A Guide to Evaluating Marine Spatial Plans

Marine spatial plans are being developed in over 40 countries around the world, to distribute human activities in marine areas more sustainably and achieve ecological, social, and economic objectives. Monitoring and evaluation are often considered only after a plan has been developed. This guide will help marine planners and managers, monitor and evaluate the success of marine plans in achieving real results and outcomes. This report emphasizes the importance of early integration of monitoring and evaluation in the planning process, the importance of measurable and specific objectives, clear management actions, relevant indicators and targets, and involvement of stakeholders throughout the planning process.

Signal reconstruction from the magnitude of subspace components

We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature conditions, that require at least a quadratic number of subspaces. Moreover, we address reconstruction under the erasure of a subset of the norms; using the concepts of $p$-fusion frames and list decoding, we propose an algorithm that outputs a finite list of candidate signals, one of which is the correct one. In the random setting, we show that a set of subspaces chosen at random and of cardinality scaling linearly in the ambient dimension allows for exact reconstruction with high probability by solving the feasibility problem of a semidefinite program

Metric entropy, n-widths, and sampling of functions on manifolds

We first investigate on the asymptotics of the Kolmogorov metric entropy and nonlinear n-widths of approximation spaces on some function classes on manifolds and quasi-metric measure spaces. Secondly, we develop constructive algorithms to represent those functions within a prescribed accuracy. The constructions can be based on either spectral information or scattered samples of the target function. Our algorithmic scheme is asymptotically optimal in the sense of nonlinear n-widths and asymptotically optimal up to a logarithmic factor with respect to the metric entropy

The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals. Our results solve a few open problems stated in the recent literature. Furthermore, we show how the algebraic estimation problem can be solved by a closed-form algebraic estimation technique, termed ideal regression, providing non-asymptotic success guarantees

Optimal configurations of lines and a statistical application

Motivated by the construction of confidence intervals in statistics, we study optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$. For small $d$, we determine line sets that numerically minimize a wide variety of potential functions among all configurations of $2^d-1$ lines through the origin. Numerical experiments verify that our findings enable to assess efficiently the tightness of a bound arising from the statistical literature.Comment: 13 page