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  • Learning Basic Mathematics

    - by NeedsToKnow
    I'm going to just come out and say it. I'm 20 and can't do maths. Two years ago I passed the end-of-high-school mathematics exam (but not at school), and did pretty well. Since then, I haven't done a scrap of mathematics. I wondered just how bad I had gotten, so I was looking at some simple algebra problems. You know, the kind you learn halfway through highschool. 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 Couldn't do them. I've got half a year left until I start a Computer Science undergraduate degree. I love designing and creating programs, and I remember I loved mathematics back when I did it. Basically, I've had a pretty bad education, but I want to be knowledgable in these areas. I was thinking of buying some high school textbooks and reading them, but I'm not sure this is the right way to go. I need to start off at some basic level and work towards a greater understanding. My question is: What should I study, how should I study, and what books can you recommend? Thanks!

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  • Need some help understanding this problem

    - by Legend
    I was wondering if someone could help me understand this problem. I prepared a small diagram because it is much easier to explain it visually. Problem I am trying to solve: 1. Constructing the dependency graph Given the connectivity of the graph and a metric that determines how well a node depends on the other, order the dependencies. For instance, I could put in a few rules saying that node 3 depends on node 4 node 2 depends on node 3 node 3 depends on node 5 But because the final rule is not "valuable" (again based on the same metric), I will not add the rule to my system. 2. Execute the request order Once I built a dependency graph, execute the list in an order that maximizes the final connectivity. First and foremost, I am wondering if I constructed the problem correctly and if I should be aware of any corner cases. Secondly, is there a closely related algorithm that I can look at? Currently, I am thinking of something like Feedback Arc Set or the Secretary Problem but I am a little confused at the moment. Any suggestions? PS: I am a little confused about the problem myself so please don't flame on me for that. If any clarifications are needed, I will try to update the question.

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  • Fast dot product for a very special case

    - by psihodelia
    Given a vector X of size L, where every scalar element of X is from a binary set {0,1}, it is to find a dot product z=dot(X,Y) if vector Y of size L consists of the integer-valued elements. I suggest, there must exist a very fast way to do it. Let's say we have L=4; X[L]={1, 0, 0, 1}; Y[L]={-4, 2, 1, 0} and we have to find z=X[0]*Y[0] + X[1]*Y[1] + X[2]*Y[2] + X[3]*Y[3] (which in this case will give us -4). It is obvious that X can be represented using binary digits, e.g. an integer type int32 for L=32. Then, all what we have to do is to find a dot product of this integer with an array of 32 integers. Do you have any idea or suggestions how to do it very fast?

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  • approximating log10[x^k0 + k1]

    - by Yale Zhang
    Greetings. I'm trying to approximate the function Log10[x^k0 + k1], where .21 < k0 < 21, 0 < k1 < ~2000, and x is integer < 2^14. k0 & k1 are constant. For practical purposes, you can assume k0 = 2.12, k1 = 2660. The desired accuracy is 5*10^-4 relative error. This function is virtually identical to Log[x], except near 0, where it differs a lot. I already have came up with a SIMD implementation that is ~1.15x faster than a simple lookup table, but would like to improve it if possible, which I think is very hard due to lack of efficient instructions. My SIMD implementation uses 16bit fixed point arithmetic to evaluate a 3rd degree polynomial (I use least squares fit). The polynomial uses different coefficients for different input ranges. There are 8 ranges, and range i spans (64)2^i to (64)2^(i + 1). The rational behind this is the derivatives of Log[x] drop rapidly with x, meaning a polynomial will fit it more accurately since polynomials are an exact fit for functions that have a derivative of 0 beyond a certain order. SIMD table lookups are done very efficiently with a single _mm_shuffle_epi8(). I use SSE's float to int conversion to get the exponent and significand used for the fixed point approximation. I also software pipelined the loop to get ~1.25x speedup, so further code optimizations are probably unlikely. What I'm asking is if there's a more efficient approximation at a higher level? For example: Can this function be decomposed into functions with a limited domain like log2((2^x) * significand) = x + log2(significand) hence eliminating the need to deal with different ranges (table lookups). The main problem I think is adding the k1 term kills all those nice log properties that we know and love, making it not possible. Or is it? Iterative method? don't think so because the Newton method for log[x] is already a complicated expression Exploiting locality of neighboring pixels? - if the range of the 8 inputs fall in the same approximation range, then I can look up a single coefficient, instead of looking up separate coefficients for each element. Thus, I can use this as a fast common case, and use a slower, general code path when it isn't. But for my data, the range needs to be ~2000 before this property hold 70% of the time, which doesn't seem to make this method competitive. Please, give me some opinion, especially if you're an applied mathematician, even if you say it can't be done. Thanks.

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  • seo custom domains

    - by BamBam
    I'm trying to do the following: I have website like apartments.com. sometimes, I want to expand to different cities, so for SEO purposes, I might create a separate domain like bostonapartments.com or newyorkapartments.com for only boston and new york apartments. bostonapartments.com and the main domain apartments.com are all hosted on 1 server. what I did was I used Virtual Host apache config to direct bostonapartments.com to a directory on that server, and then used an iframe to load content for bostonapartments.com from apartments.com. So all the content will be hosted on apartments.com, but bostonapartments.com will get the content from apartments.com. how can I accomplish this effectively in a scalable way using php, apache, mysql? btw, I do not own apartments.com, I'm just using that as an example.

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  • Extend and Overload MS and Point Types

    - by dr d b karron
    Do I have make my own Point and Vector types to overload them ? Why does this not work ? namespace System . windows { public partial struct Point : IFormattable { public static Point operator * ( Point P , double D ) { Point Po = new Point ( ); return Po; } } } namespace SilverlightApplication36 { public partial class MainPage : UserControl { public static void ShrinkingRectangle ( WriteableBitmap wBM , int x1 , int y1 , int x2 , int y2 , Color C ) { wBM . DrawRectangle ( x1 , y1 , x2 , y2 , Colors . Red ); Point Center = Mean ( x1 , y1 , x2 , y2 ); wBM . SetPixel ( Center , Colors.Blue , 3 ); Point P1 = new Point ( x1 , y1 ); Point P2 = new Point ( x1 , y2 ); Point P3 = new Point ( x1 , y2 ); Point P4 = new Point ( x2 , y1 ); const int Steps = 10; for ( int i = 0 ; i < Steps ; i++ ) { double iF = (double)(i+1) / (double)Steps; double jF = ( 1.0 - iF ); Point P11 = **P1 * jF;** } }

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  • Fixing VB6 inaccurate mathmetical results due to rounding

    - by jay
    Try running this in a .VBS file MsgBox(545.14-544.94) You get a neat little answer of 0.199999999999932! This rounding issue also occurs unfortunately in Sin(2 * pi) since VB can only ever see the (user defined) variable pi as accurate as 3.14159265358979. Is rounding it manually (and loosing accuracy) the only way to improve the result? What is the most effective way of dealing with this kind of problem?

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  • Position elements without overlap

    - by eWolf
    I have a number of rectangular elements that I want to position in a 2D space. I calculate an ideal position for each element. Now my problem is that many elements overlap as very often the ideal positions are concentrated in one region. I want to avoid overlap as much as possible (doesn't have to be perfect, though). How can I do this? I've heard physics simulations are suitable for this - is that correct? And can anyone provide an example/tutorial? By the way: I'm using XNA, if you know any .NET library that does exactly this job - tell me!

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  • How to write an intersects for Shapes in android

    - by Rafael T
    I have an written an Object called Shape which has a Point representing the topLeftCorner and a Dimension with represents its width and height. To get the topRightCorner I can simply add the width to the topLeftPoint.x. I use to rotate them on a certain degree around their center. The problem after the rotation is, that my intersects(Shape) method fails, because it does not honor the rotation of the Shapes. The rotation will be the same for each Shape. My current implementation looks like this inside my Shape Object: public boolean intersects(Shape s){ // functions returning a Point of shape s return intersects(s.topLeft()) || intersects(s.topRight()) || intersects(s.bottomLeft()) || intersects(s.bottomRight()) || intersects(s.leftCenter()) || intersects(s.rightCenter()) || intersects(s.center()); } public boolean intersects(Point p){ return p.x >= leftX() && p.x <= rightX() && p.y >= topY() && p.y <= bottomY(); } Basically I need functions like rotatedLeftX() or rotatedTopRight() to work properly. Also for that calculation I think it doesn't matter when the topLeft point before a rotation of ie 90 will turn into topRight... I already read this and this Question here, but do not understand it fully.

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  • How to maintain decimal precision in calculations

    - by Blankman
    I need to sum 2 decimal values together, then divide by 2 and convert to string. My calculation currently is trimming to 2 decimal places, but I want to keep as many decimals as I can. city.Latitude = ( (lat.North + lat.South) / 2 ).ToString(); the values for lat.North and lat.Souch are like: 55.32342322

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  • Distance between hyperplanes

    - by michael dillard
    I'm trying to teach myself some machine learning, and have been using the MNIST database (http://yann.lecun.com/exdb/mnist/) do so. The author of that site wrote a paper in '98 on all different kinds of handwriting recognition techniques, available at http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf. The 10th method mentioned is a "Tangent Distance Classifier". The idea being that if you place each image in a (NxM)-dimensional vector space, you can compute the distance between two images as the distance between the hyperplanes formed by each where the hyperplane is given by taking the point, and rotating the image, rescaling the image, translating the image, etc. I can't figure out enough to fill in the missing details. I understand that most of these are indeed linear operators, so how does one use that fact to then create the hyperplane? And once we have a hyperplane, how do we take its distance with other hyperplanes?

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  • CoreDumpDirectory isn't working on ubuntu; getting segmentation fault with php

    - by siran
    I'm trying to solve a segmentation fault. This message appears in my apache-error.log: [notice] child pid 3979 exit signal Segmentation fault (11) I've tried disabling some apache and php modules but I'm still getting the same error. I've also tried putting this in apache2.conf: CoreDumpDirectory /tmp/apache2-gdb-dump and then chmod 777, chown www-data... so that the server can write. I can see no core-dump files to give me a hint on the error. Does anybody have an idea why CoreDumpDirectory isn't working on Ubuntu?

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  • A simple algorithm for polygon intersection

    - by Elazar Leibovich
    I'm looking for a very simple algorithm for computing the polygon intersection/clipping. That is, given polygons P, Q, I wish to find polygon T which is contained in P and in Q, and I wish T to be maximal among all possible polygons. I don't mind the run time (I have a few very small polygons), I can also afford getting an approximation of the polygons' intersection (that is, a polygon with less points, but which is still contained in the polygons' intersection). But it is really important for me that the algorithm will be simple (cheaper testing) and preferably short (less code). edit: please note, I wish to obtain a polygon which represent the intersection. I don't need only a boolean answer to the question of whether the two polygons intersect.

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  • Function to get X, Y position of an object orbiting a point, given a distance and angle in radians?

    - by Jake Petroules
    I am trying to code a function for a camera that orbits a point. Assume a 3d coordinate plane where Z is up. Ignore Z. Let's say the camera's position starts at (0, 0, z). The object to orbit is at, say (50, 50, z). So we have a distance of ~70 units. Calling the function with {(50, 50, z), 70, x} where x is the position in orbit, in radians, should return where the position of the camera should be. I believe this involves cos and tan but my trig isn't that great... point3d getCameraPosition(point3d objectPosition, float distance, float rotationRadians) { // ??? }

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  • Scientific Algorithms that can produce imagery, pseudocode perhaps?

    - by Ross
    Hello, I have a client who are based in the field of mathematics. We are developing, amongst other things, a website. I like to create a mock-up of a drawing tool that an produce some imagery in the background based on some scientific algorithms. The intention being that the may client, later, may create there own. (They use emacs for everything, great client.) I'm look for an answer of where or what to go looking for. Not code specific, pseudocode even, as we can adapt and have not yet settled on a platform. I'm afraid my mathematic stops at the power of two and some trigonometry. Appreciated if they're are any mathematics related students/academics how could enlighten me? What to search for will be accepted? Edit: To summarise/clarify, I want to draw pretty pictures (the design perspective). I want them to have some context (i.e. not just for the sake of pretty images but have some explanation available). In essence I would to create a rendering engine which we can draw the images and we set the style parameters: line, colour, etc... But to pursue this option I want to experiment myself. Thanks Ross

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  • Amazon Web Services Apache Server

    - by Samnsparky
    I am trying to get a feel for the costs imposed by running apache on AWS continually. Assuming that the service is scarcely used, does anyone know how many cpu hours that would eat up in a month just by sitting there and running? I understand that this is slightly impractical but I am trying to figure out what the cost of entry is to deploy an application on this platform (as compared to GAE). I suspect it to be small but I would like to know.

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  • Adding Colours (Colors) Together like Paint (Blue + Yellow = Green, etc)

    - by glenstorey
    I'm making an iOS game using cocos2d libraries. Lets say you have two objects that have two separate colours - defined in RGB as Blue: 0,0,255 Yellow: 255,255,0 I want to add blue and yellow to make green. To over complicate things, let's say that the Blue object is bigger than the Yellow object (for the sake of argument let's say that the ratio is 2:1), I'm adding twice as much blue as yellow - how to I calculate this new (light green) colour correctly. I understand LAB * Color Space is useful for this sort of 'natural colour' kind of thing, but I'm not sure how to use it - especially in the context of a cocos2d object which (AFAIK) is limited to using RGB in its colour schemes. I'd really appreciate practical help on how to implement this. Thanks heaps!

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  • Looking for framework for plotting scientific data: 2d/3d ...

    - by Ivan
    I need to visualize some scientific calculations. I generally prefer reusing code if there is already a good available instead of inventing wheels each time, that's why I am asking. I need a C# code to draw charts (just outputting a bitmap is ok) of 2d (y=f(x)) and 3d (z=f(x,y)) digital data sets (where any axis can be float, int or datetime), sometimes combined. If I go here and click 3D in the navigation bar on the left, there I can see what I need. But the cheapest version costs $759 there, looks scary for a hobby project of an east-european student :-(

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  • Looking for interesing formula

    - by Thinker
    I'm creating a game, where players can make an alloy. To make it less predictable, and more interesting, I thought that durability and hardness of an alloy can't be calculated by simple formula, because it will be extremely easy to find extrema, where alloy have best statistics. So the questions is, is there any formula for a function, where extrema can be found only by investigating all points? Input values will be in percents: 0.0%-100.0%. I think, it should look like this: half sound wave

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  • Reverse engineering a bezier curve

    - by Martin
    Given a few sample points on a bézier curve, is it possible to work out the set of possible parameters of the curve? In my specific application there is a limited set of endpoints the curve may have, so I want to generate the set of possible curves, enumerate all of them and pick out all the ones which may end on a valid end point.

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