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  • f# types' properties in inconsistent order and of slightly differing types

    - by philbrowndotcom
    I'm trying to iterate through an array of objects and recursively print out each objects properties. Here is my object model: type firmIdentifier = { firmId: int ; firmName: string ; } type authorIdentifier = { authorId: int ; authorName: string ; firm: firmIdentifier ; } type denormalizedSuggestedTradeRecommendations = { id: int ; ticker: string ; direction: string ; author: authorIdentifier ; } Here is how I am instantiating my objects: let getMyIdeasIdeas = [| {id=1; ticker="msfqt"; direction="buy"; author={authorId=0; authorName="john Smith"; firm={firmId=12; firmName="Firm1"}};}; {id=2; ticker="goog"; direction="sell"; author={authorId=1; authorName="Bill Jones"; firm={firmId=13; firmName="ABC Financial"}};}; {id=3; ticker="DFHF"; direction="buy"; author={authorId=2; authorName="Ron James"; firm={firmId=2; firmName="DEFFirm"}};}|] And here is my algorithm to iterate, recurse and print: let rec recurseObj (sb : StringBuilder) o= let props : PropertyInfo [] = o.GetType().GetProperties() sb.Append( o.GetType().ToString()) |> ignore for x in props do let getMethod = x.GetGetMethod() let value = getMethod.Invoke(o, Array.empty) ignore <| match value with | :? float | :? int | :? string | :? bool as f -> sb.Append(x.Name + ": " + f.ToString() + "," ) |> ignore | _ -> recurseObj sb value for x in getMyIdeas do recurseObj sb x sb.Append("\r\n") |> ignore If you couldnt tell, I'm trying to create a csv file and am printing out the types for debugging purposes. The problem is, the first element comes through in the order you'd expect, but all subsequent elements come through with a slightly different (and confusing) ordering of the "child" properties like so: RpcMethods+denormalizedSuggestedTradeRecommendationsid: 1,ticker: msfqt,direction: buy,RpcMethods+authorIdentifierauthorId: 0,authorName: john Smith,RpcMethods+firmIdentifierfirmId: 12,firmName: Firm1, RpcMethods+denormalizedSuggestedTradeRecommendationsid: 2,ticker: goog,direction: sell,RpcMethods+authorIdentifierauthorName: Bill Jones,RpcMethods+firmIdentifierfirmName: ABC Financial,firmId: 13,authorId: 1, RpcMethods+denormalizedSuggestedTradeRecommendationsid: 3,ticker: DFHF,direction: buy,RpcMethods+authorIdentifierauthorName: Ron James,RpcMethods+firmIdentifierfirmName: DEFFirm,firmId: 2,authorId: 2, Any idea what is going on here?

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  • Emulator TCP Packet Size

    - by jpspringall
    Has anyone tried to do a tcp client server app using the emulator using the pc as a server and the phone as the client? I've got a bit of an issue where its only sending one packet, ie 1491 bytes of data regardless of how much there actually is to send, from the client(Phone) to the server(PC) Thanks James

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  • searching a list of tuples in python

    - by hdx
    So I have a list of tuple like: [(1,"juca"),(22,"james"),(53,"xuxa"),(44,"delicia")] I want this list for a tuple whose number value is equal to something. So that if I do search(53) it will return 2 Is is an easy way to do that?

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  • django link format words joined with hypens

    - by soField
    href="http://www.torontolife.com/daily/daily-dish/restauranto/2010/03/10/best-new-restaurants-2010-james-chatto-names-five-honourable-mentions/"Best new restaurants 2010: honourable mentions is django has built in mechanism to format links above i mean words joined with hypens how can achieve this ?

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  • jQuery Stop non-css animation

    - by Mark
    I'm trying to stop a non-css animation: http://jsbin.com/aqute4/4/edit Button 1 starts the animation nicely, totally lost on how to stop it though, since .stop() seems to need a DOM element... rather than a random object. Thanks in advance. PS: Original code comes from: http://james.padolsey.com/javascript/fun-with-jquerys-animate/

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  • Importing ShapeFiles into Oracle XE

    - by WeeJames
    Hi, I'm looking to import one of the Shapefiles supplied with the Ordnance Survey Boundary-Line opensource set into Oracle XE. http://data.gov.uk/dataset/os-boundary-line Unfortunately I'm completely unsure how to go about this, despite much Googling. Anyone got any pointers or tips or a link to a guide? Cheers James

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  • HTTPS only on specific page with .htaccess

    - by JamWaffles
    Hi all I have a URL such as http://www.domain.com/index.php?p=register. I want to redirect that to use HTTPS (SSL) with .htaccess, but only on this, and a couple of other pages (the login page, etc), but not the entire site. The URLs don't point to directories, but are used to dynamically include different files. Can someone give me a pointer or an example of how to get a single page redirect to HTTPS please? Thanks, James

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  • XML Path needed

    - by user3696029
    I have the following XML file: <?xml version="1.0" encoding="UTF-8"?> <bookstore> <book category="COOKING"> <title lang="en">Everyday Italian</title> <author>Giada De Laurentiis</author> <year>2005</year> <price>30.00</price> </book> <book category="CHILDREN"> <title lang="en">Harry Potter</title> <author>J K. Rowling</author> <year>2005</year> <price>29.99</price> </book> <book category="WEB"> <title lang="en">XQuery Kick Start</title> <author>James McGovern</author> <author>Per Bothner</author> <author>Kurt Cagle</author> <author>James Linn</author> <author>Vaidyanathan Nagarajan</author> <year>2003</year> <price>49.99</price> </book> <book category="WEB"> <title lang="en">Learning XML</title> <author>Erik T. Ray</author> <year>2003</year> <price>39.95</price> </book> </bookstore> I need to write a XML path that returns a book published after 2003, category is children and I just need to display the author and title of the book? What is frustrating is that I have everything in the XPATH that wrote except I am missing the author.

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  • ASP.NET cache maximum size

    - by user352868
    Hi Guys What's the maximum size of ASP.NET cache (either deployer on a single server or out-of-process on a Web farm) you can have? If there is a limit on how big ASP.NET cache you can have, is there a workaround to increase that limit? Thanks james

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  • How i can i use the value of a variable from one class in another in objective c?

    - by user337174
    Hi i am fairly new to objective c and have been doing some iphone programming. Is it possible to look up the value of a variable in a different class? Basically what i am doing is running a function that exists in my app delegate from a view controller, but the app delegate needs to use a variable stored in the view controller from which the app delegate function was called. Make sense??? Any help would be grateful. James

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  • Query interface for iPhone CoreData store

    - by JT
    Hi, another iPhone newbie question... I have the following: NSPersistentStoreCoordinator NSManagedObjectContext NSManagedObjectModel Is it possible to run queries directly on the store (since its a sqlite DB)? I'm trying to delete all the records from a tableview, and figured a "DELETE FROM table" would be nice and quick as opposed to looping through the records and removing them manually (which i'm also struggling with). Thanks for your time, James

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  • MySQL Database Query - Codeigniter

    - by user2450349
    I am building an application with Codeigniter and need some help with a DB query. I have a table called users with the following fields: user_id, user_name, user_password, user_email, user_role, user_manager_id In my app, I pull all records from the user table using the following: function get_clients() { $this->db->select('*'); $this->db->where('user_role', 'client'); $this->db->order_by("user_name", "Asc"); $query = $this->db->get("users"); return $query->result_array(); } This works as expected, however when I display the results in the view, I also want to display a new column called Manager which will display the managers user_name field. The user_manager_id is the id of the user from the same table. Im guessing you can create an outer join on the same table but not sure. In the view, I am displaying the returned info as follows: <table class="table table-striped" id="zero-configuration"> <thead> <tr> <th>Name</th> <th>Email</th> <th>Manager</th> </tr> </thead> <tbody> <?php foreach($clients as $row) { ?> <tr> <td><?php echo $row['user_name']; ?> (<?php echo $row['user_username']; ?>)</td> <td><?php echo $row['user_email']; ?></td> <td><?php echo $row['???']; ?></td> </tr> <?php } ?> </tbody> </table> Any idea of how I can form the query and display the manager name is the view? Example: user_id user_name user_password user_email user_role user_manager_id 1 Ollie adjjk34jcd [email protected] client null 2 James djklsdfsdjk [email protected] client 1 When i query the database, i want to display results like this: Ollie [email protected] James [email protected] Ollie

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  • Right column content overflowing over my footer

    - by Sixfoot Studio
    Hi All, I know this has got something to do with a float, but I cannot seem to figure out where I am going wrong with this. Please check this page for me, the content in the right column is flowing over my footer. http://sun-eng.sixfoot.co.za/index.php?option=com_weblinks&view=categories&Itemid=48 Thanks! James

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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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  • SOA, Cloud and Service Technology Symposium a super success!

    - by JuergenKress
    SOA, Cloud and Service Technology Symposium in London was a huge success. More than 600 international attendees participated in it. Our SOA & BPM Community had a great presence there. At joint booth with the Specialized partners link consulting, eProseed and Griffiths Waite, we presented the latest product updates and had many interesting discussions with customers and speakers. Special thanks to our HQ product management team Demed, Tim, Manas for coming over right before OOW. Also a very big Thank to Matthias Ziegler from Accenture for presenting our joint presentation individually! If you missed the conference here are the key presentations links for your reference: Big Data and its impact on SOA Demed L'Her [View PDF] Building 21st Century Service-Oriented Airports Shyam Kumar [View PDF] Building Cloudy Services Anne Thomas Manes [View PDF] Community Management: The Next Wave of SOA Governance and API Management Tim E. Hall [View PDF] Elastic SOA in the Cloud Steve Millidge [View PDF] Governing Shared Services: On-Premise & In the Cloud Thomas Erl [View Video] Introducing the Cloud Computing Design Patterns Catalogue Thomas Erl and Amin Naserpour [CloudPatterns.org] Lost in Translation - Common Mistakes Interpreting Patterns Mark Simpson [View PDF] Moving Applications to the Cloud: Migration Options Anne Thomas Manes [View PDF] New Paradigms for Application Architecture: From Applications to IT Services Anne Thomas Manes [View PDF] NoSQL for Data Services, Data Virtualization & Big Data Guido Schmutz [View PDF] A Pragmatic Approach to Cloud Computing Andrea Morena [View PDF] The Successful Execution of the SOA and BPM Vision Using a Business Capability Framework: Concepts and Examples Clemens Utschig and Manas Deb [View PDF] Service Modeling & BPM Business Value Patterns Matthias Ziegler [View PDF] [Podcast] SOA Adoption in the Brazilian Ministry of Health - Case Study Ricardo Puttini and Andre Toffanello [PDF Coming Soon] SOA Environments are a Big Data Problem Markus Zirn, Splunk and Maciej Barcz [View PDF] SOA Governance at EDP: A Global Energy Company Manuel Rosa [View PDF] For all presentations please visit the SOA, Cloud and Service Technology Symposium Website SOA & BPM Partner Community For regular information on Oracle SOA Suite become a member in the SOA & BPM Partner Community for registration please visit  www.oracle.com/goto/emea/soa (OPN account required) If you need support with your account please contact the Oracle Partner Business Center. Blog Twitter LinkedIn Mix Forum Technorati Tags: SOA Symposium,Thomas Erl,SOA Community,Oracle SOA,Oracle BPM,Community,OPN,Jürgen Kress

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  • Thursday Community Keynote: "By the Community, For the Community"

    - by Janice J. Heiss
    Sharat Chander, JavaOne Community Chairperson, began Thursday's Community Keynote. As part of the morning’s theme of "By the Community, For the Community," Chander noted that 60% of the material at the 2012 JavaOne conference was presented by Java Community members. "So next year, when the call for papers starts, put-in your submissions," he urged.From there, Gary Frost, Principal Member of Technical Staff, AMD, expanded upon Sunday's Strategy Keynote exploration of Project Sumatra, an OpenJDK project targeted at bringing Java to heterogeneous computing platforms (which combine the CPU and the parallel processor of the GPU into a single piece of silicon). Sumatra entails enhancing the JVM to make maximum use of these advanced platforms. Within this development space, AMD created the Aparapi API, which converts Java bytecode into OpenCL for execution on such GPU devices. The Aparapi API was open sourced in September 2011.Whether it was zooming-in on a Mandelbrot set, "the game of life," or a swarm of 10,000 Dukes in a space-bound gravitational dance, Frost's demos, using an Aparapi/OpenCL implementation, produced stunningly faster display results. He indicated that the Java 9 timeframe is where they see Project Sumatra coming to ultimate fruition, employing the Lamdas of Java 8.Returning to the theme of the keynote, Donald Smith, Director, Java Product Management, Oracle, explored a mind map graphic demonstrating the importance of Community in terms of fostering innovation. "It's the sharing and mixing of culture, the diversity, and the rapid prototyping," he said. Within this topic, Smith, brought up a panel of representatives from Cloudera, Eclipse, Eucalyptus, Perrone Robotics, and Twitter--ideal manifestations of community and innovation in the world of Java.Marten Mickos, CEO, Eucalyptus Systems, explored his company's open source cloud software platform, written in Java, and used by gaming companies, technology companies, media companies, and more. Chris Aniszczyk, Operations Engineering,Twitter, noted the importance of the JVM in terms of their multiple-language development environment. Mike Olson, CEO, Cloudera, described his company's Apache Hadoop-based software, support, and training. Mike Milinkovich, Executive Director, Eclipse Foundation, noted that they have about 270 tools projects at Eclipse, with 267 of them written in Java. Milinkovich added that Eclipse will even be going into space in 2013, as part of the control software on various experiments aboard the International Space Station. Lastly, Paul Perrone, CEO, Perrone Robotics, detailed his company's robotics and automation software platform built 100% on Java, including Java SE and Java ME--"on rat, to cat, to elephant-sized systems." Milinkovic noted that communities are by nature so good at innovation because of their very openness--"The more open you make your innovation process, the more ideas are challenged, and the more developers are focused on justifying their choices all the way through the process."From there, Georges Saab, VP Development Java SE OpenJDK, continued the topic of innovation and helping the Java Community to "Make the Future Java." Martijn Verburg, representing the London Java Community (winner of a Duke's Choice Award 2012 for their activity in OpenJDK and JCP), soon joined Saab onstage. Verburg detailed the LJC's "Adopt a JSR" program--"to get day-to-day developers more involved in the innovation that's happening around them."  From its London launching pad, the innovative program has spread to Brazil, Morocco, Latvia, India, and more.Other active participants in the program joined Verburg onstage--Ben Evans, London Java Community; James Gough, Stackthread; Bruno Souza, SOUJava; Richard Warburton, jClarity; and Cecelia Borg, Oracle--OpenJDK Onboarding. Together, the group explored the goals and tasks inherent in the Adopt a JSR program--from organizing hack days (testing prototype implementations), to managing mailing lists and forums, to triaging issues, to evangelism—all with the goal of fostering greater community/developer involvement, but equally importantly, building better open standards. “Come join us, and make your ecosystem better!" urged Verburg.Paul Perrone returned to profile the latest in his company's robotics work around Java--including the AARDBOTS family of smaller robotic vehicles, running the Perrone MAX platform on top of the Java JVM. Perrone took his "Rumbles" four-wheeled robot out for a spin onstage--a roaming, ARM-based security-bot vehicle, complete with IR, ultrasonic, and "cliff" sensors (the latter, for the raised stage at JavaOne). As an ultimate window into the future of robotics, Perrone displayed a "head-set" controller--a sensor directed at the forehead to monitor brainwaves, for the someday-implementation of brain-to-robot control.Then, just when it seemed this might be the end of the day's futuristic offerings, a mystery voice from offstage pronounced "I've got some toys"--proving to be guest-visitor James Gosling, there to explore his cutting-edge work with Liquid Robotics. While most think of robots as something with wheels or arms or lasers, Gosling explained, the Liquid Robotics vehicle is an entirely new and innovative ocean-going 'bot. Looking like a floating surfboard, with an attached set of underwater wings, the autonomous devices roam the oceans using only the energy of ocean waves to propel them, and a single actuated rudder to steer. "We have to accomplish all guidance just by wiggling the rudder," Gosling said. The devices offer applications from self-installing weather buoy, to pollution monitoring station, to marine mammal monitoring device, to climate change data gathering, to even ocean life genomic sampling. The early versions of the vehicle used C code on very tiny industrial micro controllers, where they had to "count the bytes one at a time."  But the latest generation vehicles, which just hit the water a week or so ago, employ an ARM processor running Linux and the ARM version of JDK 7. Gosling explained that vehicle communication from remote locations is achieved via the Iridium satellite network. But because of the costs of this communication path, the data must be sent in very small bursts--using SBD short burst data. "It costs $1/kb, so that rules everything in the software design,” said Gosling. “If you were trying to stream a Netflix video over this, it would cost a million dollars a movie. …We don't have a 'big data' problem," he quipped. There are currently about 150 Liquid Robotics vehicles out traversing the oceans. Gosling demonstrated real time satellite tracking of several vehicles currently at sea, noting that Java is actually particularly good at AI applications--due to the language having garbage collection, which facilitates complex data structures. To close-out his time onstage, Gosling of course participated in the ceremonial Java tee-shirt toss out to the audience…In parting, Chander passed the JavaOne Community Chairperson baton to Stephen Chin, Java Technology Evangelist, Oracle. Onstage in full motorcycle gear, Chin noted that he'll soon be touring Europe by motorcycle, meeting Java Community Members and streaming live via UStream--the ultimate manifestation of community and technology!  He also reminded attendees of the upcoming JavaOne Latin America 2012, São Paulo, Brazil (December 4-6, 2012), and stated that the CFP (call for papers) at the conference has been extended for one more week. "Remember, December is summer in Brazil!" Chin said.

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  • Windows 8 Launch&ndash;Why OEM and Retailers Should STFU

    - by D'Arcy Lussier
    Microsoft has gotten a lot of flack for the Surface from OEM/hardware partners who create Windows-based devices and I’m sure, to an extent, retailers who normally stock and sell Windows-based devices. I mean we all know how this is supposed to work – Microsoft makes the OS, partners make the hardware, retailers sell the hardware. Now Microsoft is breaking the rules by not only offering their own hardware but selling them via online and through their Microsoft branded stores! The thought has been that Microsoft is trying to set a standard for the other hardware companies to reach for. Maybe. I hope, at some level, Microsoft may be covertly responding to frustrations associated with trusting the OEMs and Retailers to deliver on their part of the supply chain. I know as a consumer, I’m very frustrated with the Windows 8 launch. Aside from the Surface sales, there’s nothing happening at the retail level. Let me back up and explain. Over the weekend I visited a number of stores in hopes of trying out various Windows 8 devices. Out of three retailers (Staples, Best Buy, and Future Shop), not *one* met my expectations. Let me be honest with you Staples, I never really have high expectations from your computer department. If I need paper or pens, whatever, but computers – you’re not the top of my list for price or selection. Still, considering you flaunted Win 8 devices in your flyer I expected *something* – some sign of effort that you took the Windows 8 launch seriously. As I entered the 1910 Pembina Highway location in Winnipeg, there was nothing – no signage, no banners – nothing that would suggest Windows 8 had even launched. I made my way to the laptops. I had to play with each machine to determine which ones were running Windows 8. There wasn’t anything on the placards that made it obvious which were Windows 8 machines and which ones were Windows 7. Likewise, there was no easy way to identify the touch screen laptop (the HP model) from the others without physically touching the screen to verify. Horrible experience. In the same mall as the Staples I mentioned above, there’s a Future Shop. Surely they would be more on the ball. I walked in to the 1910 Pembina Highway location and immediately realized I would not get a better experience. Except for the sign by the front door mentioning Windows 8, there was *nothing* in the computer department pointing you to the Windows 8 devices. Like in Staples, the Win 8 laptops were mixed in with the Win 7 ones and there was nothing notable calling out which ones were running Win 8. I happened to hit up the St. James Street location today, thinking since its a busier store they must have more options. To their credit, they did have two staff members decked out in Windows 8 shirts and who were helping a customer understand Windows 8. But otherwise, there was nothing highlighting the Windows 8 devices and they were again mixed in with the rest of the Win 7 machines. Finally, we have the St. James Street Best Buy location here in Winnipeg. I’m sure Best Buy will have their act together. Nope, not even close. Same story as the others: minimal signage (there was a sign as you walked in with a link to this schedule of demo days), Windows 8 hardware mixed with the rest of the PC offerings, and no visible call-outs identifying which were Win 8 based. This meant that, like Future Shop and Staples, if you wanted to know which machine had Windows 8 you had to go and scrutinize each machine. Also, there was nothing identifying which ones were touch based and which were not. Just Another Day… To these retailers, it seemed that the Windows 8 launch was just another day, with another product to add to the showroom floor. Meanwhile, Apple has their dedicated areas *in all three stores*. It was dead simple to find where the Apple products were compared to the Windows 8 products. No wonder Microsoft is starting to push their own retail stores. No wonder Microsoft is trying to funnel orders through them instead of relying on these bloated retail big box stores who obviously can’t manage a product launch. It’s Not Just The Retailers… Remember when the Acer CEO, Founder, and President of Computer Global Operations all weighed in on how Microsoft releasing the Surface would have a “huge negative impact for the ecosystem and other brands may take a negative reaction”? Also remember the CEO stating “[making hardware] is not something you are good at so please think twice”? Well the launch day has come and gone, and so far Microsoft is the only one that delivered on having hardware available on the October 26th date. Oh sure, there are laptops running Windows 8 – but all in one desktop PCs? I’ve only seen one or two! And tablets are *non existent*, with some showing an early to late November availability on Best Buy’s website! So while the retailers could be doing more to make it easier to find Windows 8 devices, the manufacturers could help by *getting devices into stores*! That’s supposedly something that these companies are good at, according to the Acer CEO. So Here’s What the Retailers and Manufacturers Need To Do… Get Product Out The pivotal timeframe will be now to the end of November. We need to start seeing all these fantastic pieces of hardware ship – including the Samsung ATIV Smart PC Pro, the Acer Iconia, the Asus TAICHI 21, and the sexy Samsung Series 7 27” desktop. It’s not enough to see product announcements, we need to see actual devices. Make It Easy For Customers To Find Win8 Devices You want to make it easy to sell these things? Make it easy for people to find them! Have staff on hand that really know how these devices run and what can be done with them. Don’t just have a single demo day, have people who can demo it every day! Make It Easy to See the Features There’s touch screen desktops, touch screen laptops, tablets, non-touch laptops, etc. People need to easily find the features for each machine. If I’m looking for a touch-laptop, I shouldn’t need to sift through all the non-touch laptops to find them – at the least, I need to quickly be able to see which ones are touch. I feel silly even typing this because this should be retail 101 and I have no retail background (but I do have an extensive background as a customer). In Summary… Microsoft launching the Surface and selling them through their own channels isn’t slapping its OEM and retail partners in the face; its slapping them to wake the hell up and stop coasting through Windows launch events like they don’t matter. Unless I see some improvements from vendors and retailers in November, I may just hold onto my money for a Surface Pro even if I have to wait until early 2013. Your move OEM/Retailers. *Update – While my experience has been in Winnipeg, similar experiences have been voiced from colleagues in Calgary and Edmonton.

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  • OpenVPN Problems, connecting with Windows OpenVPC client to Linux OpenVPN

    - by Filip Ekberg
    After following this guide and connecting to the VPN Server, I get the following error: Sat Mar 06 19:43:08 2010 us=127000 NOTE: failed to obtain options consistency info from peer -- this could occur if the remote peer is running a version of OpenVPN before 1.5-beta8 or if there is a network connectivity problem, and will not necessarily prevent OpenVPN from running (0 bytes received from peer, 0 bytes authenticated data channel traffic) -- you can disable the options consistency check with --disable-occ. I am using Archlinux and installed openvpn with Pacman. I want to acheive the following: Connect to the VPN Server, being able to route certain made up hosts through it. Is this possible? openvpn --version gives me the following openvpn --version OpenVPN 2.1.1 i686-pc-linux-gnu [SSL] [LZO2] [EPOLL] built on Jan 31 2010 Originally developed by James Yonan Copyright (C) 2002-2009 OpenVPN Technologies, Inc. <[email protected]> Suggestions?

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  • OpenVPN Problems, connecting with Windows OpenVPC client to Linux OpenVPN

    - by Filip Ekberg
    After following this guide and connecting to the VPN Server, I get the following error: Sat Mar 06 19:43:08 2010 us=127000 NOTE: failed to obtain options consistency info from peer -- this could occur if the remote peer is running a version of OpenVPN before 1.5-beta8 or if there is a network connectivity problem, and will not necessarily prevent OpenVPN from running (0 bytes received from peer, 0 bytes authenticated data channel traffic) -- you can disable the options consistency check with --disable-occ. I am using Archlinux and installed openvpn with Pacman. I want to acheive the following: Connect to the VPN Server, being able to route certain made up hosts through it. Is this possible? openvpn --version gives me the following openvpn --version OpenVPN 2.1.1 i686-pc-linux-gnu [SSL] [LZO2] [EPOLL] built on Jan 31 2010 Originally developed by James Yonan Copyright (C) 2002-2009 OpenVPN Technologies, Inc. <[email protected]> Suggestions?

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  • PDC and Tech-Ed Europe Slides and Code

    - by Stephen Walther
    I spent close to three weeks on the road giving talks at Tech-Ed Europe (Berlin), PDC (Los Angeles), and the Los Angeles Code Camp (Los Angeles). I got to talk about two topics that I am very passionate about: ASP.NET MVC and Ajax. Thanks everyone for coming to all my talks! At PDC, I announced all of the new features of our ASP.NET Ajax Library. In particular, I made five big announcements: ASP.NET Ajax Library Beta Released – You can download the beta from Ajax.CodePlex.com ASP.NET Ajax Library includes the AJAX Control Toolkit – You can use the Ajax Control Toolkit with ASP.NET MVC. ASP.NET Ajax Library being contributed to the CodePlex Foundation – ASP.NET Ajax is the founding project for the CodePlex Foundation (see CodePlex.org) ASP.NET Ajax Library is receiving full product support – Complain to Microsoft Customer Service at midnight on Christmas ASP.NET Ajax Library supports jQuery integration – Use (almost) all of the Ajax Control Toolkit controls in jQuery For more details on the Ajax announcements, see James Senior’s blog entry on the Ajax announcements at: http://jamessenior.com/post/News-on-the-ASPNET-Ajax-Library.aspx In my MVC talks, I discussed the new features being introduced with ASP.NET MVC 2. Here are three of my favorite new features: Client Validation – Client validation done the right way. Do your validation in your model and let the validation bubble up to JavaScript code automatically. Areas – Divide your ASP.NET MVC application into sub-applications. Great for managing both medium and large projects. RenderAction() – Finally, a way to add content to master pages and multiple pages without doing anything strange or twisted. There are demos of all of these features in the MVC downloads below. Here are the power point and code from all of the talks: PDC – Introducing the New ASP.NET Ajax Library PDC – ASP.NET MVC: The New Stuff Tech-Ed Europe - What's New in Microsoft ASP.NET Model-View-Controller Tech-Ed Europe - Microsoft ASP.NET AJAX: Taking AJAX to the Next Level

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  • Learn Lean Software Development and Kanban Systems

    - by Ben Griswold
    I did an in-house presentation on Lean Software Development (LSD) and Kanban Systems this week.  Beyond what I had previously learned from various podcasts, I knew little about either topic prior to compiling my slide deck.  In the process of building my presentation, I learned a ton.  I found the concepts weren’t very difficult to grok; however, I found little detailed information was available online. Hence this post which is merely a list of valuable resources. Principles of Lean Thinking, Mary Poppendieck Lean Software Development, May Poppendieck Lean Programming, Mary Poppendieck Lean Software Development, Wikipedia Implementing Lean Software Thinking: From Concept to Cash, Poppendieck Lean Software Development Overview, Darrell Norton Lean Thinking: Banish Waste and Create Wealth in Your Corporation The Goal: A Process of Ongoing Improvement The Toyota Way Extreme Toyota: Radical Contradictions That Drive Success at the World’s Best Manufacturer Elegant Code Cast 17 – David Laribee on Lean / Kanban Herding Code Episode 42: Scott Bellware on BDD and Lean Development Seven Principles of Lean Software Development, Przemys?aw Bielicki Kanban Boards for Agile Project Management with Zen Author Nate Kohari Herding Code 55: Nate Kohari brings Your Moment of Zen James Shore on Kanban Systems Agile Zen Product Site A Leaner Form of Agile, David Laribee Kanban as Alternative Agile Implementation, Mark Levison Lean Software Development, Dr. Christoph Steindl Glossary of Lean Manufacturing Terms Why Pull? Why Kanban?, Corey Ladas

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  • Super Computer Built from Raspberry Pi Boards and LEGO Bricks

    - by Jason Fitzpatrick
    It was only a matter of time before someone chained together dozens of Raspberry Pi boards into a serviceable super computer; read on to see how a team of Southampton scientists built a 64-core machine using them. Image courtesy of Simon Cox and the University of Southampton. From the University of South Hampton press release: Professor Cox comments: “As soon as we were able to source sufficient Raspberry Pi computers we wanted to see if it was possible to link them together into a supercomputer. We installed and built all of the necessary software on the Pi starting from a standard Debian Wheezy system image and we have published a guide so you can build your own supercomputer.” The racking was built using Lego with a design developed by Simon and James, who has also been testing the Raspberry Pi by programming it using free computer programming software Python and Scratch over the summer. The machine, named “Iridis-Pi” after the University’s Iridis supercomputer, runs off a single 13 Amp mains socket and uses MPI (Message Passing Interface) to communicate between nodes using Ethernet. The whole system cost under £2,500 (excluding switches) and has a total of 64 processors and 1Tb of memory (16Gb SD cards for each Raspberry Pi). Professor Cox uses the free plug-in ‘Python Tools for Visual Studio’ to develop code for the Raspberry Pi. How to Get Pro Features in Windows Home Versions with Third Party Tools HTG Explains: Is ReadyBoost Worth Using? HTG Explains: What The Windows Event Viewer Is and How You Can Use It

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