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pro vyhledávání: '"Finch BE"'
Autor:
Finch, Steven
Dumitru Popa found asymptotic expansions for certain nonlinear recurrences, but left open the numerical evaluation of associated constants. We address this issue. A change of variables involving reciprocals and the algorithm of Mavecha & Laohakosol p
Externí odkaz:
http://arxiv.org/abs/2412.11806
Autor:
Finch, Steven
The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/2411.16062
Autor:
Bang, Hayeon, Choi, Eunjin, Finch, Megan, Doh, Seungheon, Lee, Seolhee, Lee, Gyeong-Hoon, Nam, Juhan
While piano music has become a significant area of study in Music Information Retrieval (MIR), there is a notable lack of datasets for piano solo music with text labels. To address this gap, we present PIAST (PIano dataset with Audio, Symbolic, and T
Externí odkaz:
http://arxiv.org/abs/2411.02551
Autor:
Finch, Steven
N. G. de Bruijn (1958) studied the asymptotic expansion of iterates of sin$(x)$ with $0 < x \leq \pi/2$. Bencherif & Robin (1994) generalized this result to increasing analytic functions $f(x)$ with an attractive fixed point at 0 and $x > 0$ suitably
Externí odkaz:
http://arxiv.org/abs/2411.01591
Autor:
Cheng, Zerui, Contente, Edoardo, Finch, Ben, Golev, Oleg, Hayase, Jonathan, Miller, Andrew, Moshrefi, Niusha, Nasery, Anshul, Nailwal, Sandeep, Oh, Sewoong, Tyagi, Himanshu, Viswanath, Pramod
Artificial Intelligence (AI) has steadily improved across a wide range of tasks. However, the development and deployment of AI are almost entirely controlled by a few powerful organizations that are racing to create Artificial General Intelligence (A
Externí odkaz:
http://arxiv.org/abs/2411.03887
The prosody of a spoken utterance, including features like stress, intonation and rhythm, can significantly affect the underlying semantics, and as a consequence can also affect its textual translation. Nevertheless, prosody is rarely studied within
Externí odkaz:
http://arxiv.org/abs/2410.24019
Autor:
Finch, Steven
We treat three recurrences involving square roots, the first of which arises from an infinite simple radical expansion for the Golden mean, whose precise convergence rate was made famous by Richard Bruce Paris in 1987. A never-before-seen proof of an
Externí odkaz:
http://arxiv.org/abs/2410.02114
Autor:
Finch, Steven
We treat three cubic recurrences, two of which generalize the famous iterated map $x \mapsto x (1-x)$ from discrete chaos theory. A feature of each asymptotic series developed here is a constant, dependent on the initial condition but otherwise intri
Externí odkaz:
http://arxiv.org/abs/2409.15175
Autor:
Finch, Steven
Standard techniques for treating linear recurrences no longer apply for quadratic recurrences. It is not hard to determine asymptotics for a specific parametrized model over a wide domain of values (all $p \neq 1/2$ here). The gap between theory and
Externí odkaz:
http://arxiv.org/abs/2409.03510