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  • Pointers to implementing a taxonomy system?

    - by petsagouris
    I am taking part in the development of a PHP CMS (yeah I know you are like, meeh). It is currently using simple tags for tagging content. What I want to do is push the whole thing to using Taxonomy but I am not sure on what to pay attention to, or how to go about structuring the whole vocabularies/terms. I'd love to be able to keep the user interaction close to that of the current simple tags and at the same time allow for more advanced usage by power users. The Drupal and the Wordpress taxonomy systems are being reviewed at the moment and they provide valuable resources. Nevertheless, it could be that someone has some simpler and more appropriate thoughts on this matter.

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  • In Drupal 6, is there a way to take a custom field from the latest post to a taxonomy term, and disp

    - by user278457
    The title for this question pretty much sums up what I'm asking. I've got a list of taxonomy terms, and I'm using a view to display the latest post to each one. I'd like to also display a custom field set up in CCK just under this. Currently, I'm just using "date updated" of the taxonomy term itself which was easy to set up in views. I'd like to drill a little deeper and get the custom "event date" field I've added to the content type last posted to the taxonomy term I'm "viewing". I've got a feeling I'm going to have to write my own database query for this. If (I can avoid that){ How do I set up such a view? } Else{ What's the best practice for including lower level database queries alongside views? }

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  • Drupal 7: Create a taxonomy term for each node and use the node title as the term name

    - by Spre3
    Is there anyway of doing this by using rules or by some custom code? I did try using rules but I can't find a way of adding a new term and set the name as the node title because the [node:title] token is not avilable. I know this is possible using the NAT module but the way this module changes the taxonomy terms hierarchy if you add a term reference field that uses the same taxonomy vocabulary which ruins the whole purpose of what I am trying to do.

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  • Ad-hoc taxonomy: owning the chess set doesn't mean you decide how the little horsey moves

    - by Roger Hart
    There was one of those little laugh-or-cry moments recently when I heard an anecdote about content strategy failings at a major online retailer. The story goes a bit like this: successful company in a highly commoditized marketplace succeeds on price and largely ignores its content team. Being relatively entrepreneurial, the founders are still knocking around, and occasionally like to "take an interest". One day, they decree that clothing sold on the site can no longer be described as "unisex", because this sounds old fashioned. Sad now. Let me just reiterate for the folks at the back: large retailer, commoditized market place, differentiating on price. That's inherently unstable. Sooner or later, they're going to need one or both of competitive differentiation and significant optimization. I can't speak for the latter, since I'm hypothesizing off a raft of rumour, but one of the simpler paths to the former is to become - or rather acknowledge that they are - a content business. Regardless, they need highly-searchable terminology. Even in the face of tooth and claw resistance to noticing the fundamental position content occupies in driving sales (and SEO) on the web, there's a clear information problem here. Dilettante taxonomy is a disaster. Ok, so this is a small example, but that kind of makes it a good one. Unisex probably is the best way of describing clothing designed to suit either men or women interchangeably. It certainly takes less time to type (and read). It's established terminology, and as a single word, it's significantly better for web readability than a phrasal workaround. Something like "fits men or women" is short, by could fall foul of clause-level discard in web scanning. It's not an adjective, so for intuitive reading it's never going to be near the start of a title or description. It would also clutter up search results, and impose cognitive load in list scanning. Sorry kids, it's just worse. Even if "unisex" were an archaism (which it isn't), the only thing that would weigh against its being more usable and concise terminology would be evidence that this archaism were hurting conversions. Good luck with that. We once - briefly - called one of our products a "Can of worms". It was a bundle in a bug-tracking suite, and we thought it sounded terribly cool. Guess how well that sold. We have information and content professionals for a reason: to make sure that whatever we put in front of users is optimised to meet user and business goals. If that thinking doesn't inform style guides, taxonomy, messaging, title structure, and so forth, you might as well be finger painting.

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  • Drupal: How can one use Context to trigger a reaction for a Taxonomy Term condition caused by a Vie

    - by jschrab
    What I would like to do is use the Context module to insert $body_classes of my choosing based on a Taxonomy Term condition. Fine, that's what the Context module is for. Seems simple enough IF your content/page source is a node that is involved with the appropriate Terms. However, I have a page generated by Views that has the appropriate Taxonomy Term id that SHOULD trigger the condition but it doesn't. Now I could set my $body_classes in a "preprocess" in template.php but I'd rather avoid that. Is this even possible in Context? Or am I just doing something wrong?

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  • Content, MetaData and Taxonomy 2 Overview of the Data Layer

    This article is cross-posted from my personal blog. In DotNetNuke version 5.3, we introduced the concept of a centralized Content store, together with the ability to apply Taxonomies (categories) to the content. We have extended this in DNN 5.4 by completing the MetaData API as well as adding Folksonomy (user tags). In this series of blogs I will explain how developers can take advantage of these new features in their own extensions. In the first blog in this series I covered the Taxonomy Manager...Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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  • Drupal workflow action access integrated with taxonomy access control?

    - by groovehunter
    hi, I am building a DMS for our intranet and use a taxonomy hierarchy because we need access control that way. All company locations manage (upload,edit) their own documents but should be able to access all. This is inherited to the child terms and works fine. Additionally we want simple 3-step workflow (draft,published,archived). So i introduced roles for editor, publisher and docadmin and set permissions for the transitions. Also triggers to effectivly (un)publish documents. But (of course) a user of role publisher can do the transition for ALL documents. But we want publisher for each company location (top taxonomy level, see above). Could this be achieved? Do i have to set it up by myself (i guess "rules" is appropriate to do this) or is there another module helping. role inheritance was a guess, but that is only about roles (naturally). "module grants" i use and checked first option. That way my thoughts are going. I hope you get my idea resp. problem. drupal 6.16 current edit: I reread the docs and found ie. http://drupal.org/node/408018 Revisioning for categorized content. Will reread that.

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  • Can Drupal Taxonomy module be used to categorize court records and briefs?

    - by DKinzer
    I'm currently working on project that involves moving a database of documents for court records and briefs over to a Drupal environment. One of the problems that we are faced with is how to index these documents. In our court district, records and briefs all have a docket number which is assigned to a case. The interesting thing is that when multiple cases merge the docket numbers associated to the case become synonymous: Case 1, documents have Doceket No. A Case 2, documents have Docket No. B If case Cases 1 and Case 2 merge, then Docket No. A = Docket No. B My first inclination is to create Docket Vocabulary and have the terms of this Taxonomy be the docket numbers. I am hoping to take advantage of the fact that terms can be synonymous. I understand that there are several functions in the Taxonomy module that I may be able to take advantage, of including: taxonomy_get_synonyms taxonomy_get_related But I'm having problems convincing my collegues that this is the way to go, and frankly I'm not certain it's the right solution either. If anyone has had a similar issue and can offer some guidance as to how to move forward, I would greatly appreciate it. Thanks! D I've asked a related question (which I would also need to answer in order to move forward with this solution): http://stackoverflow.com/questions/2656247/can-drupal-terms-in-different-taxonomies-be-synonymous

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  • Is it possible to add custom fields to a Drupal taxonomy term?

    - by user278457
    I'd like to add a date field to a drupal taxonomy term, alongside the default "title" and "description" Is there some technique/php/module that lets me do this? Is it possible to do with CCK?? I need to be able to display the new field in the same view presenting the content nodes referencing the term. At the moment, I've added a date field to the content nodes with CCK, and it's displayed by the view. But that's not exactly what I'm going for, I just want to update one date per term.

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  • Drupal: Convert taxonomy term name to term id

    - by gigantorTRON
    Using 'taxonomy: term ID' as an argument in one of my Drupal views and I'm having trouble getting it to work correctly. On the views administration page it states, "if using term name, it is generally more efficient to convert it to a term ID and use Taxonomy: Term ID rather than Taxonomy: Term Name." How does one go about converting the term name from a URL into a term ID?

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  • Drupal Views display newest content per taxonomy limit to one node

    - by digital
    Hi, I want to create a view where all 5 of my taxonomy terms are displayed and it then displays the latest node published but this is limited by 1. For Example: Tax Term 1 Latest node published Tax Term 2 Latest node published etc etc Currently I'm grouping by taxonomy term so it's displaying all nodes published then sorted by published date desc. I can't quite figure out how to limit the nodes to only show one item per taxonomy term. Any help would be greatly appreciated.

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  • Drupal: can't add the taxonomy field to Views ?

    - by Patrick
    hi, I've prepared a View for my nodes and I've selected which fields to display. I just realized that there is not the taxonomy field from Content:Taxonomy There is only Taxonomy:Term category and warning: "The content might be duplicated, use appropriate filters". Should I use this item ? What kind of filters should I use ? thanks

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  • Cladogram, tree of life, cladistics, taxonomy in JS or canvas?

    - by boblet
    Good people - I need some help to find a way to create an interactive cladogram or phylogenetic tree (yes, I have read all related posts, and do not find what I am looking for). The thing is, I need the nodes to be name-able. An example would be something like this Most scripts I find are either applets, flash, or simply do not show the node classification, ie it would skip "feliformia" in this example. This is useless to me, as I would then end up with carnivore - anonymous node - anonymous node - anonymous node - tiger, and that is not good. This tree will in theory cover all life, so it could get rather large, and get links and names in english and latin from database. So: no flash, no applets. It must be horizontal, no supertrees (circular). I have gone through this http://bioinfo.unice.fr/biodiv/Tree_editors.html but most of them seems to be either old, not displaying sub-node levels, applets, or way too complex. I imagine this would be a delightful job for canvas/jQuery..? And chances are, someone got there before me? Any pointers much appreciated. Note: if anyone out there would like to do something like this as a project, I will be happy to help, even though it would not benefit me for this project.This type of taxonomy is not as simple as it may seem, and I would be happy see this happen.

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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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  • How to Import Data Taxonomy Into Managed Metada Service in SharePoint 2010

    - by Wayne
    First, Open the Term Store Management Tool (Site Actions > Site Settings > Term Store Management) an download the sample import file. (Remember, Service Applications are configured on a per Web Application basis, so use any site collection inside a WebApp configured with your MMS.) Second, Insert your data. In the photo below, I demonstrate creating a term called USA. Under that, I create the term Alabama. Under that, 4 cities. Then under USA, a term called Alaska. The point is that the we have a hierarchy. Using the import file, we can go 7 layers deep. The last steps is Save the file, head back into the Term Store Management Tool, select/create a group, and Import the file.

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  • What is the best taxonomy from Google's perspective?

    - by ZakGottlieb
    I was wondering what the best way is to structure a new website in Google's eyes. Currently, it contains two top-level categories (X & Y), and clicking a term under either one will result in the URL: www.nameofsite.com/X/X type term, or /Y/Y type term Technically, it is correct to group all "X type terms" under X and "Y type terms" under Y, but we could probably be more granular and break all articles into 5-6 top-level categories by breaking Y up into more specific categories. Given that the current URL structure will eventually result in 1000's of "X type terms" and "Y type terms" under just two top-level categories, would it be more advisable to have several of these, as suggested? Thank you in advance.

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  • limit by taxonomy in view

    - by bratna
    I use view to show node and i set filters to taxonomy:vocabulary (select 3 taxonomy). I want set limit by vocabulary (1 vocabulary show 3 node). Anyone know how to do this? Please help me. Thanks

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  • Wordpress: Retriving posts of a specific custom category in a custom taxonomy

    - by Extrakun
    I am able to retrieve all the posts from a custom category with this call to WP_Query $q = new WP_Query(array( 'taxonomy' => 'jh-portfolio-category', 'term' => 0, 'post_type' => 'jh-portfolio' )); However, let say within the jh-portfolio-category taxonomy I have defined some sub-categories, how do I specify I wish to have posts from a specific sub-category? Changing the 'term' property to the term_id as presented in wp_term_taxonomy doesn't seem to work.

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  • Default values for Content Taxonomy fields in Drupal

    - by lazysoundsystem
    I'm trying to set the default value for a Content Taxonomy field in a hook_form_alter, but can't pin down the necessary format. I've tried this and many variations: foreach (element_children($form) as $child) { // Set $default_value. if ($form[$child]['tids']) { // This, for Content Taxonomy fields, isn't working: $form[$child]['tids']['#default_value'] = array('value' => $default_value); dsm($form[$child]['tids']['#default_value']); } else { // This, for other fields, is working: $form[$child][0]['#default_value']['value'] = $default_value; } } Can anyone tell me what I'm missing?

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  • Drupal subscriptions to taxonomy only

    - by Disco
    Playing around with the subscriptions module; i have some troubles getting it to send the right notification for right subscription. Here's the situation : I have a content-type of type 'work'; it has a cck-taxonomy field; when creating the content users choses one category in which his 'work' fulfills. In user profil, under Categories (user/3/subscriptions/taxa) I choose two categories, lets say 'house work' and 'car work'. When creating a new 'work' content I do not get the notification. But, when manually select 'content-type' in user's profile of type 'work' I get the notification e-mail but independant to which 'category' i had chosen. This is quite annoying since I only want the user to receive his notifications upon the taxonomy he has chosen, not for every new content of type 'work'. Am I missing something obvious here ?

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  • Drupal node_save and special characters.

    - by Pierre
    Hello, i'm trying to create nodes and taxonomy terms through a custom php script by using the node_save() function. I'm working on drupal 6. It's working well (thanks to previous questions on stackoverflow) except for accented letters. Indeed, when a title or a taxonomy term contain "é", "è" or "à", the sentence is cut before those special characters. For example, a title like that: "Bonjour les éléphants" will create a node with "Bonjour les " as title. I don't know if it's linked to my database or if i have to use a special encoding in php (iconv() blabla) The fact is, for drupal titles, i can not use html encoding (for example: é is é in html) because drupal will render &eacute and not é... When i create a taxonomy or a title manually, i have no problems and the accented letter is saved in the database as "é". Soo if you can help me to create terms and title with accented letters, that will be great : ) Thank you !

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  • Default values for Content Taxonomy fields in Drupal with Hierarchical Select widget

    - by lazysoundsystem
    I'm trying to set the default value for a Content Taxonomy field in a hook_form_alter, but can't pin down the necessary format. I've tried this and many variations: foreach (element_children($form) as $child) { // Set $default_value. if ($form[$child]['tids']) { // This, for Content Taxonomy fields, isn't working: $form[$child]['tids']['#default_value'] = array('value' => $default_value); dsm($form[$child]['tids']['#default_value']); } else { // This, for other fields, is working: $form[$child][0]['#default_value']['value'] = $default_value; } } Can anyone tell me what I'm missing? Edit: In response to Henrik Opel (thanks for getting involved), here is the print out of the relevant field of the form with my changes to the default fields commented out, showing the '#default_value' field I'm trying to influence. It also shows that the option widget I'm using is Hierarchical Select (could this be a factor?). In the dsm() in the code above, the changes to the default value are recognised, but they don't get processed later on. field_name_of_content_taxonomy_field (Array, 3 elements) #tree (Boolean) TRUE #weight (String, 1 characters ) 5 tids (Array, 7 elements) #title (String, 10 characters ) Vocabulary_name #type (String, 19 characters ) hierarchical_select #weight (String, 1 characters ) 5 #config (Array, 15 elements) // 15 elements here #required (String, 1 characters ) 0 #description (String, 0 characters ) #default_value (Array, 0 elements)

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  • Adding a Taxonomy Filter to a Custom Post Type

    - by ken
    There is an amazing conversation from about two years ago on the Wordpress Answer site where a number of people came up with good solutions for adding a taxonomy filter to the admin screen for your custom post types (see URL for screen I'm referring to): http://[yoursite.com]/wp-admin/edit.php?s&post_status=all&post_type=[post-type] Anyway, I loved Michael's awesome contribution but in the end used Somatic's implementation with the hierarchy option from Manny. I wrapped it in a class - cuz that's how I like to do things -- and it ALMOST works. The dropdown appears but the values in the dropdown are all looking in the $_GET property for the taxonomies slug-name that you are filtering by. For some reason I don't get anything. I looked at the HTML of the dropdown and it appears ok to me. Here's a quick screen shot for some context: You can tell from this that my post-type is called "exercise" and that the Taxonomy I'm trying to use as a filter is "actions". Here then is the HTML surrounding the dropdown list: <select name="actions" id="actions" class="postform"> <option value="">Show all Actions</option> <option value="ate-dinner">Ate dinner(1)</option> <option value="went-running">Went running(1)</option> </select> I have also confirmed that all of the form elements are within the part of the DOM. And yet if I choose "Went running" and click on the filter button the URL query string comes back without ANY reference to what i've picked. More explicitly, the page first loads with the following URL: /wp-admin/edit.php?post_type=exercise and after pressing the filter button while having picked "Went Running" as an option from the actions filter: /wp-admin/edit.php?s&post_status=all&post_type=exercise&action=-1&m=0&actions&paged=1&mode=list&action2=-1 actually you can see a reference to an "actions" variable but it's set to nothing and as I now look in detail it appears that the moment I hit "filter" on the page it resets the filter dropdown to the default "Show All Actions". Can anyone help me with this?

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