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  • Street-Fighting Mathematics

    Sanjoy Mahajan's new book lays out practical tools for educated guessing and down-and-dirty problem-solving Problem solving - Math - Recreations - Competitions - Methods and Theories

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  • Applications: The mathematics of movement, Part 1

    - by TechTwaddle
    Before you continue reading this post, a suggestion; if you haven’t read “Programming Windows Phone 7 Series” by Charles Petzold, go read it. Now. If you find 150+ pages a little too long, at least go through Chapter 5, Principles of Movement, especially the section “A Brief Review of Vectors”. This post is largely inspired from this chapter. At this point I assume you know what vectors are, how they are represented using the pair (x, y), what a unit vector is, and given a vector how you would normalize the vector to get a unit vector. Our task in this post is simple, a marble is drawn at a point on the screen, the user clicks at a random point on the device, say (destX, destY), and our program makes the marble move towards that point and stop when it is reached. The tricky part of this task is the word “towards”, it adds a direction to our problem. Making a marble bounce around the screen is simple, all you have to do is keep incrementing the X and Y co-ordinates by a certain amount and handle the boundary conditions. Here, however, we need to find out exactly how to increment the X and Y values, so that the marble appears to move towards the point where the user clicked. And this is where vectors can be so helpful. The code I’ll show you here is not ideal, we’ll be working with C# on Windows Mobile 6.x, so there is no built-in vector class that I can use, though I could have written one and done all the math inside the class. I think it is trivial to the actual problem that we are trying to solve and can be done pretty easily once you know what’s going on behind the scenes. In other words, this is an excuse for me being lazy. The first approach, uses the function Atan2() to solve the “towards” part of the problem. Atan2() takes a point (x, y) as input, Atan2(y, x), note that y goes first, and then it returns an angle in radians. What angle you ask. Imagine a line from the origin (0, 0), to the point (x, y). The angle which Atan2 returns is the angle the positive X-axis makes with that line, measured clockwise. The figure below makes it clear, wiki has good details about Atan2(), give it a read. The pair (x, y) also denotes a vector. A vector whose magnitude is the length of that line, which is Sqrt(x*x + y*y), and a direction ?, as measured from positive X axis clockwise. If you’ve read that chapter from Charles Petzold’s book, this much should be clear. Now Sine and Cosine of the angle ? are special. Cosine(?) divides x by the vectors length (adjacent by hypotenuse), thus giving us a unit vector along the X direction. And Sine(?) divides y by the vectors length (opposite by hypotenuse), thus giving us a unit vector along the Y direction. Therefore the vector represented by the pair (cos(?), sin(?)), is the unit vector (or normalization) of the vector (x, y). This unit vector has a length of 1 (remember sin2(?) + cos2(?) = 1 ?), and a direction which is the same as vector (x, y). Now if I multiply this unit vector by some amount, then I will always get a point which is a certain distance away from the origin, but, more importantly, the point will always be on that line. For example, if I multiply the unit vector with the length of the line, I get the point (x, y). Thus, all we have to do to move the marble towards our destination point, is to multiply the unit vector by a certain amount each time and draw the marble, and the marble will magically move towards the click point. Now time for some code. The application, uses a timer based frame draw method to draw the marble on the screen. The timer is disabled initially and whenever the user clicks on the screen, the timer is enabled. The callback function for the timer follows the standard Update and Draw cycle. private double totLenToTravelSqrd = 0; private double startPosX = 0, startPosY = 0; private double destX = 0, destY = 0; private void Form1_MouseUp(object sender, MouseEventArgs e) {     destX = e.X;     destY = e.Y;     double x = marble1.x - destX;     double y = marble1.y - destY;     //calculate the total length to be travelled     totLenToTravelSqrd = x * x + y * y;     //store the start position of the marble     startPosX = marble1.x;     startPosY = marble1.y;     timer1.Enabled = true; } private void timer1_Tick(object sender, EventArgs e) {     UpdatePosition();     DrawMarble(); } Form1_MouseUp() method is called when ever the user touches and releases the screen. In this function we save the click point in destX and destY, this is the destination point for the marble and we also enable the timer. We store a few more values which we will use in the UpdatePosition() method to detect when the marble has reached the destination and stop the timer. So we store the start position of the marble and the square of the total length to be travelled. I’ll leave out the term ‘sqrd’ when speaking of lengths from now on. The time out interval of the timer is set to 40ms, thus giving us a frame rate of about ~25fps. In the timer callback, we update the marble position and draw the marble. We know what DrawMarble() does, so here, we’ll only look at how UpdatePosition() is implemented; private void UpdatePosition() {     //the vector (x, y)     double x = destX - marble1.x;     double y = destY - marble1.y;     double incrX=0, incrY=0;     double distanceSqrd=0;     double speed = 6;     //distance between destination and current position, before updating marble position     distanceSqrd = x * x + y * y;     double angle = Math.Atan2(y, x);     //Cos and Sin give us the unit vector, 6 is the value we use to magnify the unit vector along the same direction     incrX = speed * Math.Cos(angle);     incrY = speed * Math.Sin(angle);     marble1.x += incrX;     marble1.y += incrY;     //check for bounds     if ((int)marble1.x < MinX + marbleWidth / 2)     {         marble1.x = MinX + marbleWidth / 2;     }     else if ((int)marble1.x > (MaxX - marbleWidth / 2))     {         marble1.x = MaxX - marbleWidth / 2;     }     if ((int)marble1.y < MinY + marbleHeight / 2)     {         marble1.y = MinY + marbleHeight / 2;     }     else if ((int)marble1.y > (MaxY - marbleHeight / 2))     {         marble1.y = MaxY - marbleHeight / 2;     }     //distance between destination and current point, after updating marble position     x = destX - marble1.x;     y = destY - marble1.y;     double newDistanceSqrd = x * x + y * y;     //length from start point to current marble position     x = startPosX - (marble1.x);     y = startPosY - (marble1.y);     double lenTraveledSqrd = x * x + y * y;     //check for end conditions     if ((int)lenTraveledSqrd >= (int)totLenToTravelSqrd)     {         System.Console.WriteLine("Stopping because destination reached");         timer1.Enabled = false;     }     else if (Math.Abs((int)distanceSqrd - (int)newDistanceSqrd) < 4)     {         System.Console.WriteLine("Stopping because no change in Old and New position");         timer1.Enabled = false;     } } Ok, so in this function, first we subtract the current marble position from the destination point to give us a vector. The first three lines of the function construct this vector (x, y). The vector (x, y) has the same length as the line from (marble1.x, marble1.y) to (destX, destY) and is in the direction pointing from (marble1.x, marble1.y) to (destX, destY). Note that marble1.x and marble1.y denote the center point of the marble. Then we use Atan2() to get the angle which this vector makes with the positive X axis and use Cosine() and Sine() of that angle to get the unit vector along that same direction. We multiply this unit vector with 6, to get the values which the position of the marble should be incremented by. This variable, speed, can be experimented with and determines how fast the marble moves towards the destination. After this, we check for bounds to make sure that the marble stays within the screen limits and finally we check for the end condition and stop the timer. The end condition has two parts to it. The first case is the normal case, where the user clicks well inside the screen. Here, we stop when the total length travelled by the marble is greater than or equal to the total length to be travelled. Simple enough. The second case is when the user clicks on the very corners of the screen. Like I said before, the values marble1.x and marble1.y denote the center point of the marble. When the user clicks on the corner, the marble moves towards the point, and after some time tries to go outside of the screen, this is when the bounds checking comes into play and corrects the marble position so that the marble stays inside the screen. In this case the marble will never travel a distance of totLenToTravelSqrd, because of the correction is its position. So here we detect the end condition when there is not much change in marbles position. I use the value 4 in the second condition above. After experimenting with a few values, 4 seemed to work okay. There is a small thing missing in the code above. In the normal case, case 1, when the update method runs for the last time, marble position over shoots the destination point. This happens because the position is incremented in steps (which are not small enough), so in this case too, we should have corrected the marble position, so that the center point of the marble sits exactly on top of the destination point. I’ll add this later and update the post. This has been a pretty long post already, so I’ll leave you with a video of how this program looks while running. Notice in the video that the marble moves like a bot, without any grace what so ever. And that is because the speed of the marble is fixed at 6. In the next post we will see how to make the marble move a little more elegantly. And also, if Atan2(), Sine() and Cosine() are a little too much to digest, we’ll see how to achieve the same effect without using them, in the next to next post maybe. Ciao!

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  • Applications: The Mathematics of Movement, Part 2

    - by TechTwaddle
    In part 1 of this series we saw how we can make the marble move towards the click point, with a fixed speed. In this post we’ll see, first, how to get rid of Atan2(), sine() and cosine() in our calculations, and, second, reducing the speed of the marble as it approaches the destination, so it looks like the marble is easing into it’s final position. As I mentioned in one of the previous posts, this is achieved by making the speed of the marble a function of the distance between the marble and the destination point. Getting rid of Atan2(), sine() and cosine() Ok, to be fair we are not exactly getting rid of these trigonometric functions, rather, replacing one form with another. So instead of writing sin(?), we write y/length. You see the point. So instead of using the trig functions as below, double x = destX - marble1.x; double y = destY - marble1.y; //distance between destination and current position, before updating marble position distanceSqrd = x * x + y * y; double angle = Math.Atan2(y, x); //Cos and Sin give us the unit vector, 6 is the value we use to magnify the unit vector along the same direction incrX = speed * Math.Cos(angle); incrY = speed * Math.Sin(angle); marble1.x += incrX; marble1.y += incrY; we use the following, double x = destX - marble1.x; double y = destY - marble1.y; //distance between destination and marble (before updating marble position) lengthSqrd = x * x + y * y; length = Math.Sqrt(lengthSqrd); //unit vector along the same direction as vector(x, y) unitX = x / length; unitY = y / length; //update marble position incrX = speed * unitX; incrY = speed * unitY; marble1.x += incrX; marble1.y += incrY; so we replaced cos(?) with x/length and sin(?) with y/length. The result is the same.   Adding oomph to the way it moves In the last post we had the speed of the marble fixed at 6, double speed = 6; to make the marble decelerate as it moves, we have to keep updating the speed of the marble in every frame such that the speed is calculated as a function of the length. So we may have, speed = length/12; ‘length’ keeps decreasing as the marble moves and so does speed. The Form1_MouseUp() function remains the same as before, here is the UpdatePosition() method, private void UpdatePosition() {     double incrX = 0, incrY = 0;     double lengthSqrd = 0, length = 0, lengthSqrdNew = 0;     double unitX = 0, unitY = 0;     double speed = 0;     double x = destX - marble1.x;     double y = destY - marble1.y;     //distance between destination and marble (before updating marble position)     lengthSqrd = x * x + y * y;     length = Math.Sqrt(lengthSqrd);     //unit vector along the same direction as vector(x, y)     unitX = x / length;     unitY = y / length;     //speed as a function of length     speed = length / 12;     //update marble position     incrX = speed * unitX;     incrY = speed * unitY;     marble1.x += incrX;     marble1.y += incrY;     //check for bounds     if ((int)marble1.x < MinX + marbleWidth / 2)     {         marble1.x = MinX + marbleWidth / 2;     }     else if ((int)marble1.x > (MaxX - marbleWidth / 2))     {         marble1.x = MaxX - marbleWidth / 2;     }     if ((int)marble1.y < MinY + marbleHeight / 2)     {         marble1.y = MinY + marbleHeight / 2;     }     else if ((int)marble1.y > (MaxY - marbleHeight / 2))     {         marble1.y = MaxY - marbleHeight / 2;     }     //distance between destination and marble (after updating marble position)     x = destX - (marble1.x);     y = destY - (marble1.y);     lengthSqrdNew = x * x + y * y;     /*      * End Condition:      * 1. If there is not much difference between lengthSqrd and lengthSqrdNew      * 2. If the marble has moved more than or equal to a distance of totLenToTravel (see Form1_MouseUp)      */     x = startPosX - marble1.x;     y = startPosY - marble1.y;     double totLenTraveledSqrd = x * x + y * y;     if ((int)totLenTraveledSqrd >= (int)totLenToTravelSqrd)     {         System.Console.WriteLine("Stopping because Total Len has been traveled");         timer1.Enabled = false;     }     else if (Math.Abs((int)lengthSqrd - (int)lengthSqrdNew) < 4)     {         System.Console.WriteLine("Stopping because no change in Old and New");         timer1.Enabled = false;     } } A point to note here is that, in this implementation, the marble never stops because it travelled a distance of totLenToTravelSqrd (first if condition). This happens because speed is a function of the length. During the final few frames length becomes very small and so does speed; and so the amount by which the marble shifts is quite small, and the second if condition always hits true first. I’ll end this series with a third post. In part 3 we will cover two things, one, when the user clicks, the marble keeps moving in that direction, rebounding off the screen edges and keeps moving forever. Two, when the user clicks on the screen, the marble moves towards it, with it’s speed reducing by every frame. It doesn’t come to a halt when the destination point is reached, instead, it continues to move, rebounds off the screen edges and slowly comes to halt. The amount of time that the marble keeps moving depends on how far the user clicks from the marble. I had mentioned this second situation here. Finally, here’s a video of this program running,

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  • Applications: The Mathematics of Movement, Part 3

    - by TechTwaddle
    Previously: Part 1, Part 2 As promised in the previous post, this post will cover two variations of the marble move program. The first one, Infinite Move, keeps the marble moving towards the click point, rebounding it off the screen edges and changing its direction when the user clicks again. The second version, Finite Move, is the same as first except that the marble does not move forever. It moves towards the click point, rebounds off the screen edges and slowly comes to rest. The amount of time that it moves depends on the distance between the click point and marble. Infinite Move This case is simple (actually both cases are simple). In this case all we need is the direction information which is exactly what the unit vector stores. So when the user clicks, you calculate the unit vector towards the click point and then keep updating the marbles position like crazy. And, of course, there is no stop condition. There’s a little more additional code in the bounds checking conditions. Whenever the marble goes off the screen boundaries, we need to reverse its direction.  Here is the code for mouse up event and UpdatePosition() method, //stores the unit vector double unitX = 0, unitY = 0; double speed = 6; //speed times the unit vector double incrX = 0, incrY = 0; private void Form1_MouseUp(object sender, MouseEventArgs e) {     double x = e.X - marble1.x;     double y = e.Y - marble1.y;     //calculate distance between click point and current marble position     double lenSqrd = x * x + y * y;     double len = Math.Sqrt(lenSqrd);     //unit vector along the same direction (from marble towards click point)     unitX = x / len;     unitY = y / len;     timer1.Enabled = true; } private void UpdatePosition() {     //amount by which to increment marble position     incrX = speed * unitX;     incrY = speed * unitY;     marble1.x += incrX;     marble1.y += incrY;     //check for bounds     if ((int)marble1.x < MinX + marbleWidth / 2)     {         marble1.x = MinX + marbleWidth / 2;         unitX *= -1;     }     else if ((int)marble1.x > (MaxX - marbleWidth / 2))     {         marble1.x = MaxX - marbleWidth / 2;         unitX *= -1;     }     if ((int)marble1.y < MinY + marbleHeight / 2)     {         marble1.y = MinY + marbleHeight / 2;         unitY *= -1;     }     else if ((int)marble1.y > (MaxY - marbleHeight / 2))     {         marble1.y = MaxY - marbleHeight / 2;         unitY *= -1;     } } So whenever the user clicks we calculate the unit vector along that direction and also the amount by which the marble position needs to be incremented. The speed in this case is fixed at 6. You can experiment with different values. And under bounds checking, whenever the marble position goes out of bounds along the x or y direction we reverse the direction of the unit vector along that direction. Here’s a video of it running;   Finite Move The code for finite move is almost exactly same as that of Infinite Move, except for the difference that the speed is not fixed and there is an end condition, so the marble comes to rest after a while. Code follows, //unit vector along the direction of click point double unitX = 0, unitY = 0; //speed of the marble double speed = 0; private void Form1_MouseUp(object sender, MouseEventArgs e) {     double x = 0, y = 0;     double lengthSqrd = 0, length = 0;     x = e.X - marble1.x;     y = e.Y - marble1.y;     lengthSqrd = x * x + y * y;     //length in pixels (between click point and current marble pos)     length = Math.Sqrt(lengthSqrd);     //unit vector along the same direction as vector(x, y)     unitX = x / length;     unitY = y / length;     speed = length / 12;     timer1.Enabled = true; } private void UpdatePosition() {     marble1.x += speed * unitX;     marble1.y += speed * unitY;     //check for bounds     if ((int)marble1.x < MinX + marbleWidth / 2)     {         marble1.x = MinX + marbleWidth / 2;         unitX *= -1;     }     else if ((int)marble1.x > (MaxX - marbleWidth / 2))     {         marble1.x = MaxX - marbleWidth / 2;         unitX *= -1;     }     if ((int)marble1.y < MinY + marbleHeight / 2)     {         marble1.y = MinY + marbleHeight / 2;         unitY *= -1;     }     else if ((int)marble1.y > (MaxY - marbleHeight / 2))     {         marble1.y = MaxY - marbleHeight / 2;         unitY *= -1;     }     //reduce speed by 3% in every loop     speed = speed * 0.97f;     if ((int)speed <= 0)     {         timer1.Enabled = false;     } } So the only difference is that the speed is calculated as a function of length when the mouse up event occurs. Again, this can be experimented with. Bounds checking is same as before. In the update and draw cycle, we reduce the speed by 3% in every cycle. Since speed is calculated as a function of length, speed = length/12, the amount of time it takes speed to reach zero is directly proportional to length. Note that the speed is in ‘pixels per 40ms’ because the timeout value of the timer is 40ms.  The readability can be improved by representing speed in ‘pixels per second’. This would require you to add some more calculations to the code, which I leave out as an exercise. Here’s a video of this second version,

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  • Stairway to T-SQL DML Level 5: The Mathematics of SQL: Part 2

    Joining tables is a crucial concept to understanding data relationships in a relational database. When you are working with your SQL Server data, you will often need to join tables to produce the results your application requires. Having a good understanding of set theory, and the mathematical operators available and how they are used to join tables will make it easier for you to retrieve the data you need from SQL Server.

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  • Ubuntu 14.04 doesn't detect my discrete GPU

    - by user258887
    I recently purchased a laptop with an Nvidia GeForce 860m, and have installed Ubuntu 14.04. On my old laptop I had 12.04, which automatically filled Additional Drivers with Nvidia drivers. But on this computer, the only thing in Additional Drivers is Qualcomm. So I manually installed Nvidia, but X Server Settings doesn't seem to detect any GPU... lspci | grep VGA reports only my integrated Intel GPU, but lspci -v reports many things, including the Nvidia GPU: 01:00.0 3D controller: NVIDIA Corporation GM107M [GeForce GTX 860M] (rev a2) Subsystem: ASUSTeK Computer Inc. Device 157d Flags: fast devsel, IRQ 16 Memory at ec000000 (32-bit, non-prefetchable) [size=16M] Memory at c0000000 (64-bit, prefetchable) [size=256M] Memory at d0000000 (64-bit, prefetchable) [size=32M] I/O ports at e000 [size=128] Expansion ROM at ed000000 [disabled] [size=512K] Capabilities: access denied Don't know what any of that means. Not sure if it's supposed to say 'access denied'... I need my GPU to do CUDA and OpenGL programming. What else can I do to figure out why this isn't working?

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  • Stairway to T-SQL DML Level 4: The Mathematics of SQL: Part 1

    A relational database contains tables that relate to each other by key values. When querying data from these related tables you may choose to select data from a single table or many tables. If you select data from many tables, you normally join those tables together using specified join criteria. The concepts of selecting data from tables and joining tables together is all about managing and manipulating sets of data. In Level 4 of this Stairway we will explore the concepts of set theory and mathematical operators to join, merge, and return data from multiple SQL Server tables. Get Smart with SQL Backup Pro Powerful centralised management, encryption and more.SQL Backup Pro was the smartest kid at school Discover why.

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  • Laptop, unable to install discrete graphics card GTX 880M

    - by FoxyShadoww
    So I've bought the GT70 2PE Dominator Pro a few weeks ago and I installed Zorin OS 9 Ultimate on it. Today I tried to install the Nvidia drivers on my laptop since it has the GTX 880M, but my system became unbootable. Can anyone help me with this issue? I will write down what I've tried so far. This is what I've tried so far: Downloaded the newest Nvidia drivers from their website. Pressed CTRL+ALT+F2 to open the terminal page thingy. Logged in and got root access. Stopped the lightdm service. Ran the NVIDIA-Linux-x86_64-340.32.run installer. Pressed the accept button and right after that it told me the following message: The distribution-provided pre-install script failed! Continue installation anyway?. When I install anyway, it will crash my system and makes it unbootable, Does anyone know how to use my GTX 880M? Do I need to enable it on boot time somehow? Thanks for the support, Sapphire ~

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  • What is the the relation between programming and mathematics?

    - by Math Grad
    Programmers seem to think that their work is quite mathematical. I understand this when you try to optimize something in performance, find the most efficient alogithm, etc.. But it patently seems false when you look at a billing application for a shop, or a systems software riddled with I/O calls. So what is it exactly? Is computation and associated programming really mathematical? Here I have in mind particularly the words of the philosopher Schopenhauer in mind: That arithmetic is the basest of all mental activities is proved by the fact that it is the only one that can be accomplished by means of a machine. Take, for instance, the reckoning machines that are so commonly used in England at the present time, and solely for the sake of convenience. But all analysis finitorum et infinitorum is fundamentally based on calculation. Therefore we may gauge the “profound sense of the mathematician,” of whom Lichtenberg has made fun, in that he says: “These so-called professors of mathematics have taken advantage of the ingenuousness of other people, have attained the credit of possessing profound sense, which strongly resembles the theologians’ profound sense of their own holiness.” I lifted the above quote from here. It seems that programmers are doing precisely the sort of mechanized base mental activity the grand old man is contemptuous about. So what exactly is the deal? Is programming really the "good" kind of mathematics, or just the baser type, or altogether something else just meant for business not to be confused with a pure discipline?

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  • GUVCVIEW errors

    - by Brian Snapp
    I had GUVCVIEW working once before. it suddenly quit working. This is the error I receive........ bt_audio_service_open: connect() failed: Connection refused (111) bt_audio_service_open: connect() failed: Connection refused (111) bt_audio_service_open: connect() failed: Connection refused (111) bt_audio_service_open: connect() failed: Connection refused (111) video device: /dev/video0 /dev/video0 - device 1 Init. Intergrated Webcam (location: usb-0000:00:1a.7-2) { pixelformat = 'YUYV', description = 'YUV 4:2:2 (YUYV)' } { discrete: width = 640, height = 480 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 352, height = 288 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 320, height = 240 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 176, height = 144 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 160, height = 120 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 1024, height = 768 } Time interval between frame: 1/9, 1/5, { discrete: width = 1280, height = 1024 } Time interval between frame: 1/9, 1/5, checking format: 1196444237 Format unavailable: 1196444237. Init v4L2 failed !! Init video returned -2 trying minimum setup ... video device: /dev/video0 /dev/video0 - device 1 Init. Intergrated Webcam (location: usb-0000:00:1a.7-2) { pixelformat = 'YUYV', description = 'YUV 4:2:2 (YUYV)' } { discrete: width = 640, height = 480 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 352, height = 288 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 320, height = 240 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 176, height = 144 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 160, height = 120 } Time interval between frame: 1/30, 1/20, 1/15, 1/10, 1/5, { discrete: width = 1024, height = 768 } Time interval between frame: 1/9, 1/5, { discrete: width = 1280, height = 1024 } Time interval between frame: 1/9, 1/5, checking format: 1448695129 Requested Format unavailable: get width 640 height 480 vid:0c45 pid:6410 driver:uvcvideo (guvcview:4079): Gtk-CRITICAL **: gtk_hscale_new_with_range: assertion `min < max' failed (guvcview:4079): Gtk-CRITICAL **: gtk_scale_set_draw_value: assertion `GTK_IS_SCALE (scale)' failed Segmentation fault I suppose the problem lies in the fact, that I cannot locate a configuration file to edit. Any help in where this file may lie? I have tried searching for any/everything related to guvcview, and have had zero success. Thank you for taking the time to read this, and hopefully providing a solution..

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  • how to apply Discrete wavelet transform on image

    - by abuasis
    I am implementing an android application that will verify signature images , decided to go with the Discrete wavelet transform method (symmlet-8) the method requires to apply the discrete wavelet transform and separate the image using low-pass and high-pass filter and retrieve the wavelet transform coefficients. the equations show notations that I cant understand thus can't do the math easily , also didn't know how to apply low-pass and high-pass filters to my x and y points. is there any tutorial that shows you how to apply the discrete wavelet transform to my image easily that breaks it out in numbers? thanks alot in advance.

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  • Mathematics - Why is Differential Calculus (MVP) in PHP a tabu?

    - by Email
    Hi I want to do a Mean-Variance-Optimization (Markowitz) but i never found anything written in php that does this. MVP needs differential calculus. Can it be done in php and why arent there any classes/works from universities? For a webapplication (regarding performance) would another language be the better choice to handle heavy calculations? Thanks so much for any help/answer on this

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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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  • Plotting an Arc in Discrete Steps

    - by phobos51594
    Good afternoon, Background My question relates to the plotting of an arbitrary arc in space using discrete steps. It is unique, however, in that I am not drawing to a canvas in the typical sense. The firmware I am designing is for a gcode interpreter for a CNC mill that will translate commands into stepper motor movements. Now, I have already found a similar question on this very site, but the methodology suggested (Bresenham's Algorithm) appears to be incompatable for moving an object in space, as it only relies on the calculation of one octant of a circle which is then mirrored about the remaining axes of symmetry. Furthermore, the prescribed method of calculation an arc between two arbitrary angles relies on trigonometry (I am implementing on a microcontroller and would like to avoid costly trig functions, if possible) and simply not taking the steps that are out of the range. Finally, the algorithm only is designed to work in one rotational direction (e.g. counterclockwise). Question So, on to the actual question: Does anyone know of a general-purpose algorithm that can be used to "draw" an arbitrary arc in discrete steps while still giving respect to angular direction (CW / CCW)? The final implementation will be done in C, but the language for the purpose of the question is irrelevant. Thank you in advance. References S.O post on drawing a simple circle using Bresenham's Algorithm: "Drawing" an arc in discrete x-y steps Wiki page describing Bresenham's Algorithm for a circle http://en.wikipedia.org/wiki/Midpoint_circle_algorithm Gcode instructions to be implemented (see. G2 and G3) http://linuxcnc.org/docs/html/gcode.html

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  • Removing the contents of a Chan or MVar in a single discrete step

    - by Bill
    I'm writing a discrete simulation where request values from multiple threads accumulate in a centralized queue. Every n milliseconds, a manager wakes up to process requests. When the manager wakes up, it should retrieve all of the contents of the central queue in a single discrete step. While processing these, any client threads attempting to submit to the queue should block. When processing completes, the queue reopens and the manager goes back to sleep. What's the best way to do this? The retry behavior of STM isn't really what I want. If I use a Chan or MVar, there's no way to prevent clients from enqueuing additional requests during processing. One approach is to use an MVar as a mutex on a Chan holding the queue. Are there other ways to do this?

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  • What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

    - by Ein Doofus
    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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  • Music and Mathematics. Finding the natural scale matemathically. Is this correct?

    - by Alfonso de la Osa
    Hi! I wrote this post Music and Mathematics, finding the Natural and the Pentathonic scales. Central A at 383,56661 Hz. Is a method to find the Natural scale. I want to discuss it and find if its true. This is the code of the reasoning in js. <script> var c = 1.714285714285714; var tot = 0; var scale = []; while(tot < (14 - c)){ tot += c; scale.push(Math.round(tot)); } if(scale.length == 8){ document.write(scale + " " + c + "<br />"); } </script>

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  • Music and Mathematics. Finding the natural scale generator. The best way?

    - by Alfonso de la Osa
    Hi! I wrote this post Music and Mathematics, finding the Natural and the Pentatonic scales. Is a method to find the Natural scale. I want to discuss it and find if its true. This is the code of the reasoning in js. <script> var c = 12/7; var tot = 0; var scale = []; while(tot < (14 - c)){ tot += c; scale.push(Math.round(tot)); } if(scale.length == 8){ document.write(scale + " " + c + "<br />"); } </script>

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  • Mathematics for Computer Science Students

    - by Ender
    To cut a long story short, I am a CS student that has received no formal Post-16 Maths education for years. Right now even my Algebra is extremely rusty and I have a couple of months to shape up my skills. I've got a couple of video lectures in my bookmarks, consisting of: Pre-Calculus Algebra Calculus Probability Introduction to Statistics Differential Equations Linear Algebra My aim as of today is to be able to read the CLRS book Introduction to Algorithms and be able to follow the Mathematical notation in that, as well as being able to confidently read and back-up any arguments written in Mathematical notation. Aside from these video lectures, can anyone recommend any good books to help teach someone wishing to go from a low-foundation level to a more advanced level of Mathematics? Just as a note, I've taken a first-year module in Analytical Modelling, so I understand some of the basic concepts of Discrete Mathematics. EDIT: Just a note to those that are looking to learn Linear Algebra using the Video Lectures I have posted up. Peteris Krumins' Blog contains a run-through of these lecture notes as well as his own commentary and lecture notes, an invaluable resource for those looking to follow the lectures too.

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  • Can basic mathematics be done in Microsoft Word?

    - by Christopher Chipps
    Is there a function of MS Word that enables users to solve basic math problems, in this case addition or subtraction? I use its platform for a budget and of course I could just use a calculator but it would be more convenient if I could solve it all in one place. For instance: (6.75 + 12.65 + 27.35) Sorry for the simplicity of this question. Wondering if MS Word had a functionality like this of some sort?

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  • Discrete seekbar in Android app?

    - by vee
    i would like to create a seekbar for an Android app that allows the user to select a value between -5 and 5 (which maps to "strongly disagree" and "strongly agree"). how do i make a seekbar with discrete values? or is there a better UI widget i could use for this? thanks.

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  • R library for discrete Markov chain simulation

    - by stevejb
    Hello, I am looking for something like the 'msm' package, but for discrete Markov chains. For example, if I had a transition matrix defined as such Pi <- matrix(c(1/3,1/3,1/3, 0,2/3,1/6, 2/3,0,1/2)) for states A,B,C. How can I simulate a Markov chain according to that transition matrix? Thanks,

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