John D. Cook | Singular Value Consulting

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A blog by John. D Cook, statistician, mathematician, consultant, manager and professor. While not all posts are directly concerned with statistics, they are all typically engaging and worthwhile.

John D. Cook | Singular Value Consulting

1d ago

I’ve read some math publications from around a century or so ago, and I wondered if I could pull off being a math professor if a time machine dropped me into a math department from the time. I think I’d come across as something of an autistic savant, ignorant of what contemporaries would think of […]
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John D. Cook | Singular Value Consulting

6d ago

Before Copernicus promoted the heliocentric model of the solar system, astronomers added epicycle on top of epicycle, creating ever more complex models of the solar system. The term epicycle is often used derisively to mean something ad hoc and unnecessarily complex. Copernicus’ model was simpler, but it was less accurate. The increasingly complex models before […]
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John D. Cook | Singular Value Consulting

6d ago

Suppose you want to interpolate a set of data points with a combination of sines and cosines. One way to approach this problem would be to set up a system of equations for the coefficients of the sines and cosines. If you have N data points, you will get a system of N equations in […]
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John D. Cook | Singular Value Consulting

1w ago

This is a quick note to mention a connection between two recent posts, namely today’s post about moments and post from a few days ago about the Laplace transform. Let f(t) be a function on [0, ∞) and F(s) be the Laplace transform of f(t). Then the nth moment of f, is equal to then nth derivative […]
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John D. Cook | Singular Value Consulting

1w ago

It’s fascinating that there’s such a thing as the World Jigsaw Puzzle Championship. The winning team of the two-person thousand-piece puzzle round can assemble a Ravensburger puzzle in less than an hour—that’s about 3 -1/2 seconds per piece. It makes you wonder, how could you measure the hardness of a jigsaw puzzle? And what would […]
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John D. Cook | Singular Value Consulting

1w ago

The use of the word “moment” in mathematics is related to its use in physics, as in moment arm or moment of inertia. For a non-negative integer n, the nth moment of a function f is the integral of xn f(x) over the function’s domain. Uniqueness If two continuous functions f and g have all […]
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John D. Cook | Singular Value Consulting

1w ago

In the early days of computing hardware (and actually before) mathematicians put a lot of effort into understanding and mitigating the limitations of floating point arithmetic. They would analyze mundane tasks such as adding a list of numbers and think carefully about the best way to carry out such tasks as accurately as possible. Now […]
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John D. Cook | Singular Value Consulting

1w ago

I’ve been writing code for the Z3 SMT solver for several months now. Here are my findings. Python is used here as the base language. Python/Z3 feels like a two-layer programming model—declarative code for Z3, imperative code for Python. In this it seems reminiscent of C++/CUDA programming for NVIDIA GPUs—in that case, mixed CPU and […]
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John D. Cook | Singular Value Consulting

2w ago

The band-limited expansion of the function f(x) is given by where sinc(x) = sin(πx)/πx. This is also called the sinc expansion, or the Whittaker cardinal after its discoverer E. T. Whittaker [1]. This is called the band-limited expansion of f because each term in the infinite sum is band-limited, i.e. only has Fourier spectrum within […]
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John D. Cook | Singular Value Consulting

2w ago

Sometimes the future state of a system depends not only on the current state (position, velocity, acceleration, etc.) but also on the previous state. Equations for modeling such systems are known as delay differential equations (DDEs), difference differential equations, retarded equations, etc. In a system with hysteresis, it matters not only where you are but […]
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