Publications by Peter Prevos
Finding antipodes using the globe and ggmap packages
The antipode of each point on the Earth’s surface—the points where the blue and yellow overlap, are the land antipodes. When I was a kid, I was was fascinated by the conundrum of what happens when you drill a hole straight through the centre of the earth. I always believed that I would turn up in Australia. But is this really the case? The...
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Trumpworld Analysis : Ownership Relations in his Business Network
You do not need a machine learning algorithm to predict that the presidency of Donald Trump will be controversial. One of the most discussed aspects of his upcoming reign is the massive potential for conflicts of interest. Trump’s complex business empire is entangled with many aspects of national and international politics. Buzzfeed has mapped...
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Euler Problem 9 : Special Pythagorean Triple
Euler Problem 9 Definition Scatter plot of the legs (a,b) of the first Pythagorean triples with a and b less than 6000. Negative values are included to illustrate the parabolic patterns. By Dearjean13 – Own work, CC BY-SA 4.0, Link A Pythagorean triple is a set of three natural numbers, , for which, . For example: . There exists exactly one P...
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SCADA spikes in Water Treatment Data
SCADA spikes are events in the data stream of water treatment plants or similar installations. These SCADA spikes can indicate problems with the process and could result in an increased risk to public health. The WSAA Health Based Targets Manual specifies a series of decision rules to assess the performance of filtration processes. For example,...
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Euler Problem 10: Summation of Primes
Euler Problem 10 asks for the summation of primes. Computationally this is a simple problem because we can re-use the prime sieve developed for problem 3. When generating a large number of primes the erratic pattern at which they occur is much more interesting than their sum. Mathematicians consider primes the basic building blocks of number theo...
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Lifting the Big Data Veil: Data Science Strategy for Water Utilities
The Data Science Venn Diagram (Conway, 2010). In my job as manager data science for a medium-sized water utility in Australia, I have developed a strategy to increased the amount of value we extract from data. Many businesses that seek the promised benefits of Big Data don’t achieve those because they don’t start with the basics. The most imp...
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Euler Problem 11: Largest Product in a Grid
Euler Problem 11 Definition In the 20×20 grid below, four numbers along a diagonal line have been marked in red. The product of these numbers is 26 × 63 × 78 × 14 = 1,788,696. What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20 by 20 grid? Solution The solution applies ...
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Percentile Calculations in Water Quality Regulations
Percentile calculations can be more tricky than at first meets the eye. A percentile indicates the value below which a percentage of observations fall. Some percentiles have special names, such as the quartile or the decile, both of which are quantiles. This deceivingly simple definition hides the various ways to determine this number. Unfortun...
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Euler Problem 12: Highly Divisible Triangular Number
The divisors of 10 illustrated with Cuisenaire rods: 1, 2, 5, and 10 (Wikipedia). Euler Problem 12 takes us to the realm of triangular numbers and proper divisors. The image on the left shows a hands-on method to visualise the number of divisors of an integer. Cuisenaire rods are learning aids that provide a hands-on way to explore mathematics. E...
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Euler Problem 13: Large Sum of 1000 Digits
Euler Problem 13 asks to add one hundred numbers with fifty digits. This seems like a simple problem where it not that most computers are not designed to deal with numbers with a lot of integers. For example: When asking R to compute this value we get 1.844674e+19, losing most of the digits and limiting the accuracy of the results. Computers s...
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