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  • Newton Game Dynamics: Making an object not affect another object

    - by Boreal
    I'm going to be using Newton in my networked action game with Mogre. There will be two "types" of physics object: global and local. Global objects will be kept in sync for everybody; these include the players, projectiles, and other gameplay-related objects. Local objects are purely for effect, like ragdolls, debris, and particles. Is there a way to make the global objects affect the local objects without actually getting affected themselves? I'd like debris to bounce off of a tank, but I don't want the tank to respond in any way.

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  • Not so long ago in a city not so far away by Carlos Martin

    - by Maria Sandu
    Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 This is the story of how the EMEA Presales Center turned an Oracle intern into a trusted technology advisor for both Oracle’s Sales and customers. It was the summer of 2011 when I was finishing my Computer Engineering studies as well as my internship at Oracle when I was offered what could possibly be THE dream job for any young European Computer Engineer. Apart from that, it also seemed like the role was particularly tailored to me as I could leverage almost everything I learned at University and during the internship. And all of it in one of the best cities to live in, not only from my home country but arguably from Europe: Malaga! A day at EPC As part of the EPC Technology pillar, and later on completely focused on WebCenter, there was no way to describe a normal day on the job as each day had something unique. Some days I was researching documentation in order to elaborate accurate answers for a customer’s question within a Request for Information or Proposal (RFI/RFP), other days I was doing heavy programming in order to bring a Proof of Concept (PoC) for a customer to life and last not but least, some days I presented to the customer via webconference the demo I built for them the past weeks. So as you can see, the role has research, development and presentation, could you ask for more? Well, don’t worry because there IS more! Internationality As the organization’s name suggests, EMEA Presales Center, it is the Center of Presales within Europe, Middle East and Africa so I got the chance to work with great professionals from all this regions, expanding my network and learning things from one country to apply them to others. In addition to that, the teams based in the Malaga office are comprised of many young professionals hailing mainly from Western and Central European countries (although there are a couple of exceptions!) with very different backgrounds and personalities which guaranteed many laughs and stories during lunch or coffee breaks (or even while working on projects!). Furthermore, having EPC offices in Bucharest and Bangalore and thanks to today’s tele-presence technologies, I was working every day with people from India or Romania as if they were sitting right next to me and the bonding with them got stronger day by day. Career development Apart from the research and self-study I’ve earlier mentioned, one of the EPC’s Key Performance Indicators (KPI) is that 15% of your time is spent on training so you get lots and lots of trainings in order to develop both your technical product knowledge and your presentation, negotiation and other soft skills. Sometimes the training is via webcast, sometimes the trainer comes to the office and sometimes, the best times, you get to travel abroad in order to attend a training, which also helps you to further develop your network by meeting face to face with many people you only know from some email or instant messaging interaction. And as the months go by, your skills improving at a very fast pace, your relevance increasing with each new project you successfully deliver, it’s only a matter of time (and a bit of self-promoting!) that you get the attention of the manager of a more senior team and are offered the opportunity to take a new step in your professional career. For me it took 2 years to move to my current position, Technology Sales Consultant at the Oracle Direct organization. During those 2 years I had built a good relationship with the Oracle Direct Spanish sales and sales managers, who are also based in the Malaga office. I supported their former Sales Consultant in a couple of presentations and demos and were very happy with my overall performance and attitude so even before the position got eventually vacant, I got a heads-up from then in advance that their current Sales Consultant was going to move to a different position. To me it felt like a natural step, same as when I joined EPC, I had at least a 50% of the “homework” already done but wanted to experience that extra 50% to add new product and soft skills to my arsenal. The rest is history, I’ve been in the role for more than half a year as I’m writing this, achieved already some important wins, gained a lot of trust and confidence in front of customers and broadened my view of Oracle’s Fusion Middleware portfolio. I look back at the 2 years I spent in EPC and think: “boy, I’d recommend that experience to absolutely anyone with the slightest interest in IT, there are so many different things you can do as there are different kind of roles you can end up taking thanks to the experience gained at EPC” /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0in; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}

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  • Matlab-Bisection-Newton-Secant , finding roots?

    - by i z
    Hello and thanks in advance for your possible help ! Here's my problem: I have 2 functions f1(x)=14.*x*exp(x-2)-12.*exp(x-2)-7.*x.^3+20.*x.^2-26.*x+12 f2(x)=54.*x.^6+45.*x.^5-102.*x.^4-69.*x.^3+35.*x.^2+16.*x-4 Make the graph for those 2, the first one in [0,3] and the 2nd one in [-2,2]. Find the 3 roots with accuracy of 6 decimal digits using a) bisection ,b) newton,c)secant.For each root find the number of iterations that have been made. For Newton-Raphson, find which roots have quadratic congruence and which don't. What is the main common thing that roots with no quadratic congruence (Newton's method)? Why ? Excuse me if i ask silly things, but i'm asked to do this with no Matlab courses and I'm trying to learn it myself. There are many issues i have with this exercise . Questions : 1.I only see 2 roots in the graph for the f1 function and 4-5 (?) roots for the function f2 and not 3 roots as the exercise says. Here's the 2 graphs : http://postimage.org/image/cltihi9kh/ http://postimage.org/image/gsn4sg97f/ Am i wrong ? Do both have only 3 roots in [0,3] and [-2,2] ? Concerning the Newton's method , how am i supposed to check out which roots have quadratic congruence and which not??? Accuracy means tolerance e=10^(-6), right ?

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  • How to find minimum of nonlinear, multivariate function using Newton's method (code not linear algeb

    - by Norman Ramsey
    I'm trying to do some parameter estimation and want to choose parameter estimates that minimize the square error in a predicted equation over about 30 variables. If the equation were linear, I would just compute the 30 partial derivatives, set them all to zero, and use a linear-equation solver. But unfortunately the equation is nonlinear and so are its derivatives. If the equation were over a single variable, I would just use Newton's method (also known as Newton-Raphson). The Web is rich in examples and code to implement Newton's method for functions of a single variable. Given that I have about 30 variables, how can I program a numeric solution to this problem using Newton's method? I have the equation in closed form and can compute the first and second derivatives, but I don't know quite how to proceed from there. I have found a large number of treatments on the web, but they quickly get into heavy matrix notation. I've found something moderately helpful on Wikipedia, but I'm having trouble translating it into code. Where I'm worried about breaking down is in the matrix algebra and matrix inversions. I can invert a matrix with a linear-equation solver but I'm worried about getting the right rows and columns, avoiding transposition errors, and so on. To be quite concrete: I want to work with tables mapping variables to their values. I can write a function of such a table that returns the square error given such a table as argument. I can also create functions that return a partial derivative with respect to any given variable. I have a reasonable starting estimate for the values in the table, so I'm not worried about convergence. I'm not sure how to write the loop that uses an estimate (table of value for each variable), the function, and a table of partial-derivative functions to produce a new estimate. That last is what I'd like help with. Any direct help or pointers to good sources will be warmly appreciated. Edit: Since I have the first and second derivatives in closed form, I would like to take advantage of them and avoid more slowly converging methods like simplex searches.

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  • How to write a code Newton Raphson code in R involving integration and Bessel function

    - by Ahmed
    I have want to estimate the parameters of the function which involves Bessel function and integration. However, when i tried to run it, i got a message that "Error in f(x, ...) : could not find function "BesselI" ". I don't know to fix it and would appreciate any related proposal. library(Bessel) library(maxLik) library(miscTools) K<-300 f <- function(theta,lambda,u) {exp(-u*theta)*BesselI(2*sqrt(t*u*theta*lambda),1)/u^0.5} F <- function(theta,lambda){integrate(f,0,K,theta=theta,lambda=lambda)$value} tt<-function(theta,lambda){(sqrt(lambda)*exp(-t*lambda)/(2*sqrt(t*theta)))(theta(2*t*lambda-1)*F(theta,lambda)} loglik <- function(param) { theta <- param[1] lambda <- param[2] ll <-sum(log(tt(theta,lambda))) } t<-c(24,220,340,620,550,559,689,543) res <- maxNR(loglik, start=c(0.001,0.0005),print.level=1,tol = 1e-08) summary(res)

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  • Row concat from this query

    - by Álvaro G. Vicario
    I have this query: SELECT DISTINCT IM.EDIFICIOS_ID, TI.TITULAR FROM IMPORTACION IM INNER JOIN I_EDIFICIO IE ON IM.IMPORTACION_ID=IE.IMPORTACION_ID INNER JOIN I_EDIFICIO_TITULAR ET ON IM.IMPORTACION_ID=ET.IMPORTACION_ID AND IE.EDIFICIO_ID=ET.EDIFICIO_ID INNER JOIN I_TITULAR TI ON IM.IMPORTACION_ID=TI.IMPORTACION_ID AND ET.TITULAR_ID=TI.TITULAR_ID WHERE TI.TITULAR IS NOT NULL AND TI.TITULAR<>'' ORDER BY IM.EDIFICIOS_ID, TI.TITULAR; that returns this result set: EDIFICIOS_ID TITULAR ------------ ------------------ 1911 Ana María García 1911 Anselmo Piedrahita 1911 Manuel López 2594 Carlos Pérez 2594 Felisa García 6865 Carlos Pérez 6865 Felisa García 8428 Carlos Pérez I want to concatenate the values from TITULAR for each EDIFICIOS_ID, so I get this: EDIFICIOS_ID TITULAR ------------ ------------------ 1911 Ana María García; Anselmo Piedrahita; Manuel López 2594 Carlos Pérez; Felisa García 6865 Carlos Pérez; Felisa García 8428 Carlos Pérez I'm trying to use the FOR XML PATH trick. I've used it in the past but, since I can't really understand how it works, I can't figure out how to apply it to this specific case. Can you provide me with some ideas?

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  • Forbes Announcing The World’s Top 20 Billionaires

    - by Suganya
    Forbes company recently conducted a survey to figure out the world’s Billionaires list and has released it listing the top 20 names of the Billionaires. The company says that for the third time in the last three years the world has a new richest man for this year. So it means that Bill Gates was beaten up by someone else in world. Who is the new richest man in the world?   Forbes.Com announced the richest man in world and this time it is not Bill Gates. But it is Carlos Slim Helu who is into Telecom industry. Carlos lives in Mexico and he had the third richest man’s place last year. Having shown a Net worth of $ 53.5 Billion, Carlos has increased $18.5 Billion in a year. Carlos swooped on the privatization of Mexico’s national telephone service during the last decade and now has achieved the world’s first richest man. Following Carlos, in the second position is Bill Gates with the Nett worth of $53 Billion. As Bill Gates requires no great introduction, lets move on to the next place. The third place is occupied by Warren Buffett followed by Mukesh Ambani and Lakshmi Mittal in fourth and fifth places respectively. The top 20 names of world’s richest people, their occupation and the Nett worth that they hold are S.No Name Nett Worth (in $ Billion) Source of Income 1 Carlos Slim Helu 53.5 Telecom 2 Bill Gates 53 Microsoft 3 Warren Buffett 47 Investments 4 Mukesh Ambani 29 Petrochemical, Oil and Gas 5 Lakshmi Mittal 28.7 Steel 6 Lawrence Ellison 28 Oracle 7 Bernard Arnault 27.5 Luxury Goods 8 Eike Batista 27 Mining, Oil 9 Amancio Ortega 25 Fashion, Retail 10 Karl Albrecht 23.5 Supermarkets 11 Ingvar Kamprad and Family 23 IKEA 12 Christy Walton and Family 22.5 Wal-Mart 13 Stefan Persson 22.4 H & M 14 Li Ka-shing 21 Diversified 15 Jim C. Walton 20.7 Wal-Mart 16 Alice Walton 20.6 Wal-Mart 17 Liliane Bettencourt 20 L’Oreal 18 S. Robson Walton 19.8 Wal-Mart 19 Prince Alwaleed bin Talal Alsaud 19.4 Diversified 20 David Thomson and Family 19 Thomson Reuters   Source: Forbes and Image Credit : kevindooley Join us on Facebook to read all our stories right inside your Facebook news feed.

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  • How to make regex variables to capture of routes

    - by Zephiro
    anyone can help me with this problem. example $uri = '/username/carlos'; => $routes[] = '/username/@name'; @name convert in variable $name capturing string "carlos" $routes[] = '/list/edit/@id:[0-9]{3}'; $routes[] = '/username/@name'; $routes[] = '/archive/*'; $routes[] = '/'; $uri = '/username/carlos'; foreach ( $routes as $pattern ) { if ( preg_match( '#^' . preg_replace( '#(?:{{)?@(\w+\b)(?:}})?#i', '(?P<\1>[\w\-\.!~\*\'"(),\s]+)', str_replace( '\*', '(.*)', preg_quote( $pattern, '/' ) ) ) . '\/?$#i', $uri, $matchs ) ) { //how to make regex for this to work : echo $name; // carlos =>$uri = '/username/carlos'; or matt => $uri = '/username/matt'; } } thanks for reading

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  • Hostname problem

    - by codeshepherd
    my hostname is newton ...when I set "127.0.0.1 Newton" in /etc/hosts .. parallels stops working.. when I set "127.0.0.1 localhost" in /etc/hosts apache installed via ports stops working.. when I add both '"127.0.0.1 localhost", and "127.0.0.1 newton" to hosts file.. parallels network doesnt work

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  • mac hostname problem

    - by codeshepherd
    my hostname is newton ...when I set "127.0.0.1 Newton" in /etc/hosts .. parallels stops working.. when I set "127.0.0.1 localhost" in /etc/hosts apache installed via ports stops working.. when I add both '"127.0.0.1 localhost", and "127.0.0.1 newton" to hosts file.. parallels network doesnt work

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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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  • Create a folder shortcut in "My Computer"

    - by Carlos Gil
    I'm trying to add shortcuts to folders in "My Computer". This .reg almost works, I can execute programs like EXPLORE.exe, but I want to open a folder in the same window. Can someone please point out how? Windows Registry Editor Version 5.00 [HKEY_CLASSES_ROOT\CLSID\{00000000-0000-0000-0000-000000000001}] @="SkyDrive" "InfoTip"="Folder Shortcuts" [HKEY_CLASSES_ROOT\CLSID\{00000000-0000-0000-0000-000000000001}\DefaultIcon] @="C:\\Users\\Carlos\\AppData\\Local\\Microsoft\\SkyDrive\\SkyDrive.exe,0" [HKEY_CLASSES_ROOT\CLSID\{00000000-0000-0000-0000-000000000001}\Shell] [HKEY_CLASSES_ROOT\CLSID\{00000000-0000-0000-0000-000000000001}\Shell\Open] @="" [HKEY_CLASSES_ROOT\CLSID\{00000000-0000-0000-0000-000000000001}\Shell\Open\Command] @="C:\\Users\\Carlos\\SkyDrive" [HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\MyComputer\NameSpace\{00000000-0000-0000-0000-000000000001}] @="SkyDrive"

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  • How to solve "java.io.IOException: error=12, Cannot allocate memory" calling Runtime#exec()?

    - by Andrea Francia
    On my system I can't run a simple Java application that start a process. I don't know how to solve. Could you give me some hints how to solve? The program is: [root@newton sisma-acquirer]# cat prova.java import java.io.IOException; public class prova { public static void main(String[] args) throws IOException { Runtime.getRuntime().exec("ls"); } } The result is: [root@newton sisma-acquirer]# javac prova.java && java -cp . prova Exception in thread "main" java.io.IOException: Cannot run program "ls": java.io.IOException: error=12, Cannot allocate memory at java.lang.ProcessBuilder.start(ProcessBuilder.java:474) at java.lang.Runtime.exec(Runtime.java:610) at java.lang.Runtime.exec(Runtime.java:448) at java.lang.Runtime.exec(Runtime.java:345) at prova.main(prova.java:6) Caused by: java.io.IOException: java.io.IOException: error=12, Cannot allocate memory at java.lang.UNIXProcess.<init>(UNIXProcess.java:164) at java.lang.ProcessImpl.start(ProcessImpl.java:81) at java.lang.ProcessBuilder.start(ProcessBuilder.java:467) ... 4 more Configuration of the system: [root@newton sisma-acquirer]# java -version java version "1.6.0_0" OpenJDK Runtime Environment (IcedTea6 1.5) (fedora-18.b16.fc10-i386) OpenJDK Client VM (build 14.0-b15, mixed mode) [root@newton sisma-acquirer]# cat /etc/fedora-release Fedora release 10 (Cambridge) EDIT: Solution This solves my problem, I don't know exactly why: echo 0 /proc/sys/vm/overcommit_memory Up-votes for who is able to explain :) Additional informations, top output: top - 13:35:38 up 40 min, 2 users, load average: 0.43, 0.19, 0.12 Tasks: 129 total, 1 running, 128 sleeping, 0 stopped, 0 zombie Cpu(s): 1.5%us, 0.5%sy, 0.0%ni, 94.8%id, 3.2%wa, 0.0%hi, 0.0%si, 0.0%st Mem: 1033456k total, 587672k used, 445784k free, 51672k buffers Swap: 2031608k total, 0k used, 2031608k free, 188108k cached Additional informations, free output: [root@newton sisma-acquirer]# free total used free shared buffers cached Mem: 1033456 588548 444908 0 51704 188292 -/+ buffers/cache: 348552 684904 Swap: 2031608 0 2031608

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  • mac hostname problem

    - by codeshepherd
    my hostname is newton ...when I set "127.0.0.1 Newton" in /etc/hosts .. parallels stops working.. when I set "127.0.0.1 localhost" in /etc/hosts apache installed via ports stops working.. when I add both '"127.0.0.1 localhost", and "127.0.0.1 newton" to hosts file.. parallels network doesnt work

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  • Nuevo Video del Curso Introducción a C# con Visual Studio 2012

    - by carlone
    Estimad@s Amig@s, Ya se encuentra publicado un Nuevo video del curso Introducción a C# con Visual Studio 2012.  13:3211WATCHEDIntroducción a C# con Visual Studio 2012: Estructuras Cíclicas (Bucle For)by Carlos Lone 35 viewsEn este video daremos una introducción al concepto de las estructuras cíclicas y aprenderemos a utilizar el Bucle For  El código de los ejemplos utilizados pueden descargarlos en https://latamcsharpvs2012.codeplex.com/ Saludos, Carlos A. Lone  

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  • Need AutoHotkey scripts

    - by Carlos
    I'm looking for someone that knows AutoHotkey that will help me create the following scripts on Windows 7; 1) Minimize window (using control/dot) 2) Closing active window (using control/left arrow) 3) Closing all windows (using control/right arrow) I've looked at their web site but know nothing about programing so I don't understand the symbols or how to use them. Any help would be appreciated. Thanks Carlos

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  • Keyboard Shortcuts in Win 7 without the CTRL + ALT

    - by Carlos
    I am knew to this site and don't know if I'm doing this correctly. I've been asked to edit my original post so I deleted my original post and starting over. I don't know why it's so hard for everyone to understand what I'm trying to do. You guys are all geniuses when it comes to computers and I'm just starting out. I started out trying to use a shortcut to display the LOCAL AREA CONNECTION window on my desktop by creating a shortcut and assigning it CTRL + , (comma). Windows didn't like that so it added ALT which ended up being CTRL + ALT + ,. Since I couldn't figure out a way to eliminate ALT as part of the shortkey keys, I am now trying a different strategy and it's not working. my latest attempt is to run the following command; ^,:: Run, explorer:: {BA126ADB-2166-11D1-B1D0-00805FC1270E} Can someone please tell me what I'm doing wrong? I'm trying, just give me a chance. Thanks, Carlos

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  • iAds on landscape

    - by Carlos Vargas
    Hey guys Im having trouble with iAds in landscape mode This is part of my code: banner = [[ADBannerView alloc]init] ; banner.currentContentSizeIdentifier = ADBannerContentSizeIdentifier480x32; [self.view addSubview:banner]; [banner release]; But is not working for me, it gives me error, gives me a SIGABRT error in the second line of the code. I am not having problems with the portrait mode... please help. Best Regards Carlos Vargas

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  • How can I keep the cpu temp low?

    - by Newton
    I have an HP pavilion dv7, I'm using ubuntu 12.04 so the overheating problem with sandybridge cpu is a lot better. However my laptop is still becoming too hot to keep on my legs. The problem is that the fan wait too much before starting, so the medium temp is too hight. When I'm using windows 7 the laptop is room-temperature cold, I've absolutely no problem. On windows the fan is always spinning very low & very silently so the heat is continuously removed, without reaching an unconfortable temp. How can I force the computer to act like that also on ubuntu? PS The bios can't let me control this kind of thing, and this is my experience with lm-sensors and fancontrol al@notebook:~$ sudo sensors-detect [sudo] password for al: # sensors-detect revision 5984 (2011-07-10 21:22:53 +0200) # System: Hewlett-Packard HP Pavilion dv7 Notebook PC (laptop) # Board: Hewlett-Packard 1800 This program will help you determine which kernel modules you need to load to use lm_sensors most effectively. It is generally safe and recommended to accept the default answers to all questions, unless you know what you're doing. Some south bridges, CPUs or memory controllers contain embedded sensors. Do you want to scan for them? This is totally safe. (YES/no): y Module cpuid loaded successfully. Silicon Integrated Systems SIS5595... No VIA VT82C686 Integrated Sensors... No VIA VT8231 Integrated Sensors... No AMD K8 thermal sensors... No AMD Family 10h thermal sensors... No AMD Family 11h thermal sensors... No AMD Family 12h and 14h thermal sensors... No AMD Family 15h thermal sensors... No AMD Family 15h power sensors... No Intel digital thermal sensor... Success! (driver `coretemp') Intel AMB FB-DIMM thermal sensor... No VIA C7 thermal sensor... No VIA Nano thermal sensor... No Some Super I/O chips contain embedded sensors. We have to write to standard I/O ports to probe them. This is usually safe. Do you want to scan for Super I/O sensors? (YES/no): y Probing for Super-I/O at 0x2e/0x2f Trying family `National Semiconductor/ITE'... No Trying family `SMSC'... No Trying family `VIA/Winbond/Nuvoton/Fintek'... No Trying family `ITE'... No Probing for Super-I/O at 0x4e/0x4f Trying family `National Semiconductor/ITE'... Yes Found unknown chip with ID 0x8518 Some hardware monitoring chips are accessible through the ISA I/O ports. We have to write to arbitrary I/O ports to probe them. This is usually safe though. Yes, you do have ISA I/O ports even if you do not have any ISA slots! Do you want to scan the ISA I/O ports? (YES/no): y Probing for `National Semiconductor LM78' at 0x290... No Probing for `National Semiconductor LM79' at 0x290... No Probing for `Winbond W83781D' at 0x290... No Probing for `Winbond W83782D' at 0x290... No Lastly, we can probe the I2C/SMBus adapters for connected hardware monitoring devices. This is the most risky part, and while it works reasonably well on most systems, it has been reported to cause trouble on some systems. Do you want to probe the I2C/SMBus adapters now? (YES/no): y Using driver `i2c-i801' for device 0000:00:1f.3: Intel Cougar Point (PCH) Module i2c-i801 loaded successfully. Module i2c-dev loaded successfully. Next adapter: i915 gmbus disabled (i2c-0) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 gmbus ssc (i2c-1) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 GPIOB (i2c-2) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 gmbus vga (i2c-3) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 GPIOA (i2c-4) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 gmbus panel (i2c-5) Do you want to scan it? (YES/no/selectively): y Client found at address 0x50 Probing for `Analog Devices ADM1033'... No Probing for `Analog Devices ADM1034'... No Probing for `SPD EEPROM'... No Probing for `EDID EEPROM'... Yes (confidence 8, not a hardware monitoring chip) Next adapter: i915 GPIOC (i2c-6) Do you want to scan it? (YES/no/selectively): y Client found at address 0x50 Probing for `Analog Devices ADM1033'... No Probing for `Analog Devices ADM1034'... No Probing for `SPD EEPROM'... No Probing for `EDID EEPROM'... Yes (confidence 8, not a hardware monitoring chip) Next adapter: i915 gmbus dpc (i2c-7) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 GPIOD (i2c-8) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 gmbus dpb (i2c-9) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 GPIOE (i2c-10) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 gmbus reserved (i2c-11) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 gmbus dpd (i2c-12) Do you want to scan it? (YES/no/selectively): y Next adapter: i915 GPIOF (i2c-13) Do you want to scan it? (YES/no/selectively): y Next adapter: DPDDC-B (i2c-14) Do you want to scan it? (YES/no/selectively): y Now follows a summary of the probes I have just done. Just press ENTER to continue: Driver `coretemp': * Chip `Intel digital thermal sensor' (confidence: 9) To load everything that is needed, add this to /etc/modules: #----cut here---- # Chip drivers coretemp #----cut here---- If you have some drivers built into your kernel, the list above will contain too many modules. Skip the appropriate ones! Do you want to add these lines automatically to /etc/modules? (yes/NO)y Successful! Monitoring programs won't work until the needed modules are loaded. You may want to run 'service module-init-tools start' to load them. Unloading i2c-dev... OK Unloading i2c-i801... OK Unloading cpuid... OK al@notebook:~$ sudo /etc/init.d/module-init-tools restart Rather than invoking init scripts through /etc/init.d, use the service(8) utility, e.g. service module-init-tools restart Since the script you are attempting to invoke has been converted to an Upstart job, you may also use the stop(8) and then start(8) utilities, e.g. stop module-init-tools ; start module-init-tools. The restart(8) utility is also available. module-init-tools stop/waiting al@notebook:~$ sudo service module-init-tools restart stop: Unknown instance: module-init-tools stop/waiting al@notebook:~$ sudo service module-init-tools start module-init-tools stop/waiting al@notebook:~$ sudo pwmconfig # pwmconfig revision 5857 (2010-08-22) This program will search your sensors for pulse width modulation (pwm) controls, and test each one to see if it controls a fan on your motherboard. Note that many motherboards do not have pwm circuitry installed, even if your sensor chip supports pwm. We will attempt to briefly stop each fan using the pwm controls. The program will attempt to restore each fan to full speed after testing. However, it is ** very important ** that you physically verify that the fans have been to full speed after the program has completed. /usr/sbin/pwmconfig: There are no pwm-capable sensor modules installed Is my case too desperate?

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  • How abstract should you get with BDD

    - by Newton
    I was writing some tests in Gherkin (using Cucumber/Specflow). I was wondering how abstract should I get with my tests. In order to not make this open-ended, which of the following statements is better for BDD: Given I am logged in with email [email protected] and password 12345 When I do something Then something happens as opposed to Given I am logged in as the Administrator When I do something Then something happens The reason I am confused is because 1 is more based on the behaviour (filing in email and password) and 2 is easier to process and write the tests.

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  • Root cannot access /dev/urandom

    - by Darren Newton
    I am trying to generate a GPG key, and I cannot generate enough entropy. So I installed rng-tools and tried following these instructions: http://serverfault.com/questions/214605/gpg-not-enough-entropy When I am logged in as root, and try to run rngd -r /dev/urandom I get the following error: can't open /dev/random: Permission denied I find this disturbing as I am root. This is Ubuntu on a virtual server (via Parallels I believe.)

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