Francois Lekien

Bio: Francois Lekien is an academic researcher from Princeton University. The author has contributed to research in topics: Interpolation & Radar. The author has an hindex of 9, co-authored 10 publications receiving 2796 citations. Previous affiliations of Francois Lekien include California Institute of Technology & Université libre de Bruxelles.

Collective Motion, Sensor Networks, and Ocean Sampling

Abstract: This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored

Tricubic interpolation in three dimensions

Abstract: The purpose of this paper is to give a local tricubic interpolation scheme in three dimensions that is both C^1 and isotropic. The algorithm is based on a specific 64 × 64 matrix that gives the relationship between the derivatives at the corners of the elements and the coefficients of the tricubic interpolant for this element. In contrast with global interpolation where the interpolated function usually depends on the whole data set, our tricubic local interpolation only uses data in a neighbourhood of an element. We show that the resulting interpolated function and its three first derivatives are continuous if one uses cubic interpolants. The implementation of the interpolator can be downloaded as a static and dynamic library for most platforms. The major difference between this work and current local interpolation schemes is that we do not separate the problem into three one-dimensional problems. This allows for a much easier and accurate computation of higher derivatives of the extrapolated field. Applications to the computation of Lagrangian coherent structures in ocean data are briefly discussed.

Quantifying Uncertainties in Ocean Predictions

Abstract: : A multitude of physical and biological processes occur in the ocean over a wide range of temporal and spatial scales. Many of these processes are nonlinear and highly variable, and involve interactions across several scales and oceanic disciplines. For example, sound propagation is infl uenced by physical and biological properties of the water column and by the seabed. From observations and conservation laws, ocean scientists formulate models that aim to explain and predict dynamics of the sea. This formulation is intricate because it is challenging to observe the ocean on a sustained basis and to transform basic laws into generic but usable models. There are imperfections in both data and model estimates. It is important to quantify such uncertainties to understand limitations and identify the research needed to increase accuracies, which will lead to fundamental progress.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination

Abstract: This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

Real-space refinement in PHENIX for cryo-EM and crystallography.

Abstract: This article describes the implementation of real-space refinement in the phenixreal_space_refine program from the PHENIX suite The use of a simplified refinement target function enables very fast calculation, which in turn makes it possible to identify optimal data-restraint weights as part of routine refinements with little runtime cost Refinement of atomic models against low-resolution data benefits from the inclusion of as much additional information as is available In addition to standard restraints on covalent geometry, phenixreal_space_refine makes use of extra information such as secondary-structure and rotamer-specific restraints, as well as restraints or constraints on internal molecular symmetry The re-refinement of 385 cryo-EM-derived models available in the Protein Data Bank at resolutions of 6 A or better shows significant improvement of the models and of the fit of these models to the target maps

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

Abstract: This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.