding of the XCh extension\", offsetof(DCAContext, xch_disable), AV_OPT_TYPE_INT, { .i64 = 0 }, 0, 1, AV_OPT_FLAG_DECODING_PARAM|AV_OPT_FLAG_AUDIO_PARAM },\n+    { NULL },\n+};\n+\n+static const AVClass dca_decoder_class = {\n+    .class_name = \"DCA decoder\",\n+    .item_name  = av_default_item_name,\n+    .option     = options,\n+    .version    = LIBAVUTIL_VERSION_INT,\n+};\n+\nAVCodec ff_dca_decoder = {\n.name            = \"dca\",\nAVCodec ff_dca_decoder = {\n.name            = \"dca\",\n+    .long_name       = NULL_IF_CONFIG_SMALL(\"DCA (DTS Coherent Acoustics)\"),\n.type            = AVMEDIA_TYPE_AUDIO,\n.id              = AV_CODEC_ID_DTS,\n.priv_data_size  = sizeof(DCAContext),\n.init            = dca_decode_init,\n.decode          = dca_decode_frame,\n.close           = dca_decode_end,\n.type            = AVMEDIA_TYPE_AUDIO,\n.id              = AV_CODEC_ID_DTS,\n.priv_data_size  = sizeof(DCAContext),\n.init            = dca_decode_init,\n.decode          = dca_decode_frame,\n.close           = dca_decode_end,\n-    .long_name       = NULL_IF_CONFIG_SMALL(\"DCA (DTS Coherent Acoustics)\"),\n.capabilities    = CODEC_CAP_CHANNEL_CONF | CODEC_CAP_DR1,\n.sample_fmts     = (const enum AVSampleFormat[]) { AV_SAMPLE_FMT_FLTP,\nAV_SAMPLE_FMT_NONE },\n.profiles        = NULL_IF_CONFIG_SMALL(profiles),\n.capabilities    = CODEC_CAP_CHANNEL_CONF | CODEC_CAP_DR1,\n.sample_fmts     = (const enum AVSampleFormat[]) { AV_SAMPLE_FMT_FLTP,\nAV_SAMPLE_FMT_NONE },\n.profiles        = NULL_IF_CONFIG_SMALL(profiles),\n+    .priv_class      = &dca_decoder_class,\n};\n};" ]
[ null ]
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http://softmath.com/math-com-calculator/factoring-expressions/algebra-1-guide.html
[ "English | Español\n\n# Try our Free Online Math Solver!", null, "Online Math Solver\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. 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https://myhomeworkhelp.com/graphing-the-mean-variance-efficient-frontier/
[ "We shall now plot graphs for our analysis. The x axis would have the portfolio risks against the y axis that contains the portfolio rewards. This graph has been plotted with reference to the table named 8.4 present on page numbered as 232. Few more portfolios were added to make us understand the graph better. Before using it the risk supplemented with reward value of the added portfolio is calculated and entered on to the table. We must now notice the pattern in the graph.", null, "Say if we choose some extra portfolios along with the range of investments that weighs on H within the range 0 to 100%, then subsequently we might conclude with what we get in fig: 8.6. Mean Variance Efficient frontier (abbreviated as MVE frontier) is what the curve obtained is named. The area under the curve gives the finest risk as well as reward portfolio. Ideally there wouldn’t be any portfolio to the North West part of this region.", null, "Those portfolios would be having a greater amount of profit for a certain specified risk, and also lesser risk meant for a known probable degree of yield. In case if such region of portfolios existed then this would have eventually be called the MVE frontier. Taking standard deviation on the x axis, we obtain a hyperbola (the name of the nature of the curve).", null, "Allowing Shorted Positions\n\nThe portfolio on the extreme left of the efficient region is termed as minimum variance range of investments. It is so called as from here a collection of funds with a reduced risk cannot be obtained.", null, "It involves considerable amount of algebra so as to find out the risk rate. With reference to the example we considered, the portfolio with a weight valued at 76.191% upon H and also 23.809% upon I. Post the calculation we see that it gets a low risk as low as 8.9%.", null, "", null, "### Customer Reviews\n\nMy Homework Help\nRated 5.0 out of 5 based on 510 customer reviews at", null, "", null, "", null, "" ]
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https://www.askmehelpdesk.com/physics/how-how-do-you-calculate-average-speed-what-formula-394037.html
[ "", null, "Ask Remember Me?", null, "freshwoman Posts: 2, Reputation: 1 New Member #1 Sep 6, 2009, 02:22 PM\nHow How do you calculate average speed? What is the formula?\nHow do you calculate average speed?", null, "freshwoman Posts: 2, Reputation: 1 New Member #2 Sep 6, 2009, 02:23 PM\n\nHow do you calculate average speed?", null, "Unknown008 Posts: 8,076, Reputation: 723 Uber Member #3 Sep 12, 2009, 01:27 AM\n\nAverage speed is the total distance covered divided by the total time.", null, "ankit.padhi.99 Posts: 1, Reputation: 1 New Member #4 Oct 25, 2010, 08:36 AM\nThe drive from Rampur to Lakmipur is a fricky one.Mr.Shah covered the uphill distance of 60 km at 35 km per hour. The return journey downhill to Rampur was easier. Mr. Shah managed a speed of 63 km per hour. What was Mr.hah's average speed for the entire journey?", null, "Unknown008 Posts: 8,076, Reputation: 723 Uber Member #5 Oct 25, 2010, 08:47 AM\n\nThe formula stays the same. What did you get?", null, "mikemoss09 Posts: 1, Reputation: 1 New Member #6 Feb 10, 2011, 04:26 PM\nTotal Distance divided by Total Time will give you your Average Speed. :)\n\n Question Tools Search this Question", null, "Show Printable Version", null, "Email this Page Search this Question: Advanced Search\n\n## Check out some similar questions!\n\nAverage Speed Formula [ 23 Answers ]\n\nHow would one write a formula to find the average speed if one knows the distance traveled and the rate of speed for each portion of the trip? 20 miles at m speed 40 miles at n speed\n\nFormula used in getting average speed [ 3 Answers ]\n\nWhat is the formula in getting the average speed?\n\nFormula for Average Speed [ 2 Answers ]\n\nWhat is the formula in getting the average speed?\n\nThe formula for the average speed? [ 3 Answers ]\n\nWhat is the formula for the average speed?\n\nFormula for average speed [ 3 Answers ]\n\nWhat is the formula for average speed??" ]
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http://zastita-prirode-smz.hr/pdf/topics-on-analysis-in-metric-spaces
[ "## Topics on Analysis in Metric Spaces by Luigi Ambrosio", null, "By Luigi Ambrosio\n\nThis e-book provides the most mathematical must haves for research in metric areas. It covers summary degree thought, Hausdorff measures, Lipschitz capabilities, protecting theorums, decrease semicontinuity of the one-dimensional Hausdorff degree, Sobolev areas of maps among metric areas, and Gromov-Hausdorff idea, all built ina normal metric atmosphere. The lifestyles of geodesics (and extra in general of minimum Steiner connections) is mentioned on basic metric areas and as an software of the Gromov-Hausdorff idea, even at times whilst the ambient area isn't really in the neighborhood compact. a quick and extremely common description of the idea of integration with admire to non-decreasing set services is gifted following the Di Giorgi approach to utilizing the 'cavalieri' formulation because the definition of the critical. in line with lecture notes from Scuola Normale, this publication offers the most mathematical must haves for research in metric areas. Supplemented with routines of various trouble it's perfect for a graduate-level brief direction for utilized mathematicians and engineers.\n\nBest applied books\n\nAdvanced Decision Making Methods Applied to Health Care\n\nThe main tough a part of making judgements within the healthiness care box on all degrees (national, nearby, institutional, sufferer) is associated with the very complexity of the method itself, to the intrinsic uncertainty concerned and its dynamic nature. This calls for not just the power to research and interpret a large number of details but in addition organize it in order that it turns into a cognitive base for applicable decision-making.\n\nPrincipia Designae － Pre-Design, Design, and Post-Design: Social Motive for the Highly Advanced Technological Society\n\nThis e-book offers a huge layout purview in the framework of “pre-design, layout, and post-design” via concentrating on the “motive of design,” which means an underlying reason behind the layout of a product. The chapters are constructed from papers in response to discussions on the “Design learn top Workshop” held in Nara, Japan, in 2013.\n\nAdditional resources for Topics on Analysis in Metric Spaces\n\nExample text\n\n33) 36 2 MRA-Based Wavelet Bases and Frames ψ (ν) (M ∗ ξ + n)ψ (κ) (M ∗ ξ + n) = n∈Zd m ν (ξ + M ∗ −1 n)ϕ(ξ + M ∗ −1 n)m κ (ξ + M ∗ −1 n)ϕ(ξ + M ∗ −1 n). 34), which reduces it to the form m ν (ξ + θkq )m κ (ξ + θkq )ϕ(ξ + θkq )ϕ(ξ + θkq ), k∈Zd q∈D(M ∗ ) where θkq = M ∗ −1 q + k. 2, we get ϕ(ξ + θkq )ϕ(ξ + θkq ) = m ν (ξ + θ0q )m κ (ξ + θ0q ) q∈D(M ∗ ) k∈Zd m ν (ξ + M ∗ −1 q)m κ (ξ + M ∗ −1 q). 32), it remains to recall that m ν (ξ + M ∗ −1 q)m κ (ξ + M ∗ −1 q) = δνκ q∈D(M ∗ ) for almost all ξ ∈ Rd .\n\nM − 1. The case where all masks are trigonometric polynomials is of special interest for engineering applications. It will be shown in Sect. 6 that starting with an appropriate trigonometric polynomial as a refinable mask, one can construct a compactly supported scaling function. It is easy to see that if all wavelet masks are also trigonometric polynomials, then all wavelet functions are compactly supported. Let us now discuss the problem of the existence of compactly supported wavelet functions.\n\nLet r, r1 ∈ D(M j ) and p, p1 ∈ D(M). , (r − r1 ) + M j ( p − p1 ) = M j+1 n for some n ∈ Zd . , r ≡ r1 (mod M j ). However, both r and r1 belong to D(M j ), which contains only one representative of each coset; hence, r = r1 . The equality ( p − p1 ) = Mn implies that p = p1 . ♦ We shall say that a set K ⊂ Rd is congruent to a set L ⊂ Rd (modulo Zd ) if the set K can be partitioned into a finite number of mutually disjoint measurable subsets K n , n = 1, . . , l N such that L= N (K n + ln ), where (K n + ln ) ∩ (K n 1 + ln 1 ) = ∅ for n = n 1 ." ]
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https://mtr04-note.coderbridge.io/2020/10/10/sequelize/
[ "# [ 筆記 ] Express 03 - ORM ＆ Sequelize\n\n## Sequelize\n\n#### 安裝：\n\n$npm install --save sequelize 依照我們所使用的資料庫，安裝對應的工具（這邊以 mysql2 做示範） # One of the following:$ npm install --save pg pg-hstore # Postgres\n$npm install --save mysql2$ npm install --save mariadb\n$npm install --save sqlite3$ npm install --save tedious # Microsoft SQL Server\n\n\n#### 使用方式：\n\nconst Sequelize = require('sequelize'); // 引入 sequelize\n\n// 填入對應的資料庫帳號\nhost: 'localhost',\ndialect: 'mysql'\n});\n\n\n#### 欄位設定：\n\nconst User = sequelize.define('user', {\n// attributes\nfirstName: {\ntype: Sequelize.STRING, // 資料型態\nallowNull: false // 是否可以為空\n},\nlastName: {\ntype: Sequelize.STRING\n// allowNull defaults to true\n}\n}, {\n// options\n});\n\n\n// Note: using force: true will drop the table if it already exists\nsequelize.sync({ force: true }).then()\n\n\nsequelize.sync({ force: true }).then(() => {\n// Now the users table in the database corresponds to the model definition\nreturn User.create({\nfirstName: 'John',\nlastName: 'Hancock'\n});\n});\n\n\nsequelize.sync({ force: true }).then(() => {\nUser.findAll().then(users => {\nconsole.log(\"All users:\", JSON.stringify(users, null, 4));\n});\n}\n\n\nsequelize.sync({ force: true }).then(() => {\nUser.findAll({ // 條件寫在 () 括號裡面用 {} 大括號包住\nwhere: { // where 裡面的內容也是用物件包住\nfirstName: 'John'\n}\n}).then(users => {\nconsole.log(\"All users:\", JSON.stringify(users, null, 4));\n});\n}\n\n\n• 如果想透過 id 來撈取資料，可以使用 findOne()，再將 id 寫在 where 條件裡\nsequelize.sync({ force: true }).then(() => {\nUser.findOne({\nwhere: {\nid: '1'\n}\n}).then(user => {\nconsole.log(user.firstName);\n});\n}\n\n• 撈取到指定資料之後，假如我們要將資料做更新，我們可以用 .then()，並且在裡頭的 function 回傳一個 user.update()\nsequelize.sync({ force: true }).then(() => {\nUser.findOne({\nwhere: {\nid: '1'\n}\n}).then(user => {\nuser.update({ // 將要更新的資料內容寫在 () 括號裡面用 {} 大括號包住\nlastName: 'hahaha'\n})\n}).then(() => {\nconsole.log('update done');\n})\n}\n\n• 要將資料做刪除，我們可以用 .then()，並且在裡頭的 function 回傳一個 user.destroy()\nsequelize.sync({ force: true }).then(() => {\nUser.findOne({\nwhere: {\nid: '1'\n}\n}).then(user => {\nuser.destroy().then(() => {\nconsole.log('destroy done');\n})\n})\n}\n\n\n## Associations 資料庫關聯\n\nconst User = sequelize.define('user', {\n// attributes\nfirstName: {\ntype: Sequelize.STRING,\nallowNull: false\n},\nlastName: {\ntype: Sequelize.STRING\n}\n});\n\nconst Comment = sequelize.define('comment', {\ncontent: {\ntype: Sequelize.STRING\n}\n});\n\nUser.hasMany(Comment); 將兩個 table 做關聯\nComment.belongsTo(User);\n\n\nsequelize.sync().then(() => {\nComment.create({\nuserId: 2,\ncontent: 'I am 2'\n}).then(() => {\nconsole.log('create done');\n});\n});\n\n\nsequelize.sync().then(() => {\nUser.findOne({\nwhere: {\nfirstName: 'John'\n},\ninclude: [comment] // 用一個陣列把要撈取的 table 一起放進來\n}).then(user => {\n})\n})\n\n\n## Sequelize CLI\n\n##### 安裝：\n$npm install --save sequelize-cli$ npx sequelize-cli init\n\n\n##### 使用方式：\n\n$npx sequelize-cli model:generate --name User --attributes firstName:string,lastName:string,email:string$ npx sequelize-cli model:generate --name Comment --attributes content:string\n\n\n'use strict';\nmodule.exports = (sequelize, DataTypes) => {\nconst Comment = sequelize.define('Comment', {\ncontent: DataTypes.STRING\n}, {});\nComment.associate = function(models) {\n// 這邊要自行加上關聯的設定\nComment.belongsTo(Models.User);\n};\nreturn Comment;\n}\n\n\n$npx sequelize-cli db:migrate 接著到 migrations 這個資料夾底下，找到 Comment 的檔案去新增 UserId 這個關聯用的欄位，存擋之後。讓 Migrations 重跑一遍，把 UserId 加進資料庫當中 $ npx sequelize-cli db:migrate:undo\n\\$ npx sequelize-cli db:migrate\n\n\n## 操縱資料\n\nconst db = require('./models');\n\n\nconst db = require('./models');\nconst User = db.User;\nconst Comment = db.Comment;\n\nUser.create({\nfirstName: 'John'\n}).then(() => {\nconsole.log('create done');\n});" ]
[ null ]
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https://community.jmp.com/t5/Discussions/How-to-select-rows-based-on-multiple-criteria/td-p/7014
[ "Share your ideas for the JMP Scripting Unsession at Discovery Summit by September 17th. We hope to see you there!\nChoose Language Hide Translation Bar\nHighlighted\n\n## How to select rows based on multiple criteria?\n\nHi,\n\nI am writing a script to Subset a data table. Following the scripting guids' coding example I can select according to a criterium:\n\nfor each row(Selected(Rowstate())=(name==\"KATIE\"));\n\nHow can I generalize this to select both KATIE and LOUISE?\n\nThis does not work:\n\nfor each row(Selected(Rowstate())=(name==\"KATIE\",\"LOUISE\"));\n\nSo what is the syntax for this?\n\nRegards\n\nPoul\n\n1 ACCEPTED SOLUTION\n\nAccepted Solutions\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nSame principle:\n\ndt = Open( \"\\$SAMPLE_DATA/Big Class.jmp\" );\n\nFor Each Row( Selected( Row State() ) = Or( contains(:name, \"ATIE\"), contains(:name, \"ISE\")) );\n\n// Or alternatively\n\ndt << Select where(  Or( contains(:name, \"ATIE\"), contains(:name, \"ISE\")) );\n\n10 REPLIES 10\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nUse Or():\n\ndt = Open( \"\\$SAMPLE_DATA/Big Class.jmp\" );\n\nFor Each Row( Selected( Row State() ) = Or( name == \"KATIE\", name == \"LOUISE\" ) );\n\n// Or alternatively\n\ndt << Select where( Or( name == \"KATIE\", name == \"LOUISE\" ) );\n\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nBut what if I want to further use 'Contains' to match the strings inly on part of the strings? Like \"ATIE\" and \"ISE\"? Regards Poul\n\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nSame principle:\n\ndt = Open( \"\\$SAMPLE_DATA/Big Class.jmp\" );\n\nFor Each Row( Selected( Row State() ) = Or( contains(:name, \"ATIE\"), contains(:name, \"ISE\")) );\n\n// Or alternatively\n\ndt << Select where(  Or( contains(:name, \"ATIE\"), contains(:name, \"ISE\")) );\n\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nHi ms,\n\nI wonder if there is way to dynamically handle name list, and still able to subset the\n\ndt = Open( \"\\$SAMPLE_DATA/Big Class.jmp\" );\n\nname_list={\"clay\",\"Alice\",\"AMY\", ...};\n\nfor(i=1,i<=nitems(name_list),i++,\n\ni_name=name_list[i];\n\ndt<<select where(name=i_name)\n\n);\n\ndt<<subset;\n\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nIs this what you are trying to accomplish, find all of the matches found in the list called \"name_list\" and then output them into a subsetted data table?\n\n``````Names Default To Here( 1 );\ndt = Open( \"\\$SAMPLE_DATA/Big Class.jmp\" );\nname_list = {\"Clay\", \"Alice\", \"AMY\"};\nFor( i = 1, i <= N Items( name_list ), i++,\ni_name = Uppercase( name_list[i] );\ndt << select where( :name == i_name, current selection( \"extend\" ) );\n);\n\ndtSub = dt << subset( selected rows( 1 ), selected columns( 0 ) );``````\nJim\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nThanks,\nI used to subset each criteria into a individual table, and then combined all of them.\nHappy New Year !\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nIf there are many strings to match, it would be tempting to use of list instead of constructing a long OR() clause. However, Contain() cannot not look for substrings in a list (of strings). A loop over the list is then required. Here's an example:\n\ndt = Open( \"\\$SAMPLE_DATA/Big Class.jmp\" );\n\nname_list = {\"ATIE\", \"ISE\", \"CLY\", \"WWW\"};\n\nn = N Items( name_list );\n\nFor Each Row(\n\nFor( i = 1, i <= n, i++,\n\nIf( (s_flag = Contains( :name[], name_list[i] )) > 0,\n\nBreak()\n\n)\n\n);\n\nSelected( Row State() ) = s_flag;\n\n);\n\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nHi, these answers were really helpfull. Now if I want to add a condition for value in another column, say I wanted to select name=\"KATIE\" and \"ROBERT\", (or even better, containing \"ATIE\"), AND sex=\"F\". Then I would have to combine the Or- condition with an and condition.\n\ndt = Open( \"\\$SAMPLE_DATA/Big Class.jmp\" );\n\nFor Each Row( Selected( Row State() ) = Or( contains(:name, \"ATIE\"), contains(:name, \"OBER\"))  And (contains(:sex, \"F\")));\n\nI already something like this, but was ot succesfull.\n\nRegards\n\nPoul\n\n(PS Obviously I used Base SAS a lot. Now I try to implement selections on tables this way around. Thanks for the help.)\n\nHighlighted\n\n## Re: How to select rows based on multiple criteria?\n\nAlmost there. The And() must enclose both arguments; for And() to be true, both its arguments must be true.\n\nThis should work:\n\nFor Each Row( Selected( Row State() ) = And(Or( contains(:name, \"ATIE\"), contains(:name, \"OBER\")),  contains(:sex, \"F\")));\n\nArticle Labels\n\nThere are no labels assigned to this post." ]
[ null ]
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http://programmingbydoing.com/a/number-puzzles-iv-a-new-hope.html
[ "• Author: Graham Mitchell\n• Filename: NumberPuzzles4.java\n\n### Number Puzzles IV: A New Hope\n\nUse nested `for` loops to find four positive integers whose sum is 45, and such that the first plus 2, the second minus 2, the third multiplied by 2, and the fourth divided by 2 are all equal.\n\nPlease note that these four numbers are integers, and not necessarily just digits. In this problem, we are no longer finding a single four-digit number; we are finding four separate numbers. However, since we are trying to generate all possible combinations, the procedure should be the same.\n\nFor those of you having trouble with the English on this one (I've noticed that students really don't like word problems), here's what that means.\n\n• The output of your program should be four numbers. They won't be negative numbers.\n• When you add the four numbers, they add up to 45.\n• If you add 2 to the first number, you get the same answer as if you had subtracted 2 from the second number.\n• If you multiply the third number by two, you also get the same answer.\n• If you divide the fourth number by two, you also get the same answer.\n\nThe following mathematical statments are also true about these numbers:\n\nA + 2 = B - 2 = C × 2 = D ÷ 2\n\nand\n\nA + B + C + D = 45\n```\n```", null, "" ]
[ null, "http://programmingbydoing.com/a/examples/cc-by-nc-sa.png", null ]
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https://morsagmon.com/blog/object-oriented-programming-with-excel-vba-part-2/
[ "Select Page\n##### In this advanced chapter of OOP with Excel VBA, we implement objects composition with a dynamic collection in Excel VBA using Class Modules. Not for the faint of heart…\n\nIn Part 1 on this exercise of implementing OOP in Excel VBA, we left off with a half-baked order object. It had some properties and a couple of methods, but its line-items were missing.\n\nToday we’re going to round up our order object to include its line-items.\n\nThinking about the right structure and arrangement of the line-items within the order object, two main characteristics should guide our thinking:\n\n1. An order may have any number of line-items. This is a one-to-many relationship.\n2. All line-items have the same structure. We’re dealing with similar records that together form a collection of records.\n\nA collection seems like a perfect structure to maintain the dynamic nature of the number of line-items per each order. But a collection of what?\n\nOne option that come to mind is a user-defined type. This would fit perfectly with the record nature of the line-item. In this approach, we would have defined a user type representing a line-item record and construct a collection of variables of that type. Instead of a collection, we could also construct an array of these line-item types.\n\nThese solutions are counter-intuitive to the object oriented programming approach we’re perfecting here and will render the elegance of our order object awkward.\n\n#### Here comes another object\n\nAs we’re now thinking “objects”, it only comes naturally that a line-item is an object!\n\nOur strategy would be to have each order object hold a collection of line-items objects.\n\nLet’s start off by implementing a new Class Module for our line-item object, I named it clsLineItem:\n\n`Private p_LineItemIndex As Integer`\n\n`Private p_Product As Long`\n\n`Private p_Qty As Integer`\n\n`Private p_Total As Single`\n\n` `\n\n`Property Get LineItemIndex() As Integer`\n\n`    LineItemIndex = p_LineItemIndex`\n\n`End Property`\n\n` `\n\n`Property Get Product() As Long`\n\n`    Product = p_Product`\n\n`End Property`\n\n` `\n\n`Property Get Quantity() As Long`\n\n`    Quantity = p_Qty`\n\n`End Property`\n\n` `\n\n`Property Get LineTotal() As Long`\n\n`    LineTotal = p_Total`\n\n`End Property`\n\n` `\n\n`Public Sub CreateLineItem(intLineIndex As Integer, lngProduct As Long, intQty As Integer, sngAmount As Single)`\n\n`   `\n\n`    p_LineItemIndex = intLineIndex`\n\n`    p_Product = lngProduct`\n\n`    p_Qty = intQty`\n\n`    p_Total = sngAmount`\n\n`End Sub`\n\n#### Order Object Composition\n\nNext, we need to adjust our clsOrder Class Module, to accommodate our collection of line-items objects.\n\nWe need to declare a private collection and implement adding and removing line-items.\n\n`Private p_colLineItems As Collection`\n\nNext, we need to change the AddLineItem and RemoveLineItem methods. When adding, we are now receiving a line-item object and simply adding it to the private collection:\n\n`Public Sub AddLineItem(itmLineItem As clsLineItem)`\n\n`    'Process new line-item here`\n\n`    p_colLineItems.Add itmLineItem`\n\n`    'Update the order's object variables`\n\n`    p_LineItemsCount = p_LineItemsCount + 1`\n\n`    p_OrderTotal = p_OrderTotal + itmLineItem.LineTotal`\n\n`End Sub`\n\nWe remove a line item by its index (line number within the order). Here it is a little tricky, as we need to fetch the line item amount before we actually remove it, so that we can update the order total variable – subtract the removed line-item’s amount from the order total. Nothing too complicated that a helper private Sub can’t polish for us:\n\n`Public Sub RemoveLineItem(intLineItemRow As Integer)`\n\n`    'Update the order's object variables while removing the line item`\n\n`    p_LineItemsCount = p_LineItemsCount - 1`\n\n`    p_OrderTotal = p_OrderTotal - RemoveLineItemFromCollection(intLineItemRow)`\n\n`End Sub`\n\n` `\n\n`Private Function RemoveLineItemFromCollection(intLineItemRow As Integer) As Single`\n\n`'Returns the line-item amount`\n\n`    Dim itmLine As clsLineItem`\n\n`   `\n\n`    iRowIndex = 0`\n\n`    For Each itmLine In p_colLineItems`\n\n`        iRowIndex = iRowIndex + 1`\n\n`        If itmLine.LineItemIndex = intLineItemRow Then`\n\n`            RemoveLineItemFromCollection = itmLine.LineTotal`\n\n`            p_colLineItems.Remove iRowIndex`\n\n`            Exit Function`\n\n`        End If`\n\n`    Next`\n\n`End Function`\n\nWe’re looping through the collection until we find our winning line-item by its row index. Same technique applies in a new method we need that returns a line-item object (it is a Function this time, not a Sub) based on a row index of that line item. This is part of the public interface and allows to query line items’ data of an order:\n\n`Public Function GetLineItem(intLineIndex As Integer) As clsLineItem`\n\n`    Dim itmLine As clsLineItem`\n\n`   `\n\n`    For Each itmLine In p_colLineItems`\n\n`        If itmLine.LineItemIndex = intLineIndex Then`\n\n`            GetLineItem = itmLine`\n\n`            Exit Function`\n\n`        End If`\n\n`    Next`\n\n`End Function`\n\nLastly, as in most cases all line items of an order are needed together, let’s offer a public method for returning the line-items collection:\n\n`Public Function GetLineItems() As Collection`\n\n`    Set GetLineItems = p_colLineItems`\n\n`End Function`\n\n##### The Complete Order Class Module\n\nAfter all adjustments, our new clsOrder Class Module should look like this:\n\n`Private p_OrderDate As Date`\n\n`Private p_LineItemsCount As Integer`\n\n`Private p_OrderTotal As Single`\n\n` `\n\n`Private p_colLineItems As New Collection`\n\n` `\n\n`Private Function RemoveLineItemFromCollection(intLineItemRow As Integer) As Single`\n\n`'Returns the line-item amount`\n\n`    Dim itmLine As clsLineItem`\n\n`   `\n\n`    iRowIndex = 0`\n\n`    For Each itmLine In p_colLineItems`\n\n`        iRowIndex = iRowIndex + 1`\n\n`        If itmLine.LineItemIndex = intLineItemRow Then`\n\n`            RemoveLineItemFromCollection = itmLine.LineTotal`\n\n`            p_colLineItems.Remove iRowIndex`\n\n`            Exit Function`\n\n`        End If`\n\n`    Next`\n\n` `\n\n`End Function`\n\n` `\n\n` `\n\n`'Properties`\n\n` `\n\n`Property Get OrderDate() As Date`\n\n`    'Return current order date`\n\n`    OrderDate = p_OrderDate`\n\n`End Property`\n\n` `\n\n`Property Let OrderDate(datOrder As Date)`\n\n`    'Store new order date`\n\n`    p_OrderDate = datOrder`\n\n`End Property`\n\n` `\n\n`Property Get LineItemsCount() As Integer`\n\n`    'Return current count of line-items`\n\n`    LineItemsCount = p_LineItemsCount`\n\n`End Property`\n\n` `\n\n`Property Get TotalAmount() As Single`\n\n`    'Return current order total`\n\n`    TotalAmount = p_OrderTotal`\n\n`End Property`\n\n` `\n\n` `\n\n`'Methods`\n\n` `\n\n`Public Sub AddLineItem(itmLineItem As clsLineItem)`\n\n`    'Process new line-item here`\n\n`    p_colLineItems.Add itmLineItem`\n\n`    'Update the order's object variables`\n\n`    p_LineItemsCount = p_LineItemsCount + 1`\n\n`    p_OrderTotal = p_OrderTotal + itmLineItem.LineTotal`\n\n`End Sub`\n\n` `\n\n`Public Sub RemoveLineItem(intLineItemRow As Integer)`\n\n`   `\n\n`    'Update the order's object variables while removing the line item`\n\n`    p_LineItemsCount = p_LineItemsCount - 1`\n\n`    p_OrderTotal = p_OrderTotal - RemoveLineItemFromCollection(intLineItemRow)`\n\n`   `\n\n`End Sub`\n\n` `\n\n` `\n\n`Public Function GetLineItem(intLineIndex As Integer) As clsLineItem`\n\n` `\n\n`    Dim itmLine As clsLineItem`\n\n`   `\n\n`    For Each itmLine In p_colLineItems`\n\n`        If itmLine.LineItemIndex = intLineIndex Then`\n\n`            GetLineItem = itmLine`\n\n`            Exit Function`\n\n`        End If`\n\n`    Next`\n\n` `\n\n`End Function`\n\n` `\n\n`Public Function GetLineItems() As Collection`\n\n`    Set GetLineItems = p_colLineItems`\n\n`End Function`\n\n#### Using our Order and LineItem Objects\n\nFinally, we can make use of our objects by re-writing our (regular) module Orders. I remind you that we are processing the following two tables into a collection of orders and printing out a report with all orders data. A more detailed explanation of some of this code is waiting for you in the first part of this Blog post.", null, "Our new Orders module now looks like this:\n\n`Sub ProcessOrders()`\n\n`    'Our orders collection`\n\n`    Dim colOrders As New Collection`\n\n`    'Our order object variable`\n\n`    Dim objOrder As clsOrder`\n\n`   `\n\n`    'Our table variable`\n\n`    Set tblOrders = ThisWorkbook.Worksheets(\"Data\").ListObjects(\"OrdersTable\")`\n\n`   `\n\n`    'Main processing loop`\n\n`    For Each rowOrder In tblOrders.ListRows`\n\n`        'Set an instance of an order object`\n\n`        Set objOrder = New clsOrder`\n\n`        'Set the date property value of our order object`\n\n`        objOrder.OrderDate = rowOrder.Range(1, 3)`\n\n`        'Call to process order's line items`\n\n`        Call ProcessOrderLineItems(objOrder, rowOrder.Range(1, 1))`\n\n`        'Add order to our orders collection`\n\n`        colOrders.Add objOrder`\n\n`    Next`\n\n`   `\n\n`    'We now have an elegant collection of orders, let's print their details:`\n\n`    Call PrintOrderReport(colOrders)`\n\n`   `\n\n`    'Release order lines table autofilter`\n\n`    ThisWorkbook.Worksheets(\"Data\").ListObjects(\"OrderLinesTable\").Range.AutoFilter`\n\n`End Sub`\n\n` `\n\n` `\n\n`Sub ProcessOrderLineItems(objOrder As clsOrder, lngOrderNumber As Long)`\n\n`    Dim iRowIndex As Integer`\n\n`    'Declaring our line-item object`\n\n`    Dim objLineItem As clsLineItem`\n\n` `\n\n`    Set tblOrdersLines = ThisWorkbook.Worksheets(\"Data\").ListObjects(\"OrderLinesTable\")`\n\n`       `\n\n`    'Filter order lines table on current order number`\n\n`    tblOrdersLines.Range.AutoFilter Field:=1, Criteria1:=\"=\" & lngOrderNumber`\n\n`    'Loop all filtered rows`\n\n`    iRowIndex = 0`\n\n`    For Each cell In Intersect(tblOrdersLines.ListColumns(1).DataBodyRange, _`\n\n`        tblOrdersLines.Range.SpecialCells(xlCellTypeVisible))`\n\n`        iRowIndex = iRowIndex + 1`\n\n`        'Process order line item`\n\n`        'We instantiate a line item object and populate it with data`\n\n`        Set objLineItem = New clsLineItem`\n\n`        objLineItem.CreateLineItem iRowIndex, cell.Offset(0, 2), cell.Offset(0, 3), cell.Offset(0, 4)`\n\n`        'Adding the line item object to the order object`\n\n`        objOrder.AddLineItem objLineItem`\n\n`    Next`\n\n`End Sub`\n\n` `\n\n` `\n\n`Sub PrintOrderReport(ByRef colOrders As Collection)`\n\n` `\n\n`    Dim colLineItems As New Collection`\n\n`    Dim lineItem As clsLineItem`\n\n`   `\n\n`    For Each ord In colOrders`\n\n`        Debug.Print \"Order Details: \", ord.OrderDate, ord.LineItemsCount, ord.TotalAmount`\n\n`        Debug.Print \"  Line Items: \"`\n\n`        Set colLineItems = ord.GetLineItems`\n\n`        For Each lineItem In colLineItems`\n\n`            Debug.Print \"  \", lineItem.LineItemIndex, lineItem.Product, lineItem.Quantity, lineItem.LineTotal`\n\n`        Next`\n\n`        Debug.Print vbCrLf 'New line space between orders`\n\n`    Next`\n\n`End Sub`\n\nWhen running the ProcessOrders Sub, we end up with the following report of our orders:\n\n`Order Details:              25/04/2020     2             107`\n\n`  Line Items:`\n\n`               1             28            2             70`\n\n`               2             33            1             37`\n\n` `\n\n` `\n\n`Order Details:              22/04/2020     1             109`\n\n`  Line Items:`\n\n`               1             32            2             109`\n\n` `\n\n` `\n\n`Order Details:              22/04/2020     3             294`\n\n`  Line Items:`\n\n`               1             10            2             90`\n\n`               2             19            2             88`\n\n`               3             16            2             116`\n\n#### Summary\n\nOver the last 4 Blog posts, we learned about objects in computer programming, OOP in general and how OOP is implemented in Excel VBA.\n\nWe demonstrated how complex use of Class Modules, or objects, is realized in Excel VBA with elaborated code modules.\n\nRemember that OOP has its advantages and disadvantages, so be familiar with its benefits and chose where it makes most sense to use.\n\nI know that this Blog series is most valuable to anyone using Excel VBA, so be a good friend and share this widely, so that we can help many other VBA programmers too." ]
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https://www.jianshu.com/p/44ae73a58ebc?utm_campaign=maleskine&utm_content=note&utm_medium=seo_notes&utm_source=recommendation
[ "Flutter基础篇：\n\nFlutter进阶篇：\n\n# 八、Dart的类与函数\n\nDart是一种面向对象的语言，具有类和基于mixin的继承。每个对象都是一个类的实例，所有类都来自`Object`。 基于`Mixin`的继承意味着虽然每个类（除了`Object`）只有一个超类，但是类体可以在多个类层次结构中重用。\n\n# （一）类的分类\n\n### （1）普通类\n\n##### 1).Dart使用`class`关键字表示一个类，对象具有由函数和数据（分别为方法和实例变量）组成的成员。\n\n``````class Test{\nvoid tests(){}\n}\nvoid main(){\nnew Test().tests();\n}\n``````\n##### 2).要在运行时获取对象的类型，可以使用Object类的`runtimeType`属性，该属性返回一个Type对象。\n\n`````` var a = 10;\nvar b = 10.0;\nvar c = '10';\nvar d = true;\nvar e = [12.5,13.1];\nvar f = {3:'5',5:'11'};\nvar t = new Test();// 这里就直接使用上面那个Test类 不再去重复写这个类了\nprint('a 的类型是： \\${a.runtimeType}'); // a 的类型是： int\nprint('b 的类型是： \\${b.runtimeType}'); // b 的类型是： double\nprint('c 的类型是： \\${c.runtimeType}'); // c 的类型是： String\nprint('d 的类型是： \\${d.runtimeType}'); // d 的类型是： bool\nprint('e 的类型是： \\${e.runtimeType}'); // e 的类型是： List<double>\nprint('f 的类型是： \\${f.runtimeType}'); // f 的类型是： _InternalLinkedHashMap<int, String>\nprint('t 的类型是： \\${t.runtimeType}'); // t 的类型是： Test\nclass Test{}\n``````\n##### 3). Dart和Java一样，使用extends关键字，表示一个类继承另一个类。\n\n`````` class Test {\nvoid test() {/*这里省略方法内部的逻辑操作*/}\n// 其他逻辑\n}\n\nclass TestChild extends Test {\n@override //@override标注在test()函数上面 表示test()函数是重写父类的。\nvoid test() {\nsuper.test();// 调用父类的test()函数\n/*这里省略方法内部的逻辑操作*/\n}\n// 其他逻辑\n}\n``````\n\n`@override`是元数据。元数据注解以字符开头@，后跟对编译时常量（如`deprecated`）的引用或对常量构造函数的调用。元数据可以出现在库，类，typedef，类型参数，构造函数，工厂，函数，字段，参数或变量声明之前以及导入或导出指令之前。您可以使用反射在运行时检索元数据。\n\n``````class Television {\n/// _Deprecated: Use [turnOn] instead._\n@deprecated\nvoid activate() {\nturnOn();\n}\n\n// Turns the TV's power on.\nvoid turnOn() {\n//...\n}\n}\n``````\n\n``````library todo;\n\nclass Todo {\nfinal String who;\nfinal String what;\nconst Todo(this.who, this.what);\n}\n\n// 以下是使用@todo注释的示例：\nimport 'todo.dart';\n@Todo('seth', 'make this do something')\nvoid doSomething() {\nprint('do something');\n}\n``````\n##### 4).静态变量\n\n``````class Test {\nstatic const num = 16;\n// ···\n}\n\nvoid main() {\nprint(Test. num); // 16\n}\n``````\n##### 5).重写操作符\n\n< + | []\n> / ^ []=\n<= ~/ & ~\n>= * << ==\n- % >>\n\n``````void main(){\nfinal a = Testoperator(2, 3);\nfinal b = Testoperator(2, 2);\nvar num1 = Testoperator(4, 5);\nvar num2= Testoperator(0,1);\nprint(a + b == num1); // true\nprint(a - b == num2); // true\n}\n\nclass Testoperator {\nfinal int x, y;\n\nTestoperator(this.x, this.y);\n\nTestoperator operator +(Testoperator o) => Testoperator(x + o.x, y + o.y);\nTestoperator operator -(Testoperator o) => Testoperator(x - o.x, y - o.y);\n\n// Override hashCode using strategy from Effective Java, Chapter 11.\n@override\nint get hashCode {\nint result = 17;\nresult = 37 * result + x.hashCode;\nresult = 37 * result + y.hashCode;\nreturn result;\n}\n\n// 如果重写了 hashCode，应该重写==操作符。\n@override\nbool operator ==(dynamic other) {\nif (other is! Testoperator) return false;\nTestoperator person = other;\nreturn (person.x == x &&\nperson.y == y);\n}\n}\n``````\n##### 6).noSuchMethod()\n\n``````void main() {\nTestMethod test = new TestMethod();\ndynamic f = test.foo;\n// Invokes `Object.noSuchMethod`, not `TestMethod.noSuchMethod`, so it throws.\nf(42);\n}\n\nclass TestMethod {\n// 除非你重写noSuchMethod，否则使用不存在的成员会导致NoSuchMethodError\n// Unless you override noSuchMethod, using a\n// non-existent member results in a NoSuchMethodError.\n@override\nvoid noSuchMethod(Invocation invocation) {\nprint('You tried to use a non-existent member: ' +\n'\\${invocation.memberName}');\n}\ndynamic foo();\n}\n``````\n\n• 1.接收处有静态类型dynamic\n• 2.接收处定义了一个未实现的方法（abstract也是OK的）的静态类型dynamic，接收器的动态类型的实现与类`noSuchMethod()` 中的实现不同Object。\n有关更多信息，请参阅非正式 `noSuchMethod`转发规范\n\n### （2）抽象类\n\n##### 1).使用abstract修饰符定义抽象类（无法实例化的类）。抽象类对于定义接口非常有用，通常还有一些实现。如果希望抽象类看起来是可实例化的，请定义工厂构造函数。\n\n``````// 此类声明为abstract，因此无法实例化\nabstract class Test {\n//定义构造函数，字段，方法...\n\n// 抽象方法\nvoid test();\n}\n``````\n##### 2).隐式接口\n\n``````void main() {\nprint(sayHello(Person('李四'))); // 你好 张三. 我是 李四.\nprint(sayHello(PersonImpl())); // 你好 张三 你知道我是谁吗？\n}\n\n// Person类 隐式接口包含hello()\nclass Person {\n// 在接口中，但是仅在此库中可见。\nfinal _name;\n\n// 不在接口中,因为这是一个构造函数\nPerson(this._name);\n\n// 在接口中\nString hello(String who) => '你好 \\$who. 我是 \\$_name.';\n}\n\n// Person接口的实现\nclass PersonImpl implements Person {\nget _name => '';\n\nString hello(String name) => '你好 \\$name 你知道我是谁吗？';\n}\n\nString sayHello(Person person) => person.hello('张三');\n\nclass ZhangSan implements Run,Life {\n//...\n}\nclass Run {}\nclass Life {}\n``````\n\n### （3）可调用的类（Callable Class）\n\n``````void main() {\nvar test = new Test();\nvar result = test(166.6665,\"Flutter真好玩\",672);\nprint(\"\\$result\");// 666.666 Flutter真好玩 666\n}\nclass Test {\n// 必须是call函数\ncall(double a, String b, int c) => '\\${a*4} \\${b} \\${c-6}';\n}\n``````\n\n### （4）枚举类型\n\n##### 2). 枚举中的每个值都有一个index getter，它返回枚举声明中值的从零开始的位置。例如，第一个值具有索引0，第二个值具有索引1。\n``````assert(Color.red.index == 0);\nassert(Color.green.index == 1);\nassert(Color.blue.index == 2);\n``````\n##### 3).要获取枚举中所有值的列表，请使用枚举values常量。\n``````List<Color> colors = Color.values;\nassert(colors == Color.blue);\n``````\n##### 4).您可以在switch语句中使用枚举，如果您不处理所有枚举值，您将收到警告。\n``````var aColor = Color.blue;\nswitch (aColor) {\ncase Color.red:\nprint('Red');\nbreak;\ncase Color.green:\nprint('Green');\nbreak;\ndefault: // 你没有这个 你会看到一个警告\nprint(aColor); // 'Color.blue'\n}\n``````\n##### 5).枚举类型的限制条件：\n• 1.你不能在子类，`mixin` 或者实现枚举。\n• 2.你不能显式实例化枚举。\n\n### （5）mixin\n\nMixins是一种在多个类层次结构中重用类代码的方法。\n\n##### 1).要实现 mixin，请创建一个扩展Object的类，并且不声明构造函数。除非您希望mixin可用作常规类，否则请使用mixin关键字而不是class。\n\n``````// 声明mixin\n// 专家\nmixin Expert {\n// 发现和解决难题\nbool solveProblems = false;\n// 精通数据结构和算法\nbool dataStructureAndAlgorithms = false;\n// 会架构设计\nbool architectureDesign = false;\n// 性能优化\nbool performanceOptimization = false;\n// 熟练掌握计算机系统\nbool computerSystem = false;\n\nvoid develop() {\n// 娱乐节目\nif (solveProblems) {\nprint('发现和解决难题');\n}\nif (dataStructureAndAlgorithms) {\nprint('精通数据结构和算法');\n}\nif (architectureDesign) {\nprint('会架构设计');\n}\nif (performanceOptimization) {\nprint('熟练掌握性能优化');\n}\nif (computerSystem) {\nprint('熟练掌握计算机系统');\n}\n}\n}\n\n// 特性\n\n// 有效率的\nmixin Efficient {\nvoid getEfficientAttrs() {\nprint('有效率的');\n}\n}\n\n// 和蔼的\nmixin Kind {\nvoid getKindAttrs() {\nprint('和蔼的');\n}\n}\n\n// 软件架构师\nclass SoftwareArchitect {\nSoftwareArchitect() {\nprint('软件架构师');\n}\n}\n``````\n##### 2).要使用 mixin，请使用with关键字后跟一个或多个mixin名称。以下示例显示了两个使用mixins的类。\n``````void main() {\n// 姓名：张三\n// 发现和解决难题\n// 精通数据结构和算法\n// 会架构设计\nACompanySoftwareArchitect architect1 = new ACompanySoftwareArchitect('张三');\narchitect1.develop();\nprint('====');\n// 姓名：李四\n// 发现和解决难题\n// 精通数据结构和算法\n// 会架构设计\n// 熟练掌握性能优化\n// 熟练掌握计算机系统\n// 有效率的\n// 和蔼的\nBCompanySoftwareArchitect architect2 = new BCompanySoftwareArchitect('李四');\narchitect2.develop();\narchitect2.getEfficientAttrs();\narchitect2.getKindAttrs();\n}\n\n// 使用mixin\n// A公司的软件架构师，继承自软件架构师，拥有专家的特性。\nclass ACompanySoftwareArchitect extends SoftwareArchitect with Expert {\nString name;\nACompanySoftwareArchitect(String name) {\nthis.name = name;\nprint('姓名：' + name);\nsolveProblems = true;\ndataStructureAndAlgorithms = true;\narchitectureDesign = true;\n}\n\n@override\nvoid develop() {\nsuper.develop();\n}\n}\n\n// B公司的软件架构师，继承自软件架构师，\nclass BCompanySoftwareArchitect extends SoftwareArchitect\nwith Expert, Efficient, Kind {\nString name;\n\nBCompanySoftwareArchitect(String name) {\nthis.name = name;\nprint('姓名：' + name);\nsolveProblems = true;\ndataStructureAndAlgorithms = true;\narchitectureDesign = true;\nperformanceOptimization = true;\ncomputerSystem = true;\n}\n}\n``````\n##### 3).要指定只有某些类型可以使用mixin。例如，所以你的mixin可以调用它没有定义的方法， 用于on指定所需的超类。\n\n`mixin SoftwareDeveloper on ACompanySoftwareArchitect{}`\n\n# （二）泛型\n\n### （1）为什么使用泛型？\n\n##### 1).正确指定泛型类型可以生成更好的代码。\n\n``````var names = List<String>();\nnames.addAll(['Seth', 'Kathy', 'Lars']);\n// 报错 The argument type 'int' can't be assigned to the parameter type 'String'.\nnames.add(42);\n``````\n##### 2).您可以使用泛型来减少代码重复。\n\n``````abstract class ObjectCache {\nObject getByKey(String key);\nvoid setByKey(String key, Object value);\n}\n``````\n\n``````abstract class StringCache {\nString getByKey(String key);\nvoid setByKey(String key, String value);\n}\n``````\n\n``````class Test1 extends ObjectCache {\n@override\nObject getByKey(String key) {\nreturn 'object cache';\n}\n\n@override\nvoid setByKey(String key, Object value) {\nreturn null;\n}\n}\n\nclass Test2 extends StringCache {\n@override\nString getByKey(String key) {\nreturn 'String cache';\n}\n\n@override\nvoid setByKey(String key, String value) {\nreturn null;\n}\n}\n``````\n\n``````abstract class Cache<T> {\nT getByKey(String key);\n}\n``````\n\n``````print(new Test1().getByKey('123'));\nprint(new Test2().getByKey('456'));\n``````\n\n### （2）使用集合文字\n\n`list``map`文字可以参数化。参数化文字就像你已经看到的文字一样，除了你在开始括号之前添加 `<type>`（对于list）或 `<keyType, valueType>`（对于map）。\n\n``````var numbers = <String>['11', '22', '33'];\nvar pages = <String, String>{\n'index.html': 'Homepage',\n'store.html': 'Store',\n'mine.html': 'Mine'\n};\n``````\n\n### （3）使用带有构造函数的参数化类型\n\n``````var names = List<String>();\nnames.addAll(['Seth', 'Kathy', 'Lars']);\nvar nameSet = Set<String>.from(names);\n``````\n\n``````var views = Map<int, View>();\n``````\n\n### （4）泛型集合及其包含的类型\n\nDart的泛型类型是具体的。也就说，它们在运行时会会携带类型信息。\n\n``````var names = List<String>();\nnames.addAll(['Seth', 'Kathy', 'Lars']);\nprint(names is List<String>); // true\nprint(names.runtimeType); // List<String>\n``````\n\n### （5）限制参数类型\n\n``````abstract class SomeBaseClass {\n// 其他操作\n}\n\nclass Foo<T extends SomeBaseClass> {\nString toString() {\nreturn \"Instance of Foo<\\$T>\";\n}\n}\n\nclass Extender extends SomeBaseClass {\n//其他操作\n}\n``````\n\n``````void main() {\nvar someBaseClassFoo = Foo<SomeBaseClass>();\nvar extenderFoo = Foo<Extender>();\nprint(someBaseClassFoo.toString());// Instance of Foo<SomeBaseClass>\nprint(extenderFoo.toString());// Instance of Foo<SomeBaseClass>\n}\n``````\n\n``````var foo = Foo();\n``````\n\n//等同于print(foo.toString());\n\n``````print(foo);// Instance of Foo<SomeBaseClass>\n``````\n\n### （6）使用泛型方法\n\n``````新版本的Dart的泛型方法，允许在方法和函数上使用类型参数。（但它同样适用于实例方法，静态方法，顶级函数，本地函数甚至lambda表达式。）\n\n``````\n`````` T first<T>(List<T> data) {\n// 做一些初始工作或错误检查...\nT tmp = data;\n// 做一些额外的检查或处理...\nreturn tmp;\n}\n``````\n\n• 1). 在函数的返回类型（T）中\n• 2). 在参数类型（List<T>）中\n• 3). 在局部变量的类型（T tmp）\n\n``````class Test {\nstatic int f<M, N>(int x) => 3;\nint m<M, N>(int y) => 5;\n}\n``````\n\n// 作为参数\n\n``````void functionTypedParameter<T>(T callback){}\n``````\n\n// 声明一个本地泛型函数`本身`\n\n``````void localFunction(){\nT itself<T>(T thing) => thing;\n}\n``````\n\n// 将泛型函数表达式绑定到局部变量。\n\n``````void functionExpression(){\nvar lambda = <T>(T thing) => thing;\n}\n``````\n\n``````void main() {\nList<String> data = [\"张三\",\"李四\",\"王五\"];\nvar result = first(data);\nprint(result);\n}\n``````\n\n# （三）函数\n\n### （1）普通函数\n\nDart是一种真正的面向对象的语言，所以即使是函数也是对象，函数属于`Function`类型。可以通过函数指定变量或者把函数作为其他函数的参数。\n\n##### 1）函数的简写。\n\n1.对于只有一个表达式的函数，可以简写。\n\n`````` void main(){\nrunApp(new MyApp());\n}\n``````\n\n``````void main() => runApp(new MyApp());\n``````\n\n【注意：】`main`函数是程序的入口，不管是纯Dart代码，还是Flutter项目，或者其他语言，基本都是`main`函数是入口函数。\n\n2.返回值为`void`时，可以省略`void`关键字（开发中不建议这么做）。\n\n``````void _incrementCounter(){\n//...\n}\n``````\n\n``````_incrementCounter(){\n//...\n}\n``````\n\n【注意】函数属于Function类型，可以通过断言assert(XXX is Funtion);判断出结果，返回值必须是具体类型或者省略，如果返回值写为void，编译器有错误提示。\n\n``````void testMethod (){\n//...\n}\n``````\n\n##### 2）普通参数与可选参数\n\nDart的函数最好玩的就是这个可选参数了，就是可以声明多个参数，使用时可以调用其中的某一个或者多个参数，与参数位置无关。\n\n1.可选参数的基本使用\n\n``````// 工作：地址、公司名、工资、工作时长、公司人数\nvoid work(\nString address,\nString cpompany,\ndouble money,\nString workTime,\nint workerNumbers) {\n//TODO:...\n}\n``````\n\n``````void main() {\n// 缺一个参数都会报错\nwork('hangzhou','XXCompany',1000000.00,'9:00-5:00',500);\n}\n``````\n\n``````void work2({\nString address,\nString cpompany,\ndouble money,\nString workTime,\nint workerNumbers}) {\n//TODO:...\n}\n``````\n\n``````void main() {\n//你随意使用其中的参数都是可以的，例如我使用了其中的参数1，参数4和参数5\nwork2(address:'hangzhou', workTime:'9:00-5:00', workerNumbers:500);\n}\n``````\n\n2.可选参数默认的值\n\n``````void work3({\nString address = 'hangzhou',\nString cpompany = ' XXCompany ',\ndouble money,\nString workTime,\nint workerNumbers}) {\n//TODO:...\n}\n``````\n\n3.普通函数参数为list或者map的默认值\n\n``````void work4(\nString address,\n[String cpompany = 'XXCompany',\ndouble money,\nString workTime,\nint workerNumbers]) {\n//TODO:...\n}\n``````\n\n4.可变参数为list或者map的默认值\n\n``````void work5({\nList<int> list = const [10, 20, 30],\nMap<String, String> gifts = const {\n'cpompany':'XXCompany',\n'money':'50000',\n'workTime':'9:00-5:00',\n}}) {\n//TODO:...\n}\n``````\n##### 3）函数作为一个参数传给另一个函数\n\n``````// 函数作为参数传给另一个函数\nvoid main() {\n// 例如main.dart里面FloatingActionButton的onPressed参数引入了一个_incrementCounter()函数\n// floatingActionButton: new FloatingActionButton(onPressed: _incrementCounter,),\n}\n\nvoid _incrementCounter() {\n// setState(() {\n// _counter++;\n// });\n}\n``````\n##### 4）匿名函数\n\n``````void _incrementCounter() {\nsetState(() {\n_counter++;\n});\n}\n``````\n\n``````List list = [10, 7, 23];\nlist.forEach((item) {\nprint('\\$item');\n});\n``````\n\n##### 5）函数作用域\n\nDart是一种具有语法范围的语言，变量的范围是静态确定的，只需通过代码布局来确定。通过花括号向外查看，可以确定变量是否在范围内。\n\n``````// main函数里面可以输出topLevel和insideMain的值。\n// myFunction函数里面可以输出topLevel、insideMain和insideFunction的值。\n// nestedFunction函数里面可以输出topLevel、insideMain、insideFunction和insideNestedFunction的值。\nbool topLevel = true;\nvoid main() {\nvar insideMain = true;\nvoid myFunction() {\nvar insideFunction = true;\nvoid nestedFunction() {\nvar insideNestedFunction = true;\nprint('topLevel\\r');\nprint(topLevel);\nprint('insideMain\\r');\nprint(insideMain);\nprint('insideFunction\\r');\nprint(insideFunction);\nprint('insideNestedFunction\\r');\nprint(insideNestedFunction);\n}\n// print('topLevel\\r');\n// print(topLevel);\n// print('insideMain\\r');\n// print(insideMain);\n// print('insideFunction\\r');\n// print(insideFunction);\n// 调用函数nestedFunction\nnestedFunction();\n}\n// 调用函数myFunction\nmyFunction();\n// print('topLevel\\r');\n// print(topLevel);\n// print('insideMain\\r');\n// print(insideMain);\n}\n``````\n##### 6）闭包\n\n• a. 内部函数为有参数的匿名函数示例：\n``````void main() {\nvar result = test();\nprint(result(2.0));//结果为：12.56\n}\n\nFunction test(){\nconst PI = 3.14;\nreturn (double r) => r * r * PI;\n}\n``````\n• b. 内部函数为无参数的匿名函数示例：\n``````void main() {\nvar result2 = test2();\nprint(result2());//结果为：3.14\n}\n\nFunction test2() {\nconst PI = 3.14;\nreturn () => PI;\n}\n``````\n##### 7）等价函数\n``````//函数也是对象\n\nvoid topMethod() {} // 一个顶级函数\n\nclass Demo {\nstatic void staticMethod() {} //一个静态方法\nvoid caseMethod() {} //实例方法\n}\n\nvoid main() {\nvar compareVar;\n\n// 比较顶级的函数\ncompareVar = topMethod;\nprint(topMethod == compareVar);\n\n// 比较静态方法\ncompareVar = Demo.staticMethod;\nprint(Demo.staticMethod == compareVar);\n\n// 比较实例方法\nvar demo1 = Demo(); // Demo类的实例1\nvar demo2 = Demo(); // Demo类的实例2\nvar y = demo2;\ncompareVar = demo2.caseMethod;\n\n//这些闭包指向同一个实例demo2，所以它们相等。\nprint(y.caseMethod == compareVar);\n\n//这些闭包是指不同的实例，所以他们不平等。\nprint(demo1.caseMethod != demo2.caseMethod);\n}\n``````\n##### 8）函数别名\n\n``````class Demo {\nFunction funs;\nDemo (int f(Object a, Object b)) {\nfuns = f;\n}\n}\n\nint test(Object a, Object b) => 0;\n\nvoid main() {\nDemo demo = Demo(test);\n// funs是一个函数，但它是哪一种类型的函数?\nprint(demo.funs is Function); // true\n}\n``````\n\n1. 给Function取一个别名叫做`TypedefFuns`\n``````typedef TypedefFuns = int Function(Object a, Object b);\n``````\n1. Demo类里的构造方法使用这个别名\n``````class Demo {\nTypedefFuns funs;\nDemo(this.funs);\n}\n``````\n1. 使用Demo类，传入一个函数。这里给Demo类传入了一个函数`test`。如果想知道然后判断`demo.funs`属于哪一种类型。\n``````int test(Object a, Object b) => 0;\n\nvoid main() {\nDemo demo = Demo(test);\nprint(demo.funs is Function); // true\nprint(demo.funs is Demo); // false\n}\n``````\n\n``````typedef TypedefFuns2<T> = int Function(T a, T b);\nint test2(int a, int b) => a - b;\nvoid main() {\nprint(test2 is TypedefFuns2<int>); // True\n}\n``````\n##### 9）getter 和 setter\n\n`getter``setter`是提供对象属性的读写访问权限的特殊方法。所有实例变量都生成一个隐式getter方法。非final实例变量也会生成隐式setter方法。使用get和set关键字通过实现getter和setter来创建其他属性。\n\n• 1.使用getter和setter，可以从实例变量开始。\n\n``````void main() {\nvar rect = Rectangle(3, 4, 20, 15);\nprint(rect.left == 3); // true\nrect.right = 12;\nprint(rect.left == -8); // true\n}\n\nclass Rectangle {\nnum left, top, width, height;\n\nRectangle(this.left, this.top, this.width, this.height);\n\nnum get right => left + width;\nset right(num value) => left = value - width;\nnum get bottom => top + height;\nset bottom(num value) => top = value - height;\n}\n``````\n\n• 2.实例变量的隐式getter和setter方法\n\n``````class Point {\nnum x;\nnum y;\n}\n\nvoid main() {\nvar point = Point();\npoint.x = 4; // Use the setter method for x.\nassert(point.x == 4); // Use the getter method for x.\nassert(point.y == null); // Values default to null.\n}\n``````\n\n``````class Point2 {\nnum x = 10;\nnum y = 5;\nPoint2 p = new Point2();//p在构造函数之前执行\nPoint2(){}\n}\nvoid main() {\nvar point2 = Point2();\npoint2.x = 4; //\n}\n``````\n##### 10）抽象方法\n\n``````abstract class Test {\n//定义实例变量和方法...\n\n//定义一个抽象方法\nvoid doSomething();\n}\n\nclass TestImpl extends Test {\n// 抽象方法的实现\nvoid doSomething(){\n// 具体的实现...\n}\n}\n``````\n##### 11）静态方法\n\n``````void main() {\nprint(Point.area(5, 4));// 10\n}\nclass Point {\nstatic num area(num x, num y) {\nreturn (x * y)/2;\n}\n}\n``````\n\n### （2）构造函数\n\n##### 1).最常见的构造函数形式，即生成构造函数，创建一个类的新实例。\n\n``````class Test {\nint x, y;\n\nTest(int x, int y) {\nthis.x = x;//this.x指向的是当前Test类里面的变量int x\nthis.y = y;\n}\n}\nvoid main(){\n// 使用Test构造函数创建Test对象\nvar test = new Test(5, 15);\n}\n``````\n##### 2).Dart具有语法糖，可以将构造函数参数赋值给实例变量。\n``````class Test {\nnum x, y;\n\n// 构造函数运行之前设置x和y\nTest(this.x, this.y) {\nprint('x:\\$x, y:\\$y');\n}\n}\n\nclass Test {\nnum x, y;\n\n// 构造函数运行之前设置x和y\nTest(this.x, this.y);\n}\n``````\n##### 3).默认构造函数（空参构造）\n\n`````` class Test{\n// 如果不写 默认就是空参构造\nTest(){}\n}\n``````\n##### 4).命名构造函数\n\nJava可以做到方法重载（也就是：多个同名不同参数构造函数），但是Dart不可以这么做。Dart提供了命名构造。使用命名构造函数为类实现多个构造函数或提供更多的解释说明。\n\n``````class Test{\nnum x, y;\n\n// 命名构造\nTest.help() {\nx = 5;\ny = 10;\nprint('x=\\${x}, y = \\${y}');\n}\n}\nvoid main(){\nTest.help();// 调用命名构造函数\n}\n``````\n\n``````void main() {\n// 先执行Test类的空参构造， 再执行TestChild类的空参构造。\nnew TestChild();\n// 调用时会报错\n//new TestChild.help();\n}\n\nclass Test{\nvar x, y;\nTest(){\nprint('这是 Test 类的空参构造');\n}\n// 命名构造不能被继承\nTest.help(){\nx = 5;\ny = 10;\nprint('Test.help() 命名函数 x=\\${x}, y = \\${y}');\n}\n}\n\nclass TestChild extends Test{\nvar x, y;\nTestChild(){\nprint('这是 TestChild 类的空参构造');\n}\n// 加上与父类相同的命名构造就不会错 注释了就会报错\n// TestChild.help(){\n// x = 3;\n// y = 2;\n// print('TestChild.help() 命名函数 x=\\${x}, y = \\${y}');\n// }\n}\n``````\n\n##### 6).构造函数调用流程\n\n`初始化列表 -> 超类的无参数构造函数 -> 主类的无参数构造函数`,\n\n``````Test 空参构造\nTestChild 有参构造\n\n``````\n\n``````void main() {\nvar result = new TestChild.area(3, 4);\nprint('面积为：\\${result.area}');\n}\n\nclass Test {\nnum width;\nnum height;\nnum area;\n\n// 必须加上空参构造，如果注释掉 它的子类会报错\nTest() {\nprint('Test 空参构造');\n}\n\nTest.area(width, height)\n: width = width,\nheight = height,\narea = width * height {\nprint('Test 有参构造');\n}\n}\n\nclass TestChild extends Test {\n\nnum width;\nnum height;\nnum area;\n\nTestChild() {\nprint('TestChild 空参构造');\n}\n\nTestChild.area(num width, num height)\n: area = (width * height)/2 {\nprint('TestChild 有参构造');\n}\n}\n``````\n\n1. 在调用构造函数之前会计算超类构造函数的参数，所以参数可以是一个表达式。\n``````void main(){\nnew TestChild();\n}\n\nclass Test{\nstatic String data;\nTest() {\nprint('Test 空参构造，data: \\$data');\n}\n\nTest.area(String datas) {\nprint('Test.area 命名函数，data: \\$datas');\n}\n}\n\nclass TestChild extends Test {\n// 参数可以是一个表达式\nTestChild() : super.area(getDefaultData()) {\nprint('TestChild 空参函数 调用父类的命名构造');\n}\n\nstatic String getDefaultData(){\nreturn 'TestChild的数据 getDefaultData';\n}\n}\n``````\n\n`````` Test.area 命名函数，data: TestChild的数据 getDefaultData\nTestChild 空参函数 调用父类的命名构造\n``````\n• 2.超类构造参数不能使用this关键字。例如：参数可以调用静态方法，但是不能调用实例方法。\n例如上例中的`Test.area`，修改一下就会报错：\n``````Test.area(this.width, this.height)\n: width = width,\nheight = height,\narea = width * height {\nprint('Test 有参构造');\n}\n``````\n##### 7).重定向构造函数\n\n``````void main() {\nvar result = new Test(4, true, '数字', 10);\nprint('abcd分别是：\\${result.a},\\${result.b},\\${result.c},\\${result.d}');\n}\n\nclass Test {\nnum a;\nbool b;\nString c;\nnum d;\n// 主构造函数\nTest(this.a, this.b, this.c, this.d);\n\n// 委托给主构造函数\nTest.test1(num x,bool y) : this(x, y,'', 0);\nTest.test2(num a,bool b, String c) : this(a, b, c, 0);\nTest.test3(num a,bool b, String c,num d) : this(a, b, c, d);\n}\n``````\n\n##### 8).常量构造函数\n• 1.如果您的类生成永远不会更改的对象，则可以使这些对象成为编译时常量。为此，请定义`const`构造函数并确保所有实例变量都是`final`。要使用const构造函数创建编译时常量，请将`const`关键字放在构造函数名称之前。\n示例代码：\n``````void main() {\nvar result = new Test(4, 10);\nprint('x=\\${result.x}, y:=\\${result.y}'); // x=4, y=10\nprint(Test.origin.x); // 5\nprint(Test.origin.y); // 1\n\nvar a = const Test(1, 1);\nvar b = const Test(1, 1);\n// 他们是相同示实例\nprint(a == b); // true\n\nclass Test {\nstatic final Test origin = const Test(5, 1);\nfinal num x;\nfinal num y;\nconst Test(this.x, this.y);\n}\n``````\n• 2.常量上下文中的const构造函数\n\n``````// 这里有很多const关键字\nconst pointAndLine = const {\n'point': const [const ImmutablePoint(0, 0)],\n'line': const [const ImmutablePoint(1, 10), const ImmutablePoint(-2, 11)],\n};\nclass ImmutablePoint{\nconst ImmutablePoint(int a, int b);\n}\n``````\n\n``````// 只有一个const, 它建立了常量上下文\nconst pointAndLine2 = {\n'point': [ImmutablePoint(0, 0)],\n'line': [ImmutablePoint(1, 10), ImmutablePoint(-2, 11)],\n};\n``````\n\n``````var a = const ImmutablePoint(1, 1); //创建一个常量\nvar b = ImmutablePoint(1, 1); // 不创建常量\nassert(!identical(a, b)); // 不是同一个实例\n``````\n##### 9).工厂构造函数\n\n`factory`是在实现不总是创建其类的新实例的构造函数时使用关键字。例如，工厂构造函数可能从缓存中返回实例，或者它可能返回子类型的实例。\n\n``````class Test{\nfinal String name;\nstatic Map<String, Test> _cache = new Map<String, Test>();\nfactory Test(String name) {\nif (_cache.containsKey(name)) {\nreturn _cache[name];\n} else {\nfinal symbol = new Test._internal(name);\n_cache[name] = symbol;\nreturn symbol;\n}\n}\nTest._internal(this.name);\nvoid test(){\nprint('调用了test()');\n}\n}\nvoid main(){\nvar a = new Test('abc');\nvar b = new Test('abc');\n// 检查两个是否引用的相同的对象\nprint(identical(a, b)); // true\nnew Test('abc').test();\n}\n``````\n\n``````true\n\n``````\n\n• 1.工厂构造函数无权访问`this`\n• 2.可以创建子类的实例（例如：取决于传递的参数）。\n• 3.返回缓存的实例而不是新的实例。\n• 4.可以使用new关键字，也可以不使用。（上例中可以这样写：Test('abc').test()）\n• 5.工厂构造函数没有初始化列表（没有 :super()）\n\n``````// factory实现的单例\nclass Singleton {\nfactory Singleton() => const Singleton._internal_();\nconst Singleton._internal_();\n}\n\nvoid main() {\nprint(new Singleton() == new Singleton());\nprint(identical(new Singleton(), new Singleton()));\n}\n``````\n\n### （3）初始化列表\n\n##### 1).可以在构造函数体运行之前初始化实例变量，用逗号分隔初始化。\n\n``````class Test1 {\nvar x, y;\nTest1(var x, var y)\n: x = x,\ny = y {\nprint('Test1 有参构造初始化');\n}\n}\n``````\n\n``````class Test2{\nvar x,y;\nTest2.from(Map<String, num> json)\n: x = json['x'],\ny = json['y'] {\nprint('Test2.from(): (\\$x, \\$y)');\n}\n}\n``````\n##### 2). 在实际应用开发中，可以使用`assert`在初始化列表用来校验输入参数。\n\n``````class Test1 {\nvar x, y;\n\nTest1(var x, var y) : assert(x >= 0) {\nprint('Test1(): (\\$x, \\$y)');\n}\n\n}\n``````\n\n``````class Test2 {\nvar x, y;\nTest2.withAssert(this.x, this.y) : assert(x >= 0) {\nprint('Test2.withAssert(): (\\$x, \\$y)');\n}\n}\n``````\n##### 3).如果没有更多实际操作内容，可以简写。\n\n``````class Test1 {\nvar x, y;\n\nTest1(var x, var y) : assert(x >= 0);\n\n}\n``````\n\n``````class Test2{\nvar x, y;\nTest2.withAssert(this.x, this.y) : assert(x >= 0);\n}\n``````\n##### 4).如果要把构造的初始化和`assert`校验同时使用，可以采用这种方式：\n\n``````class Test1{\nvar x, y;\nTest1(var x, var y) : assert(x > 0){\nthis.x = x;\nthis.y = y;\nprint('Test1 有参构造初始化');\n}\n}\n``````\n##### 5).设置`final`字段，初始化程序时更方便。\n``````import 'dart:math';\n\n// 设置final字段，初始化程序时更方便\n\nvoid main() {\nvar p = new Test1(4, 3);\nprint('长方形的对角线长度：\\${p.hypotenuse}');\n}\n\nclass Test1 {\nfinal num width;\nfinal num height;\nfinal num hypotenuse;\n\nTest1(width, height)\n: width = width,\nheight = height,\nhypotenuse = sqrt(width * width + height * height);\n}\n``````\nFlutter&Dart" ]
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https://stats.stackexchange.com/questions/435241/bivariate-exponential-distribution-s-t-with-controllable-correlation-and-s
[ "# Bivariate exponential distribution $(S, T)$ with controllable correlation and $S\\leq T$\n\nI am trying to define a bivariate exponential distribution $$(S, T)$$ with marginals $$S\\sim\\mathrm{Exp}(\\lambda_S)$$ and $$T\\sim\\mathrm{Exp}(\\lambda_T)$$ for $$\\lambda_S > \\lambda_T$$. I would like the joint distribution of $$S$$ and $$T$$ to have two properties:\n\n1. $$\\rho(S, T)$$ can be controlled by some parameter of the joint distribution\n2. $$S\\leq T$$\n\nThe literature has many examples of distributions that fulfill one of these two properties. For instance, the BVE of Marshall and Olkin (1967) can be constructed from independent random variables $$\\tilde S, \\tilde T$$, and $$C$$ and selected constant $$\\lambda_C < \\lambda_T$$ as\n\n\\begin{align*} \\tilde S &\\sim \\mathrm{Exp}(\\lambda_S-\\lambda_C) \\\\ \\tilde T &\\sim \\mathrm{Exp}(\\lambda_T-\\lambda_C) \\\\ C &\\sim \\mathrm{Exp}(\\lambda_C) \\\\ S &= \\min(\\tilde S, C) \\\\ T &= \\min(\\tilde T, C) \\end{align*}\n\nHere, $$S$$ and $$T$$ have the desired marginal distributions, and $$\\lambda_C$$ controls the degree to which they are correlated (requirement 1). However, we cannot guarantee that $$S\\leq T$$ (requirement 2).\n\nAlternately, we could use independent random variables $$\\tilde S$$ and $$T$$ to construct\n\n\\begin{align*} \\tilde S &\\sim \\mathrm{Exp}(\\lambda_S-\\lambda_T) \\\\ T &\\sim \\mathrm{Exp}(\\lambda_T) \\\\ S &= \\min(\\tilde S, T) \\end{align*}\n\nAgain, $$S$$ and $$T$$ have the desired marginal distributions. This time $$S\\leq T$$ (requirement 2), but we have no way to control the correlation (requirement 1).\n\nIs there a bivariate exponential distribution that meets both of my requirements?\n\nConsider $$E \\sim \\mathcal{E}( \\lambda_S - \\lambda_C)$$ and $$C \\sim \\mathcal{E}(\\lambda_C)$$. Now define \\begin{align*} S & = \\min \\{ E , C \\} \\\\ T & = \\min \\{ a E , C\\} \\end{align*} where $$a = \\frac{ \\lambda_S - \\lambda_C}{\\lambda_T - \\lambda_C} > 1 .$$\n\nYou get $$S \\sim \\mathcal {E}(\\lambda_S)$$ and $$T \\sim \\mathcal{E} (\\lambda_T)$$, by construction $$S \\leq T$$ and you have some ability to control correlation between two variables. Analytically, $$\\rho(S,T) = \\frac{\\lambda_S+\\lambda_C(1-\\lambda_T/\\lambda_S-\\lambda_S/\\lambda_T)}{\\lambda_S-\\lambda_C} .$$ If $$\\lambda_C \\approx 0$$ you get $$S \\approx E$$ and $$S\\approx a E$$ hence $$\\rho \\approx 1$$, but if $$\\lambda_C \\approx \\lambda_T$$ then $$T \\approx C$$ and $$S \\approx \\min\\{E, C\\}$$, meaning $$\\rho\\approx\\lambda_T/\\lambda_S$$.\n\nWith the following simulation I obtained an estimation of $$0.625$$ for the correlation with $$\\lambda_S = 2$$, $$\\lambda_T = 1.1$$ and $$\\lambda_C = 1$$ (analytically we know $$\\rho(S,T)=\\frac{139}{220}\\approx 0.632$$).\n\nset.seed(1234)\nlambda_S = 2; lambda_T = 1.1; lambda_C = 1\na = (lambda_S -lambda_C)/(lambda_T -lambda_C)\n\nE = rexp(10000, lambda_S - lambda_C)\nC = rexp(10000, lambda_C)\n\nS = apply(rbind(E,C), 2, min)\nTT = apply(rbind( a*E,C), 2, min)\n\ncor(S, TT)\n# 0.6254737\n\n\nChanging $$\\lambda_S = 10$$ gives $$\\rho(S,T)=\\frac{1979}{9900}\\approx 0.200$$." ]
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https://www.colorhexa.com/114a39
[ "# #114a39 Color Information\n\nIn a RGB color space, hex #114a39 is composed of 6.7% red, 29% green and 22.4% blue. Whereas in a CMYK color space, it is composed of 77% cyan, 0% magenta, 23% yellow and 71% black. It has a hue angle of 162.1 degrees, a saturation of 62.6% and a lightness of 17.8%. #114a39 color hex could be obtained by blending #229472 with #000000. Closest websafe color is: #003333.\n\n• R 7\n• G 29\n• B 22\nRGB color chart\n• C 77\n• M 0\n• Y 23\n• K 71\nCMYK color chart\n\n#114a39 color description : Very dark cyan - lime green.\n\n# #114a39 Color Conversion\n\nThe hexadecimal color #114a39 has RGB values of R:17, G:74, B:57 and CMYK values of C:0.77, M:0, Y:0.23, K:0.71. Its decimal value is 1133113.\n\nHex triplet RGB Decimal 114a39 `#114a39` 17, 74, 57 `rgb(17,74,57)` 6.7, 29, 22.4 `rgb(6.7%,29%,22.4%)` 77, 0, 23, 71 162.1°, 62.6, 17.8 `hsl(162.1,62.6%,17.8%)` 162.1°, 77, 29 003333 `#003333`\nCIE-LAB 27.605, -22.914, 4.945 3.418, 5.312, 4.716 0.254, 0.395, 5.312 27.605, 23.441, 167.821 27.605, -20.54, 8.355 23.047, -13.859, 4.002 00010001, 01001010, 00111001\n\n# Color Schemes with #114a39\n\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #4a1122\n``#4a1122` `rgb(74,17,34)``\nComplementary Color\n• #114a1d\n``#114a1d` `rgb(17,74,29)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #113f4a\n``#113f4a` `rgb(17,63,74)``\nAnalogous Color\n• #4a1d11\n``#4a1d11` `rgb(74,29,17)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #4a113f\n``#4a113f` `rgb(74,17,63)``\nSplit Complementary Color\n• #4a3911\n``#4a3911` `rgb(74,57,17)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #39114a\n``#39114a` `rgb(57,17,74)``\n• #224a11\n``#224a11` `rgb(34,74,17)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #39114a\n``#39114a` `rgb(57,17,74)``\n• #4a1122\n``#4a1122` `rgb(74,17,34)``\n• #030c09\n``#030c09` `rgb(3,12,9)``\n• #072119\n``#072119` `rgb(7,33,25)``\n• #0c3529\n``#0c3529` `rgb(12,53,41)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #165f49\n``#165f49` `rgb(22,95,73)``\n• #1b7359\n``#1b7359` `rgb(27,115,89)``\n• #1f8869\n``#1f8869` `rgb(31,136,105)``\nMonochromatic Color\n\n# Alternatives to #114a39\n\nBelow, you can see some colors close to #114a39. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #114a2b\n``#114a2b` `rgb(17,74,43)``\n• #114a30\n``#114a30` `rgb(17,74,48)``\n• #114a34\n``#114a34` `rgb(17,74,52)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #114a3e\n``#114a3e` `rgb(17,74,62)``\n• #114a43\n``#114a43` `rgb(17,74,67)``\n• #114a47\n``#114a47` `rgb(17,74,71)``\nSimilar Colors\n\n# #114a39 Preview\n\nThis text has a font color of #114a39.\n\n``<span style=\"color:#114a39;\">Text here</span>``\n#114a39 background color\n\nThis paragraph has a background color of #114a39.\n\n``<p style=\"background-color:#114a39;\">Content here</p>``\n#114a39 border color\n\nThis element has a border color of #114a39.\n\n``<div style=\"border:1px solid #114a39;\">Content here</div>``\nCSS codes\n``.text {color:#114a39;}``\n``.background {background-color:#114a39;}``\n``.border {border:1px solid #114a39;}``\n\n# Shades and Tints of #114a39\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #020a08 is the darkest color, while #f9fefc is the lightest one.\n\n• #020a08\n``#020a08` `rgb(2,10,8)``\n• #061a14\n``#061a14` `rgb(6,26,20)``\n• #0a2a20\n``#0a2a20` `rgb(10,42,32)``\n• #0d3a2d\n``#0d3a2d` `rgb(13,58,45)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #155a45\n``#155a45` `rgb(21,90,69)``\n• #186a52\n``#186a52` `rgb(24,106,82)``\n• #1c7a5e\n``#1c7a5e` `rgb(28,122,94)``\n• #208a6a\n``#208a6a` `rgb(32,138,106)``\n• #239a76\n``#239a76` `rgb(35,154,118)``\n• #27aa83\n``#27aa83` `rgb(39,170,131)``\n• #2bba8f\n``#2bba8f` `rgb(43,186,143)``\n• #2eca9b\n``#2eca9b` `rgb(46,202,155)``\n``#3ad2a4` `rgb(58,210,164)``\n``#4ad5ac` `rgb(74,213,172)``\n``#5ad9b3` `rgb(90,217,179)``\n``#6addba` `rgb(106,221,186)``\n• #7ae0c2\n``#7ae0c2` `rgb(122,224,194)``\n• #8ae4c9\n``#8ae4c9` `rgb(138,228,201)``\n• #9ae8d0\n``#9ae8d0` `rgb(154,232,208)``\n• #a9ebd8\n``#a9ebd8` `rgb(169,235,216)``\n• #b9efdf\n``#b9efdf` `rgb(185,239,223)``\n• #c9f3e6\n``#c9f3e6` `rgb(201,243,230)``\n• #d9f6ee\n``#d9f6ee` `rgb(217,246,238)``\n• #e9faf5\n``#e9faf5` `rgb(233,250,245)``\n• #f9fefc\n``#f9fefc` `rgb(249,254,252)``\nTint Color Variation\n\n# Tones of #114a39\n\nA tone is produced by adding gray to any pure hue. In this case, #2d2e2e is the less saturated color, while #03583f is the most saturated one.\n\n• #2d2e2e\n``#2d2e2e` `rgb(45,46,46)``\n• #2a322f\n``#2a322f` `rgb(42,50,47)``\n• #263531\n``#263531` `rgb(38,53,49)``\n• #233932\n``#233932` `rgb(35,57,50)``\n• #1f3c33\n``#1f3c33` `rgb(31,60,51)``\n• #1c4035\n``#1c4035` `rgb(28,64,53)``\n• #184336\n``#184336` `rgb(24,67,54)``\n• #154738\n``#154738` `rgb(21,71,56)``\n• #114a39\n``#114a39` `rgb(17,74,57)``\n• #0e4e3a\n``#0e4e3a` `rgb(14,78,58)``\n• #0a513c\n``#0a513c` `rgb(10,81,60)``\n• #06553d\n``#06553d` `rgb(6,85,61)``\n• #03583f\n``#03583f` `rgb(3,88,63)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #114a39 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
[ null ]
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https://www.economics.ku.dk/staff/vip/?pure=en%2Fpublications%2Fcomparing-linear-probability-model-coefficients-across-groups(08f9bd9a-280a-4e3e-b785-ee1864687833)%2Fexport.html
[ "## Comparing linear probability model coefficients across groups\n\nResearch output: Contribution to journalJournal articleResearchpeer-review\n\n#### Standard\n\nComparing linear probability model coefficients across groups. / Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt.\n\nIn: Quality and Quantity, Vol. 49, No. 5, 09.2015, p. 1823-1834.\n\nResearch output: Contribution to journalJournal articleResearchpeer-review\n\n#### Harvard\n\nHolm, A, Ejrnæs, M & Karlson, KB 2015, 'Comparing linear probability model coefficients across groups', Quality and Quantity, vol. 49, no. 5, pp. 1823-1834. https://doi.org/10.1007/s11135-014-0057-0\n\n#### APA\n\nHolm, A., Ejrnæs, M., & Karlson, K. B. (2015). Comparing linear probability model coefficients across groups. Quality and Quantity, 49(5), 1823-1834. https://doi.org/10.1007/s11135-014-0057-0\n\n#### Vancouver\n\nHolm A, Ejrnæs M, Karlson KB. Comparing linear probability model coefficients across groups. Quality and Quantity. 2015 Sep;49(5):1823-1834. https://doi.org/10.1007/s11135-014-0057-0\n\n#### Author\n\nHolm, Anders ; Ejrnæs, Mette ; Karlson, Kristian Bernt. / Comparing linear probability model coefficients across groups. In: Quality and Quantity. 2015 ; Vol. 49, No. 5. pp. 1823-1834.\n\n#### Bibtex\n\n@article{08f9bd9a280a4e3eb785ee1864687833,\ntitle = \"Comparing linear probability model coefficients across groups\",\nabstract = \"This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons.\",\nauthor = \"Anders Holm and Mette Ejrn{\\ae}s and Karlson, {Kristian Bernt}\",\nyear = \"2015\",\nmonth = sep,\ndoi = \"10.1007/s11135-014-0057-0\",\nlanguage = \"English\",\nvolume = \"49\",\npages = \"1823--1834\",\njournal = \"Quality and Quantity\",\nissn = \"0033-5177\",\npublisher = \"Springer\",\nnumber = \"5\",\n\n}\n\n#### RIS\n\nTY - JOUR\n\nT1 - Comparing linear probability model coefficients across groups\n\nAU - Holm, Anders\n\nAU - Ejrnæs, Mette\n\nAU - Karlson, Kristian Bernt\n\nPY - 2015/9\n\nY1 - 2015/9\n\nN2 - This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons.\n\nAB - This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons.\n\nU2 - 10.1007/s11135-014-0057-0\n\nDO - 10.1007/s11135-014-0057-0\n\nM3 - Journal article\n\nVL - 49\n\nSP - 1823\n\nEP - 1834\n\nJO - Quality and Quantity\n\nJF - Quality and Quantity\n\nSN - 0033-5177\n\nIS - 5\n\nER -\n\nID: 162898477" ]
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https://iter01.com/657351.html
[ "# 論文資訊\n\nTitle：《Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning》\nAuthors：Jiwoong Park、Minsik Lee、H. Chang、Kyuewang Lee、J. Choi\nSources：2019 IEEE/CVF International Conference on Computer Vision (ICCV)\nOthers：44 Citations, 44 References\n\n# Abstract\n\n本文提出一個完全對稱的自編碼器，其中 解碼器 基於 Laplacian sharpening  設計 ，編碼器  基於 Laplacian smoothing 設計。此外還設計了一種基於  latent representation 和  affinity matrix  的代價函式。\n\n# 1. Introduction\n\n在機器學習和資料探勘領域，使用圖資料做以下研究：\n\n• node clustering\n• dimensionality reduction\n• social network analysis\n• chemical property prediction of a molecular graph\n• image segmentation\n\n卷積方法產生限制的原因：\n\n• Low computational efficiency due to eigendecomposition or singular value decomposition.\n• Only showing a shallow relationship between nodes.\n\n近年來，一個被稱為幾何深度學習（ geometric deep learning） 的新興領域，將深度神經網路模型推廣到 非歐幾里得域 （ non-Euclidean domains），比如： meshes、 manifolds、 graphs。其中，利用自編碼器框架尋找圖的 geometrical structures 的深層潛在表示正越來越受到關注。\n\n首先嚐試的是   VGAE  它由一個  Graph Convolutional Network (GCN)  encoder   和一個  matrix outerproduct decoder  組成，如 Figure 1 (a) 所示。\n\n作為  VGAE  的一種變體，ARVGA 採用了 VGAE 的  adversarial approach。然而 VGAE 和  ARVGA  重建   affinity matrix  $A$，而不是節點   feature matrix  $X$，因此，解碼器部分不能是可學習的，故， graphical feature 不能在解碼器部分中使用。\n\n之後，提出了  MGAE，它使用具有線性啟用函式的堆疊單層圖自動編碼器和邊緣化過程 如 Figure 1 (b)所示。但是， since the MGAE reconstructs the feature matrix of nodes without hidden layers, it cannot manipulate the dimension of the latent representation and performs a linear mapping.", null, "本文提出了一種新的圖卷積自編碼器框架，該框架具有對稱的自編碼器架構，並在編碼和解碼過程中同時使用圖和節點屬性，如 Figure 1(c)  所示 。\n\nVGAE  的編碼器可以解釋為一種特殊形式的   Laplacian smoothing  ，它計算每個節點的新表示加權區域性平均的鄰居和本身。\n\n本文使用切比雪夫多項式（Chebyshev polynomial）的形式表示拉普拉斯銳化以構造一個 Laplacian sharpening  的解碼器。\n\n本文貢獻如下：\n\n• 提出了第一個完全對稱的圖卷積自編碼器，它在整個編碼-解碼過程中同時利用了圖的結構和節點屬性。\n• 推導了一種新的數值穩定形式的防止神經網路數值不穩定的解碼器。\n• 設計了一個計算高效的子空間聚類代價來同時尋找影像聚類任務的潛在表示和潛在親和矩陣。\n\n# 2. Preliminaries\n\n## 2.1. Basic notations on graphs\n\n• A graph is represented as  $\\mathcal{G}=(\\mathcal{V}, \\mathcal{E}, A)$\n• $\\mathcal{V}$  denotes the node set with  $v_{i} \\in \\mathcal{V}$  and  $|\\mathcal{V}|=n$.\n• $\\mathcal{E}$ denotes the edge set with  $\\left(v_{i}, v_{j}\\right) \\in \\mathcal{E}$.\n• $A \\in \\mathbb{R}^{n \\times n}$ denotes an affinity matrix which encodes pairwise affinities between nodes.\n• $D \\in \\mathbb{R}^{n \\times n}$  denotes a degree matrix which is a diagonal matrix with  $D_{i i}=\\sum_{j} A_{i j}$ .\n• Unnormalized graph Laplacian  $\\Delta$  is defined by  $\\Delta=D-A$  .\n• Symmetric graph Laplacian  $L$  is defined by  $L=I_{n}-D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$ .\n• Random walk graph Laplacian  $L_{r w}$ is defined by $L_{r w}=I_{n}-D^{-1} A$\n• $I_{n} \\in \\mathbb{R}^{n \\times n}$  denotes an identity matrix.\n• $\\Delta$, $L$  and  $L_{r w}$ are positive semidefinite matrices.\n\n## 2.2. Spectral convolution on graphs\n\n可以發現 2.2 節的內容在《第三代GCN》已經將的很清楚了，所以下面不再詳細展開介紹。\n\nA spectral convolution on a graph is the multiplication of an input signal $x \\in \\mathbb{R}^{n}$ with a spectral filter $g_{\\theta}=\\operatorname{diag}(\\theta)$ parameterized by the vector of Fourier coefficients $\\theta \\in \\mathbb{R}^{n}$ as follows:\n\n$g_{\\theta} * x=U g_{\\theta} U^{T} x\\quad \\quad \\quad (1)$\n\nwhere\n\n• $U$ is the matrix of eigenvectors of the symmetric graph Laplacian $L=U \\Lambda U^{T}$ .\n• $U^{T} x$ is the graph Fourier transform of the input $x$ ,\n• $g_{\\theta}$ is a function of the eigenvalues of $L$ .\n• $g_{\\theta}(\\Lambda)$ , where $\\Lambda$ is the diagonal matrix of eigenvalues of $L$ .\n\n一般圖卷積帶來的問題：this operation is inappropriate for large-scale graphs since it requires an eigendecomposition to obtain the eigenvalues and eigenvectors of $L$ .\n\n解決辦法：the spectral filter $g_{\\theta}(\\Lambda)$ was approximated by $K^{t h}$ order Chebyshev polynomials in previous works . By doing so, the spectral convolution on the graph can be approximated as\n\n$g_{\\theta} * x \\approx U \\sum\\limits _{k=0}^{K} \\theta_{k}^{\\prime} T_{k}(\\tilde{\\Lambda}) U^{T} x=\\sum\\limits _{k=0}^{K} \\theta_{k}^{\\prime} T_{k}(\\tilde{L}) x\\quad \\quad \\quad (2)$\n\nwhere\n\n• $T_{k}(\\cdot)$ denote the Chebyshev polynomials .\n• $\\theta^{\\prime}$ denote a vector of the Chebyshev coefficients.\n• $\\tilde{\\Lambda}$ is $\\frac{2}{\\lambda_{\\max }} \\Lambda-I_{n}$.\n• $\\lambda_{\\max }$ denotes the largest eigenvalue of $L$.\n• $\\tilde{L}$ is $U \\tilde{\\Lambda} U^{T}=\\frac{2}{\\lambda_{\\max }} L-I_{n}$.\n\nIn the GCN , the Chebyshev approximation model was simplified by setting $K=1$, $\\lambda_{\\max } \\approx 2$ and $\\theta=\\theta_{0}^{\\prime}= -\\theta_{1}^{\\prime}$ . This makes the spectral convolution simplified as follows:\n\n$g_{\\theta} * x \\approx \\theta\\left(I_{n}+D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}\\right) x \\quad \\quad \\quad (3)$\n\nHowever, repeated application of $I_{n}+D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$ can cause numerical instabilities in neural networks since the spectral radius of $I_{n}+D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$ is $2$ , and the Chebyshev polynomials form an orthonormal basis when its spectral radius is $1$ . To circumvent this issue, the GCN uses renormalization trick:\n\n$I_{n}+D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}} \\rightarrow \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} \\quad \\quad \\quad (4)$\n\nwhere $\\tilde{A}=A+I_{n}$ and $\\tilde{D}_{i i}=\\sum_{j} \\tilde{A}_{i j}$ . Since adding selfloop on nodes to an affinity matrix cannot affect the spectral radius of the corresponding graph Laplacian matrix , this renormalization trick can provide a numerically stable form of $I_{n}+D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$ while maintaining the meaning of each elements as follows:\n\n$\\left(I_{n}+D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}\\right)_{i j}=\\left\\{\\begin{array}{ll}1 & i=j \\\\A_{i j} / \\sqrt{D_{i i} D_{j j}} & i \\neq j\\end{array}\\right.\\quad \\quad \\quad (5)$\n\n$\\left(\\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}}\\right)_{i j}=\\left\\{\\begin{array}{ll}1 /\\left(D_{i i}+1\\right) & i=j \\\\A_{i j} / \\sqrt{\\left(D_{i i}+1\\right)\\left(D_{j j}+1\\right)} & i \\neq j\\end{array}\\right.\\quad \\quad \\quad (6)$\n\nFinally, the forward-path of the GCN can be expressed by\n\n$H^{(m+1)}=\\xi\\left(\\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} H^{(m)} \\Theta^{(m)}\\right)\\quad \\quad \\quad (7)$\n\nwhere $H^{(m)}$  is the activation matrix in the $m^{t h}$  layer and $H^{(0)}$  is the input nodes' feature matrix $X$. $\\xi(\\cdot)$  is a nonlinear activation function like $\\operatorname{ReLU}(\\cdot)=\\max (0, \\cdot)$, and $\\Theta^{(m)}$  is a trainable weight matrix. The GCN presents a computationally efficient convolutional process (given the assumption that $\\tilde{A}$  is sparse) and achieves an improved accuracy over the state-of-the-art methods in semi-supervised node classification task by using features of nodes and geometric structure of graph simultaneously.\n\n## 2.3. Laplacian smoothing\n\nLi et al. show that GCN is a special form of Laplacian smoothing.\n\nLaplacian smoothing equation:\n\n$x_{i}^{(m+1)}=(1-\\gamma) x_{i}^{(m)}+\\gamma \\sum\\limits_{j} \\frac{\\tilde{A}_{i j}}{\\tilde{D}_{i i}} x_{j}^{(m)}\\quad \\quad \\quad (8)$\n\nWhere:\n\n• $\\tilde{A}=A+I_{n}$.\n• $\\tilde{D}=D+I_{n}$.\n• $x_{i}^{(m+1)}$ is the new representation of $x_{i}^{(m)}$.\n• $\\gamma (0<\\gamma \\leq 1)$ is a regularization parameter which controls the importance between itself and its neighbors.\n\nRewrite the above equation in a matrix form as follows:\n\n\\begin{aligned}X^{(m+1)} &=(1-\\gamma) X^{(m)}+\\gamma \\tilde{D}^{-1} \\tilde{A} X^{(m)} \\\\&=X^{(m)}-\\gamma\\left(I_{n}-\\tilde{D}^{-1} \\tilde{A}\\right) X^{(m)} \\\\&=X^{(m)}-\\gamma \\tilde{L}_{r w} X^{(m)}\\end{aligned}\\quad \\quad \\quad (9)\n\nTips:\n\nRandom walk normalized Laplacian\n\n$L^{r w}=D^{-1} L=I-D^{-1} A$\n\nSymmetric normalized Laplacian\n\n$L^{\\text {sys }}=D^{-1 / 2} L D^{-1 / 2}=I-D^{-1 / 2} A D^{-1 / 2}$\n\nWe set  $\\gamma=1$  and replace $\\tilde{L}_{r w}$  with  $\\tilde{L}$ , then Eq. (9) is changed into\n\n$X^{(m+1)}=\\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} X^{(m)}$\n\nThis equation is the same as the renormalized version of spectral convolution in Eq. (7).\n\n# 3 The proposed method\n\nOur mode is GALA (Graph convolutional Autoencoder using Laplacian smoothing and sharpening).\n\nIn GALA, there are  $M$  layers in total, from the first to $\\frac{M}{2}$  th layers for the encoder and from the  $\\left(\\frac{M}{2}+1\\right)$ th to  $M$  th layers for the decoder where  $M$  is an even number.\n\n• The encoder part of GALA is designed to perform the computationally efficient spectral convolution on the graph with a numerically stable form of Laplacian smoothing in the Eq. (7) .\n• Its decoder part is designed to be a special form of Laplacian sharpening . By this decoder part, GALA reconstructs the feature matrix of nodes directly, instead of yielding an affinity matrix as in the existing VGAE-related algorithms whose decoder parts are incomplete.\n\n## 3.1 Laplacian sharpening\n\nThe encoder performs Laplacian smoothing that makes the latent representation of each node similar to those of its neighboring nodes.\n\nLaplacian sharpening is a process that makes the reconstructed feature of each node farther away from the centroid of its neighbors.\n\nLaplacian sharpening equation:\n\n$x_{i}^{(m+1)}=(1+\\gamma) x_{i}^{(m)}-\\gamma \\sum\\limits _{j} \\frac{A_{i j}}{D_{i i}} x_{j}^{(m)}\\quad \\quad \\quad (10)$\n\nWhere:\n\n• $x_{i}^{(m+1)}$ is the new representation of $x_{i}^{(m)}$.\n• $\\gamma (0<\\gamma \\leq 1)$ is a regularization parameter which controls the importance between itself and its neighbors.\n\nThe matrix form of Eq. (10) :\n\n\\begin{aligned}X^{(m+1)} &=(1+\\gamma) X^{(m)}-\\gamma D^{-1} A X^{(m)} \\\\&=X^{(m)}+\\gamma\\left(I_{n}-D^{-1} A\\right) X^{(m)} \\\\&=X^{(m)}+\\gamma L_{r w} X^{(m)}\\end{aligned}\\quad \\quad \\quad (11)\n\nWe set  $\\gamma=1$  and replace $\\tilde{L}_{r w}$  with  $\\tilde{L}$ , then Eq. (10) is changed into\n\n$X^{(m+1)}=(2 I_{n}-D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}})X^{(m)}$\n\nWe express Laplacian sharpening in the form of Chebyshev polynomial  and simplify it with\n\n• $K=1$\n• $\\lambda_{\\max } \\approx 2$\n• $\\theta=\\frac{1}{2} \\theta_{0}^{\\prime}=\\theta_{1}^{\\prime}$\n\nThen, a decoder layer can be expressed by\n\n$H^{(m+1)}=\\xi\\left(\\left(2 I_{n}-D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}\\right) H^{(m)} \\Theta^{(m)}\\right)\\quad \\quad \\quad (12)$\n\nWhere:\n\n• $H^{(m)}$  is the matrix of the activation in the  $m^{t h}$  layer,\n• $2 I_{n}-D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$  is a special form of Laplacian sharpening,\n• $\\xi(\\cdot)$  is the nonlinear activation function like  $\\operatorname{ReLU}(\\cdot) =\\max (0, \\cdot)$ ,\n• $\\Theta^{(m)}$  is a trainable weight matrix.\n\nThe spectral radius of  $2 I_{n}-D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$  is 3 , repeated application of this operator can be numerically instable.\n\n若 $\\boldsymbol{A}=\\left(a_{i j}\\right)$ 是複數域上的 $\\mathrm{n}$ 階方陣，又 $\\lambda_{1}, \\lambda_{2}, \\ldots, \\lambda_{n}$ 是 $A$ 的全部特徵值，則\n\n$\\rho(\\boldsymbol{A})= \\underset{1 \\leq i \\leq n}{max} |\\lambda_{i}|$\n\nFrom previous articles,we know that\n\n$D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$ range  $[ -1,1]$\n\nSo we need to find a  numerically stable form of Laplacian sharpening.\n\n## 3.2 Numerically stable Laplacian sharpening\n\nTo find a new representation of Laplacian sharpening whose spectral radius is $1$ .\n\nA signed graph is denoted by  $\\Gamma=(\\mathcal{V}, \\mathcal{E}, \\hat{A})$  which is induced from the unsigned graph  $\\mathcal{G}=(\\mathcal{V}, \\mathcal{E}, A)$ .\n\nEach element in  $\\hat{A}$  has the same absolute value with  $A$ , but its sign is changed into minus or keeps plus.\n\nThe degree matrix $\\hat{D}$ can be defined as $\\hat{D}_{i i}=\\sum\\limits _{j}\\left|\\hat{A}_{i j}\\right|$ .\n\nThus,we can construct\n\n• unnormalized graph Laplacian  $\\hat{\\Delta}=\\hat{D}-\\hat{A}$.\n• symmetric graph Laplacian  $\\hat{L}=I_{n}-\\hat{D}^{-\\frac{1}{2}} \\hat{A} \\hat{D}^{-\\frac{1}{2}}$  of the signed graph.\n\nThe range of the eigenvalue of  $\\hat{L}$  is  $[0,2]$ , thus the spectral radius of  $\\hat{D}^{-\\frac{1}{2}} \\hat{A} \\hat{D}^{-\\frac{1}{2}}$  is $1$ for any choice of  $\\hat{A}$\n\nUsing this result, instead of Eq. (12):\n\n$H^{(m+1)}=\\xi\\left(\\hat{D}^{-\\frac{1}{2}} \\hat{A} \\hat{D}^{-\\frac{1}{2}} H^{(m)} \\Theta^{(m)}\\right)\\quad \\quad \\quad (13)$\n\nWhere:\n\n• $\\hat{A}=2 I_{n}-A$\n• $\\hat{D}=2 I_{n}+D$\n\n$\\hat{D}^{-\\frac{1}{2}} \\hat{A} \\hat{D}^{-\\frac{1}{2}}$ 計算方式如下：\n\n$\\left(\\hat{D}^{-\\frac{1}{2}} \\hat{A} \\hat{D}^{-\\frac{1}{2}}\\right)_{i j}=\\left\\{\\begin{array}{ll}2 /\\left(D_{i i}+2\\right) & i=j \\\\-A_{i j} / \\sqrt{\\left(D_{i i}+2\\right)\\left(D_{j j}+2\\right)} & i \\neq j\\end{array}\\right.\\quad \\quad \\quad (14)$\n\nWhich has the same meaning with the original one given by\n\n$\\left(2 I_{n}-D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}\\right)_{i j}=\\left\\{\\begin{array}{ll}2 & i=j \\\\-A_{i j} / \\sqrt{D_{i i} D_{j j}} & i \\neq j\\end{array}\\right.\\quad \\quad \\quad (15)$\n\n目的：\n\n• 將譜半徑變成 $1$。\n• $\\hat{D}^{-\\frac{1}{2}} \\hat{A} \\hat{D}^{-\\frac{1}{2}}$  保留了和  $2 I_{n}-D^{-\\frac{1}{2}} A D^{-\\frac{1}{2}}$  的性質。\n\nSumary, the numerically stable decoder layer of GALA is given as\n\n$H^{(m+1)}=\\xi\\left(\\hat{D}^{-\\frac{1}{2}} \\hat{A} \\hat{D}^{-\\frac{1}{2}} H^{(m)} \\Theta^{(m)}\\right),\\left(m=\\frac{M}{2}, \\ldots, M-1\\right)\\quad \\quad \\quad (16)$\n\nWhere\n\n• $\\hat{A}=2 I_{n}-A$\n• $\\hat{D}=2 I_{n}+D$\n\nThe encoder layer of GALA is given as\n\n$H^{(m+1)}=\\xi\\left(\\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} H^{(m)} \\Theta^{(m)}\\right),\\left(m=0, \\ldots, \\frac{M}{2}-1\\right)\\quad \\quad \\quad (17)$\n\nWhere\n\n• $\\tilde{A}=I_{n}+A$\n• $\\tilde{D}=I_{n}+D$\n\nBoth encoder and decoder propagation functions, Eqs. (16) and (17), are both $\\mathcal{O}(m p c)$.\n\n• $m$ is the cardinality of edges in the graph.\n• $p$ is the feature dimension of the previous layer.\n• $c$ is the feature dimension of the current layer.\n\nIn Table 1, we show the reason why the Laplacian smoothing is not appropriate to the decoder and the necessity of numerically stable Laplacian sharpening by node clustering experiments.", null, "• Laplacian smoothing decoder (Eq. 7) shows the lowest performances, since Laplacian smoothing which makes the representation of each node similar to those of its neighboring nodes conflicts with the purpose of reconstruction cost.\n• A numerically instable form of Laplacian sharpening decoder (Eq. 12) shows higher performance compared to smoothing decoder because the role of Laplacian sharpening coincide with reconstructing the node feature.\n• The performance of proposed numerically stable Laplacian sharpening decoder (Eq. 16) significantly higher than others, since it solves instability issue of neural network while maintaining the meaning of original Laplacian sharpening.\n\nThe basic cost function of GALA is given by\n\n$\\min _{\\bar{X}} \\frac{1}{2}\\|X-\\bar{X}\\|_{F}^{2}\\quad \\quad \\quad (18)$\n\nWhere\n\n• $\\bar{X}$  is the reconstructed feature matrix of nodes.\n• the column of  $\\bar{X}$  corresponds to the output of the decoder for an input feature of a node.\n• $\\|\\cdot\\|_{F}$  denotes the Frobenius norm.\n\n## 3.3. Subspace clustering cost for image clustering\n\nFor image clustering tasks,we add  an element of subspace clustering to the proposed method.\n\n$\\underset{\\bar{X}, H, A_{H}}{min} \\frac{1}{2}\\|X-\\bar{X}\\|_{F}^{2}+\\frac{\\lambda}{2}\\left\\|H-H A_{H}\\right\\|_{F}^{2}+\\frac{\\mu}{2}\\left\\|A_{H}\\right\\|_{F}^{2}\\quad \\quad \\quad (19)$\n\nWhere\n\n• $H \\in \\mathbb{R}^{k \\times n}$  denotes the latent representations (i.e., the output of the encoder).\n• $A_{H} \\in \\mathbb{R}^{n \\times n}$  denotes the affinity matrix which is a new latent variable for subspace clustering,\n• $\\lambda$, $\\mu$  are the regularization parameters.\n\nThe second term of Eq. (19) aims at the self-expressive model of subspace clustering and the third term of Eq. (19) is for regularizing  $A_{H}$ .\n\nIf we only consider minimizing  $A_{H}$ , the problem becomes:\n\n$\\underset{A_{H}}{min} \\frac{\\lambda}{2}\\left\\|H-H A_{H}\\right\\|_{F}^{2}+\\frac{\\mu}{2}\\left\\|A_{H}\\right\\|_{F}^{2}\\quad \\quad \\quad (20)$\n\nWe can easily obtain the analytic solution\n\n$A_{H}^{*}=(H^{T} H+\\frac{\\mu}{\\lambda} I_{n})^{-1} H^{T} H$\n\nBy using this analytic solution and singular value decomposition, we derive a computationally efficient subspace clustering cost function as follows :\n\n$\\underset{\\bar{X}, H}{min} \\frac{1}{2}\\|X-\\bar{X}\\|_{F}^{2}+\\frac{\\mu \\lambda}{2} \\operatorname{tr}\\left(\\left(\\mu I_{k}+\\lambda H H^{T}\\right)^{-1} H H^{T}\\right)\\quad \\quad \\quad (21)$\n\nSome benefits are it can reduce the computational burden significantly.\n\n• The above problem can be solved by  $k \\times k$  matrix inversion instead of  $n \\times n$ matrix inversion.  from  $\\mathcal{O}\\left(n^{3}\\right)$  to  $\\mathcal{O}\\left(k^{3}\\right)$ .\n• $k$ is the dimension of latent representation.\n\n## 3.4. Training\n\n• We train GALA to minimize Eq. (18) by using the ADAM algorithm.\n• We train GALA deterministically by using the full batch in each training epoch and stop when the cost is converged.\n• We set the learning rate to $1.0 × 10^{-4}$ for training and train GALA in an unsupervised way without any cluster labels.\n\n• First, in the pre-training stage, the training method is the same as that of minimizing Eq. (18).\n• After pre-training, we fine-tune GALA to minimize Eq. (21) using ADAM.\n\nAfter the training process are over, we construct  $k$  nearest neighborhood graph using attained latent representations  $H^{*}$ . Then we perform spectral clustering and get the clustering performance.\n\nIn the case of image clustering, after all training processes are over, we construct the optimal affinity matrix  $A_{H}^{*}$  noted in the previous subsection by using the attained latent representation matrix  $H^{*}$  from GALA. Then we perform spectral clustering on the affinity matrix and get the optimal clustering with respect to our cost function.\n\n# 4. Experiments\n\n## 4.1. Datasets\n\nFour network datasets\n\n• Cora\n• Citeseer\n• Wik\n• Pubmed\n\nEvery network dataset has the feature matrix $X$ and the affinity matrix $A$ .\n\nThree image datasets\n\n• COIL20\n• YALE\n• MNIST\n\nEvery image dataset has the feature matrix $X$ only.\n\n• Node clustering.\n\n## 4.2. Experimental settings\n\nThree metrics:\n\n• accuracy (ACC)\n• normalized mutual information (NMI)\n\nFor average in 50 times.\n\n## 4.3. Comparing methods\n\n• Using features only.\n• Kmeans\n• Using network structures only.\n• Spectral\n• Big-Clam\n• DeepWalk\n• GraEnc\n• DNGR\n• Using both\n• Circles\n• RTM\n• RMSC\n• Using both with spectral convolution on graphs\n• GAE\n• VGAE\n• MGAE\n• ARGA\n• ARVGA", null, "## 4.4. Node clustering results\n\nThe experimental results of node clustering are presented in Table 2.", null, "• For every dataset, the methods which use features and network structures simultaneously show better performance than the methods which use only one of them.\n• Use both features and network structures, algorithms with neural network models which exploit spectral convolution on graphs present outstanding performance since they can learn deeper relationships between nodes than the methods which do not use spectral convolution on graphs.\n• GALA shows superior performance to other methods.\n• MGAE, which is the state-of-the-art graph convolutional autoencoder algorithm, by about 6.15%, 6.56% and 8.68% on ACC, NMI and ARI.\n• The better performance of GALA comes from the better decoder design based on the numerically stable form of Laplacian sharpening both and full utilizing of graph structure and node attributes in the whole autoencoder framework.\n\nWe conduct another node clustering experiment on a large network dataset (Pubmed), and the results are reported in Table 5.", null, "• GALA outperforms every baselines and state-of-the-art graph convolution algorithms.\n\n## 4.5. Image clustering results\n\nThe experimental results of image clustering are presented in Table 4.\n\nWe report both GALA’s performance of reconstruction cost only case and the subspace clustering cost added case (GALA+SCC).", null, "• GALA outperforms several baselines and the state-of-the-art graph convolution algorithms for most of the cases.\n• The proposed subspace clustering cost term contributes to improve the performance of the image clustering.\n\n## 4.6. Ablation studies\n\nWe validate the effectiveness of the proposed stable decoder and the subspace clustering cost by image clustering experiments on the three image datasets (COIL20, YALE and MNIST).\n\nThere are four configurations as shown in Table 6.", null, "• The numerically stable form of Laplacian sharpening and subspace clustering cost are helpful to find the latent representations.\n• Stable decoder with the reconstruction cost only outperforms the state-of-the-art algorithms in most cases\n\n$\\underset{\\bar{X}, H}{min} \\frac{1}{2}\\|X-\\bar{X}\\|_{F}^{2}+\\gamma \\mathbb{E}_{H}[\\log p(\\hat{A} \\mid H)]$\n\nwhere\n\n• $H$  is the latent representation,\n• $\\hat{A}=\\operatorname{sigmoid}\\left(H H^{T}\\right)$  is the reconstructed affinity matrix and\n• $\\gamma$  is the regularization parameter.\n\nThe results are shown in Table 7", null, "• Our model outperforms the compared methods in terms of the link prediction task as well as the node clustering task.\n\n## 4.8. Visualization\n\n• The encoder makes the feature of each node becomes similar with its neighbors.\n• The decoder makes the features of each node distinguishable with its neighbors using the geometrical structure of the graphs.\n\nWe visualize the distribution of learned latent representations and the input features of each node in two-dimensional space using t-SNE as shown in Figure 3.", null, "• From the visualization, we can see that GALA is wellclustering the data according to their corresponding labels even though GALA performs in an unsupervised manner.\n• We can see through the red dotted line in embedding results of the latent representation on YALE that GALA embeds the representation of nodes better than the compared methods by minimizing inter-cluster affinity and maximizing intra-cluster affinity\n\n# 5. Conclusions\n\n• We designed a symmetric graph convolutional autoencoder architecture where the encoder performs Laplacian smoothing while the decoder performs Laplacian sharpening.\n• To prevent numerical instabilities, we designed a new representation of Laplacian sharpening with spectral radius one by incorporating the concept of the signed graph.\n• To enhance the performance of image clustering tasks, we added a subspace clustering cost term to the reconstruction cost of the autoencoder." ]
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https://mephistolessiveur.info/relationship-between-and/obtaining-information-from-the-graph-of-a-functional-relationship.php
[ "# Obtaining information from the graph of a functional relationship\n\n### Graphs of Functions", null, "Argomenti trattati: function, functions, graph, inverse. in which case the inverse relation is the inverse function: the inverse relation is the relation obtained by. curve on the graph. So how do we find the equation of curve from the graph ( curve on the graph is similar to the graph of the quadratic function)? c is very easy to obtain, it is just the point where your curve intersects the y-axis. b is the . Then, propose a mathematical relationship that governs these variables. Usually . In Section we defined a function as a special type of relation; one in which each The graph of a function f is the set of points which satisfy the equation y = f(x). . Putting all of this information together and plotting additional points, we get.\n\nThus, a circle is not the graph of a function. Vertical line test We see that we can draw a vertical line, for example the dotted line in the drawing, which cuts the circle more than once. Therefore the circle is not a function. Does this graph pass the vertical line test?\n\n## Functions and Graphs\n\nIt passes the vertical line test. Therefore, it is the graph of a function. It does not pass the vertical line test because the vertical line we have drawn cuts the graph twice, so it is not the graph of a function. Definition A one to one function is a function which associates distinct arguments with distinct values; that is, every unique argument produces a unique result.\n\nIt is not necessary for all elements in a co-domain to be mapped. And then we get to x is equal to 4, where it seems like this thing that could be a function is somewhat defined.\n\nIt does try to associate 4 with things. But what's interesting here is it tries to associate 4 with two different things. All of a sudden in this thing that we think might have been a function, but it looks like it might not be, we don't know.\n\nDo we associate 4 with 5?\n\n### Functions and Graphs\n\nOr do we associate it with negative 1? So this thing right over here is actually a relation. You can have one member of the domain being related to multiple members of the range. But if you do have that, then you're not dealing with a function. So once again, because of this, this is not a function.", null, "It's not clear that when you input 4 into it, should you output 5? Or should you output negative 1? And sometimes there's something called the vertical line test that tells you whether something is a function.", null, "When it's graphically defined like this, you literally say, OK, when x is 4, if I draw a vertical line, do I intersect the function at two places or more? It could be two or more places. And if you do, that means that there's two or more values that are related to that value in the domain.\n\n## Recognizing functions from graph\n\nThere's two or more outputs for the input 4. And if there are two or more outputs for that one input, then you're not dealing with a function. You're just dealing with a relation. The approximations -1,4 and 2,-8 are not very close to the real relative extreme points, so we will use the zoom and trace features to improve the approximations.\n\nWhen you click the Trace button, a point on the graph of f is indicated with a small circle.", null, "The coordinates of that point are reported in the two text boxes near the Trace button. If you select a larger Step Size from the pull down menu, then the trace point moves farther with each click. It is possible to move faster with the enter key than with the mouse. Using the default view, the lowest point found while tracing near the minimum point is 1. Note that this is not the exact location of the minimum point.\n\nWe need to look at the trace points on either side of this point to get an idea of how close we are. Find this trace point, make sure that the Step Size is set to 1, and then find the points on either side of this point." ]
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http://conceptmap.cfapps.io/wikipage?lang=en&name=Archimedes%27_principle
[ "# Archimedes' principle\n\nArchimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.\n\n## Explanation\n\nIn On Floating Bodies, Archimedes suggested that (c. 250 BCE):\n\nAny object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object.\n\nArchimedes' principle allows the buoyancy of an object partially or fully immersed in a fluid to be calculated. The downward force on the object is simply its weight. The upward, or buoyant, force on the object is that stated by Archimedes' principle, above. Thus, the net force on the object is the difference between the magnitudes of the buoyant force and its weight. If this net force is positive, the object rises; if negative, the object sinks; and if zero, the object is neutrally buoyant - that is, it remains in place without either rising or sinking. In simple words, Archimedes' principle states that, when a body is partially or completely immersed in a fluid, it experiences an apparent loss in weight that is equal to the weight of the fluid displaced by the immersed part of the body(s).\n\n## Formula\n\nConsider a cuboid immersed in a fluid, with one (hence two: top and bottom) of its sides orthogonal to the direction of gravity (assumed constant across the cube's stretch). The fluid will exert a normal force on each face, but only the normal forces on top and bottom will contribute to buoyancy. The pressure difference between the bottom and the top face is directly proportional to the height (difference in depth of submersion). Multiplying the pressure difference by the area of a face gives a net force on the cuboid – the buoyancy, equaling in size the weight of the fluid displaced by the cuboid. By summing up sufficiently many arbitrarily small cuboids this reasoning may be extended to irregular shapes, and so, whatever the shape of the submerged body, the buoyant force is equal to the weight of the displaced fluid.\n\n${\\text{ weight of displaced fluid}}={\\text{weight of object in vacuum}}-{\\text{weight of object in fluid}}\\,$\n\nThe weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). The weight of the object in the fluid is reduced, because of the force acting on it, which is called upthrust. In simple terms, the principle states that the buoyant force (Fb) on an object is equal to the weight of the fluid displaced by the object, or the density (ρ) of the fluid multiplied by the submerged volume (V) times the gravity (g)\n\nWe can express this relation in the equation:\n\n$F_{b}=\\rho gV$\n\nwhere $F_{b}$  (Fa in the figure) denotes the buoyant force applied onto the submerged object, $\\rho$  denotes the density of the fluid, $V$  represents the volume of the displaced fluid and $g$  is the acceleration due to gravity. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy.\n\nSuppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting on it. Suppose that, when the rock is lowered into the water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyant force: 10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea-floor. It is generally easier to lift an object through the water than it is to pull it out of the water.\n\nFor a fully submerged object, Archimedes' principle can be reformulated as follows:\n\n${\\text{apparent immersed weight}}={\\text{weight of object}}-{\\text{weight of displaced fluid}}\\,$\n\nthen inserted into the quotient of weights, which has been expanded by the mutual volume\n\n${\\frac {\\text{density of object}}{\\text{density of fluid}}}={\\frac {\\text{weight}}{\\text{weight of displaced fluid}}}$\n\nyields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volume is\n\n${\\frac {\\text{density of object}}{\\text{density of fluid}}}={\\frac {\\text{weight}}{{\\text{weight}}-{\\text{apparent immersed weight}}}}.\\,$\n\n(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.)\n\nExample: If you drop wood into water, buoyancy will keep it afloat.\n\nExample: A helium balloon in a moving car. When increasing speed or driving in a curve, the air moves in the opposite direction to the car's acceleration. However, due to buoyancy, the balloon is pushed \"out of the way\" by the air and will drift in the same direction as the car's acceleration.\n\nWhen an object is immersed in a liquid, the liquid exerts an upward force, which is known as the buoyant force, that is proportional to the weight of the displaced liquid. The sum force acting on the object, then, is equal to the difference between the weight of the object ('down' force) and the weight of displaced liquid ('up' force). Equilibrium, or neutral buoyancy, is achieved when these two weights (and thus forces) are equal.\n\n## Forces and equilibrium\n\nThe equation to calculate the pressure inside a fluid in equilibrium is:\n\n$\\mathbf {f} +\\operatorname {div} \\,\\sigma =0$\n\nwhere f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:\n\n$\\sigma _{ij}=-p\\delta _{ij}.\\,$\n\nHere δij is the Kronecker delta. Using this the above equation becomes:\n\n$\\mathbf {f} =\\nabla p.\\,$\n\nAssuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function:\n\n$\\mathbf {f} =-\\nabla \\Phi .\\,$\n\nThen:\n\n$\\nabla (p+\\Phi )=0\\Longrightarrow p+\\Phi ={\\text{constant}}.\\,$\n\nTherefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative force field. Let the z-axis point downward. In this case the field is gravity, so Φ = −ρfgz where g is the gravitational acceleration, ρf is the mass density of the fluid. Taking the pressure as zero at the surface, where z is zero, the constant will be zero, so the pressure inside the fluid, when it is subject to gravity, is\n\n$p=\\rho _{f}gz.\\,$\n\nSo pressure increases with depth below the surface of a liquid, as z denotes the distance from the surface of the liquid into it. Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the pressure on the bottom being greater. This difference in pressure causes the upward buoyancy force.\n\nThe buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known. The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is in contact with the fluid:\n\n$\\mathbf {B} =\\oint \\sigma \\,d\\mathbf {A} .$\n\nThe surface integral can be transformed into a volume integral with the help of the Gauss theorem:\n\n$\\mathbf {B} =\\int \\operatorname {div} \\sigma \\,dV=-\\int \\mathbf {f} \\,dV=-\\rho _{f}\\mathbf {g} \\int \\,dV=-\\rho _{f}\\mathbf {g} V$\n\nwhere V is the measure of the volume in contact with the fluid, that is the volume of the submerged part of the body, since the fluid doesn't exert force on the part of the body which is outside of it.\n\nThe magnitude of buoyancy force may be appreciated a bit more from the following argument. Consider any object of arbitrary shape and volume V surrounded by a liquid. The force the liquid exerts on an object within the liquid is equal to the weight of the liquid with a volume equal to that of the object. This force is applied in a direction opposite to gravitational force, that is of magnitude:\n\n$B=\\rho _{f}V_{\\text{disp}}\\,g,\\,$\n\nwhere ρf is the density of the fluid, Vdisp is the volume of the displaced body of liquid, and g is the gravitational acceleration at the location in question.\n\nIf this volume of liquid is replaced by a solid body of exactly the same shape, the force the liquid exerts on it must be exactly the same as above. In other words, the \"buoyancy force\" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to\n\n$B=\\rho _{f}Vg.\\,$\n\nThe net force on the object must be zero if it is to be a situation of fluid statics such that Archimedes principle is applicable, and is thus the sum of the buoyancy force and the object's weight\n\n$F_{\\text{net}}=0=mg-\\rho _{f}V_{\\text{disp}}g\\,$\n\nIf the buoyancy of an (unrestrained and unpowered) object exceeds its weight, it tends to rise. An object whose weight exceeds its buoyancy tends to sink. Calculation of the upwards force on a submerged object during its accelerating period cannot be done by the Archimedes principle alone; it is necessary to consider dynamics of an object involving buoyancy. Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be applied alone. For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor.\n\nIn order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero), therefore;\n\n$mg=\\rho _{f}V_{\\text{disp}}g,\\,$\n\nand therefore\n\n$m=\\rho _{f}V_{\\text{disp}}.\\,$\n\nshowing that the depth to which a floating object will sink, and the volume of fluid it will displace, is independent of the gravitational field regardless of geographic location.\n\n(Note: If the fluid in question is seawater, it will not have the same density (ρ) at every location. For this reason, a ship may display a Plimsoll line.)\n\nIt can be the case that forces other than just buoyancy and gravity come into play. This is the case if the object is restrained or if the object sinks to the solid floor. An object which tends to float requires a tension restraint force T in order to remain fully submerged. An object which tends to sink will eventually have a normal force of constraint N exerted upon it by the solid floor. The constraint force can be tension in a spring scale measuring its weight in the fluid, and is how apparent weight is defined.\n\nIf the object would otherwise float, the tension to restrain it fully submerged is:\n\n$T=\\rho _{f}Vg-mg.\\,$\n\nWhen a sinking object settles on the solid floor, it experiences a normal force of:\n\n$N=mg-\\rho _{f}Vg.\\,$\n\nAnother possible formula for calculating buoyancy of an object is by finding the apparent weight of that particular object in the air (calculated in Newtons), and apparent weight of that object in the water (in Newtons). To find the force of buoyancy acting on the object when in air, using this particular information, this formula applies:\n\nBuoyancy force = weight of object in empty space − weight of object immersed in fluid\n\nThe final result would be measured in Newtons.\n\nAir's density is very small compared to most solids and liquids. For this reason, the weight of an object in air is approximately the same as its true weight in a vacuum. The buoyancy of air is neglected for most objects during a measurement in air because the error is usually insignificant (typically less than 0.1% except for objects of very low average density such as a balloon or light foam).\n\n### Simplified model\n\nA simplified explanation for the integration of the pressure over the contact area may be stated as follows:\n\nConsider a cube immersed in a fluid with the upper surface horizontal.\n\nThe sides are identical in area, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force resulting from hydrostatic pressure, exerted perpendicular to the plane of the surface of each side.\n\nThere are two pairs of opposing sides, therefore the resultant horizontal forces balance in both orthogonal directions, and the resultant force is zero.\n\nThe upward force on the cube is the pressure on the bottom surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal bottom surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the bottom surface.\n\nSimilarly, the downward force on the cube is the pressure on the top surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top surface.\n\nAs this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.\n\nThis means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the volume of the cube, and the downward force on the cube is its weight, in the absence of external forces.\n\nThis analogy is valid for variations in the size of the cube.\n\nIf two cubes are placed alongside each other with a face of each in contact, the pressures and resultant forces on the sides or parts thereof in contact are balanced and may be disregarded, as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy of two cubes in contact is the sum of the buoyancies of each cube. This analogy can be extended to an arbitrary number of cubes.\n\nAn object of any shape can be approximated as a group of cubes in contact with each other, and as the size of the cube is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence.\n\nAngled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.\n\n## Refinements\n\nArchimedes' principle does not consider the surface tension (capillarity) acting on the body. Moreover, Archimedes' principle has been found to break down in complex fluids.\n\nThere is an exception to Archimedes' principle known as the bottom (or side) case. This occurs when a side of the object is touching the bottom (or side) of the vessel it is submerged in, and no liquid seeps in along that side. In this case, the net force has been found to be different from Archimedes' principle, owing to the fact that since no fluid seeps in on that side, the symmetry of pressure is broken. \n\n## Principle of flotation\n\nArchimedes' principle shows the buoyant force and displacement of fluid. However, the concept of Archimedes' principle can be applied when considering why objects float. Proposition 5 of Archimedes' treatise On Floating Bodies states that\n\nAny floating object displaces its own weight of fluid.\n\nIn other words, for an object floating on a liquid surface (like a boat) or floating submerged in a fluid (like a submarine in water or dirigible in air) the weight of the displaced liquid equals the weight of the object. Thus, only in the special case of floating does the buoyant force acting on an object equal the objects weight. Consider a 1-ton block of solid iron. As iron is nearly eight times as dense as water, it displaces only 1/8 ton of water when submerged, which is not enough to keep it afloat. Suppose the same iron block is reshaped into a bowl. It still weighs 1 ton, but when it is put in water, it displaces a greater volume of water than when it was a block. The deeper the iron bowl is immersed, the more water it displaces, and the greater the buoyant force acting on it. When the buoyant force equals 1 ton, it will sink no farther.\n\nWhen any boat displaces a weight of water equal to its own weight, it floats. This is often called the \"principle of flotation\": A floating object displaces a weight of fluid equal to its own weight. Every ship, submarine, and dirigible must be designed to displace a weight of fluid at least equal to its own weight. A 10,000-ton ship's hull must be built wide enough, long enough and deep enough to displace 10,000 tons of water and still have some hull above the water to prevent it from sinking. It needs extra hull to fight waves that would otherwise fill it and, by increasing its mass, cause it to submerge. The same is true for vessels in air: a dirigible that weighs 100 tons needs to displace 100 tons of air. If it displaces more, it rises; if it displaces less, it falls. If the dirigible displaces exactly its weight, it hovers at a constant altitude.\n\nWhile they are related to it, the principle of flotation and the concept that a submerged object displaces a volume of fluid equal to its own volume are not Archimedes' principle. Archimedes' principle, as stated above, equates the buoyant force to the weight of the fluid displaced.\n\nOne common point of confusion[by whom?] regarding Archimedes' principle is the meaning of displaced volume. Common demonstrations involve measuring the rise in water level when an object floats on the surface in order to calculate the displaced water. This measurement approach fails with a buoyant submerged object because the rise in the water level is directly related to the volume of the object and not the mass (except if the effective density of the object equals exactly the fluid density).\n\n## Eureka\n\nArchimedes reportedly exclaimed \"Eureka\" after he realized how to detect whether a crown is made of impure gold. While he did not use Archimedes' principle in the widespread tale and only used displaced water for measuring the volume of the crown, there is an alternative approach using the principle: Balance the crown and pure gold on a scale in the air and then put the scale into water. According to Archimedes' principle, if the density of the crown differs from the density of pure gold, the scale will get out of balance under water." ]
[ null ]
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https://math.stackexchange.com/questions/889175/conditional-return-time-of-simple-random-walk?noredirect=1
[ "# Conditional return time of simple random walk\n\nConsider a simple symmetric random walk on $\\mathbb{Z}$, $(S_t)_{t \\geq 0}$. Call $\\tau_k = \\min\\{t \\in \\mathbb{N}\\, : \\, \\, S_t =k \\}$, the hitting time of $k \\in \\mathbb{N}$. Call $\\tau^* = \\min\\{t >0\\, : \\, \\, S_t =0 \\}$, the return time to the origin. Let $c<1$ be a positive constant.\n\nIs there a way to compute the next formula explicitly?\n\n$$\\sum_{k=1}^{\\infty} \\sum\\limits_{j=1}^{\\infty} P ( \\tau_k = j \\, | \\, \\tau_k < \\tau^*) \\cdot c^{j-1}$$\n\n• For starters can you compute $P(\\tau_k\\lt\\tau^*)$?\n– Did\nAug 7, 2014 at 10:05\n• Yes, let's say we know that…. Aug 7, 2014 at 10:54\n• Perhaps a bound could be $\\frac{P(\\tau^* > j)}{P(\\tau_j < \\tau^*)}$, just using the bound $P(\\tau_k < \\tau^*) > P(\\tau_j < \\tau^*)$. But is $P(\\tau^* > j)$ know exactly? Aug 7, 2014 at 10:58\n• No, how do YOU compute THE EXACT VALUE of $P(\\tau_k\\lt\\tau^*)$?\n– Did\nAug 7, 2014 at 11:01\n• The first step must be right. Thus $P(\\tau_k < \\tau^*) =$p P(SRW starting from 1 reaches k before 0)$and it comes from the gambler ruin problem. Aug 7, 2014 at 11:07 ## 1 Answer To have$\\tau_k < \\tau^*$, the first step of the walk must be in the positive direction. So, we may as well start the walk at position$1$: let$X_1$,$X_2$,$X_3$,$\\ldots$be i.i.d. with$\\mathbb{P}(X_i=1)=\\mathbb{P}(X_i=-1)={1\\over 2}$, let$T_n:=1+\\sum_{1\\le i\\le n} X_i\\ \\ (n\\in\\mathbb{Z}_{\\ge 0})$, and let$\\mu_k:=\\min \\{n\\in\\mathbb{Z}_{\\ge 0}\\mid T_n=k\\}$. We then want to compute $$\\sum_{k\\ge 1} \\mathbb{E}[c^{\\mu_k}\\mid \\mu_k<\\mu_0],$$ where the$-1$in the exponent has disappeared because we started the walk at what was formerly time$1$. Fix some$A>0$and let$M_n:=c^n A^{T_n}$; if$A+A^{-1}=2/c$,$M_n$will be a martingale. Then, by the optional stopping theorem, \\begin{eqnarray*} A=M_0&=& \\mathbb{E}[M_{\\min(\\mu_k, \\mu_0)}]\\\\ &=& \\mathbb{P}(\\mu_k<\\mu_0) \\mathbb{E}[c^{\\mu_k}\\mid \\mu_k < \\mu_0] A^k+ \\mathbb{P}(\\mu_k>\\mu_0) \\mathbb{E}[c^{\\mu_0}\\mid \\mu_k > \\mu_0]. \\ \\ (*) \\end{eqnarray*} The equation$A+A^{-1}=2/c$has two positive roots. Let$A_0$be the one greater than$1$; the other will then be$A_0^{-1}$. Setting$A:=A_0$and$A:=A_0^{-1}$in$(*)$then gives two linear equations. Subtracting one from the other and solving gives $$\\mathbb{P}(\\mu_k<\\mu_0) \\mathbb{E}[c^{\\mu_k}\\mid \\mu_k < \\mu_0] = {A_0-A_0^{-1}\\over A_0^k-A_0^{-k}}= {1\\over A_0^{k-1}+A_0^{k-3}+\\cdots+A_0^{-(k-3)}+A_0^{-(k-1)}}.\\ \\ (**)$$ Letting$c\\to 1$,$A_0\\to 1$as well. In this case$(**)$becomes $$\\mathbb{P}(\\mu_k<\\mu_0) = \\frac{1}{k},$$ which can also be found by using the optional stopping theorem with the martingale$T_n$. Dividing this into$(**)$gives $$\\mathbb{E}[c^{\\mu_k}\\mid \\mu_k < \\mu_0] = k {A_0-A_0^{-1}\\over A_0^k-A_0^{-k}},$$ so the answer is $$\\sum_{k\\ge 1} k {A_0-A_0^{-1}\\over A_0^k-A_0^{-k}}.$$ • Nice the idea of using the optional stopping theorem! However, in (*), shouldn't the second term in the right hand side contain$c^{μ_0}$instead of$c^{μ_k}\\$? Mar 20, 2015 at 11:17\n• Yes, it should. I corrected this mistake. Mar 20, 2015 at 22:25" ]
[ null ]
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https://business.totalenergies.uk/information-centre/energy-essentials/how-read-your-business-energy-invoicebill
[ "1. To calculate the gas used, subtract the previous read from the present for each meter.\n2. Multiply the figure by the Correction Factor (CF).\n3. To calculate the number of M3 used, multiply this figure by the Conversion Factor (shown below in the table and on the reverse of your invoice). Please ignore this part of the calculation if your meter is already measured in M3.\n4. Multiply this figure by the Calorific Value (CV).\n5. Divide this figure by 3.6 to convert to kWh.\n6. Multiply the number of kWh by the unit price to calculate the cost per meter.\n7. Add together the cost of each meter to calculate the total cost, excluding VAT.\n8. VAT is added at 20% unless any exemptions apply.\n9. Apply CCL at the current rate, found here unless any reductions apply.\n10. The sum of these calculations amounts to the total gas sale.\n\n#### Meter Unit Conversion Factor\n\n MCUF HCUF Thousands of Cubic Feet 28.317 Hundreds of Cubic Feet 2.8317 Tens of Cubic Feet 0.28317 One Cubic Foot 0.028317 Hundreds of Cubic Metres 100 Tens of Cubic Metres 10 Tenths of Cubic Metres 0.1\n\n#### How to calculate your non-half-hourly electricity invoice\n\n1. To calculate the number of billed units (electricity consumed), deduct the present meter read from the previous one.\n2. Multiply the billed units by their respective price.\n3. Non-half hourly meters may have several different readings. The time periods and prices these refer to are stated in your contract.\nThese meter readings may be actual, customer or estimate as indicated on your invoice.\n4. The total (consumption) is the consumption for all readings for the period of use. The total cost associated with the total consumption is also stated.\n5. Multiply the billed units of Standing Charge by price (if applicable).\n6. Multiply the billed units of Capacity Charge by price (if applicable).\n7. Add together Capacity Charge and Standing Charge to get the total other charges.\n8. Apply CCL at the current rate, found here unless any reductions apply.\n9. VAT applied at 20.0% unless exemptions apply.\n10. The sum of these calculations amounts to the total electricity sale.\n\n#### How to calculate your half-hourly electricity invoice\n\n1. Billed units are calculated for the period of use, and they are measured in kWh.\n2. These units are then multiplied by their respective prices.\n3. Half-hourly meters may have up to six consumption periods. The time periods and prices these refer to are stated in your contract.\n4. The total (consumption) is the consumption for all consumption periods for the period of use. The total cost associated with the total consumption is also stated.\n5. Multiply the billed units of Standing Charge by Price (if applicable).\n6. Multiply the billed units of Capacity Charge by Price (if applicable).\n7. Add together Capacity Charge and Standing Charge to get total other charges (if applicable). Please note that there may be charges specific to your individual contract.\n8. Apply CCL at the current rate, found here unless any reductions apply.\n9. VAT is added at 20.0% unless any exemptions apply.\n10. The sum of these calculations amounts to the total electricity sale.\n\n#### Invoice Definitions\n\n A A after a meter reading indicates actual read taken by the data collector or agents working on its behalf E after a meter reading indicates an estimated read C after a meter reading indicates a read given by the customer S after a meter reading indicates a read that has been agreed between two gas or electricity companies when the supply has transferred from one to the other This is the unit of measure for energy consumed This is a government energy tax on Industrial and Commercial consumption, subject to VAT To calculate CCL multiply Total Consumption by the rate assigned to gas or electricity (reductions may be applicable) A unique number that identifies the specific point of entry of the gas supply into the property A fixed meter specific factor applied to take into account the effect of temperature and pressure on actual gas flow. It is a legal requirement to include this factor in the calculation of our invoices. This represents the amount of heat or energy in a given volume of gas. An average calorific value is calculated monthly by the transporter and allows for any periodic or regional variations in the quality of natural gas. It is a legal requirement that we include this factor in the calculation of our invoices\n\n## TotalEnergies Gas & Power Gas Invoice\n\n#### Click on the image to enlarge it", null, "## TotalEnergies Gas & Power Electricity Invoice Sample\n\n#### Click on the image to enlarge it", null, "" ]
[ null, "https://v2totalgpuk-backoffice-twf4biz.aqa.tgscloud.net/sites/g/files/wompnd2326/f/atoms/image/totalenergies-gas1.jpg", null, "https://v2totalgpuk-backoffice-twf4biz.aqa.tgscloud.net/sites/g/files/wompnd2326/f/atoms/image/invoice-mock-uplabeled-1.jpg", null ]
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https://www.groundai.com/project/multi-robot-routing-for-persistent-monitoring-with-latency-constraints/
[ "Multi-Robot Routing for Persistent Monitoring with Latency Constraints\n\n# Multi-Robot Routing for Persistent Monitoring with Latency Constraints\n\n## Abstract\n\nIn this paper we study a multi-robot path planning problem for persistent monitoring of an environment. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum time spent by the robots between visits to that vertex, called the latency, and the objective is to find the minimum number of robots that can satisfy these latency constraints. The decision version of this problem is known to be PSPACE-complete. We present a approximation algorithm for the problem where is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show through simulations that in most of the cases the heuristic algorithm gives better solutions than the approximation algorithm. We evaluate our algorithms on large problem instances in a patrolling scenario and in a persistent scene reconstruction application. We also compare the algorithms with an existing solver on benchmark instances.\n\n\\DeclareFloatStyle\n\n## I Introduction\n\nWith the rapid development in field robotics, teams of robots can now perform long term monitoring tasks. Examples of such tasks include infrastructure inspection  to detect presence of anomalies or failures; patrolling for surveillance [2, 3] to detect threats in the environment; 3D reconstruction of scenes [4, 5] in changing environments; informative path planning  for observing dynamic properties of an area; and forest fire monitoring . In such persistent monitoring scenarios, locations in an environment need to be visited repeatedly by a team of robots. Since the duration of the events, or the rate of change of the properties to be monitored, can be different for different locations, each location will have a different latency constraint, which specifies the maximum time allowed between consecutive visits to that location. In this paper we study the problem of finding a set of paths that continually visit a set of locations while collectively satisfying the latency constraints on each location.\n\nWe represent the locations of interest in the environment as the vertices of a graph. The edge weights give the travel time between the vertices and each vertex has a latency constraint that defines the maximum allowed time between two consecutive visits to that vertex. The problem is to find walks on the graph for the minimum number of robots that can satisfy the latency constraints.\n\nRelated Work: Persistent monitoring problems have been extensively studied in the literature [8, 9, 10, 11]. In , persistent coverage using multiple robots in a continuous environment is considered. The problem of determining a visit sequence for a set of locations along with the time spent at each location to gather information is considered in [13, 14]. For the problem with latency constraints, the authors in  use incomplete greedy heuristics to find if a single robot can satisfy the constraints on all vertices of a graph. They show that if a solution exists, then a periodic solution also exists. In this paper, we consider the multi-robot problem and our objective is to minimize the number of robots that can satisfy the latency constraints on the given graph. This problem has been considered in [16, 17], where it is called Cyclic Routing of Unmanned Aerial Vehicles. The decision version of the problem for a single robot is shown to be PSPACE-complete in . The authors also show that the length of even one period of a feasible walk can be exponential in the size of the problem instance. In , the authors propose a solver based on Satisfiability Modulo Theories (SMT). To apply an SMT solver, they impose an upper bound on the length of the period of the solution. Since an upper bound is not known a priori, the solver will not return the optimal solution if the true optimal period exceeds the bound. The authors generate a library of test instances, but since their algorithm scales exponentially with the problem size, they solve instances up to only 7 vertices. We compare our algorithms with their solver and show that our algorithms run over times faster on average and return solutions with the same number of robots on of the benchmark instances provided by .\n\nA related single robot problem is studied in  where each vertex has a weight associated with it and the objective is to minimize the maximum weighted latency (time between consecutive visits) for an infinite walk. The authors provide an approximation algorithm for this problem. The authors in  study the single robot problem for a security application where the length of attack on each vertex of the graph is given. To intercept all possible attacks, they design an algorithm to repeatedly patrol all vertices with the maximum revisit time to each vertex less than its length of attack.\n\nTimed automata have been used to model general multi-robot path planning problems  as the clock states can capture the concurrent time dependent motion. In , temporal logic constraints are used to specify high level mission objectives to be achieved by a set of robots. The routing problem with latency constraints can also be modeled as a timed automaton since multiple robots may require synchronization to satisfy the latency constraints. A timed automaton based solution to the problem is presented in , however it is shown to perform more poorly than the SMT-based approach in , which we use as a comparison for our proposed algorithms.\n\nSeveral vehicle routing problems are closely related to persistent monitoring with latency constraints. In the vehicle routing problem with time windows , customers have to be served within their time windows by several vehicles with limited capacity. The goal is to minimize the number of vehicles required. Since the problem does not require repeated visits, the length of the resulting tour is polynomially bounded, and thus the problem is in NP. In the deadline-TSP , the vertices have deadlines for first visits. In the period vehicle routing problem , the problem is to design routes for each day of a given period where each customer may require a number of visits (in a given number of allowable combinations) during this period. The main difference between these problems and the cyclic routing problem with latency constraints is that the latency constraints need to be satisfied indefinitely which makes it harder than these problems.\n\nContributions: We present a approximation algorithm for the problem where is the ratio of the maximum and the minimum latency constraints (Section IV). We also provide an algorithm for the problem of minimizing the maximum weighted latency with multiple robots and show that an approximation algorithm for this problem yields a bi-criterion approximation for our problem. We present an orienteering based heuristic algorithm to solve the problem and prove its completeness (Section V). We show through simulations that the heuristic algorithm gives better solutions than the approximation algorithm. We evaluate the performance of the algorithms on large problem instances in a patrolling scenario and in an image collection application for 3D scene reconstruction. We also compare our algorithms against an existing solver on benchmark instances (Section VI).\n\n## Ii Background and Notation\n\nGiven a directed graph with edge lengths for each , a simple walk in graph is defined as a sequence of vertices such that for each . An infinite walk is a sequence of vertices such that for each . Given walks and , represents the concatenation of the walks. Given a finite walk , an infinite periodic walk is constructed by concatenating infinite copies of W together, and is denoted by . A cycle is a simple walk that starts and ends at the same vertex with no other vertex appearing more than once.\n\nIn general, a walk can stay for some time at a vertex before traversing the edge towards the next vertex. Therefore we define a timed walk in graph as a sequence , where is an ordered pair that represents the holding time that the walk spends at vertex , such that for each . The definitions of infinite walk and periodic walk can be extended to infinite timed walk and periodic timed walk. A walk with ordered pairs of the form becomes a simple walk. The vertices traversed by walk are given by and the length of walk is given by . Since we are considering a multi-robot problem, synchronization between the walks is important. Given a set of walks on graph , we assume that at time , each robot is at the first vertex of its walk , and will spend the holding time at that vertex before moving to .\n\nGiven a graph and length , the Minimum Cycle Cover Problem (MCCP) is to find minimum number of cycles that cover the whole graph such that the length of the longest cycle is at most . This problem is NP-hard and a -approximation algorithm for MCCP is given in .\n\nGiven a graph with vertex weights for , and length , the Orienteering problem is to find a path from vertex to of length at most such that the sum of the weights on the vertices in the path is maximized. This problem is also NP-hard and a -approximation is given in .\n\n## Iii Problem Statement\n\nLet be a directed weighted graph with edge lengths for each . The edge lengths are metric and represent the time taken by the robot to travel between the vertices. The latency constraint for each vertex is denoted by and represents the maximum time allowed between consecutive visits to . The time taken by the robots to inspect a vertex can be added to the length of the incoming edges of that vertex to get an equivalent metric graph with zero inspection times and modified latency constraints . Hence, we assume that the time required by the robots to inspect a vertex is zero. We formally define the problem statement after the following definition.\n\n###### Definition III.1 (Latency).\n\nGiven a set of infinite walks on a graph , let represent the arrival time for the walks to vertex . Similarly, let represent the departure time from vertex . Then the latency of vertex on walks is defined as the maximum time spent away from vertex by the walks, i.e., .\n\n###### Problem III.2 (Minimizing Robots with Latency Constraints).\n\nGiven the latency constraints , the optimization problem is to find a set of walks with minimum cardinality such that .\n\nThe decision version of the problem is to determine whether there exists a set of walks such that for all . Note that a general solution to Problem III.2 will be a set of timed walks with possibly non-zero holding times.\n\nIn this problem definition, the graph and its edge lengths capture the robot motion in the environment. This graph can be generated from a probabilistic roadmap, or any other environment decomposition method. The latency constraints provide the maximum allowable time between visits to a vertex. For example, in dynamic scene reconstruction, each vertex corresponds to a viewpoint . The latency constraints may encode the maximum staleness of information that can be tolerated for the voxels captured at that viewpoint.\n\n### Iii-a Multiple Robots on the Same Walk\n\nIn multi-robot problems that involve finding cycles or tours in a graph, equally placing robots on a tour reduces the cost of that tour by a factor of  . That is not true for Problem III.2: if a periodic walk gives latency on vertex , equally spacing more robots on one period of that walk does not necessarily reduce the latency for that vertex. Figure 1 gives an example of such a walk. The latency of vertices and on the walk are and respectively. The length of one period of the walk is . If we place another robot following the first robot with a lag of units, the latency of vertex remains the same. If we place the second robot at a lag of unit, the latency will reduce to for vertex and for vertices and . Hence we need more sophisticated algorithms than finding a walk for a single robot and adding more robots on that walk until the constraints are satisfied, unless that walk is a cycle.", null, "Fig. 1: A graph with three vertices and the walk (a,b,a,c). The length of shown edges is one. Equally placing two robots on this walk does not halve the latencies.\n\n## Iv Approximation Algorithm\n\nSince Problem III.2 is PSPACE-complete, we resort to finding approximate and heuristic solutions to the problem. In this section, we present an approximation algorithm for the problem.\n\n### Iv-a O(logρ) Approximation\n\nWe first mention a simple approach to the problem and then improve it incrementally to get the approximation algorithm. One naive solution is to find a TSP tour of the graph and equally place robots on that tour to satisfy all the latency constraints. However, a single vertex with a very small can result in a solution with the number of robots proportional to . To solve this issue, we can partition the vertices of the graph such that the latencies in one partition are close to each other, and then place robots on the TSP tour of each partition. If more than one robot is required for a partition , then another approach is to solve the MCCP for that partition. The benefit of using the MCCP over placing multiple robots on a TSP is that if all the vertices in had the same latency requirement, then we have a guarantee on the number of cycles required for that partition. However, a general solution to the problem might not consist of simple cycles. Lemma IV.2 relates solutions consisting of cycles to general solutions and shows that a solution consisting of cycles will have latencies no more than twice that of any general solution with same number of robots. Therefore, if we solve the MCCP on a partition with its latency constraints multiplied by two, we have a guarantee on the number of cycles. We can then use the naive idea from TSP based solutions and place multiple robots on each cycle to satisfy the latency constraints.\n\nThe approximation algorithm is given in Algorithm 1. The first four lines of the algorithm partition the vertices according to their latency constraints. For each of those partitions, the function MCCP called in line 8 uses an approximation algorithm for the minimum cycle cover problem from . Then, the appropriate number of robots are placed on each cycle returned by the MCCP function to satisfy the latency constraints. We will need the following definition to establish the approximation ratio of Algorithm 1. A similar relaxation technique was used in .\n\n###### Definition IV.1.\n\nLet . The latency constraints of the problem are said to be relaxed if for any vertex , its latency constraint is updated from to such that is the smallest integer for which .\n\nWe will also need the following lemma that follows from Lemma 2 in  and we omit the proof for brevity.\n\n###### Lemma IV.2.\n\nFor any set of walks on an undirected metric graph with vertices , there exists a set of walks on with , such that each walk is a cycle of vertices , and the sets partition , and .\n\nThe following proposition gives the approximation factor of Algorithm 1.\n\n###### Proposition IV.3.\n\nGiven an undirected metric graph with latency constraints for , Algorithm 1 constructs walks such that for all and , where is the minimum number of robots required to satisfy the latency constraints and is the approximation factor of MCCP.\n\n###### Proof.\n\nGiven that robots will satisfy the latency constraints , they will also satisfy the relaxed constraints since . Therefore, there exists a set of at most walks such that for , .\n\nUsing Lemma IV.2, given the set , cycles can be constructed in such that the latency of each vertex in is at most . Hence, running an approximation algorithm for Minimum Cycle Cover Problem (MCCP) on the subgraph with vertices and with maximum cycle length will not return more than cycles.\n\nSince MCCP returns cycles, equally placing robots on each cycle will reduce the latency of each vertex on that cycle by a factor of . As for each , we will need to place at most robots on each cycle.\n\nFinally, since there are at most partitions , the algorithm will return walks. ∎\n\nRuntime: Since we run the approximation algorithm for MCCP on partitions of the graph, the runtime of Algorithm 1 is the same as that of the approximation algorithm of MCCP. That is because the runtime of MCCP is superlinear, so if , then for .\n\n###### Remark IV.4 (Heuristic Improvements).\n\nInstead of finding cycles using MCCP for each partition in line 8 of the algorithm, we can also equally place robots on the Traveling Salesman Tour of to get a feasible solution. In practice, we use both of these methods and pick the solution that gives the lower number of robots for each . This modification can return better solutions to the problem but does not improve the approximation guarantee established in Proposition IV.3.\n\n### Iv-B Relation to Min Max Weighted Latency\n\nThe approximation algorithm and analysis presented above helps in formulating an algorithm for the multi-robot version of a related problem. In , the authors study in detail the problem of minimizing the maximum weighted latency of a graph given a single robot. Here we define the multiple robot version of the problem.\n\n###### Problem IV.5 (Minimizing Maximum Weighted Latency:).\n\nGiven a graph with weights for , and a set of walks , the weighted latency of is defined as . Given the number of robots , the problem of minimizing maximum weighted latency is to find a set of infinite walks such that the cost is minimized.\n\nWithout loss of generality, is assumed to be normalized such that . In this section we relate this problem to Problem III.2.\n\nIn [Algorithm 2], an approximation algorithm for the single robot version of Problem IV.5 is given. We will refer to that approximation algorithm as MinMaxLatencyOneRobot, which returns a walk in graph such that the maximum weighted latency of that walk is not more than , where is the ratio of maximum to minimum vertex weights in and is the optimal maximum weighted latency for one robot in . We use this approximation algorithm as a subroutine in Algorithm 2 for minimizing the maximum weighted latency with multiple robots.\n\n###### Proposition IV.6.\n\nGiven an instance of Problem IV.5, Algorithm 2 constructs walks such that the maximum weighted latency of the graph is not more than if and otherwise, where and is the maximum weighted latency of the single optimal walk.\n\n###### Proof.\n\nThe maximum vertex weight in the subgraph constructed at line 8 of the algorithm will be at most , whereas the minimum vertex weight in will be at least . Hence the ratio of the maximum to minimum vertex weights in will be at most . Therefore, the approximation algorithm for one robot will return a walk such that the maximum weighted latency of will not be more than . Moreover, and hence if , the maximum weighted latency will be at most .\n\nThe TSP tour of is an optimal solution when all the vertex weights in are equal. Since the vertex weights within differ by a factor of at most, and the approximation factor of TSP tour in metric graphs is , the maximum weighted latency of the TSP tour will be at most . Equally placing will decrease the latency of all the vertices by a factor of . ∎\n\nNote that Algorithm 2 bounds the cost of the solution by a function of the optimal cost of a single robot. This algorithm shows that robots can asymptotically decrease the weighted latency given by a single walk by a factor of , which is not straightforward for this problem as discussed in Section III-A.\n\nNow we show that if there is an approximation algorithm for Problem IV.5, it can be used to solve Problem III.2 using the optimal number of robots but with the latency constraints relaxed by a factor . This is referred to as a -bi-criterion algorithm  for Problem III.2.\n\n###### Proposition IV.7.\n\nIf there exists an -approximation algorithm for Problem IV.5, then there exists a -bi-criterion approximation algorithm for Problem III.2.\n\nWe will need the following lemma relating the two problems to prove the proposition. Given an instance of the decision version of Problem III.2 with robots, let us define an instance of Problem IV.5 by assigning , where .\n\n###### Lemma IV.8.\n\nAn instance of the decision version of Problem III.2 is feasible if and only if the optimal maximum weighted latency is at most for the corresponding instance of Problem IV.5.\n\n###### Proof.\n\nIf the optimal set of walks has a cost more than , then for some vertex . Hence the latency constraint for that vertex is not satisfied and the set of walks is not feasible.\n\nIf the optimal set of walks has a cost at most , then for all . Hence, . So, the latency constraints are satisfied for all vertices and is feasible. ∎\n\n###### Proof of Proposition iv.7.\n\nIf a problem instance of Problem III.2 with robots is feasible, then by Lemma IV.8 the optimal set of walks has a cost at most . The -approximation algorithm for the corresponding Problem IV.5 will return a set of walks with a cost no more than . Hence, , for all .\n\nHence, we can use binary search to find the minimum number of robots for which the -approximation algorithm for the corresponding Problem IV.5 results in a latency at most for all . This will be the minimum number of robots for which the problem is feasible. ∎\n\n## V Heuristic Algorithms\n\nThe approximation algorithm for Problem III.2 presented in Section IV is guaranteed to provide a solution within a fixed factor of the optimal solution. In this section, we propose a heuristic algorithm based on the orienteering problem, which in practice provides high-quality solutions.\n\n### V-a Partitioned Solutions\n\nIn general, walks in a solution of the problem may share some of the vertices. However, sharing the vertices by multiple robots requires coordination and communication among the robots. Such strategies may also require the robots to hold at certain vertices for some time before traversing the next edge, in order to maintain synchronization. This is not possible for vehicles that must maintain forward motion, such as fixed-wing aircraft. The following example illustrates that if vertices are shared by the robots, lack of coordination or perturbation in edge weights can lead to large errors in latencies.\nExample: Consider the problem instance shown in Figure 2. An optimal set of walks for this problem is given by where , and . Note that walk starts by staying on vertex , while leaves vertex and leaves vertex . Also note that any partitioned solution will need robots. Moreover, if the length of edge changes from to , (e.g., if the robot’s speed increases slightly) the latencies of vertices and will keep changing with time and will go up to . Hence, a small deviation in robot speed can result in a large impact on the monitoring objective.", null, "Fig. 2: A problem instance with an optimal set of walks that share vertices. The latency constraints for each vertex are written inside that vertex. The edge lengths are labeled with the edges. The optimal walks are {W1,W2,W3} where W1=((a,1),(b,1)), W2=((b,0),(c,0)) and W3=((c,0),(d,1),(c,1)).\n\nSince the above mentioned issues will not occur if the robots do not share the vertices of the graph, and the problem is PSPACE-complete even for a single robot, we focus on finding partitioned walks in this section. The general greedy approach used in this section is to find a single walk that satisfies latency constraints on a subset of vertices . Note that we do not know beforehand, but a feasible walk on a subset of vertices will determine . We then repeat this process of finding feasible walks on the remaining vertices of the graph until the whole graph is covered.\n\n### V-B Greedy Algorithm\n\nWe now consider the problem of finding a single walk on the graph that satisfies the latency constraints on the vertices in . Given a robot walking on a graph, let represent the vertex occupied by the robot after traversing edges (after steps) of the walk. Also, at step , let the maximum time left until a vertex has to be visited by the robot for its latency to be satisfied be represented by . If that vertex is not visited by the robot within that time, we say that the vertex expired. Hence, the vector represents the time to expiry for each vertex. At the start of the walk, , and evolves according to the following equation:\n\n si(k)={r(i)if p(k)=isi(k−1)−l(p(k−1),p(k))otherwise. (1)\n\nWe will use the notation without the step if it is clear that we are talking about the current time to expiry. An incomplete greedy heuristic for the decision version of the problem with is presented in . The heuristic is to pick the vertex with minimum value of as the next vertex to be visited by the robot. This heuristic does not ensure that all the vertices on the walk will have their latency constraints satisfied since the distance to a vertex to be visited might get larger than . To overcome this, we propose a modification to the heuristic to apply it to our problem. Given a walk on graph , the function PeriodicFeasibility determines whether the periodic walk is feasible on the vertices that are visited by . This can be done simply in by traversing the walk and checking if the time to expiry for any of the visited vertices becomes negative. Given this function, the simple greedy algorithm is to pick the vertex subject to the constraint that PeriodicFeasibility returns true, where is the walk traversed so far. The algorithm terminates when all the vertices are either expired, or covered by the walk.\n\n### V-C Orienteering Based Greedy Algorithm\n\nAlgorithm 3 also finds partitioned walks by finding a feasible walk on a subset of vertices and then considering the remaining subgraph. The idea is to visit more vertices on the way to the greedily picked vertex. From the current vertex , the target vertex is picked greedily as described in Section V-B. Then the time is calculated in line 12 which is the maximum time to go from to for which the periodic walk remains feasible. In line 17, Orienteering finds a path in the vertices from to of length at most maximizing the sum of the weights on the vertices of the path. The set represents the expired vertices whose latencies cannot be satisfied by the current walk, and they will be considered by the next robot. The vertices with less time to expiry are given more importance in the path by setting weight for vertex . The vertices that are already in the walk will remain feasible, and so their weight is discounted by a small number to encourage the path to explore unvisited vertices.\n\n###### Lemma V.1.\n\nAlgorithm 3 returns a feasible solution, i.e., for the set of walks returned by Algorithm 3, , for all .\n\n###### Proof.\n\nThe vertices covered by the walk added to the solution in line 21 are removed from the set of vertices before finding the rest of the walks. Hence the latencies of the vertices will be satisfied by only . We will show that every time is appended in line 17, it remains feasible on .\n\nstarts from a single vertex , and hence is feasible at the start. Let us denote as the walk before line 17 and as the walk after line 17. Due to line 12, if is feasible in a particular iteration, then will remain feasible. Hence the only vertices than can possibly have their latency constraints violated in are in the orienteering path from to . Consider any vertex in the path from to returned by the Orienteering function in line 17. If , then because of line 12. If , then and by line 14, . As is only visited once in , . ∎\n\nAn approximation algorithm for Orienteering can be used in line 17 of Algorithm 3. In our implementation, we used an ILP formulation to solve Orienteering. To improve the runtime in practice, we pre-process the graph before calling the Orienteering solver to consider only the vertices such that . We show in the next section that although the runtime of Algorithm 3 is more than that of Algorithm 1, it can still solve instances with up to vertices in a reasonable amount of time, and it finds better solutions.\n\n## Vi Simulation Results\n\nWe now present the performance of the algorithms presented in the paper. For the approximation algorithm, we used the LKH implementation  to find the TSP of the graphs instead of the Christofides approximation algorithm . This results in the loss of approximation guarantee but gives better results in practice. The orienteering paths in Algorithm 3 were found using the ILP formulation from  and the ILP’s were solved using the Gurobi solver .\n\n### Vi-a Patrolling an Environment\n\nThe graphs for the problem instances were generated randomly in a real world environment. The scenario represents a ground robot monitoring the University of Waterloo campus. Vertices around the campus buildings represent the locations to be monitored and a complete weighted graph was created by generating a probabilistic road-map to find paths between those vertices. Figure 3 shows the patrolling environment. To generate random problem instances of different sizes, random vertices were chosen from the original graph. The latency constraints were generated uniformly randomly between and where was chosen randomly between and for each instance. Here TSP represents the TSP length of the graph found using LKH.\n\nFor each graph size, random instances were created. The average run times of the algorithms are presented in Figure 4. As expected, Algorithm 3 is considerably slower than the approximation and simple greedy algorithms due to multiple calls to the ILP solver. However, as shown in Figure 5, Algorithm 3 also gives the minimum number of robots for most of these instances.", null, "Fig. 3: The environment used for generation of random instances. The red dots represent the vertices to be monitored and the green dots represent the vertices in the PRM used to find shortest paths between red vertices.", null, "Fig. 4:\n\n### Vi-B Persistent 3D Scene Reconstruction\n\nAnother application of our algorithms is in capturing images for 3D reconstruction of a scene. Since existing algorithms focus on computing robot paths to map a static scene [5, 4], our algorithms could be applied to persistently monitor and thus maintain an up-to-date reconstruction of a scene that changes over time. To demonstrate this, we create problem instances using a method similar to . The viewpoints were generated on a grid around the building to be monitored. For each viewpoint, five camera angles were randomly generated, and best angle was selected for each viewpoint based on a view score that was calculated assuming a square footprint for the camera. For each camera angle, equally placed rays were projected onto the building within the footprint and a score was calculated based on the distance and incidence angle of the ray. This calculation is similar to that in , although they used a more detailed hemisphere coverage model.\n\nAfter selecting the viewing angles, the final score of a camera pose was evaluated as in  by greedily picking the best viewpoint first and evaluating the marginal score of other viewpoints. The resulting graph had vertices. The latencies were set such that the most informative viewpoint is visited every minutes and on average each viewpoint is visited every minutes. Algorithm 3 found a solution in seconds using two walks, as shown in Figure 7. Note that Algorithm 1 returned a solution with robots.", null, "Fig. 7: The walks returned by Algorithm 3 to continually monitor the mausoleum of the Taj Mahal. The cones at each viewpoint show the camera angle. Note that the walk on the left is not a tour, as it visits the vertex with least latency twice within a period. The walk on the right is a tour and it visits the vertices that the first robot was unable to cover.\n\n### Vi-C Comparison with Existing Algorithms in Literature\n\nIn [21, 16] the authors propose an SMT (Satisfiability Modulo Theory) based approach using Z3 solver  to solve the decision version of the problem. The idea is to fix an upper bound on the period of the solution and model the problem as a constraint program. The authors also provide benchmark instances for the decision version of the problem. We tested our algorithms on the benchmark instances provided and compare the results to the SMT based solver provided by .\n\nOut of 300 benchmark instances, given a time limit of 10 minutes, the Z3 solver returned 182 instances as satisfiable with the given number of robots. We ran our algorithms for each instance and checked if the number of robots returned are less than or equal to the number of robots in the benchmark instance. The approximation algorithm satisfied instances whereas Algorithm 3 satisfied instances. The four satisfiable instances that Algorithm 3 was unable to satisfy had optimal solutions where the walks share the vertices, and Algorithm 3 returned one more robot than the optimal in all those instances. The drawback of the constraint program to solve the problem is the scalability. It spent an average of seconds on satisfiable instances whereas Algorithm 3 spent ms on those instances on average. Moreover, on one such instance where Algorithm 3 returned one more robot than the Z3 solver, Z3 solver spent 194 seconds as compared to ms for Algorithm 3. Note that these differences are for benchmark instances having up to vertices. As shown above, Algorithm 3 takes seconds for vertex instances whereas we were unable to solve instances with even vertices within an hour using the Z3 solver. Hence, the scalability of the Z3 based solver hinders its use for problem instances of practical sizes.\n\n## Vii Conclusion and Future Work\n\nIn this paper we presented and analyzed an approximation and a heuristic algorithm for the problem of finding the minimum number of robots that can satisfy the latency constraints for the vertices in a graph. We demonstrated the performance of the algorithms through simulations. We also presented and analyzed an algorithm for minimizing the maximum latency given multiple robots. Finding the relation between the partitioned optimal solution and a general optimal solution is an interesting direction for future work.\n\n### References\n\n1. G. Cabrita, P. Sousa, L. Marques, and A. De Almeida, “Infrastructure monitoring with multi-robot teams,” in Int. Conf. on Intelligent Robots and Systems, 2010, pp. 18–22.\n2. N. Basilico, N. Gatti, and F. Amigoni, “Patrolling security games: Definition and algorithms for solving large instances with single patroller and single intruder,” Artificial Intelligence, vol. 184, pp. 78–123, 2012.\n3. A. B. Asghar and S. L. Smith, “Stochastic patrolling in adversarial settings,” in IEEE American Control Conf., 2016, pp. 6435–6440.\n4. M. Roberts, D. Dey, A. Truong, S. Sinha, S. Shah, A. Kapoor, P. Hanrahan, and N. Joshi, “Submodular trajectory optimization for aerial 3D scanning,” in Int. Conf. on Computer Vision, 2017, pp. 5334–5343.\n5. A. Bircher, K. Alexis, M. Burri, P. Oettershagen, S. Omari, T. Mantel, and R. Siegwart, “Structural inspection path planning via iterative viewpoint resampling with application to aerial robotics,” in IEEE Int. Conf. on Robotics and Automation, 2015, pp. 6423–6430.\n6. N. Cao, K. H. Low, and J. M. Dolan, “Multi-robot informative path planning for active sensing of environmental phenomena: A tale of two algorithms,” in Int. Conf. on Autonomous Agents and Multi-Agent Systems, 2013, pp. 7–14.\n7. L. Merino, F. Caballero, J. R. Martínez-De-Dios, I. Maza, and A. Ollero, “An unmanned aircraft system for automatic forest fire monitoring and measurement,” Journal of Intelligent & Robotic Systems, vol. 65, no. 1-4, pp. 533–548, 2012.\n8. P. F. Hokayem, D. Stipanovic, and M. W. Spong, “On persistent coverage control,” in IEEE Conf. on Decision and Control, 2007, pp. 6130–6135.\n9. N. Nigam and I. Kroo, “Persistent surveillance using multiple unmanned air vehicles,” in IEEE Aerospace Conf., 2008, pp. 1–14.\n10. N. Nigam, S. Bieniawski, I. Kroo, and J. Vian, “Control of multiple uavs for persistent surveillance: algorithm and flight test results,” IEEE Transactions on Control Systems Technology, vol. 20, no. 5, pp. 1236–1251, 2012.\n11. Y. Elmaliach, N. Agmon, and G. A. Kaminka, “Multi-robot area patrol under frequency constraints,” Annals of Mathematics and Artificial Intelligence, vol. 57, no. 3-4, pp. 293–320, 2009.\n12. J. M. Palacios-Gasós, E. Montijano, C. Sagues, and S. Llorente, “Multi-robot persistent coverage using branch and bound,” in IEEE American Control Conf., 2016, pp. 5697–5702.\n13. X. Yu, S. B. Andersson, N. Zhou, and C. G. Cassandras, “Optimal visiting schedule search for persistent monitoring of a finite set of targets,” in IEEE American Control Conf., 2018, pp. 4032–4037.\n14. ——, “Optimal dwell times for persistent monitoring of a finite set of targets,” in American Control Conf., 2017, pp. 5544–5549.\n15. J. Las Fargeas, B. Hyun, P. Kabamba, and A. Girard, “Persistent visitation under revisit constraints,” in IEEE Int. Conf. on Unmanned Aircraft Systems, 2013, pp. 952–957.\n16. N. Drucker, M. Penn, and O. Strichman, “Cyclic routing of unmanned aerial vehicles,” in Int. Conf. on AI and OR Techniques in Constriant Programming for Combinatorial Optimization Problems.   Springer, 2016, pp. 125–141.\n17. H.-M. Ho and J. Ouaknine, “The cyclic-routing uav problem is pspace-complete,” in Int. Conf. on Foundations of Software Science and Computation Structures.   Springer, 2015, pp. 328–342.\n18. S. Alamdari, E. Fata, and S. L. Smith, “Persistent monitoring in discrete environments: Minimizing the maximum weighted latency between observations,” The International Journal of Robotics Research, vol. 33, no. 1, pp. 138–154, 2014.\n19. M. M. Quottrup, T. Bak, and R. Zamanabadi, “Multi-robot planning: A timed automata approach,” in IEEE Int. Conf. on Robotics and Automation, vol. 5, 2004, pp. 4417–4422.\n20. A. Ulusoy, S. L. Smith, X. C. Ding, C. Belta, and D. Rus, “Optimality and robustness in multi-robot path planning with temporal logic constraints,” The International Journal of Robotics Research, vol. 32, no. 8, pp. 889–911, 2013.\n21. N. Drucker, “Cyclic routing of unmanned aerial vehicles,” Master’s thesis, Technion – Israel Institute of Technology, Israel, 2014.\n22. O. Bräysy and M. Gendreau, “Vehicle routing problem with time windows, part I: Route construction and local search algorithms,” Transportation Science, vol. 39, no. 1, pp. 104–118, 2005.\n23. J. N. Tsitsiklis, “Special cases of traveling salesman and repairman problems with time windows,” Networks, vol. 22, no. 3, pp. 263–282, 1992.\n24. N. Christofides and J. E. Beasley, “The period routing problem,” Networks, vol. 14, no. 2, pp. 237–256, 1984.\n25. W. Yu and Z. Liu, “Improved approximation algorithms for some min-max and minimum cycle cover problems,” Theoretical Computer Science, vol. 654, pp. 45–58, 2016.\n26. C. Chekuri, N. Korula, and M. Pál, “Improved algorithms for orienteering and related problems,” ACM Transactions on Algorithms, vol. 8, no. 3, p. 23, 2012.\n27. Y. Chevaleyre, “Theoretical analysis of the multi-agent patrolling problem,” in IEEE Int. Conf. on Intelligent Agent Technology, 2004, pp. 302–308.\n28. R. K. Iyer and J. A. Bilmes, “Submodular optimization with submodular cover and submodular knapsack constraints,” in Advances in Neural Information Processing Systems, 2013, pp. 2436–2444.\n29. K. Helsgaun, “An effective implementation of the Lin–Kernighan traveling salesman heuristic,” European Journal of Operational Research, vol. 126, no. 1, pp. 106–130, 2000.\n30. N. Christofides, “Worst-case analysis of a new heuristic for the travelling salesman problem,” Carnegie-Mellon Univ Pittsburgh Pa Management Sciences Research Group, Tech. Rep., 1976.\n31. A. N. Letchford, S. D. Nasiri, and D. O. Theis, “Compact formulations of the steiner traveling salesman problem and related problems,” European Journal of Operational Research, vol. 228, no. 1, pp. 83–92, 2013.\n32. Gurobi, “Gurobi optimizer,” 2018. [Online]. Available: http://www.gurobi.com\n33. L. De Moura and N. Bjørner, “Z3: An efficient SMT solver,” in Int. Conf. on Tools and Algorithms for the Construction and Analysis of Systems.   Springer, 2008, pp. 337–340.\nYou are adding the first comment!\nHow to quickly get a good reply:\n• Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.\n• Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.\n• Your comment should inspire ideas to flow and help the author improves the paper.\n\nThe better we are at sharing our knowledge with each other, the faster we move forward.\nThe feedback must be of minimum 40 characters and the title a minimum of 5 characters", null, "", null, "", null, "" ]
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[ "# 秩－零化度定理\n\n（重定向自秩-零化度定理\n\n$\\operatorname {rank} \\mathrm {A} +\\operatorname {nullity} \\mathrm {A} =n.$", null, "$\\operatorname {dim} (\\operatorname {Im} \\mathrm {T} )+\\operatorname {dim} (\\operatorname {Ker} \\mathrm {T} )=\\operatorname {dim} \\mathrm {V}$", null, "$\\operatorname {rank} \\mathrm {A} +\\operatorname {nullity} \\mathrm {A} =\\operatorname {dim} \\mathrm {V} .$", null, "## 证明\n\n$\\mathrm {V}$ 是一个有限维线性空间，其维度$\\operatorname {dim} \\mathrm {V} =n$ 。对一个从$\\mathrm {V}$ 射到$\\mathrm {F}$ 的线性变换$\\mathrm {T}$ ，它的$\\operatorname {Ker} \\mathrm {T}$ $\\mathrm {V}$ 的一个子空间。设 ${\\mathfrak {B}}_{k}=\\left(e_{1},e_{2}\\cdots ,e_{p}\\right)$ $\\operatorname {Ker} \\mathrm {T}$ 的一组基（$p\\leqslant n$ ）。根据基扩充定理${\\mathfrak {B}}_{k}$ 可以被扩充为$\\mathrm {V}$ 的一组基：${\\mathfrak {B}}=\\left(e_{1},e_{2}\\cdots ,e_{n}\\right)$ 。除了${\\mathfrak {B}}_{k}$ $p$ 个向量以外，另外的$n-p$ 个向量$\\left(e_{p+1},\\cdots ,e_{n}\\right)$ 是一组线性无关的向量。设$\\mathrm {H}$ 是它们张成的子空间，那么$\\mathrm {V}$ 是子空间$\\operatorname {Ker} \\mathrm {T}$ $\\mathrm {H}$ 直和\n\n$\\mathrm {V} =\\operatorname {Ker} \\mathrm {T} \\oplus \\mathrm {H}$\n\n{\\begin{aligned}\\mathrm {T} _{\\mathrm {H} }:\\mathrm {H} &\\rightarrow \\operatorname {Im} \\mathrm {T} \\\\u&\\mapsto \\mathrm {T} (u)\\end{aligned}}\n\n1. $\\mathrm {T} _{\\mathrm {H} }$ 是一个单射，因为$\\forall u,v\\in \\mathrm {H}$ $\\mathrm {T} (u)=\\mathrm {T} (v)\\Rightarrow \\mathrm {T} (u-v)=0\\Rightarrow u-v\\in \\mathrm {H} \\cap \\operatorname {Ker} \\mathrm {T} \\Rightarrow u-v=0\\Rightarrow u=v$\n2. $\\mathrm {T} _{\\mathrm {H} }$ 是一个满射，因为$\\forall v\\in \\operatorname {Im} \\mathrm {T}$ $\\exists u\\in \\mathrm {V} ,$ ，使得$\\ v=\\mathrm {T} (u)$ ，而且$u=a+b$  ，其中$a\\in \\operatorname {Ker} \\mathrm {T} ,\\ b\\in \\mathrm {H}$ 。 于是 $v=\\mathrm {T} (u)=\\mathrm {T} (a+b)=\\mathrm {T} (a)+\\mathrm {T} (b)\\ =\\mathrm {T} (b)$ ，其中$b\\in \\mathrm {H}$ ，所以$\\mathrm {T} _{\\mathrm {H} }$ 是一个满射\n\n$\\operatorname {dim} (\\mathrm {H} )=\\operatorname {dim} (\\operatorname {Im} \\mathrm {T} ).$\n\n$\\operatorname {dim} (\\operatorname {Im} \\mathrm {T} )+\\operatorname {dim} (\\operatorname {Ker} \\mathrm {T} )=\\operatorname {dim} (\\mathrm {V} ),$\n\n$\\operatorname {rank} \\mathrm {T} +\\operatorname {nullity} \\mathrm {T} =\\operatorname {dim} (\\mathrm {V} ).$ :59\n\n## 其他表达形式及推广\n\n0 → UVR → 0\n\ndim(U) + dim(R) = dim(V)\n\n0 → V1V2 → ... → Vr → 0\n\n$\\sum _{i=1}^{r}(-1)^{i}\\dim(V_{i})=0.$\n\nindex T = dim(ker T) - dim(coker T)\n\nindex T = dim(V) - dim(W)\n\n## 参考资料\n\n1. ^ Steven Roman. Advanced Linear Algebra. Springer(GTM135, Edition II). 2005. ISBN 9780387247663." ]
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https://www.techscience.com/jai/v4n1/47728/html
[ "[BACK]\n Journal on Artificial IntelligenceDOI:10.32604/jai.2022.027839", null, "Article\n\nOptimizing the Multi-Objective Discrete Particle Swarm Optimization Algorithm by Deep Deterministic Policy Gradient Algorithm\n\nXi an High-Tech Institute, Xi an, 710025, China\n*Corresponding Author: Yao Jun-Ping. Email: [email protected]\nReceived: 26 January 2022; Accepted: 09 March 2022\n\nAbstract: Deep deterministic policy gradient (DDPG) has been proved to be effective in optimizing particle swarm optimization (PSO), but whether DDPG can optimize multi-objective discrete particle swarm optimization (MODPSO) remains to be determined. The present work aims to probe into this topic. Experiments showed that the DDPG can not only quickly improve the convergence speed of MODPSO, but also overcome the problem of local optimal solution that MODPSO may suffer. The research findings are of great significance for the theoretical research and application of MODPSO.\n\nKeywords: Deep deterministic policy gradient; multi-objective discrete particle swarm optimization; deep reinforcement learning; machine learning\n\n1  Introduction\n\nParticle swarm optimization (PSO), a swarm intelligence algorithm, was proposed by Bai et al. in 1995. PSO is inspired by foraging behaviors of bird, information about the food will be shared among these birds. PSO can solve optimization problems with a continuous solution space, but it is invalid in discrete solution space optimization problem. Therefore, Zheng proposed binary particle swarm optimization (BPSO) in 1997, and later, a variant of BPSO called discrete particle swarm optimization (DPSO) was put forward. For BPSO cannot solve combination optimization problem with ordered structure expression and constraint condition , therefore DPSO is more widely used than BPSO. However, DPSO cannot solve multi-objective problems in practical applications. Drawing lessons from the multi-objective particle swarm optimization (MOPSO) proposed by Feng et al. in 2002, the multi-objective discrete particle swarm optimization (MODPSO) combines DPSO with MOPSO, can make up for the shortcomings of DPSO.\n\nThe static hyperparameter configuration has been proved to be an important factor constraining the performance of PSO, especially in convergence speed and local optimal solution. Therefore, Lu et al. explored dynamic setting of PSO hyperparameters based on deep deterministic policy gradient (DDPG) in 2021.\n\nThe configuration of hyperparameters of MODPSO and PSO is static. For example, value of the positive acceleration constant is usually 2 in MODPSO and PSO , this means static hyperparameter configuration of MODPSO may be an important factor constraining the performance of the algorithm as well as PSO. Therefore, determining whether DDPG can improve the performance of MODPSO is of great significance for promoting the theoretical research and real-world application of MODPSO.\n\nIn this logic, this paper explored whether DDPG could improve the performance of MODPSO, basic idea is that DDPG initially generates random hyperparameters for MODPSO, MODPSO gives good or bad reward to DDPG after adopting these hyperparameters, DDPG will generates new hyperparameters for MODPSO according to the reward from MODPSO. Steps of MODPSO are presented in Section 2. Frame of DDPG is presented in Section 3. Steps of deep deterministic policy gradient multi-objective discrete particle swarm optimization (DDPGMODPSO) is presented in Section 4, which is the development of MODPSO. Experimental results are presented in Section 5. Conclusion is presented in Section 6.\n\n2  MODPSO\n\nTo compare DDPGMODPSO and MODPSO, the fitness function proposed by Sun et al. was adopted, and the calculation method is as follow.\n\n{Min(Cost)=Mini=1mTi,process×[3.66+0.002×(j=1nSdj,memory+k=1hSmk,memory)]}Min(Time)=Min(i=1mTi,process)(1)\n\nMaterialized view is an important term in database and data house, the above multi-objective function is about to reduce cost and time of materialized view. i represents the ith query, j represents the jth base table, k represents the kth materialized view, Ti,process represents time used for the ith query, Sdj,memory represents storage used for the jth base table, Smk,memory represents storage used for the kth materialized view.\n\nThe MODPSO process designed by Sun et al. is as follows.\n\nInput: Discrete solution space;\n\npositive acceleration constants c1 and c2;\n\nnumber of particles;\n\nnumber of training epochs.\n\nOutput: Optimal solution.\n\nStep 1: Initialize the particle swarm, determine particle speed and position randomly, and deal with the illegal position.\n\nStep 2: Calculate individual fitness values Cost(xi(t)) and Time(xi(t)).\n\nStep 3: If individual fitness values greater than individual optimal fitness values, update the individual optimal fitness values as follows.\n\n{Cost(pbesti)>Cost(xi(t))Time(pbesti)>Time(xi(t))(2)\n\n{Cost(pbesti)=Cost(xi(t))Time(pbesti)=Time(xi(t))pbesti=xi(t)(3)\n\nStep 4: If individual optimal fitness values greater than global optimal fitness values, update the global optimal fitness values as follows.\n\n{Cost(gbesti)>Cost(xi(t))Time(gbesti)>Time(xi(t))(4)\n\n{Cost(gbesti)=Cost(xi(t))Time(gbesti)=Time(xi(t))gbesti=xi(t)(5)\n\nStep 5: Update velocity for each particle.\n\nvi(t)=vi(t1)+ρ1×(xpbestixi(t))+ρ2×(xgbestxi(t))(6)\n\nwhere random number ρ1=r1×c1, ρ2=r2×c2, r1U(0, 1), r2U(0, 1).\n\nStep 6: Update particle position as follows.\n\n{xi(t)=xi(t1)+vi(t)t=t+1(7)\n\nDeal with the illegal position.\n\nStep 7: Judge whether the training is terminated. If it is terminated, output the result; otherwise, go to Step 2.\n\nIt is necessary to noted that illegal position means position not in the discrete solution space, the way we deal with illegal position is replace it by the nearest position in the discrete solution space.\n\n3  DDPG\n\nDDPG was proposed by Zhao et al. in 2015, it combines deterministic policy gradient (DPG) and deep Q-network (DQN) with the actor-critic algorithm as a framework. Fig. 1 shows the structure of DDPG, which is mainly composed of Environment (MODPSO), Agent (Actor Network and Critic Network), State (st and st+1), Action (at) and Reward (rt).", null, "Figure 1: Structure of DDPG\n\nThe components of the DDPG are specified as follows.\n\n(1)   Environment\n\nActor network and critic network obtain the optimal hyperparameters c1 and c2 by continuously interacting with MODPSO, and then apply c1 and c2 to MODPSO, so MODPSO is set as the Environment here.\n\n(2)   Agent\n\nSince actor network and critic network are the only elements that can interact with the Environment, the actor network and the critic network are used as Agent here.\n\n(3)   Action\n\nActions are c1 and c2.\n\n(4)   State\n\nState have six dimensions. The first five dimensions represent the change in the average fitness value of MODPSO in the past, and the last dimension represents the current number of training epochs of MODPSO. The calculation method is as follows.\n\nsit=fitmeant+4ifitmeant+3i(8)\n\ns5t=tTmax(9)\n\nwhere sit represents state vector of the t-th training epoch and the i-th dimension. The value range of i is [0, 4]. Where Tmax indicates the maximum number of training epochs and fitment indicates the average fitness value of particles in the t-th training epochs of MODPSO.\n\n(5)   Reward\n\nState of the Environment is transferred, and Environment then gives Reward to Agent according to Agent's action. The setting of Reward is related to whether the global optimal fitness value has changed. The calculation method is as follows.\n\nri={1,Global optimal fitness value changed1,Global optimal fitness value not changed(10)\n\n4  DDPGMODPSO\n\nInspired by deep deterministic policy gradient particle swarm optimization (DDPGPSO) proposed by Lu et al. , this paper proposed DDPGMODPSO. DDPG initially generates random hyperparameters for MODPSO, MODPSO gives good or bad reward to DDPG after adopting these hyperparameters, then DDPG will generates new hyperparameters for MODPSO according the reward from MODPSO.\n\nThe DDPGMODPSO process designed in the this work is as follows.\n\nInput: Discrete solution space;\n\nthe number of particles;\n\nnumber of training epochs for MODPSO Tmax;\n\nnumber of training epochs for DDPG Trainmax.\n\nOutput: Optimal solution.\n\nStep 1: Randomly initialize the parameters of the current policy network μ(s|θμ) and current Q-network Q(s,a|θQ), i.e., θμ, and θQ.\n\nStep 2: Randomly initialize the parameters of target policy network μ(s|θμ) and target Q-network Q(s,a|θQ): θμθμ, θQθQ.\n\nStep 3: Initialize experience replay pool R.\n\nStep 4: Execute Step 1 to Step 4 of the MODPSO algorithm.\n\nStep 5: While episode is less than Trainmax.\n\nStep 6: Initialize a random process to explore Action;\n\nStep 7: Receive initial observations s1 of Environment (particle swarm).\n\nStep 8: While t is less than Tmax.\n\nStep 9: Choose Action according to the current strategy and explore noise. The specific process is as follows.\n\nat=μ(st|θμ)+Nt(11)\n\nStep 10: Execute Action at in Environment, then observe Reward rt and new State st+1;\n\nStep 11: Save (st, at, rt, st+1) to R as a data set for training the current network;\n\nStep 12: Randomly sample a minimum batch of N groups of data from R as training data of the current Q-network, and set yi.\n\nyi=ri+γQ(si+1,μ(si+1|θμ)|θQ)(12)\n\nStep 13: Update current Q-network by minimizing the loss function, and the minimum loss function is expressed as follows.\n\nL=1Ni=0N(yiQ(si,ai|θQ))2(13)\n\nStep 14: Use the gradient of the sample to update actor network as follows.\n\nθμJ1Ni(aQ(s,a|θQ)|s=si,a=μ(si)θμμ(s|θμ)|s=si)(14)\n\nStep 15: Update target network.\n\nθQτθQ+(1τ)θQ(15)\n\nθμτθμ+(1τ)θμ(16)\n\nwhere τ is the parameter update rate, which is generally set at 0.0001.\n\nStep 16: t++.\n\nStep 17: episode++.\n\nStep 18: Save the weights of the trained actor network;\n\nStep 19: Execute Step1 to Step 4 of the MODPSO algorithm;\n\nStep 20: While t is less than Tmax.\n\nStep 21: Calculate the current State and update the global optimal fitness value.\n\nStep 22: According to current policy network μ(s|θμ) and current State, get the current Action, calculate c1 and c2;\n\nStep 23: Execute Step 5 to Step 6 of the MODPSO algorithm.\n\nStep 24: t++.\n\n5  Experimental Results and Analysis\n\n5.1 Experimental Setup\n\nThe discrete solution space (the experimental data) in this paper is the same as Sun et al. . Tab. 1 shows the specifics of the data.", null, "Tab. 2 shows the setup of MODPSO.", null, "Tab. 3 shows the setup of actor network.", null, "Tab. 4 shows the setup of critic network.", null, "5.2 Result and Analyses\n\nTen sets of experiments were carried out on MODPSO and DDPGMODPSO separately, experimental result is showd in Tab. 5.", null, "As showed in Fig. 2, DDPGMODPSO outperformed MODPSO.\n\nAs showed in Fig. 3, Among the 10 experiments, MODPSO only found the global optimal value in two experiments, while DDPGMODPSO found the global optimal value in seven experiments. Therefore, DDPGMODPSO is significantly better than MODPSO in finding the global optimal fitness value.\n\nAs is showed in Fig. 4, In the two experiments in which MODPSO found the global optimal fitness value, MODPSO took an average of 56 steps to reach the global optimal fitness value; in the seven experiments in which DDPGMODPSO found the global optimal fitness value, DDPGMODPSO took an average of 41 steps. Therefore, DDPGMODPSO converges faster than MODPSO.", null, "Figure 2: Experimental result", null, "Figure 3: Number of times the global optimal value was found", null, "Figure 4: Average number of steps the global optimal value was found\n\n6  Conclusion\n\nIn the present work, we explored how the DDPG can improve the performance of MODPSO. Experiments revealed that DDPGMODPSO outperformed MODPSO in discovering the optimal fitness value and converged faster than the latter. Therefore, it was verified that DDPG can significantly improve the global optimal fitness value discovery capability and convergence speed of MODPSO.\n\nFunding Statement: The authors received no specific funding for this study.\n\nConflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.\n\n## References\n\n1. B. Bai, Z. W. Guo, C. Zhou, W. Zhang and J. Y. Zhang, “Application of adaptive reliability importance sampling-based extended domain PSO on single-mode failure in reliability engineering,” Information Sciences, vol. 546, pp. 42–59, 2020.\n2. R. Z. Zheng, “An improved discrete particle swarm optimization for airline crew rostering problem,” in Proc. of the 2020 IEEE Congress on Evolutionary Computation, Piscataway, USA, pp. 1–7, 2020.\n3. L. C. Shen, X. H. Huo and Y. F. Niu, “Survey of discrete particle swarm optimization algorithm,” Systems Engineering and Electronics, vol. 30, no. 10, pp. 1986–1990, 2008.\n4. Q. Feng, Q. Li, W. Quan and M. Pei, “Research review of multi-objective particle swarm optimization algorithm,” Chinese Journal of Engineering, vol. 43, no. 6, pp. 745–753, 2021.\n5. H. X. Lu, S. Y. Yin, G. L. Gong, Y. Liu and G. Chen, “Particle swarm algorithm based on depth deterministic policy gradient,” Journal of University of Electronic Science and Technology of China, vol. 50, no. 2, pp. 199–206, 2021.\n6. Z. X. Cai, L. Y. Liu, J. F. Cai and B. F. Chen Artificial Intelligence and its Applications, 5st ed., Beijing, China: Tsinghua University Press, pp. 184–189, 201\n7. Y. Y. Sun, J. P. Yao, X. J. Li and Y. J. Wang, “Materialized view selection in cloud environment based on multi-objective discrete particle swarm optimization,” Journal of China Academy of Electronics, vol. 16, no. 7, pp. 661–668, 2021.\n8. Y. P. Lin, L. L. Chen and J. Z. Zou, “Application of hybrid feature selection algorithm based on PSO in fatigue driving,” Computer Engineering, vol. 45, no. 2, pp. 278–283, 2019.\n9. X. Y. Zhao and S. F. Ding, “A review of deep reinforcement learning research,” Computer Science, vol. 45, no. 7, pp. 1–6, 2018.", null, "This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited." ]
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https://math.stackexchange.com/questions/29935/f3-g3-1-for-two-meromorphic-functions
[ "# $f^3 + g^3=1$ for two meromorphic functions\n\nCan you find two non-constant meromorphic functions $f,g$ such that $f^3 +g^3=1$?\n\n• If there is one pair, then the identity, $$\\left(\\frac{x^3y + y}{x y^3 + x}\\right)^3+\\left(\\frac{x^3 - y^3}{x y^3 + x}\\right)^3=1,\\quad \\text{if}\\; x^3+y^3=1$$ should lead to many more parametrizations. – Tito Piezas III Jan 9 '17 at 15:28\n\nYes. According to remark 2 on p.236 of Remmert's book, Classical topics in complex function theory, Springer GTM 172, a (more or less) explicit example can be given by using the Weierstrass $\\wp$-function associated to the triangular lattice $\\{m + n e^{2\\pi i /3}\\,:\\,m,n \\in \\mathbb{Z}\\}$. This function satisfies the differential equation $$(\\wp')^2 = 4 \\wp^3 - g_2 \\wp - g_3 \\qquad \\text{with}\\; g_2 = 0 \\; \\text{and} \\; g_3 = \\pm \\frac{\\Gamma\\big(\\frac{1}{3}\\big)^{18}}{(2\\pi)^6}.$$\n\nPutting $a = \\frac{1}{2} \\sqrt{\\phantom{|}g_{3}}$ and $b = \\dfrac{1}{\\sqrt{24a}}$ the functions $$f = \\frac{a + b\\, \\wp'}{\\wp} \\qquad \\text{and} \\qquad g = \\frac{a - b\\,\\wp'}{\\wp}$$ satisfy $f^3 + g^3 = 1$ by the above differential equation (the values of $a$ and $b$ are found using the ansatz $\\big(a + b\\,\\wp'\\big)^3 + \\big(a - b\\,\\wp'\\big)^3 = \\wp^3$ and the differential equation).\n\nObserve however that the zeroes of $\\wp$ and the poles of $\\wp'$ are poles of both $f$ and $g$ and indeed, according to the proposition on the same page this is necessarily the case (by a beautiful application of Picard's theorem). In fact, this proposition states: If $f$ and $g$ are meromorphic functions on $\\mathbb{C}$ satisfying $\\,f^n + g^n = 1$ for some $n \\geq 3$ then $f$ and $g$ are both either constant or they have common poles. Added: In fact, as user8268 points out in his comment below, one can even show that there are actually no non-constant such functions for $n \\geq 4$ (thanks a lot for that!). This is also alluded to by Remmert in his remark 1 on the same page 236.\n\nSee Remmert's book for further details.\n\nFollowing the links on the Wikipedia page I stumbled over Hans Lundmark's beautiful page on elliptic functions where you can find some domain coloring plots of some $\\wp$-functions towards the end of the page.\n\n• for $f^n+g^n=1$ (assuming they are meromorphic functions defined on all $\\mathbb{C}$): such functions would give you a holomorphic map from $\\mathbb{C}$ to the (compactification of) the Riemann surface $x^n+y^n=1$, which is of genus $>1$ if $n>3$. The universal cover of the Riemann surface is thus the unit disc $D$, and the map would lift to a holomorphic map $\\mathbb{C}\\to D$, which must be constant by Liuoville thm. Hence no non-constant $f,g$ for $n>3$. – user8268 Mar 30 '11 at 14:45\n• @user8268: Very nice, thanks for this remark (in fact, this is remark 1 in Remmert's book which I skipped, unfortunately). @joriki: thanks for the correction! – t.b. Mar 30 '11 at 14:54\n• (to include some numbers to my previous comment:) the genus of $x^n+y^n=1$ is (as computed e.g. by Riemann-Hurwitz formula) $g=(n-1)(n-2)/2$. For $n=1$ we get $g=1$, so the universal covering of the surface is $\\mathbb{C}$, hence $x$ and $y$ pull-back to meromorphic functions satisfying $f^3+g^3=1$ - which is as non-explicit proof of their existence as it gets :) – user8268 Mar 30 '11 at 15:04\n• ...sorry I meant \"for $n=3$\" – user8268 Mar 30 '11 at 15:12\n• New address: users.mai.liu.se/hanlu09/complex – Hans Lundmark Aug 14 '15 at 10:24\n\nAs an addendum of sorts to Theo's answer, the two functions $f$ and $g$ in the answer can be simplified through the use of the homogeneity relations\n\n$$\\wp\\left(cz;\\frac{g_2}{c^4},\\frac{g_3}{c^6}\\right)=\\frac1{c^2}\\wp\\left(z;g_2,g_3\\right),\\quad \\wp^\\prime\\left(cz;\\frac{g_2}{c^4},\\frac{g_3}{c^6}\\right)=\\frac1{c^3}\\wp^\\prime\\left(z;g_2,g_3\\right)$$\n\nFocusing on the case of positive $g_3$ (the treatment for negative $g_3$ is similar), we have\n\n$$f(z)=\\frac{3+\\sqrt{3}\\wp^\\prime\\left(\\frac{\\Gamma(1/3)^3}{2\\pi}z;0,1\\right)}{6\\wp\\left(\\frac{\\Gamma(1/3)^3}{2\\pi}z;0,1\\right)},\\quad g(z)=\\frac{3-\\sqrt{3}\\wp^\\prime\\left(\\frac{\\Gamma(1/3)^3}{2\\pi}z;0,1\\right)}{6\\wp\\left(\\frac{\\Gamma(1/3)^3}{2\\pi}z;0,1\\right)}$$\n\nwhere now only \"equianharmonic case\" Weierstrass elliptic functions are involved.\n\nIf these functions are plotted in the complex plane, a hexagonal structure similar to what is observed for the Dixon elliptic functions can be seen. This suggests that there might be a relationship between these functions and the Dixon elliptic functions.\n\nIn particular, using the homogeneity relations, one can show that\n\n$$f(z)=-\\frac{\\mathrm{cm}\\left(\\frac{\\Gamma(1/3)^3}{2\\pi}\\sqrt{3}z\\right)}{\\mathrm{sm}\\left(\\frac{\\Gamma(1/3)^3}{2\\pi}\\sqrt{3}z\\right)}$$\n\nAs promised, here are plots of $f(z)$ on the real line:", null, "a contour plot of the real and imaginary parts of $f(z)$:", null, "and plots of a single \"hexagonal tile\" of $f(z)$:", null, "", null, "Plots of $g(z)$ are similar since $g(z)=f(-z)$.\n\n• I'll edit this answer later to include pictures and show the equivalence with the Dixon elliptic functions. – J. M. is a poor mathematician Jul 21 '11 at 9:09\n• I hope you haven't forgotten... I'd love to see those pictures! – t.b. Jul 23 '11 at 0:59\n• Don't worry @Theo, I haven't; once I get to a Mathematica machine I'll post those pictures post-haste. – J. M. is a poor mathematician Jul 23 '11 at 1:01\n• Very nice! Thanks a lot! – t.b. Jul 27 '11 at 13:15\n• @J.M. : I have created this new Wikipedia article. \"J.M.\", could you perhaps add some information to it, including graphics? en.wikipedia.org/wiki/Dixon%27s_elliptic_functions $\\qquad$ – Michael Hardy Aug 23 '16 at 18:33\n\nAs I mentioned in this other post, A.C. Dixon studied in 1890 a class of elliptic functions based on inverting the Abelian integral\n\n$$\\int\\frac{\\mathrm dt}{\\left(1-t^3\\right)^{2/3}}$$\n\n(actually, he studied a more general class of elliptic functions based on the cubic $x^3+y^3-3\\alpha xy=1$, but I'll confine myself to the case $\\alpha=0$ and refer the interested to Dixon's paper for the general case.)\n\nIn particular, there are the two Dixon elliptic functions $\\mathrm{sm}(z,0)=\\mathrm{sm}(z)$ and $\\mathrm{cm}(z,0)=\\mathrm{cm}(z)$ that satisfy $\\mathrm{sm}^3(z)+\\mathrm{cm}^3(z)=1$ and a bunch of other identities, and can be expressed in terms of Weierstrass $\\wp$:\n\n$$\\mathrm{sm}(z)=\\frac{6\\wp\\left(z;0,\\frac1{27}\\right)}{1-3\\wp^\\prime\\left(z;0,\\frac1{27}\\right)}$$\n\n$$\\mathrm{cm}(z)=\\frac{3\\wp^\\prime\\left(z;0,\\frac1{27}\\right)+1}{3\\wp^\\prime\\left(z;0,\\frac1{27}\\right)-1}$$\n\nBoth have the independent periods $\\pi_3=B\\left(\\frac13,\\frac13\\right)$ (where $B(a,b)$ is the beta function) and $\\pi_3\\exp(2i\\pi/3)$, and have poles at the points $z=\\frac23\\pi_3+k\\pi_3,\\;k\\in\\mathbb Z$ in the real line, as well as having a total of three poles and three zeros in each \"fundamental hexagon\". As can be surmised, these are related to the general solutions in Theo's answer, due to the fact that the Weierstrass function satisfies homogeneity relations.\n\n• More general \"hyprgoniometric functions\" were studied by Lundberg in 1879(!) that satisfy relations of the form $s^n+c^n=1$; see this and this for instance. – J. M. is a poor mathematician May 9 '11 at 16:00\n• Hm, that is an interesting remark about $x^n+y^n=1$. Can you kindly look at this MO post? – Tito Piezas III Jan 7 '17 at 14:17\n• @Tito, it has been quite a while since I last touched it, but I think the sticking point I had was inverting the associated Abelian integrals (so that the inverses will automatically satisfy the general relation). The only extent of my knowledge on that was that (generalized) theta functions would be involved but I could not find the required identities in easily accessible references. – J. M. is a poor mathematician Jan 7 '17 at 14:21\n• Can you kindly look at this related post on the Dixonian functions? :) – Tito Piezas III Jan 9 '17 at 16:44" ]
[ null, "https://i.stack.imgur.com/iinhb.png", null, "https://i.stack.imgur.com/kX3gN.png", null, "https://i.stack.imgur.com/lZdM6.png", null, "https://i.stack.imgur.com/M0JAD.png", null ]
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https://qpqu.hargaqu.co/identifying-parts-of-a-parabola.html
[ "Example sentences with the word parabola. parabola example sentences. In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or Apollonian parabola ; a 2 x = y 3 is the cubic parabola , a 3 x...\nSal rewrites the equation y=-5x^2-20x+15 in vertex form (by completing the square) in order to identify the vertex of the corresponding parabola.\n1) Introduction to the Parabola The graph of a quadratic function is a U-shaped curve called a parabola. The point at which the curve changes direction is called the vertex. If the parabola opens upward, then the vertex is a minimum point and its y-value is the minimum value of the function. If the parabola opens downward, then the vertex is\n- [Voiceover] What I have attempted to draw here in yellow is a parabola, and as we've already seen in previous videos, a parabola can be defined as the set of all points that are equidistant to a point and a line, and the point is called the focus of the parabola, and the line is called the directrix of the parabola.\nUse vertex form to write the equation of the parabola. 9. Identify the vertex and the y-intercept of the graph of the function y =−3(x +2)2 +5. 10. Write y =2x2 +12x 14 in vertex form. Write the equation of the parabola in vertex form. 11. vertex ( –4 , 3), point (4, 131) 12. vertex (0, 3), point ( –4 , –45 )\nIf the parabola is symmetric about y-axis, we will have square for the variable x.So the given parabola will open rightward or leftward. x² = -4ay is the standard equation of the parabola which is symmetric about y axis and open downward. Let us look into some example problems to understand the above...\nEnglish Parts of Speech. Parts of a Sentence. Gerunds and Infinitives. English Modal Verbs.Dec 31, 2020 · x2 + y2= r2. Find the coordinates of the focus, axis, the equation of the directrix and latus rectum of the parabola y2 = 16x. Solution: In this equation, y2 is there, so the coefficient of x is positive so the parabola opens to the right. Comparing with the given equation y2 = 4ax, we find that a = 4.\nParabolas, Part 1 Conic Sections: Parabolas, Part 1. In this video, I discuss a quick way to roughly sketch a parabola. Nothing about directrix and focus in this video (look in part 2!). I simply find the vertex, x and y intercepts and do a quick graph. Lecture 2 Play Video: Parabolas, Part 2 (Directrix and Focus)\nfootball or diving sketch with key parts labeled. Exit Ticket – Diving or football problem signed off by teacher/expert at end of class. Homework – A Closer Look – Quadratics in Action Day 4 ‐ Domain and Range for Situations Warm Up - Review of parts of parabola, identifying domain and range of images\nA parabola has an axis of symmetry x — lies on the graph of the parabola. Let the graph of g be a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) = — 3. Write a rule for g. 36): -Ll(KE3) Identify the focus, directrix, and axis of symmetry of f (x) 16 ('00 Write the equation of the parabola, focus a vertex\nMar 17, 2020 · Check Point researchers detailed the activity of a prolific cyber-criminal known as ‘Dton’ that earned at least $100,000 US from his operations. Over the past few months, experts at Check Point have monitored the activity of a prolific cyber-criminal known as ‘Dton’. The man is active at least since 2013 and already earned at least […] Identify the concavity of the parabola by analyzing the quadratic expression. Find the – and -intercepts of a quadratic function. Find the vertex of a parabola by completing the square and by using the vertex formula. Find the equation of the axis of symmetry. Graph a parabola by labeling the – and -intercepts, the vertex and the axis of symmetry. 4. Give three examples of parabolas in the real world. • • • 5. What is a problem that can be solved with a quadratic function? 6. Use the picture at the right to tell what the axis of symmetry does. Axis of Symmetry Lesson 3: Investigating the Parts of a Parabola Unit 10: Introduction to Quadratics and Their Transformations This file ... The latus rectum of a parabola is the chord that passes through the focus and is perpendicular to the axis of the parabola. LSL’ Latus Ractum = 2 (4 a. a) 2\\left( \\sqrt{4a.a} \\right) 2 (4 a. a ) = 4a (length of latus Rectum) Note: – Two parabola are said to be equal if their latus rectum are equal. Parametric co-ordinates of Parabola If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph. This activity includes a parabola graphic organizer for students to label in relation to real-world scenarios. Available in printable form and digital for Google Slides.Add more iMath activities to the pho... Parabola. A u-shaped curve with certain specific properties. Note: It is a common error to call any u-shaped curve a parabola. A parabola must satisfy the conditions listed above, and a parabola always has a quadratic equation. Example: For the quadratic function , identify the vertex, the y-intercept, x-intercept(s), and the axis of symmetry. Graph the function. Graph the points identified above: vertex, point on . y-axis, points on. x-axis. Then draw the smooth curve of a parabola through the points. The . y-coordinate of the vertex represents Parabolas are of course not the only non-linear curves of importance - others being e.g. x 2+y = 1 (circle), x 2 4 + y 9 = 1 (ellipse), xy = 1 (hyperbola) - but they are the only ones discussed here. The shape of the parabola will be obtained experimentally i.e., by plotting enough points to see what the curve looks like. A second technique to identifying the curve of the parametric equations is to try to eliminate the parameter from the equations. This will result in an equation involving only x and y which we may recognize. For example, let's look again at the previous example. Since x = 2t then solving for t gives t = x/2. A parabola opening up has a minimum, while a parabola opening down has a maximum. All of the points on a parabola define a parabola. However, the vertex is the point in which the y value is only used for one point on the parabola. A parabola is a single curve: it does not have separate parts. Parabolas can open upward or downward. “Up like a cup” “Down like a frown :( “ To open upward, a>0. To open downward, a<0. Vertex of a upward parabola is the minimum. Vertex of a downward parabola is the maximum. Domain: Always all real numbers. Range: y ≤ or ≥ the vertex. Photo Links The main cables hang in the shape of a parabola. Find the equation of the parabola. Then, determine how high the main cable is 20 meters from the center. 2) The outer door of an airplane hangar is in the shape of a parabola. As you've noted in the details to the question, a parabola has an equation of the form $Ax^2\\pm 2\\sqrt{AC}\\, xy + Cy^2+ Dx + Ey + F = 0$ That's a special case of the generic equation for a conic section [math]Ax... 1. Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. 2. Find the vertex, focus, and directrix of (x-2)^2=12 (y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled. 3. Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. Once it is in standard form we can identify t.. See full list on mathsisfun.com Problem 34E from Chapter 11.5: Identifying a Parabola Using Rotation of Axes(a) Use rotatio... (a) Use rotation of axes to show that the following equation represents a parabola. Properties of parabolas Vertex form Graphing quadratic inequalities Factoring quadratic expressions Solving quadratic equations w/ square roots Solving quadratic equations by factoring Completing the square Solving equations by completing the square Solving equations with the quadratic formula The discriminant Get introduced to parabola; learn how to find equation of a parabola, equation of directrix. Follow BYJU'S way of learning. Conic Sections - Parabola. Parabola is locus of all points which are equally spaced from a fixed line and a fixed point. Parabolas can open upward or downward. “Up like a cup” “Down like a frown :( “ To open upward, a>0. To open downward, a<0. Vertex of a upward parabola is the minimum. Vertex of a downward parabola is the maximum. Domain: Always all real numbers. Range: y ≤ or ≥ the vertex. Photo Links This puzzle worksheet has 12 problems in which the students have the opportunity to practice graphing quadratic equations (from standard and vertex form), while also identifying the key characteristics of the parabola: 1. Axis of Symmetry 2. Vertex 3. Domain 4. Range (I used this as a homework assig Parabolas are of course not the only non-linear curves of importance - others being e.g. x 2+y = 1 (circle), x 2 4 + y 9 = 1 (ellipse), xy = 1 (hyperbola) - but they are the only ones discussed here. The shape of the parabola will be obtained experimentally i.e., by plotting enough points to see what the curve looks like. Define parabola. parabola synonyms, parabola pronunciation, parabola translation, English dictionary definition of parabola. parabola Any point on a parabola is the same distance parabola - a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve. Start by defining a domain, that is the bounded set of x values over which you want to average the rate of change. Then apply the standard rate of change formula ... Examples and Results on Normal to a Parabola | Co-Normal Points. In this lesson examples on normal to a parabola has been discussed along with results. Also the concept of conormal points has been explained. Graph the parabola y = f (x) for the given quadratic inequality f (x) ≥ 0 or f (x) ≤ 0. Find the vertex and the intercepts. Plot the points and graph the parabola. Identify the values of x for which the part of the parabola will either be negative or positive depending on the inequalities. Identify the concavity of the parabola by analyzing the quadratic expression. Find the – and -intercepts of a quadratic function. Find the vertex of a parabola by completing the square and by using the vertex formula. Find the equation of the axis of symmetry. Graph a parabola by labeling the – and -intercepts, the vertex and the axis of symmetry. (y − 2) = 3 (x − 5) 2 foci 3x2 + 2x + 5y − 6 = 0 vertices x = y2 axis (y − 3) 2 = 8 (x − 5) The Vertex of a Parabola The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x 2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. Graph the parabola y = f (x) for the given quadratic inequality f (x) ≥ 0 or f (x) ≤ 0. Find the vertex and the intercepts. Plot the points and graph the parabola. Identify the values of x for which the part of the parabola will either be negative or positive depending on the inequalities. I am being told to find the intervals on which the function is increasing or decreasing. It is a normal positive parabola with the vertex at$(3,0).$The equation could be$y = (x-3)^2,$but my confusion comes from the interval on which the parabola is increasing: I would think increasing is$(3,\\infty)...\nOff campus housing fsu\nDimplex thermostat troubleshootingLamb jackpot shows in texas 2020\nChapter 5 quiz 1 glencoe geometry answers\nDeviation approval mail\n1989 toyota corolla sr5\nCloset organizer onlineSsl vs tls handshakeWebdriverio typescriptHow to charge lenovo thinkpad penLego technic lamborghini gallardoBosch dishwasher rinse aid dispenser leakingMarvin gaye trouble man piano sheetKimber target 10mm\nFirewall log format huawei\nPrice percentage oscillator thinkorswim\nJson insert mysql\nSunbeam electric blanket controller flashing\nData keluaran hk 2020 harian\nNetsuite external id field\nForza horizon 3 club\nOrbi remote management web\nRibbon cable connectors digikey\nChicago electric 10 inch miter saw blade guard replacement\nAmazon under consideration to application submitted\nHazbin hotel x male reader one shots\nQuinte fiable\nCeiling tile suppliers near me9mm carry compensator\nExamples and Results on Normal to a Parabola | Co-Normal Points. In this lesson examples on normal to a parabola has been discussed along with results. Also the concept of conormal points has been explained.complete the square to identify what type of conic you have, identify the key parts indicated and then graph conic. parabola: vertex,focus, directrix, focal diameter. ellipse: center,vertices, foci, eccentricity. hyperbola: center, vertices, foci, slope of\nBlender sculpting not workingCnw sd80mac\n1. The figure below shows a graph of the function of f(x) in the coordinate plane. 0.25 0.5 0.75 L .25 1.75 Part A: Identify the following key features of the graph: The latus rectum of a parabola is the chord that passes through the focus and is perpendicular to the axis of the parabola. LSL’ Latus Ractum = 2 (4 a. a) 2\\left( \\sqrt{4a.a} \\right) 2 (4 a. a ) = 4a (length of latus Rectum) Note: – Two parabola are said to be equal if their latus rectum are equal. Parametric co-ordinates of Parabola A2.4.1 Describe connections between the geometric definition and the algebraic equations of the conic sections (parabola, circle, ellipse, hyperbola). A2.4.2 Identify specific characteristics (Center, vertex, foci, directrix, asymptotes etc.) of conic sections from their equation or graph. A2.4.3 Use the techniques of translations and rotation of axis in the coordinate plane to graph conic sections.\nIdentify the signs of a, b and c in each of the following: View Answer An equilateral triangle is inscribed in the parabola y 2 = 4 a x , where one vertex is at the vertex of the parabola.\nMsi gt 710 1gb driver\nThis file cannot be previewed file explorer windows 10\nBedford county tn accident today\nDec 16, 2016 · The Super Mario Effect - Tricking Your Brain into Learning More | Mark Rober | TEDxPenn - Duration: 15:09. TEDx Talks Recommended for you\nA 6 kg object is slides down a frictionless 10m rampRoof shingles liquidators\nThe vertex of any parabola has an x-value equal to − b 2 a. After finding the x-value of the vertex, substitute it into the original equation to find the corresponding y-value. This y-value is a maximum if the parabola opens downward, and it is a minimum if the parabola opens upward. We can easily identify that the parabola is opening left or right. Since the coefficient in front of the x term is positive, we can say that the parabola will open to the right. The focus will be to the right of the vertex, and the directrix will be a vertical line that is the same distance to the left of the vertex that the focus is to the right. In Exercises 37–40, write an equation of the parabola shown. (See Example 4.) 37. 39. In Exercises 41–46, identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with p = 1 and vertex (0, 0). 41. xy € =1 8 (x−3)2+2 43. € =1 16 (y−3)2+1\nDirect deposit cardsLabradoodle for sale florida\nAug 05, 2020 · August 5, 2020 – Today, Ariadne Labs and The Learning Accelerator announced the launch of The Parabola Project, an initiative that aims to rapidly develop evidence-informed tools to help school system leaders identify options for school reopening during the COVID-19 pandemic. The Parabola Project draws on expertise from both the education and ... This calculator will find either the equation of the parabola from the given parameters or the axis of symmetry, eccentricity, latus rectum, length of the latus rectum, focus, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the entered parabola.\nOgl horror character sheetsInferences worksheet pdf\nYou could have also discovered the x = 5 dividing point by finding the vertex of the parabola. You can find the vertex of parabola by rewriting the original equation so that we have . From the last form, we can read the vertex as (5, -10). We are only interested in the x-part of the point, the 5. The identify function is . The graph of the ...\nTeams dial planAmr500 pulley size\nIt just moved the the vertex, it moved it along the y axis the plus 2 took the exact same parabola shape moved it up 2 the minus 3 same parabola shape moved down 3. It looks like these guys are actually wider and skinnier but they're not it's hard to tell on this little screen but all of these parabolas are equally wider skinny that's going to ...\nGiant schnauzer for sale in texasCode impact analysis document template\nIdentify the vertex of the parabola. Write your answer as an ordered pair. I recommend decimals here. e. How long after the ball was released does it take for the ball to reach its maximum height, and how high is it? f. Going back to the original equation from part a, substitute zero for y and apply the quadratic formula. North Carolina NCTest Version. 2. powered by The kinds of supporting materials used in paragraphs depend on the topic sentence and the purpose of the paragraph as part of a whole written composition.\nJerr dan rollback bed for saleSwan island dahlias\nWhen a is zero, your parabola is really a line and the x values are already sorted in the correct order when b is positive or in the reverse order when b is negative. So when a isn't zero, find the apex: x0 = - b / (2*a) Now find the value in your sorted list of x values that is closest to x: i = index(x: min(|x - x0|)) Add point i to the list ... Identify the concavity of the parabola by analyzing the quadratic expression. Find the – and -intercepts of a quadratic function. Find the vertex of a parabola by completing the square and by using the vertex formula. Find the equation of the axis of symmetry. Graph a parabola by labeling the – and -intercepts, the vertex and the axis of symmetry.\nSpeer gold dot 224 bullets2006 buick lucerne life expectancy\nCharacteristics of Parabolas. Learning Outcomes. Identify the vertex, axis of symmetry, $y$-intercept, and minimum or maximum value of a Given a quadratic function in general form, find the vertex. Define the domain and range of a quadratic function by identifying the vertex as a maximum...The vertex form of a parabola's equation is generally expressed as: y = a(x-h) 2 +k (h,k) is the vertex as you can see in the picture below If a is positive then the parabola opens upwards like a regular \"U\".\nRaceme ultra rsa unlock cableConvert fbx to sfb\nPart of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. Identify the signs of a, b and c in each of the following: View Answer An equilateral triangle is inscribed in the parabola y 2 = 4 a x , where one vertex is at the vertex of the parabola.\nWorksheet polarity of bonds answer key12v 200ah deep cycle battery\nParabola homework assignment help for a view from the bridge catherine essay October 25, 2020 art term paper ideas However, edison and charles desavary, help parabola homework assignment who was stationary, and the measurement of support on the direction of the influence of the." ]
[ null ]
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https://www.gradesaver.com/textbooks/math/algebra/college-algebra-6th-edition/chapter-2-functions-and-graphs-exercise-set-2-6-page-297/13
[ "## College Algebra (6th Edition)\n\n$(-∞,0)∪(0,3)∪(3,∞)$\nMaking $x=0,3$ results in an undefined function, so those values are excluded from the domain. $h(x)=\\frac{4}{\\frac{3}{x}-1}$ $(-∞,0)∪(0,3)∪(3,∞)$" ]
[ null ]
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https://quant.stackexchange.com/questions/17138/garch-for-covariance-matrix/17147
[ "# Garch for covariance matrix?\n\nI have seen plenty of literature about GARCH on estimation volatility. how about covariance? There are plenty of risk models depending on the covariance matrix.\n\nI guess we can assume the correlation is constant and volatility changes. But in reality in super volatile moment correlation between stocks increases.\n\nOr there is a separate model for estimating correlation?\n\n## 2 Answers\n\nI think you're looking for multivariate GARCH models of which this is an overview paper.\n\nMultivariate GARCH models have one big drawback: they are pretty hard to estimate due to the number of correlations. This paper by Caporin and McAleer might be of interest in that regard.\n\nNot sure your question is about having a process for covariance or to have multivariate GARCH.\n\nThe standard viewpoint on a stochastic volatility for covariance is to use a Whishart process. See for instance Philipov, A. and M. E. Glickman (2006, July) Multivariate stochastic volatility via wishart processes. Journal of Business & Economic Statistics 24 (3), 313-328. You will find all the formulas.\n\nJust note in dimension one, it is like using a Gamma distribution for your volatility, using a \"time serie\" (a stochastic process) on the parameter $\\beta$. I.e.\n\n$$X_t|\\sigma^2_t \\sim {\\cal N}(0, \\sigma_t)$$\n\nand\n\n$$\\sigma_t^{-2}|\\alpha,\\beta_t\\sim \\Gamma(\\alpha,\\beta_t).$$" ]
[ null ]
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https://ras.football/2020/02/11/rodney-clemons-ras/
[ "# Rodney Clemons RAS", null, "### Rodney Clemons RAS\n\nRodney Clemons went undrafted for the NFL out of Southern Methodist in 2020.\n\nHe recorded a Relative Athletic Score of 3.35, out of a possible 10.0. RAS is a composite metric on a 0 to 10 scale based on the average of all of the percentile for each of the metrics the player completed either at the Combine or pro day.\n\nHe had a recorded height of 5115 that season, recorded as XYYZ where X is feet, YY is inches, and Z is eighths of an inch. That correlates to 5 feet, 11 and 5/8 of an inch or 71.625 inches, or 181.9275 centimeters. This correlates to a 4.28 score out of 10.0.\n\nHe recorded a weight of 209 in pounds, which is approximately 95 kilograms. This correlates to a 8.19 score out of 10.0.\n\nBased on his weight, he has a projected 40 yard dash time of 4.59. This is calculated by taking 0.00554 multiplied by his weight and then adding 3.433.\n\nAt the Combine, he recorded a 40 yard dash of 4.71 seconds. This was a difference of 0.12 seconds from his projected time. This forty time correlates to a 1.93 score out of 10.0.\n\nUsing Bill Barnwell’s calculation, this Combine 40 time gave him a Speed Score of 84.94.\n\nThe time traveled between the 20 and 40 yard lines is known as the Flying Twenty. As the distance is also known, we can calculate the player’s speed over that distance. The time he traveled the last twenty yards at the Combine was 1.96 seconds. Over 20 yards, we can calculate his speed in yards per second to 10.2. Taking into account the distance in feet (60 feet), we can calculate his speed in feet per second to 30.61. Breaking it down further, we can calculate his speed in inches per second to 367.35. Knowing the feet per second of 30.61, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 20.9 in the last 20 yards of his run.\n\nAt the Combine, he recorded a 20 yard split of 2.75 seconds. This correlates to a 1.74 score out of 10.0.\n\nWe can calculate the speed traveled over the second ten yards of the 40 yard dash easily, as the distance and time are both known. The time he traveled the second ten yards at the Combine was 1.1 seconds. Over 10 yards, we can calculate his speed in yards per second to 9.09. Taking into account the distance in feet (30 feet), we can calculate his speed in feet per second to 27.27. Breaking it down further, we can calculate his speed in inches per second to 327.27. Knowing the feet per second of 27.27, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 18.6 in the second ten yards of his run.\n\nAt the Combine, he recorded a 10 yard split of 1.65 seconds. This correlates to a 2.19 score out of 10.0.\n\nThe time he traveled the first ten yards at the Combine was 1.65 seconds. Over 10 yards, we can calculate his speed in yards per second to 6.0. Taking into account the distance in feet (30 feet), we can calculate his speed in feet per second to 18.0. Breaking it down further, we can calculate his speed in inches per second to 218.0. Knowing the feet per second of 18.0, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 12.3 in the first ten yards of his run.\n\nAt the Combine, he recorded a bench press of 21 repetitions of 225 pounds. This correlates to a 9.23 score out of 10.0.\n\nAt the Combine, he recorded a vertical jump of 33.5 inches. This correlates to a 3.83 score out of 10.0.\n\nAt the Combine, he recorded a broad jump of 910, which is recorded as FII or FFII . where F is feet and I is inches. This correlates to a 4.48 score out of 10.0.\n\nThis player did not have a recorded 5-10-5 or 20 yard short shuttle for the Combine in the RAS database.\n\nThis player did not have a recorded 3 cone L drill for the Combine in the RAS database.\n\nThis player did not record any measurements at their pro day that we were able to find. If they recorded Combine measurements, they stood on them.\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]
[ null, "https://ras.football/wp-content/uploads/2020/04/Rodney-Clemons-RAS-18547-740x430.png", null ]
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https://www.general-relativity.net/2018/04/exercise-104-super-luminal-effects.html
[ "## Wednesday, 11 April 2018\n\n### Exercise 1.04 Super luminal effects\n\n#### The question was\n\nProjection effects can trick you into thinking that an astrophysical object is moving “superluminally”. Consider a quasar that ejects gas with speed v at an angle θ with respect to the line-of-sight of the observer. Projected onto the sky, the gas appears to travel perpendicular to the line of sight with angular speed vapp/D, where D is the distance to the quasar and vapp is the apparent speed. Derive an expression for vapp in terms of v and θ. Show that, for appropriate values of v and θ, vapp can be greater than 1.\n\nPSR J0108-1431, the closest known pulsar to the Earth, is 280 light years distant . If the ejected gas position was measured at times a year apart, the angular difference in position α would be 1/128 = 0.0078125. We remember that sin's and tan's of very small angles are very close to the angle.\nI don't know why we have to bring relativity into this, so I haven't. Consider the diagram below, α is unrealistically big for visibility.\n\nOur famous observer is at O and the pulsar is at P. The ejected gas arrives at G after, say a year, and it's velocity v is represented by PG. The apparent velocity vapp isis represented by the line PGapp. We added the line PQ at right angles to OGapp and passing thru P. By simple geometry, we get angles in this order:\nStarting at O: PGO = π - α - θ then QGP = α + θ\nStarting at Gapp: PGappO = π/2 - α then QPGapp = α\ncalculating  PQ in two different ways we get\nPQ = vapp cos α   = v sin (α + θ)\nTherefore\nvapp   = v sin (α + θ) / cos α\nThis is not quite what was wanted, but for maximum leverage we obviously want v = π/2 - α so v lies along PQ. We then get\nvapp   = v / cos α\n\nLet's assume the gas comes from PSR J0108-1431 and that it's velocity is 0.99997, vapp is 1.000000517. If v is 0.99996, vapp is 0.999990517. It's a close run thing.\n\n#### Embarassing\n\nSadly my answer was completely wrong as I discovered when I looked at the UCSB answer, which was very clear. They have a slightly different illustration (from Hartle). O is the Observer again and N is the pulsar. They also do not use relativity but they do take account of the fact that if the cloud is moving rapidly towards the observer, the time taken for the light to arrive will be shorter, making the apparent velocity larger. That was at least one of my mistakes.", null, "From Hartle via UCSB\nThe formula they arrive at is\nvapp   = v sin θ / (1 - v cos θ)\nI have omitted a c because, for us, it is always 1.\n\nThis gives much more exciting results. For example at v=0.99, the apparent velocity can reach nearly 7 times the speed of light! Here is a graph of vapp vs θ for a more modest v = 0.95.", null, "vapp vs θ for v = 0.95" ]
[ null, "https://2.bp.blogspot.com/-fN0Je2ubJDc/W3KZd47dvPI/AAAAAAABDCc/VacFeo-THxsNwKqUFGk8FbkzvlwkSwaKwCLcBGAs/s1600/pic1.png", null, "https://4.bp.blogspot.com/-17lAs-5Tqio/W3Kaf-dZlLI/AAAAAAABDCk/15FgWhGJYQcpVJD1RsAejD2dayiEkDPkACLcBGAs/s1600/pic1.png", null ]
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https://artofproblemsolving.com/wiki/index.php/2005_AMC_10B_Problems/Problem_3
[ "# 2005 AMC 10B Problems/Problem 3\n\n## Problem\n\nA gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?", null, "$\\textbf{(A) } \\frac{1}{10} \\qquad \\textbf{(B) } \\frac{1}{9} \\qquad \\textbf{(C) } \\frac{1}{3} \\qquad \\textbf{(D) } \\frac{4}{9} \\qquad \\textbf{(E) } \\frac{5}{9}$\n\n## Solution\n\nAfter the first day, there is", null, "$1-\\left(\\dfrac{1}{3}\\cdot1\\right)=\\frac{2}{3}$ gallons left. After the second day, there is a total of", null, "$\\dfrac{2}{3}-\\left(\\dfrac{1}{3}\\times\\dfrac{2}{3}\\right)=\\dfrac{2}{3}-\\dfrac{2}{9}=\\dfrac{4}{9}$. Therefore, the fraction of the original amount of paint that is left is", null, "$\\dfrac{\\dfrac{4}{9}}{1}=\\boxed{\\textbf{(D) }\\frac{4}{9}}$.\n\nAnother way to do this is just to simply find the gain everyday and subtract from the remaining you had before.\n\nThe problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.", null, "" ]
[ null, "https://latex.artofproblemsolving.com/0/b/a/0ba0ca373308de801b689211a795cc68ab848a29.png ", null, "https://latex.artofproblemsolving.com/4/8/b/48b262b6d4eab460fa3ba443162cc38243c1a8c0.png ", null, "https://latex.artofproblemsolving.com/f/9/8/f98128e02b6d4d069b975edbf97183e8707009ea.png ", null, "https://latex.artofproblemsolving.com/b/5/8/b58d1d908613ef43bf08ef810eaf4ef016c80ef5.png ", null, "https://wiki-images.artofproblemsolving.com//8/8b/AMC_logo.png", null ]
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https://www.onlinemathlearning.com/trigonometry-common-core-regents-january-2017.html
[ "", null, "# Algebra 2/Trigonometry Common Core Regents Exam - January 2017\n\nRelated Topics:\nMore Lessons for the Regents High School Exam\nMore Lessons for Algebra\n\nHigh School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Algebra 2/Trigonometry (Common Core) Regents High School Examination January 2017.\n\n### Algebra 2/Trigonometry Common Core Regents New York State Exam - January 2017, Questions 1 - 39\n\nThe following are questions from the past paper\nRegents High School Algebra 2/Trigonometry, January 2017 Exam (pdf).\nScroll down the page for the step by step solutions.\n\nAlgebra 2/Trigonometry - January 2017 Regents - Questions and solutions 1 - 14\n\n1. What is 510° expressed in radian measure?\n2. Four surveys are described below. Which survey methodology would lead to the least biased conclusion?\n(1) One hundred randomly chosen heart surgeons were polled by telephone about how to get children to eat healthier foods.\n(2) A country and western radio station asked one hundred of its listeners to call a telephone number and answer a question about rap music.\n(3) From calls made to one hundred randomly generated telephone numbers, people replied to a question about television shows they watch.\n(4) The first one hundred people who left the World of Baseball Bookstore replied to a question about the importance of baseball to society\n3. When factored completely, x4 - 13x2 + 36 is equivalent to\n4. Which ordered pair is a solution to the system below?\nx2 - 4y2 = 16\ny = x - 4\n5. Three freshmen, five sophomores, and four juniors are on the school’s chess team. The coach must select three students to attend the citywide tournament. Which expression could be used to determine how many different groups of three students can be made from this team?\n6. A survey of high school girls found that the mean number of text messages sent per day by the girls was 62, with a standard deviation of 12. If a normal distribution is assumed, which interval represents the number of texts sent by 68.2% of the girls?\n7. The expression 93/2 ˙ 271/2 is equivalent to\n8. The ratio Arc cos1/2 / Arc tan 1 is equal to\n9. Which summation will not produce 2 + 4 + 6 + 8 + 10 + 12?\n10. The expression 1/3√6(3m √2 - k √3) is equivalent to\n11. If log3(x + 1) - log3x = 2, then x equals\n12. Which relation is not a function?\n13. What is the area of parallelogram ABCD if AB = 4, AD = 5√3, and m∠A = 60?\n14. The maximum point on the graph of the equation y = f(x) is (2,3). What is the maximum point on the graph of the equation y = f(x - 4)?\n\nAlgebra 2/Trigonometry - January 2017 Regents - Questions and solutions 15 - 27\n\n15. The formula of the nth term of the sequence 3, -6, 12, -24, 48. . . is\n16. The expression 3/(a-1) + 3/(1-a) is equivalent to\n17. The product of (2√2 + 5i) and (2√2 - 5i) is\n18. Which quadratic equation has roots with a sum of 7/6 and a product of -1/2?\n19. The range of the function f(x) = 3|x - 4| - 5 is\n20. The graph of the equation y = mx passes through the point\n21. If sin θ = 1/2 , and θ terminates in Quadrant II, what is the value of cscθ ˙ cotθ?\n22. A circle has a radius of 12 units. For this circle, which expression incorrectly states the length of the arc intercepted by the given central angle?\n23. How many different four-letter arrangements can be made from the letters in the word “CHAIRS,” if the same letter may be used only once?\n24. The sets below represent test scores for two students in Mrs. Silvio’s trigonometry class.\nMichelle: {71, 68, 84, 88}\nValerie: {78, 82, 76, 80}\nWhich statement correctly describes the relationship between the two students’ test scores?\n25. A support wire 20 meters long runs from the top of a utility pole to a point on the ground 17 meters from the base of the pole. What is the measure, to the nearest minute, of the angle formed by the pole and the wire?\n26. If f(x) = 3x - 2 and f-1(x) = (x+2)/3, then f ⚬ f-1(x) equals\n27. The graph of f(x) is shown below. Which graph represents f-1(x)?\n\nAlgebra 2/Trigonometry - January 2017 Regents - Questions and solutions 28 - 39\n\n28. The number of bacteria that grow in a petri dish is approximated by the function G(t) = 500e0.216t, where t is time, in minutes. Use this model to approximate, to the nearest integer, the number of bacteria present after one half-hour.\n29. Determine the exact value of (27/64)-2/3 as a fraction in simplest form.\n30. State the conjugate of 7 - √-48 expressed in simplest a + bi form.\n31. Express 12x-5y5/24x-3y-2 in simplest form, using only positive exponents.\n32. In a theater with 30 rows, the number of seats in a row increases by two with each successive row. The front row has 15 seats. Find the total seating capacity of the theater.\n33. Given f(x) = x2 and g(x) = x - 3, express g(f(x + 2)) as a polynomial in simplest form.\n34. Sketch an angle of 250° in standard position and then express cos 250° as a cosine function of a positive acute angle.\n35. Solve the inequality x2 - 3x - 4 > 0 algebraically for x.\n36. The table below shows the minimum hourly wage, in U.S. dollars, for selected years since 1955. Write the linear regression equation for this set of data, rounding all values to three decimal places. State the strength and direction indicated by the correlation coefficient\n37. Solve the system of equations algebraically for x and y:\n38. A rocket is shot vertically into the air. Its height, h, at any time, t, in seconds, can be modeled by the equation h = -16t2 + 184t. Determine algebraically, the number of seconds it will take the rocket to reach a height of 529 feet.\n39. Forces of 22 pounds and 43 pounds act on an object at an angle of 52°. Determine, to the nearest pound, the magnitude of the resultant force. Find, to the nearest degree, the angle between the smaller force and the resultant force.\n\nRotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.\n\nYou can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.", null, "" ]
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http://c.biancheng.net/ml_alg/sklearn-knn.html
[ "# sklearn实现KNN分类算法\n\nPyhthon Sklearn 机器学习库提供了 neighbors 模块，该模块下提供了 KNN 算法的常用方法，如下所示：\n\nKNeighborsClassifier KNN 算法解决分类问题\nKNeighborsRegressor KNN 算法解决回归问题\nNearestNeighbors 基于无监督学习实现KNN算法\nKDTree 无监督学习下基于 KDTree 来查找最近邻的分类算法\nBallTree 无监督学习下基于 BallTree 来查找最近邻的分类算法\n\n```#加载红酒数据集\n#KNN分类算法\nfrom sklearn.neighbors import KNeighborsClassifier\n#分割训练集与测试集\nfrom sklearn.model_selection import train_test_split\n#导入numpy\nimport numpy as np\n#加载数据集\n#查看数据集对应的键\nprint(\"红酒数据集的键:\\n{}\".format(wine_dataset.keys()))\nprint(\"数据集描述:\\n{}\".format(wine_dataset['data'].shape))\n\n# data 为数据集数据;target 为样本标签\n#分割数据集，比例为 训练集：测试集 = 8:2\nX_train,X_test,y_train,y_test=train_test_split(wine_dataset['data'],wine_dataset['target'],test_size=0.2,random_state=0)\n\n#构建knn分类模型，并指定 k 值\nKNN=KNeighborsClassifier(n_neighbors=10)\n\n#使用训练集训练模型\nKNN.fit(X_train,y_train)\n\n#评估模型的得分\nscore=KNN.score(X_test,y_test)\nprint(score)\n#给出一组数据对酒进行分类\nX_wine_test=np.array([[11.8,4.39,2.39,29,82,2.86,3.53,0.21,2.85,2.8,.75,3.78,490]])\npredict_result=KNN.predict(X_wine_test)\nprint(predict_result)\nprint(\"分类结果：{}\".format(wine_dataset['target_names'][predict_result]))```\n\n```红酒数据集的键:\ndict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names'])\n\n(178, 13)\n0.75", null, "" ]
[ null, "http://c.biancheng.net/templets/new/images/material/qrcode_mp.png", null ]
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https://answers.everydaycalculation.com/gcf/4-9
[ "Solutions by everydaycalculation.com\n\n## What is the GCF of 4 and 9?\n\nThe gcf of 4 and 9 is 1.\n\n#### Steps to find GCF\n\n1. Find the prime factorization of 4\n4 = 2 × 2\n2. Find the prime factorization of 9\n9 = 3 × 3\n3. To find the gcf, multiply all the prime factors common to both numbers:\n\nTherefore, GCF = 1\n\nThe greatest common factor (gcf) is also known as greatest common divisor (gcd) or highest common factor (hcf).\n\n#### GCF Calculator\n\nEnter two numbers separate by comma. To find gcf of more than two numbers, click here." ]
[ null ]
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