SDLS: a Matlab package for solving conic least-squares problems

This document is an introduction to the Matlab package SDLS (Semi-Definite Least-Squares) for solving least-squares problems over convex symmetric cones. The package is shortly presented through the addressed problem, a sketch of the implemented algorithm, the syntax and calling sequences, a simple numerical example and some more advanced features. The implemented method consists in solving the dual problem with a quasi-Newton algorithm. We note that SDLS is not the most competitive implementation of this algorithm: efficient, robust, commercial implementations are available (contact the authors). Our main goal with this Matlab SDLS package is to provide a simple, user-friendly software for solving and experimenting with semidefinite least-squares problems. Up to our knowledge, no such freeware exists at this date

Locally symmetric submanifolds lift to spectral manifolds

In this work we prove that every locally symmetric smooth submanifold gives rise to a naturally defined smooth submanifold of the space of symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs to the locally symmetric manifold. We also present an explicit formula for the dimension of the spectral manifold in terms of the dimension and the intrinsic properties of the locally symmetric manifold

An efficient dual algorithm to solve conic least-square problems

Theme 4 - Simulation et optimisation de systemes complexes - Projet NUMOPTAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.2001 n.4212 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Recommendations for quantifying and reducing uncertainty in climate projections of species distributions.

Projecting the future distributions of commercially and ecologically important species has become a critical approach for ecosystem managers to strategically anticipate change, but large uncertainties in projections limit climate adaptation planning. Although distribution projections are primarily used to understand the scope of potential change-rather than accurately predict specific outcomes-it is nonetheless essential to understand where and why projections can give implausible results and to identify which processes contribute to uncertainty. Here, we use a series of simulated species distributions, an ensemble of 252 species distribution models, and an ensemble of three regional ocean climate projections, to isolate the influences of uncertainty from earth system model spread and from ecological modeling. The simulations encompass marine species with different functional traits and ecological preferences to more broadly address resource manager and fishery stakeholder needs, and provide a simulated true state with which to evaluate projections. We present our results relative to the degree of environmental extrapolation from historical conditions, which helps facilitate interpretation by ecological modelers working in diverse systems. We found uncertainty associated with species distribution models can exceed uncertainty generated from diverging earth system models (up to 70% of total uncertainty by 2100), and that this result was consistent across species traits. Species distribution model uncertainty increased through time and was primarily related to the degree to which models extrapolated into novel environmental conditions but moderated by how well models captured the underlying dynamics driving species distributions. The predictive power of simulated species distribution models remained relatively high in the first 30 years of projections, in alignment with the time period in which stakeholders make strategic decisions based on climate information. By understanding sources of uncertainty, and how they change at different forecast horizons, we provide recommendations for projecting species distribution models under global climate change