14 problems

RKHA Leibniz-rule conjecture. An analogous characterization should hold for unitary groups of composition operators on RKHAs: satisfying the Leibniz rule should characterize genera…

Analytic-choice conjecture. The degree lies strictly above every $\lim^{(n)}$; hence $\mathrm{SCI}_{\mathrm{TTE}}=\infty$, and it may coincide with a known “analytic choice” princi…

Let $\cX=\{x_j\}_{j=1}^d$ be a set of data points and, for each $x_j\in\cX$, let $\cX_j=\{x_j,u_{jl},x_{jl}^+\}_{l=1}^{d_j}$ be collected data triplets satisfying the stated assump…

Prevalence conjecture. If the ergodic transformation $T\in\mathrm{MPT}$ has discrete spectrum, then $\mathcal{U}=\mathcal{U}_T$ has a prevalent set of cyclic vectors in $L^2_\mu$.

Slow-convergence conjecture. The convergence of the bounds as $\alpha$ increases is slow because, for degree-$\alpha$ polynomial $\varphi$, the expression for $\mathcal{L}\varphi$…

Let $N$ be the number of cells in an elementary cellular automaton, and consider the maximum period of its dynamics and the associated Koopman eigenvalues on the unit circle. Diver…

Let $N$ be the number of cells in an elementary cellular automaton, and let $csigma$ denote the set of different Koopman eigenvalues in the limit $N\to\infty$. Let $\aleph_0$ and…

The fluidic pinball is an unsteady flow around three cylinders arranged on an equidistant triangle, governed by the two-dimensional incompressible Navier–Stokes equations. Chaotic-…

The robotic fish is considered in a confined space, where collisions with the side wall and unmodeled boundary conditions may affect its trajectory-tracking performance. Wall-colli…

Convolutional-coordinate error-bound conjecture. Although these coordinates are observed to be optimally parsimonious for finite discrete spectrum systems, restrictive error bounds…

Polynomial derivative and error-bound conjecture. A polynomial bound should exist for the derivatives of the singular components in terms of $k$, and consequently a polynomial or e…

A continuous spectrum is a continuous range of observed frequencies, as occurs in nonlinear systems such as the Duffing oscillator; Koopman models may use deep neural networks (DNN…

Let a dynamical system have a bounded attractor with a basin of attraction that can be properly “coordinatized”. Let the associated Koopman operator act on a natural space of obser…

Let a dynamical system have a basin of attraction that can be properly “coordinatized”, and let its associated Koopman operator act on a natural space of observables. Polynomial-ri…