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  • google search rankings and trends api

    - by Drakkhen
    I'm looking to find an api or program or interface to get the following information. I would like to see the amount of times a particular search term was used and its /weekly/monthly/yearly breakdown along with its rank in a particular page. I've found googlesearchpositionfinder.com and google.com/trends but i have 5000 terms to search for by hand is not happening. I've also found www.juiceanalytics.com/openjuice/programmatic-google-trends-api but it doesn't allow me to do a break down for a period of 2 years. Basically i'm trying to create a ranking of search phrases, the weeks(period) they were more popular and how a particular site(e.g urban dictionary) showed up in googles search rankings for the terms.

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  • Minimum 4 Characters or Show Nothing - PHP

    - by ali
    Hi, I want to show up only words with minimum 4 Characters, actually I can limit the hits and show only words with min. 100 hits - but how can I set a min. character length? thank you! function sm_list_recent_searches($before = '', $after = '', $count = 20) { // List the most recent successful searches. global $wpdb, $table_prefix; $count = intval($count); $results = $wpdb->get_results( "SELECT `terms`, `datetime` FROM `{$table_prefix}searchmeter_recent` WHERE 100 < `hits` ORDER BY `datetime` DESC LIMIT $count"); if (count($results)) { foreach ($results as $result) { echo '<a href="'. get_settings('home') . '/search/' . urlencode($result->terms) . '">'. htmlspecialchars($result->terms) .'</a>'.", "; } } }

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  • Can I use string concatenation to define a class CONST in PHP?

    - by selfsimilar
    I know that you can create global constants in terms of each other using string concatenation: define('FOO', 'foo'); define('BAR', FOO.'bar'); echo BAR; will print 'foobar'. However, I'm getting an error trying to do the same using class constants. class foobar { const foo = 'foo'; const foo2 = self::foo; const bar = self::foo.'bar'; } foo2 is defined without issue, but declaring const bar will error out Parse error: syntax error, unexpected '.', expecting ',' or ';' I've also tried using functions like sprintf() but it doesn't like the left paren any more than the string concatenator '.'. So is there any way to create class constants in terms of each other in anything more than a trivial set case like foo2?

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  • Is there a way to optimise finding text items on a page (not regex)

    - by Jeepstone
    After seeing several threads rubbishing the regexp method of finding a term to match within an HTML document, I've used the Simple HTML DOM PHP parser (http://simplehtmldom.sourceforge.net/) to get the bits of text I'm after, but I want to know if my code is optimal. It feels like I'm looping too many times. Is there a way to optimise the following loop? //Get the HTML and look at the text nodes $html = str_get_html($buffer); //First we match the <body> tag as we don't want to change the <head> items foreach($html->find('body') as $body) { //Then we get the text nodes, rather than any HTML foreach($body->find('text') as $text) { //Then we match each term foreach ($terms as $term) { //Match to the terms within the text nodes $text->outertext = str_replace($term, '<span class="highlight">'.$term.'</span>', $text->outertext); } } } For example, would it make a difference to determine check if I have any matches before I start the loop maybe?

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  • woocommerce show attribute description when selecting a variable

    - by user2916995
    I'm trying to figure out a way to display custom text based on the users selection of the variable product. The attribute is 'pricing' and the tag is deposit - which I've added a text description to when adding the attribute. So I'm trying to make this text appear when the user selects 'deposit' But the code I'm using in 'content-single-product.php' is displaying the text all the time no matter what variable is selected or not. <?php $my_taxonomy = 'pa_pricing'; $terms = wp_get_post_terms( $post->ID, $my_taxonomy ); echo term_description($terms[0]->term_id, $my_taxonomy); ?> I only want the text to be displayed after the user has selected pricing 'deposit' Can someone help me with this?

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  • How to extract data from Google Analytics and build a data warehouse (webhouse) from it?

    - by nkaur301
    I have click stream data such as referring URL, top landing pages, top exit pages and metrics such as page views, number of visits, bounces all in Google Analytics. I am required to build a data warehouse from scratch(which I believe is known as web-house) from this data. My questions are:- 1)Is it possible? Every day data increases (some in terms of metrics or measures such as visits and some in terms of new referring sites), how would the process of loading the warehouse go about? 2)What ETL tool would help me to achieve this? Pentaho I believe has a way to pull out data from Google Analytics, has anyone used it? How does that process go? Any references, links would be appreciated besides answers.

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  • Legal Issue: Remove/Hide links on Google Login page

    - by Rowell
    For the background: I'm developing a device application which offers connection to Google Drive. My end-users will need to login to their Google Account and authorize my application to access their Google Drive. I'm using OAuth 2.0 to do this. But my concern is that I don't want users to navigate away from my application using the links on the Google Login page. Basically, I don't want them to use my application to browse the internet. Question: Will I violate any terms of service/usage if I hide or change the href the links using GreaseMonkey or TamperMonkey? The changes will only be on the client side and I won't alter any processing at all. I already checked https://developers.google.com/terms/ but I found no item related to modifying the pages on client side. Thanks in advance.

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  • fail2ban custom action to permanent ban IPs from China

    - by John Magnolia
    When a IP address gets banned how can I check if the banned IP address is from China. If yes, then add it to the permanent ban list. I have found this nice guide which write the banned IP to file. Reason: I am getting a lot of brute force attacks from China daily, thankfully fail2ban is helping restrict this although they appear to be getting worse and they are just changing their IP Address. Or even better would be if there was a maintained database of known hacker IP addresses. Example 1 Hi, The IP 60.169.78.77 has just been banned by Fail2Ban after 4 attempts against vsftpd. Here are more information about 60.169.78.77: % [whois.apnic.net node-7] % Whois data copyright terms http://www.apnic.net/db/dbcopyright.html inetnum: 60.166.0.0 - 60.175.255.255 netname: CHINANET-AH descr: CHINANET anhui province network descr: China Telecom descr: A12,Xin-Jie-Kou-Wai Street descr: Beijing 100088 country: CN admin-c: CH93-AP tech-c: JW89-AP mnt-by: APNIC-HM mnt-routes: MAINT-CHINANET-AH mnt-lower: MAINT-CHINANET-AH status: ALLOCATED PORTABLE changed: [email protected] 20040721 source: APNIC person: Chinanet Hostmaster nic-hdl: CH93-AP e-mail: [email protected] address: No.31 ,jingrong street,beijing address: 100032 phone: +86-10-58501724 fax-no: +86-10-58501724 country: CN changed: [email protected] 20070416 mnt-by: MAINT-CHINANET source: APNIC person: Jinneng Wang address: 17/F, Postal Building No.120 Changjiang address: Middle Road, Hefei, Anhui, China country: CN phone: +86-551-2659073 fax-no: +86-551-2659287 e-mail: [email protected] nic-hdl: JW89-AP mnt-by: MAINT-NEW changed: [email protected] 19990818 source: APNIC Regards, Fail2Ban Example 2 Hi, The IP 60.169.78.81 has just been banned by Fail2Ban after 4 attempts against vsftpd. Here are more information about 60.169.78.81: % [whois.apnic.net node-6] % Whois data copyright terms http://www.apnic.net/db/dbcopyright.html inetnum: 60.166.0.0 - 60.175.255.255 netname: CHINANET-AH descr: CHINANET anhui province network descr: China Telecom descr: A12,Xin-Jie-Kou-Wai Street descr: Beijing 100088 country: CN admin-c: CH93-AP tech-c: JW89-AP mnt-by: APNIC-HM mnt-routes: MAINT-CHINANET-AH mnt-lower: MAINT-CHINANET-AH status: ALLOCATED PORTABLE changed: [email protected] 20040721 source: APNIC person: Chinanet Hostmaster nic-hdl: CH93-AP e-mail: [email protected] address: No.31 ,jingrong street,beijing address: 100032 phone: +86-10-58501724 fax-no: +86-10-58501724 country: CN changed: [email protected] 20070416 mnt-by: MAINT-CHINANET source: APNIC person: Jinneng Wang address: 17/F, Postal Building No.120 Changjiang address: Middle Road, Hefei, Anhui, China country: CN phone: +86-551-2659073 fax-no: +86-551-2659287 e-mail: [email protected] nic-hdl: JW89-AP mnt-by: MAINT-NEW changed: [email protected] 19990818 source: APNIC Regards, Fail2Ban Example 3 Hi, The IP 222.133.244.99 has just been banned by Fail2Ban after 4 attempts against vsftpd. Here are more information about 222.133.244.99: % [whois.apnic.net node-6] % Whois data copyright terms http://www.apnic.net/db/dbcopyright.html inetnum: 222.133.244.96 - 222.133.244.127 netname: LCZFFHQ country: CN descr: liaochenggovermentfanghuoqiang admin-c: DS95-AP tech-c: DS95-AP status: ASSIGNED NON-PORTABLE changed: [email protected] 20060122 mnt-by: MAINT-CNCGROUP-SD source: APNIC route: 222.132.0.0/14 descr: CNC Group CHINA169 Shandong Province Network country: CN origin: AS4837 mnt-by: MAINT-CNCGROUP-RR changed: [email protected] 20060118 source: APNIC person: Data Communication Bureau Shandong nic-hdl: DS95-AP e-mail: [email protected] address: No.77 Jingsan Road,Jinan,Shandong,P.R.China phone: +86-531-6052611 fax-no: +86-531-6052414 country: CN changed: [email protected] 20050330 mnt-by: MAINT-CNCGROUP-SD source: APNIC Regards, Fail2Ban

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  • Developer Developer Developer Scotland 2010

    - by Chris Hardy (ChrisNTR)
    This past weekend, I headed up to Glasgow thanks to Plip for driving and Dave Sussman for some light entertainment to do a session on C# on the iPhone with MonoTouch. I had already presented a session similar to this one at DDD8 in Reading, which you can watch on Vimeo ( http://vimeo.com/9150434 ) but in this session I covered more topics such as the new 3.3.1 section of the new terms of service Apple released. I also showed a Twitter example written in MonoTouch, which was reused from the DDD8 session...(read more)

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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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  • Learn WinRT or Unity 3d?

    - by user1582878
    I am not sure where to ask advices about career development, so I am sorry if I am wrong. My question is what is better for me to learn, Win 8 and metro style applications or try to focus on some 3d engine, like Unity 3d? On the one hand I`ve got enought experience in c# and programming for business applications (WinForms and WPF), on the other hand I was always been fasinated by the creation of computer games and have strong math background. Which is better in terms of my career and new job opportunities?

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  • The right way to start out in game development/design [closed]

    - by Marco Sacristão
    Greetings everyone I'm a 19 year old student looking for some help in the field of game development. This question may or may not seem a bit overused, but the fact is that game development has been my life long dream, and after several hours of search I've realized that I've been going in circles for the past three or four months whilst doing such research on how to really get down and dirty with game development, therefor I decided to ask you guys if you could help me out at all. Let me start off with some information about me and things i've already learned about GameDev which might help you out on helping me out (wordplay!): I'm not an expert programmer, but I do have knowledge on how to program in several languages including C and Java (Currently learning Java in my degree in Computer Engineering), but my methodology might not be most correct in terms of syntax (hence my difficulty in starting out, i'm afraid that the starting point might not be the most correct, and it would deploy a wrongful development methodology that would be to corrected later on, in terms of game development or other projects). I have yet to work in a project as large as a game, never in my learning curve of programming I've done a project to the scale of a video game, only very small software (PHP Front-ends and Back-ends, with some basic JQuery and CSS knowledge). I'm not the biggest mathematician or physicist, but I already know that is not a problem, because there are several game engines already available for use and integration with home-made projects (Box2D, etc). I've also learned about some libraries that could be included in said projects, to ease out some process in game development, like SDL for example. I do not know how sprites, states, particles or any specific game-related techniques work. With that being said, you can see that I have some ideas on game development, but I have absolutely no clue on how to design and produce a game, or even how game-like mechanics work. It does not have to be a complex game just to start out, I'd rather learn the basic of game design (Like 2D drawing, tiling, object collision) and test that out in a language that I feel comfortable in which could be later on migrated to other platforms, as long that what I've learned is the correct way to do things, and not just something that I've learned from some guy on Youtube by replicating that code on the video. I'm sorry if my question is not in the best format possible, but I've got so many questions on my mind that are still un-answered that I don't know were to start! Thank you for reading.

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  • Website Title Tags For SEO - Creating Excellent Title Tags

    What are title tags? One of the most basic, but important things you can do for your website (in terms of search engine optimisation - SEO), is to ensure that each and every page has its own unique, keyword rich title tag. The title tag can be found at the top of your source code within the and tags (on a web page, click on View Source Code to view the page code).

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  • When Less is More

    - by aditya.agarkar
    How do you reconcile the fact that while the overall warehouse volume is down you still need more workers in the warehouse to ship all the orders? A WMS customer recently pointed out this seemingly perplexing fact in a customer conference. So what is going on? Didn't we tell you before that for a warehouse the customer is really the "king"? In this case customers are merely responding to a low overall low demand and uncertainty. They do not want to hold down inventory and one of the ways to do that is by decreasing the order size and ordering more frequently. Overall impact to the warehouse? Two words: "More work!!" This is not all. Smaller order sizes also mean challenges from a transportation perspective including a rise in costlier parcel or LTL shipments instead of cheaper TL shipments. Here is a hypothetical scenario where a customer reduces the order size by 10% and increases the order frequency by 10%. As you can see in the following table, the overall volume declines by 1% but the warehouse has to ship roughly 10% more lines. Order Frequency (Line Count)Order Size (Units)Total VolumeChange (%)10010010,000 -110909,900-1% If you want to see how "Less is More" in graphical terms, this is how it appears: Even though the volume is down, there is going to be more work in the warehouse in terms of number of lines shipped. The operators need to pick more discrete orders, pack them into more shipping containers and ship more deliveries. What do you do differently if you are facing this situation?In this case here are some obvious steps to take:Uno: Change your pick methods. If you are used to doing order picks, it needs to go out the door. You need to evaluate batch picking and grouping techniques. Go for cluster picking, go for zone picking, pick and pass...anything that improves your picker productivity. More than anything, cluster picking works like a charm and above all, its simple and very effective. Dos: Are you minimize "touch" points in your pick process? Consider doing one step pick, pack and confirm i.e. pick and pack stuff directly into shipping cartons. Done correctly the container will not require any more "touch" points all the way to the trailer loading. Use cartonization!Tres: Are the being picked from an optimized pick face? Are the items slotted correctly? This needs to be looked into. Consider automated "pull" or "push" replenishment into your pick face and also make sure that high demand items are occupying the golden zones.  Cuatro: Are you tracking labor productivity? If not there needs to be a concerted push for having labor standards in place. Hope you found these ideas useful.

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  • Dual-licensing LGPL 2.1 and LGPL 3

    - by user594694
    I maintain a software, a small PHP library, that is released under the LGPL version 3 license (LGPLv3). Someone wants to use the library in their software which has the GPL version 2 license. This license compatibility matrix suggests this is not possible without changing the licensing terms of one of the software. I have been requested to dual-license my code under LGPLv2.1 and LGPLv3. Does it make sense, and what might the drawbacks be? Thank you.

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  • example.com/blog vs blog.example.com [duplicate]

    - by Mario Duarte
    Possible Duplicate: Subdomain versus subdirectory I'm about to start my own blog (adding it to a domain already owned by me) and I'm wondering what is the best way to set it up. There are two common alternatives for blogs: domain.com/blog and blog.domain.com. My question is: what are the advantages and disadvantages and of each alternative and which one do you think is the best? (in terms of SEO, etc)

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  • Using the BackgroundWorker in a Silverlight MVVM Application

    - by axshon
    With Silverlight 4 and the Entity Framework you get a lot of work done on your behalf in terms of standard UI CRUD-style operations. Validations and I/O are pretty easy to accommodate out of the box. But sometimes you need to perform some long running tasks either on the client or on the server via service calls. To prevent your UI from hanging and annoying your users, you should consider placing these operations on a background thread. The BackgroundWorker object is the perfect solution for this...(read more)

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  • How can I add "Show desktop" docklet to docky?

    - by DandyWalker
    I have some missing docklets in docky I used to use before. The most important one I remember is "Show desktop" which is important for me. I tried removing and installing it several times but no use I can't find it in the docklet's part of the settings. I tried searching for something like docky-extras in aptitude and synaptic package manager and tried different terms and combination but seems like there is no such thing. So how can I add the missing docklet?

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  • Introduction to Developing Mobile Web Applications in ASP.NET MVC 4

    - by bipinjoshi
    As mobile devices are becoming more and more popular, web developers are also finding it necessary to target mobile devices while building their web sites. While developing a mobile web site is challenging due to the complexity in terms of device detection, screen size and browser support, ASP.NET MVC4 makes a developer's life easy by providing easy ways to develop mobile web applications. To that end this article introduces you to the basics of developing web sites using ASP.NET MVC4 targeted at mobile devices.http://www.binaryintellect.net/articles/7a33d6fa-1dec-49fe-9487-30675d0a09f0.aspx

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  • A Brief Discussion On Visual Studio 2010 Top Features

    In this article I will describe about some new features of Visual Studio 2010 which I explored till now. These features are really very useful in terms of productive development. This article is mainly targeted for beginners of Visual Studio 2010 but everybody can get benefit on the same.

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  • Python Forgiveness vs. Permission and Duck Typing

    - by darkfeline
    In Python, I often hear that it is better to "beg forgiveness" (exception catching) instead of "ask permission" (type/condition checking). In regards to enforcing duck typing in Python, is this try: x = foo.bar except AttributeError: pass else: do(x) better or worse than if hasattr(foo, "bar"): do(foo.bar) else: pass in terms of performance, readability, "pythonic", or some other important factor?

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