Latest posts tagged with #Chebyshev on Bluesky
Adaptive Neurons for Dynamic Weighting in Neural Networks
Adaptive neurons compute weights as functions using Chebyshev polynomial coefficients. Evaluated on 145 datasets, the model outperformed a MLP on 121, matched 24, and improved in 8% of cases. getnews.me/adaptive-neurons-for-dyn... #adaptivelearning #chebyshev
Chebyshev Coefficient Decay on Tiny Intervals and Quadrature Impact
Researchers derived formulas showing Chebyshev coefficients shrink proportionally to powers of the interval length L as it narrows, with a fixed number of nodes. Read more: getnews.me/chebyshev-coefficient-de... #chebyshev #spectralmethods
(2) Given that there is only one such sequence {z_j}, "c" only appears once on the tree.
Like holy fuck. #MarkovNumbers #MarkovNumber #Chebyshev #ChebyshevPolynomial #ChebyshevPolynomials #Unicity
Okay, actually, this is a total proof outline. Given "c" and treating "b" as a variable, identity III demands strict {z_j} values for each and every "j," in order for the reduced coefficient on each (1.5b)^i to line up with the #ChebyshevPolynomial. #MarkovNumber #MarkovNumbers #Unicity #Chebyshev
#MarkovNumbers #Unicity #Chebyshev #ChebyshevPolynomial #MarkovNumber this is getting close to the generating function for Chebyshev...
#MarkovNumbers #Unicity #Chebyshev #ChebyshevPolynomial #MarkovNumber this is getting close to the generating function for Chebyshev...
Whoops! Corrected #Chebyshev evolution for #MarkovNumbers towards proving #Unicity
Σ(i=0→i=n)(z_n-i*(x_l/z_0)^i)
=z_0*U_n(3y_m/2)
where z_k is the kth Markov number on a branch; z_0 (which is y_m+1) is the base of the branch; y_m is the "host" of that branch; and x_l is the "host" of y_m's branch
I think this game is just about over, and the big winner has my initials. #sine and #cosine of the #logarithm of #markovnumbers in order appear to oscillate with perfectly level routine. I'll have to derive how #sinh and #cosh relate to sin and cosine of ln. #markovnumbers #unicity #chebyshev
Conference presentation subject from this summer. This was a collaboration with math curriculum specialist Samaya Williams, Dustin Ragland from Ableton, and myself. The app was built in MAX MSP & RNBO. Dewey Hulsey did our web design. #music #mued #academia #maxmsp #chebyshev
"Number the next orientations by a method each expansion of a #CayleyDickson Construction, Webster. Then watch what #MarkovNumber Tree branches do in terms of sequentially finer rotations, and #Unicity how they cleverly dodge intercepting one another."
I think I may have it. #Chebyshev
