Published as: arxiv.org/pdf/2304.03442.pdf Generative Agents: Interactive Simulacra of Human Behavior by Park et al.
AI Agents Behaving Like Humans by Prompt Engineering (2023)
Source. See sections: "Example 1 - N even", "Example 2 - N odd" and "Representation in terms of sines and cosines" of www.statlect.com/matrix-algebra/discrete-Fourier-transform-of-a-real-signal
The transform still has complex numbers.
Summary:Therefore, we only need about half of to represent the signal, as the other half can be derived by conjugation.
- is real
"Representation in terms of sines and cosines" from www.statlect.com/matrix-algebra/discrete-Fourier-transform-of-a-real-signal then gives explicit formulas in terms of .
NumPy for example has "Real FFTs" for this: numpy.org/doc/1.24/reference/routines.fft.html#real-ffts
DFT of with 25 points
. Source at: numpy/fft_plot.py. This plot illustrates how the DFT of a real signal is symmetric around the middle point, and so only half of the transform points are needed to reconstruct the original signal. We also see how the phase of the sinusoids determines if their DFT components are real or imaginary.An efficient algorithm to calculate the discrete Fourier transform.
Leo Szilard: The Genius Behind the Bomb
. Source. 1992. TODO an external link to the production? Producers credited at end: Helen Weiss and Alain Jehlen. As indicated at: archive.org/details/TheGeniusBehindtheBomb it was apparently produced by WGBH, public radio station from Boston.Ciro Santilli does the same via Google searches and Twitter/Reddit searches for himself, you can't invent anything new nowadays:
Kibo was known for his high-volume but thoughtful posts, but achieved Usenet celebrity circa 1991 by writing a small script to grep his entire Usenet feed for instances of his name, and then answering personally whenever and wherever he was mentioned, giving the illusion that he was personally reading the entire feed.
Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.
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