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  • Justo Balderas 1:27 pm on May 23, 2017 Permalink | Reply
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    Dibs 

    Dibs pa? Ahaha

    Week 5: Synthesis


    • 1] Vectors dahil sa “you are a vector” thing sa post na “we are vectors”.
      2] Matrices dahil sa quote ni Margot Gerritsen, at dahil narin sa movie na The Matrix.
      3] Symmetry dahil shinare ko yung fractal music video sa kakilala kong grad ng music. Nalaman ko sa kanya na ganun daw yung music noong kapanahunan pa nila Bach, nakasulat lang. Wala pang recording, kaya para mapakinggan, kailangang tugtugin. Kaya yung mga demographic daw ni Bach, na-aappreciate yung patterns na ginawa niya kasi binabasa daw talaga nila.
      4] Change of basis dahil dun sa skewed/distorted picture thing ala photoshop.
    • Relationship.
      :)) Mema/meta nalang eh noh.
    • Yes naman, sipag magbasa oh. Salamat sa mga contributions nyo sa applications nung wk. 2, 3, & 4. Marami akong natutunan at narealize ko, dapat pala inaraw araw ko yung pagche-check ng post, hindi yung isahan lang at ‘at the end of the sem’ pa, kasi nakakamotivate nga talaga to learn kapag nakikita mo yung mga application.
     
  • Justo Balderas 5:56 pm on May 21, 2017 Permalink | Reply
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    Quickly multiply two big integers via Fourier Transform 

    Week 4: Laplace and Fourier Transform


    The fastest known algorithms for the multiplication of very large integers use the “polynomial multiplication method” which uses Fourier transform. [5]

     

    Multiplying huge integers is an operation that occurs in many fields of Computational Science: Cryptography, Number theory, just to name a few. The problem is that traditional approaches to multiplication require O(n2) multiplication operations, where n is the number of digits. To see why, assume for example that we want to multiply the numbers 123 and 456. The normal way to do this is shown below.

    We see that for two integers of length 3, this multiplication requires 3 x 3 = 9 operations, hence its O(n2complexity. Executing an O(n2) algorithm for huge n is very costly, so that is why it is preferred to use more efficient algorithms when multiplying huge integers. One way to do this more efficient (in O(n log(n))), is by using FFT’s (Fast Fourier Transforms).[4]

    So how?

    “a number can indeed be divided on a decimal basis and the product of two of them is equivalent to the convolution product which on its turn can be handled fastly with FFT.”[3]

    1] Represent the integer as a polynomial

    2] Use the multiplication algorithm for polynomials using FFT

    3] O(n) carry-propagation step

    Sources:

    [1] https://www.quora.com/What-are-some-non-obvious-applications-of-the-Fourier-transform/answer/Lionel-Chiron (visited on May 21, 2017).

    [2] https://math.stackexchange.com/questions/116674/what-is-the-fastest-way-to-multiply-two-digit-numbers#comment271358_116674 (visited on May 21, 2017).

    [3] https://www.quora.com/What-are-the-major-applications-of-the-Fast-Fourier-Transform-FFT-to-algorithms-in-Computer-Science/answer/John-McGonagle (visited on May 21, 2017).

    [4] (2017). Cs.rug.nl. Retrieved 21 May 2017, from http://www.cs.rug.nl/~ando/pdfs/Ando_Emerencia_multiplying_huge_integers_using_fourier_transforms_paper.pdf

    [5] https://en.wikipedia.org/wiki/Discrete_Fourier_transform#Polynomial_multiplication (visited on May 21, 2017).
    [6] https://en.wikipedia.org/wiki/Multiplication_algorithm#Fourier_transform_methods (visited on May 21, 2017).

     
  • Justo Balderas 5:45 pm on May 21, 2017 Permalink | Reply
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    Ball Is Life 

    Week 3: Symmetric Matrices


    DIBS: Symmetry in basketball (equipment/ball)

    “I will never look at a (traditional) NBA basketball the same again” – This is just right after researching for this post. *amazed meme* *my whole life has been a lie meme*

    Ever since 7 years old, I thought basketball looks like this.

    3 plane

    expectation

    Little did I know, it is just like a tennis ball or baseball traditionally made by joining two complementary (symmetric) pieces.

    baseball

    deconstructed baseball

    In basketball, what you should see from one side is different from what you have on the other. Below’s a photo of the different flows of the leather patches in the front and rear view.

    2 different plane

    leather patches

    So the first animation (gif) should be…

    2 plane reflective symmetry

    reality (on most, if not all traditional basketball)

    Each leather patch embraces the other. Here’s an animation.

    2 plane of symmetry

    animation

     

    Here’s a real life example. Observe the 2 leather patches carefully. (sorry for the low resolution ‘.gif’, here’s the link for the video source: youtu.be/DQc8miHqdqQ?t=2m20s )

    real basketball

    NBA basketball (Spalding brand)

    Basketballs have two planes of reflective symmetry, as do tennis balls. But these balls also have a 2-fold rotational symmetry. A cube has nine planes of mirror symmetry, while some soccer balls have fifteen![2]

    sources:
    [1] https://blender.stackexchange.com/questions/41298/asymmetrical-basketball  (visited on May 21, 2017).
    [2] John Horton Conway. The Symmetries of Things, p. 12
    [3] https://math.stackexchange.com/questions/688749/number-of-reflection-symmetries-of-a-basketball (visited on May 21, 2017).

     
  • Justo Balderas 5:44 pm on May 21, 2017 Permalink | Reply
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    Real Estate 

    Week 2: Vectors


    DIBS: 3D weight matrices in modeling real estate prices

    “Vector” can be pretty much just a fancy word for “list”. Specifically, an ordered list of numbers. [1]

    For example, let’s say that you were doing some analytics about house prices, and the only features you cared about were square footage and price. You might model each house with a pair of numbers: the first indicating square footage, and the second indicating price. Since the length of this vector or list is two (a pair), this is two dimensional or 2D. [1]

    2d vector house price
    This is a very simplified way of knowing house prices in real estate. There are other factors such as amenities (parking, good view, bedrooms, etc.) or even floor level (level 1, level 2, level 3, etc.). An example would be “3D weight matrices in modeling real estate prices”.[2]

    sources:
    [1] 3Blue1Brown. Vectors, what even are they? URL: https://youtu.be/fNk_zzaMoSs (visited on May 20, 2017).

    [2] (2017). Int-arch-photogramm-remote-sens-spatial-inf-sci.net. Retrieved 20 May 2017, from http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLII-2-W2/123/2016/isprs-archives-XLII-2-W2-123-2016.pdf

     
  • Justo Balderas 12:34 am on January 20, 2017 Permalink | Reply
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    Justo 

    Week 1: Introduce yourself


    • Hi, I’m Justin Balderas. ‘Justin’: baka ‘di ako tumingin agad. ‘Justo’: Yaaaaan, sure titingin agad ako. 😀
    • Huhu, nakakahiya, pero palag-palag.
    • Greatest weakness. Sa basketball lang ako nagiging analytical. Nyahaha. Jk. ‘Di ko kasi agad nakita yung payoff nung bago pa ako mag high school eh, kaya eto, mahina ang pundasyon.
    • G.
     
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