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  • Web Crawler for Learnign Topics on Wikipedia

    - by Chris Okyen
    When I want to learn a vast topic on wikipedia, I don't know where to start. For instance say I want to learn about Binary Stars, I then have to know other things linked on that pages and linked pages on all the linked pages and so on for the specified number of levels. I want to write a web crawler like HTTracker or something similiar, that will display a heiarchy of the links on a certain page and the links on those linked pages.I wish to use as much prewritten code as possible. Here is an example: Pretending we are bending the rules by grabing links from only the first sentence of each pages The example archives and "processes" two levels deep The page is Ternary operation The First Level In mathematics a ternary operation is an N-ary operation The Second Level Under Mathmatics: Mathematics (from Greek µ???µa máthema, “knowledge, study, learning”) is the abstract study of topics encompassing quantity, structure, space, change and others; it has no generally accepted definition. Under N-ary In logic,mathematics, and computer science, the arity i/'ær?ti/ of a function or operation is the number of arguments or operands that the function takes Under Operation In its simplest meaning in mathematics and logic, an operation is an action or procedure which produces a new value from one or more input values ------------------------------------------------------------------------- I need some way to determine what oder to approach all these wiki pages to learn the concept ( in this case ternary operations )... Following along with this exmpakle, one way to show the path to read would a printout flowout like so: This shows that the first sentence of the Mathematics page doesn't link to the first sentence of pages linked on ternary page two levels deep. (Please tell me how I should explain this ) --- In otherwords, the child node of the top pages first sentence, ternary_operation, does not have any child nodes that reference the children of the top pages other children nodes- N-ary and operation. Thus it is safe to read this first. Since N-ary has a link to operations we shoudl read the operation page second and finally read the N-ary page last. Again, I wish to use as much prewritten code as possible, and was wondering what language to use and what would be the simpliest way to go about doing this if there isn't already somethign out there? Thank You!

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  • Wikipedia A* pathfinding algorithm takes a lot of time

    - by Vee
    I've successfully implemented A* pathfinding in C# but it is very slow, and I don't understand why. I even tried not sorting the openNodes list but it's still the same. The map is 80x80, and there are 10-11 nodes. I took the pseudocode from here Wikipedia And this is my implementation: public static List<PGNode> Pathfind(PGMap mMap, PGNode mStart, PGNode mEnd) { mMap.ClearNodes(); mMap.GetTile(mStart.X, mStart.Y).Value = 0; mMap.GetTile(mEnd.X, mEnd.Y).Value = 0; List<PGNode> openNodes = new List<PGNode>(); List<PGNode> closedNodes = new List<PGNode>(); List<PGNode> solutionNodes = new List<PGNode>(); mStart.G = 0; mStart.H = GetManhattanHeuristic(mStart, mEnd); solutionNodes.Add(mStart); solutionNodes.Add(mEnd); openNodes.Add(mStart); // 1) Add the starting square (or node) to the open list. while (openNodes.Count > 0) // 2) Repeat the following: { openNodes.Sort((p1, p2) => p1.F.CompareTo(p2.F)); PGNode current = openNodes[0]; // a) We refer to this as the current square.) if (current == mEnd) { while (current != null) { solutionNodes.Add(current); current = current.Parent; } return solutionNodes; } openNodes.Remove(current); closedNodes.Add(current); // b) Switch it to the closed list. List<PGNode> neighborNodes = current.GetNeighborNodes(); double cost = 0; bool isCostBetter = false; for (int i = 0; i < neighborNodes.Count; i++) { PGNode neighbor = neighborNodes[i]; cost = current.G + 10; isCostBetter = false; if (neighbor.Passable == false || closedNodes.Contains(neighbor)) continue; // If it is not walkable or if it is on the closed list, ignore it. if (openNodes.Contains(neighbor) == false) { openNodes.Add(neighbor); // If it isn’t on the open list, add it to the open list. isCostBetter = true; } else if (cost < neighbor.G) { isCostBetter = true; } if (isCostBetter) { neighbor.Parent = current; // Make the current square the parent of this square. neighbor.G = cost; neighbor.H = GetManhattanHeuristic(current, neighbor); } } } return null; } Here's the heuristic I'm using: private static double GetManhattanHeuristic(PGNode mStart, PGNode mEnd) { return Math.Abs(mStart.X - mEnd.X) + Math.Abs(mStart.Y - mEnd.Y); } What am I doing wrong? It's an entire day I keep looking at the same code.

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  • How to analyse Wikipedia article's data base with R?

    - by Tal Galili
    Hi all, This is a "big" question, that I don't know how to start, so I hope some of you can give me a direction. And if this is not a "good" question, I will close the thread with an apology. I wish to go through the database of Wikipedia (let's say the English one), and do statistics. For example, I am interested in how many active editors (which should be defined) Wikipedia had at each point of time (let's say in the last 2 years). I don't know how to build such a database, how to access it, how to know which types of data it has and so on. So my questions are: What tools do I need for this (besides basic R) ? MySQL on my computer? RODBC database connection? How do you start planning for such a project?

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  • Importing wikipedia database dumb - kills navicat - anyone got any ideas?

    - by Ali
    Ok guys I've downloaded the wikipedia xml dump and its a whopping 12 GB of data :\ for one table and I wanted to import it into mysql databse on my localhost - however its a humongous file 12GB and obviously navicats taking its sweet time in importing it or its more likely its hanged :(. Is there a way to include this dump or atleast partially at most you know bit by bit. Let me correct that its 21 GB of data - not that it helps :\ - does any one have any idea of importing humongous files like this into MySQL database.

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  • How much one can trust the information published in the wikipedia? [closed]

    - by AKN
    Wikipedia has answers for many question almost in all categories. Let it be Technical Sports Personalities Important events (this day, that day) Scientific terms etc... I know the source of contents are from volunteers (Please correct me if I'm wrong here). But what measures they have to ensure that contents are properly written. Even if they have admin/moderator and all that, they may not be experts in all areas. So how do they validate the appropriateness of the content?

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  • How is the filesystem of Wikipedia designed?

    - by Heo
    I read about FHS, and I started to consider the file system of wikipedia. On the one hand, I feel it is a security risk to let everyone know it. On the other hand, it is necessary for developers. For example, is there some rule to know where are all sitemaps and their indices located? So: How is the file system of Wikipedia designed?

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  • Why hill climbing is called anytime algorithm?

    - by crucified soul
    From wikipedia, Anytime algorithm In computer science an anytime algorithm is an algorithm that can return a valid solution to a problem even if it's interrupted at any time before it ends. The algorithm is expected to find better and better solutions the more time it keeps running. Hill climbing Hill climbing can often produce a better result than other algorithms when the amount of time available to perform a search is limited, such as with real-time systems. It is an anytime algorithm: it can return a valid solution even if it's interrupted at any time before it ends. Hill climbing algorithm can stuck into local optima or ridge, after that even if it runs infinite time, the result won't be any better. Then, why hill climbing is called anytime algorithm?

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • Filtering Wikipedia's XML dump: error on some accents

    - by streetpc
    I'm trying to index Wikpedia dumps. My SAX parser make Article objects for the XML with only the fields I care about, then send it to my ArticleSink, which produces Lucene Documents. I want to filter special/meta pages like those prefixed with Category: or Wikipedia:, so I made an array of those prefixes and test the title of each page against this array in my ArticleSink, using article.getTitle.startsWith(prefix). In English, everything works fine, I get a Lucene index with all the pages except for the matching prefixes. In French, the prefixes with no accent also work (i.e. filter the corresponding pages), some of the accented prefixes don't work at all (like Catégorie:), and some work most of the time but fail on some pages (like Wikipédia:) but I cannot see any difference between the corresponding lines (in less). I can't really inspect all the differences in the file because of its size (5 GB), but it looks like a correct UTF-8 XML. If I take a portion of the file using grep or head, the accents are correct (even on the incriminated pages, the <title>Catégorie:something</title> is correctly displayed by grep). On the other hand, when I rectreate a wiki XML by tail/head-cutting the original file, the same page (here Catégorie:Rock par ville) gets filtered in the small file, not in the original… Any idea ? Alternatives I tried: Getting the file (commented lines were tried wihtout success): FileInputStream fis = new FileInputStream(new File(xmlFileName)); //ReaderInputStream ris = ReaderInputStream.forceEncodingInputStream(fis, "UTF-8" ); //(custom function opening the stream, reading it as UFT-8 into a Reader and returning another byte stream) //InputSource is = new InputSource( fis ); is.setEncoding("UTF-8"); parser.parse(fis, handler); Filtered prefixes: ignoredPrefix = new String[] {"Catégorie:", "Modèle:", "Wikipédia:", "Cat\uFFFDgorie:", "Mod\uFFFDle:", "Wikip\uFFFDdia:", //invalid char "Catégorie:", "Modèle:", "Wikipédia:", // UTF-8 as ISO-8859-1 "Image:", "Portail:", "Fichier:", "Aide:", "Projet:"}; // those last always work

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  • Mahout - Error when try out wikipedia exmaples

    - by Li'
    Note this post is similar to Caused by: java.lang.ClassNotFoundException: classpath but different error message. When I try to run Wikipedia Bayes Example from https://cwiki.apache.org/confluence/display/MAHOUT/Wikipedia+Bayes+Example When I ran the following command : lis-macbook-pro:mahout-distribution-0.8 Li$ mahout wikipediaXMLSplitter -d examples/temp/enwiki-latest-pages-articles10.xml -o wikipedia/chunks -c 64 I got error message: MAHOUT_LOCAL is set, so we don't add HADOOP_CONF_DIR to classpath. MAHOUT_LOCAL is set, running locally SLF4J: Class path contains multiple SLF4J bindings. SLF4J: Found binding in [jar:file:/Users/Li/File/Java/mahout-distribution-0.8/examples/target/mahout-examples-0.8-job.jar!/org/slf4j/impl/StaticLoggerBinder.class] SLF4J: Found binding in [jar:file:/Users/Li/File/Java/mahout-distribution-0.8/examples/target/dependency/slf4j-jcl-1.7.5.jar!/org/slf4j/impl/StaticLoggerBinder.class] SLF4J: See http://www.slf4j.org/codes.html#multiple_bindings for an explanation. SLF4J: Actual binding is of type [org.slf4j.impl.JCLLoggerFactory] Oct 21, 2013 4:25:47 PM org.slf4j.impl.JCLLoggerAdapter warn WARNING: Unable to add class: wikipediaXMLSplitter java.lang.ClassNotFoundException: wikipediaXMLSplitter at java.net.URLClassLoader$1.run(URLClassLoader.java:202) at java.security.AccessController.doPrivileged(Native Method) at java.net.URLClassLoader.findClass(URLClassLoader.java:190) at java.lang.ClassLoader.loadClass(ClassLoader.java:306) at sun.misc.Launcher$AppClassLoader.loadClass(Launcher.java:301) at java.lang.ClassLoader.loadClass(ClassLoader.java:247) at java.lang.Class.forName0(Native Method) at java.lang.Class.forName(Class.java:171) at org.apache.mahout.driver.MahoutDriver.addClass(MahoutDriver.java:236) at org.apache.mahout.driver.MahoutDriver.main(MahoutDriver.java:127) I am using Hadoop 1.2 and Mahout 0.8. mahout-distribution-0.8/bin has been added to $PATH. $MAHOUT_LOCAL is set to "True", so it runs locally. I dont know why I got "Unable to add class: wikipediaXMLSplitter"

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  • Wikipedia abandonne Google Maps et passe à OpenStreetMap pour ses applications mobiles, la première version pour iOS est disponible

    Wikipedia passe à OpenStreetMap Et abandonne Google Maps pour ses applications mobiles, la version iOS disponible Après Apple pour iPhoto, c'est au tour de Wikipedia de passer à OpenStreetMap, l'alternative collaborative et open source aux Google Maps. Ce choix concerne les applications mobiles (iOS et Android) de l'encyclopédie. Ses applications proposent à un utilisateur de le géolocaliser et d'afficher les éléments intéressants (bâtiments, musées, évènements historiques, etc.) à proximité. [IMG]http://ftp-developpez.com/gordon-fowler/Wikipedia%20appli.png[/IMG]

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  • Own mediawiki/wikipedia naming convention for pages

    - by Andy M
    I recently installed a mediawiki at home and I'm looking for a way to name pages. Let's say I have the following structure : Main - Dev - C# - Tips Main - Cooking - Mexixan Cooking - Tips Main - Annoying my girlfriend - Tips Each final page is a different Tips page. Naming them only "tips" won't work because I need three different pages. Now, I could name each of my tips page with its "path" (ex: main_cooking_mexican_cooking_tips) but it looks cumbersome and the problem is that, whenever I'll change the structure of my mediawiki, some pages will need to change their name in order to be corrects. Does it exist some convention to follow regarding this ? Thanks for your help !

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  • dbpedia auto-suggest labels

    - by Sid
    Wikipedia has a auto-suggest feature on its search field. If you for instance type in "mars" it lists a few items including Mars, Marseille, Marsh. I am looking to implement something similar working off the latest DBpedia export (wikipedia in database form). If I do a search for all labels in the labels_en.nt file that DBpedia offer that begin with "mars" then, even if I remove ones that redirect on to others that are listed, I end up with a huge list. In trying to understand how wikipedia does this I noticed that I'm actually querying this URL which returns a JSON string. Now my problem is that I don't know how wikipedia narrows the list down. Perhaps it does so based on page popularity. The higher views/edits a page has the higher it goes in this suggestion box. If so, does DBpedia export this information?

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  • nearest neighbor - k-d tree - wikipedia proof.

    - by user123930
    On the wikipedia entry for k-d trees, an algorithm is presented for doing a nearest neighbor search on a k-d tree. What I don't understand is the explanation of step 3.2. How do you know there isn't a closer point just because the difference between the splitting coordinate of the search point and the current node is greater than the difference between the splitting coordinate of the search point and the current best?

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  • Wikipedia article's

    - by Algorist
    Hi, I am doing a project, for which I need to know all the wikipedia article names(I don't need the content). Is there a place where I can download this data. Thank you Bala

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  • How can I create Wikipedia's footnote highlighting solely with jQuery

    - by andrew.bachman
    I would like to duplicate Wikipedia's footnote highlighting from in-text citation click solely in jQuery and CSS classes. I found a webpage that describes how to do so with CSS3 and then a JavaScript solution for IE. I would like however to do so solely with jQuery as the site I'm doing it on already has a bunch of jQuery elements. I've come up with a list of the process. In-Text Citation Clicked Replace highlight class with standard footnote class on <p> tag of footnotes that are already highlighted. Add highlight to the appropriate footnote Use jQuery to scroll down the page to appropriate footnote. I've come up with some jQuery so far but I'm extremely new to it relying heavy on tutorials and plugins to this point. Here is what I have with some plain English for the parts I haven't figured out yet. $('.inlineCite').click(function() { $('.footnoteHighlight').removeClass('footnoteHighlight').addClass('footnote'); //add highlight to id of highlightScroll //scroll to footnote with matching id }); If I had a method to pass a part of the selector into the function and turn it into a variable I believe I could pull it off. Most likely I'm sure one of you gurus will whip something up that puts anything I think I have done to shame. Any help will be greatly appreciated so thank you in advance. Cheers.

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  • Why Wikipedia doesn't appear as a referral in Google Analytics' Traffic sources?

    - by Rober
    One of my clients has a website and got not spammy backlinks in a Wikipedia article. When I test it for SEO purposes with Google Analytics (from different IPs), apparently there is no referral information. On the Real-Time view my test visit is visible but with There is no data for this view in the referrals subview. And this visits appear as (direct) / (none) on the Traffic sources view. Wikipedia is not hiding in any way its links origin, since it is shown in the server visits log. Is Google ignoring Wikipedia as a referral? Am I missing anything else? Update: Now it works, several days after the link was active. Maybe something is detecting for how long the link was there so that it doesn't work just from the beggining, as a security measure? Many visits are actually not recorded.

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  • MediaWiki styling for iPhone

    - by Brian Ashe
    When you visit en.wikipedia.org with an iPhone you are forwarded to en.m.wikipedia.org which is formatted beautifully for the device. I have MediaWiki on my own server and I'd love to have this formatting available when I visit my site with my iPhone. Is there an easy way to enable this? I've gotten as far as www.mediawiki.org/wiki/Manual:$wgHandheldForIPhone and http://www.mediawiki.org/wiki/Extension:MobileSkin but nothing is jumping out at me.

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  • How to create a Semantic Network like wordnet based on Wikipedia?

    - by Forbidden Overseer
    I am an undergraduate student and I have to create a Semantic Network based on Wikipedia. This Semantic Network would be similar to Wordnet(except for it is based on Wikipedia and is concerned with "streams of text/topics" rather than simple words etc.) and I am thinking of using the Wikipedia XML dumps for the purpose. I guess I need to learn parsing an XML and "some other things" related to NLP and probably Machine Learning, but I am no way sure about anything involved herein after the XML parsing. Is the starting step: XML dump parsing into text a good idea/step? Any alternatives? What would be the steps involved after parsing XML into text to create a functional Semantic Network? What are the things/concepts I should learn in order to do them? I am not directly asking for book recommendations, but if you have read a book/article that teaches any thing related/helpful, please mention them. This may include a refernce to already existing implementations regarding the subject. Please correct me if I was wrong somewhere. Thanks!

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  • Parsing Wiki XML Dumps ver0.4 just got tough

    - by syed
    Hello, I am trying to parse Wikipedia XML Dump using "Parse-MediaWikiDump-1.0.4" along with "Wikiprep.pl" script. I guess this script works fine with ver0.3 Wiki XML Dumps but not with the latest ver0.4 Dumps. I get the following error. Can't locate object method "page" via package "Parse::MediaWikiDump::Pages" at wikiprep.pl line 390. Also, under the "Parse-MediaWikiDump-1.0.4" documentation @ http://search.cpan.org/~triddle/Parse-MediaWikiDump-1.0.4/lib/Parse/MediaWikiDump/Pages.pm, I read "LIMITATIONS Version 0.4 This class was updated to support version 0.4 dump files from a MediaWiki instance but it does not currently support any of the new information available in those files." Any work arounds would help me get to the next level. Note: one may wonder why cannot we directly use SAX or STAX parser instead, wikipedia dump is a 25GB plus single file, stack/memory issues are obvious. Hence, the above perl script resolves this issue but currently I am stuck with this version problem.

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  • Redirecting search results into an ASP.NET page

    - by Arjun Vasudevan
    I've an ASP.NET page with a textbox and a option from user of the following choices: Wikipedia, Google, Dictionary.com, Flickr, Google images. The user enters a word(s) in the textbox and selects a choice among the following. Depending on the choice select by the user I wish to return the following. Wikipedia: Return the content and link to the page corresponding to the topic about the word. Google: Return the top 10 results of google search for this word. Flickr: Return a few images atmost 10 images from flickr search GoogleImage: Return a few images from google image search. Dictionary: Return the meaning of the word. How can I do that?

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