17 problems

Unique smoothest spectral submanifold conjecture. Just as in the time-periodic and time-quasiperiodic cases, a unique member of the $W(E,t)$ family of manifolds should be smoother…

Interface-residual conjecture. The quantity $\eta^\Gamma$ can indicate the modelling error caused by replacing the 2D model by the 0D one, and can therefore drive the choice of the…

Let $cmathcal{E}_cperp$ be the natural orthogonal-complement effective subspace defined above, and let $coverline{\bm p}$ be the vector defined in Corollary corresponding to…

Let $\delta^{(\star\star)}_{\Omega_t \to \Omega}$ denote the alternative criterion for comparing a template domain $\Omega_t$ with a target domain $\Omega$, and distinguish the for…

Let $G_k=[g_k^{(1)},g_k^{(2)},\ldots,g_k^{(K)}]$ be a sequence of input sets whose ranges approximate surface distributions at the observable boundary $S\subset\partial\Omega$ as…

Let $\Sigma\subset\mathbb{C}$ be the set of spectral points, and let $V_0$ and $Q_0$ be the solution basis and Lanczos matrix corresponding to the background $q_0=0$. Let $T$ be th…

Optimal space-time reduction conjecture. Optimal space-time reduction can be achieved by an NAR model when the $K$-mode Galerkin system preserves the CFL number of the full model.

Minimality conjecture. If $(\cC(s), \cK(s))$ is $\C^n$--observable and $(\cK(s), \cB(s))$ is $\C^n$--reachable, then there is no lower-order realization, constructible via Petrov--…

Let the new data representation be the eigenbasis-based representation constructed from a Fokker–Planck operator for bundles of numerical simulations. Complexity-reduction conjectu…

Model Boundary Approximation Method (MBAM) is a method for approximating models by exploring their parameter-space boundaries. MBAM conjecture. MBAM may provide a framework for the…

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

Let $\boldsymbol{\mu}$ be a parameter vector, let $\mathcal{D}$ be its parameter domain, and let sampling points be selected in $\mathcal{D}$ for constructing approximation spaces…

Let a biochemical network have drift matrix $A(x_{ss})$ in its dynamics linearised about a stable steady state $x_{ss}$. A network is nearly monotone if removing some interactions…

Let $U$ be the snapshot matrix used in the two-dimensional formulation, and let $U^*U$ be its Gram matrix. Let Algorithm 1.2D denote the matrix-valued inversion algorithm defined i…

Let $v$ be a smooth velocity, and let $\overline{u}_j$ and $\overline{w}_j$ denote the orthogonalized primal and dual snapshots, with widths measured by $\widehat{\gamma}_j^0$ and…

Let $A$ be the relevant self-adjoint operator, let $\tau$ be the sampling interval, let $\eta_0(\mu)$ be the spectral density in the data representation, and let…

Let a biochemical reaction network be augmented with differential equations for conservation laws of its fast truncated subsystem, and solve the tropical equilibration problem for…