On the performance of algorithms for the minimization of ℓ1\ell_1-penalized functionals

The problem of assessing the performance of algorithms used for the minimization of an $\ell_1$-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of `approximation isochrones' is introduced. Five different iterative minimization algorithms are tested and compared, as well as two warm-start strategies. Both well-conditioned and ill-conditioned problems are used in the comparison, and the contrast between these two categories is highlighted.Comment: 18 pages, 10 figures; v3: expanded version with an additional synthetic test problem

Toward standard practices for sharing computer code and programs in neuroscience

Computational techniques are central in many areas of neuroscience and are relatively easy to share. This paper describes why computer programs underlying scientific publications should be shared and lists simple steps for sharing. Together with ongoing efforts in data sharing, this should aid reproducibility of research.This article is based on discussions from a workshop to encourage sharing in neuroscience, held in Cambridge, UK, December 2014. It was financially supported and organized by the International Neuroinformatics Coordinating Facility (http://www.incf.org), with additional support from the Software Sustainability institute (http://www.software.ac.uk). M.H. was supported by funds from the German federal state of Saxony-Anhalt and the European Regional Development Fund (ERDF), Project: Center for Behavioral Brain Sciences

Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems

This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto a state-space manifold having reduced dimensionality and possessing a Kahler potential of multi-linear form. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given, and methods for quantum state optimization by Dantzig selection are given.Comment: 104 pages, 13 figures, 2 table

ActivePapers: a platform for publishing and archiving computer-aided research

International audienceThe lack of replicability and reproducibility of scientific studies based on computational methods has lead to serious mistakes in published scientific findings, some of which have been discovered and publicized recently. Many strategies are currently pursued to improve the situation. This article reports the first conclusions from the ActivePapers project, whose goal is the development and application of a computational platform that allows the publication of computational research in a form that enables installation-free deployment, encourages reuse, and permits the full integration of datasets and software into the scientific record. The main finding is that these goals can be achieved with existing technology, but that there is no straightforward way to adapt legacy software to such a framework