10 problems

Conditioning conjecture. The global optima of the underlying optimization problem are among the best-conditioned eigenvalues of the rectangular multiparameter eigenvalue problem.

Chen's conjecture. The established sufficient condition $\alpha\leq 1/3$ for strong consistency of the stochastic-gradient identification algorithm is inherently conservative; the…

Radius-selection conjecture. The stagnation radius satisfies

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…

Consider coarse-graining algorithms for dynamical systems, including methods based on weak formulations of the governing equations. Weak-form improvement conjecture. The weak form…

Let $\Phi$ be the regression matrix, let $\hat{\eta}_{\operatorname*{EB}}$ be the empirical Bayes hyper-parameter estimator, and let $\eta_{\operatorname*{b}}^{*}$ denote its limit…

Let EMP I be a minimal excitation and measurement pattern for a cascade network, and distinguish its first and last modules along the cascade. The first module's accuracy is not im…

The estimation methods RLS, SRLS, and KRLS are compared, where the uncertainty set in each method represents possible disturbances or model uncertainty in the system-identification…

Let an excitation and measurement placement (EMP) be an allocation of excitations and measurements in a dynamic network, and let the covariance matrix refer to the theoretical cova…

A networked dynamical system (NDS) is constructed from interconnected subsystems, whose (pseudo) free pole parameters (FPPs) describe subsystem dynamics. Connections determining st…