Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$; hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201

Bipartite Graph Learning for Autonomous Task-to-Sensor Optimization

NPS NRP Technical ReportThis study addresses the question of how machine learning/artificial intelligence can be applied to identify the most appropriate 'sensor' for a task, to prioritize tasks, and to identify gaps/unmet requirements. The concept of a bipartite graph provides a mathematical framework for task-to-sensor mapping by establishing connectivity between various high-level tasks and the specific sensors and processes that must be invoked to fulfil those tasks and other mission requirements. The connectivity map embedded in the bipartite graph can change depending on the availability/unavailability of resources, the presence of constraints (physics, operational, sequencing), and the satisfaction of individual tasks. Changes can also occur according to the valuation, re-assignment and re-valuation of the perceived task benefit and how the completion of a specific task (or group of tasks) can contribute to the state of knowledge. We plan to study how machine learning can be used to perform bipartite learning for task-to-sensor planning.Naval Special Warfare Command (NAVSPECWARCOM)N9 - Warfare SystemsThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Bipartite Graph Learning for Autonomous Task-to-Sensor Optimization

NPS NRP Executive SummaryThis study addresses the question of how machine learning/artificial intelligence can be applied to identify the most appropriate 'sensor' for a task, to prioritize tasks, and to identify gaps/unmet requirements. The concept of a bipartite graph provides a mathematical framework for task-to-sensor mapping by establishing connectivity between various high-level tasks and the specific sensors and processes that must be invoked to fulfil those tasks and other mission requirements. The connectivity map embedded in the bipartite graph can change depending on the availability/unavailability of resources, the presence of constraints (physics, operational, sequencing), and the satisfaction of individual tasks. Changes can also occur according to the valuation, re-assignment and re-valuation of the perceived task benefit and how the completion of a specific task (or group of tasks) can contribute to the state of knowledge. We plan to study how machine learning can be used to perform bipartite learning for task-to-sensor planning.Naval Special Warfare Command (NAVSPECWARCOM)N9 - Warfare SystemsThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Bipartite Graph Learning for Autonomous Task-to-Sensor Optimization

NPS NRP Project PosterThis study addresses the question of how machine learning/artificial intelligence can be applied to identify the most appropriate 'sensor' for a task, to prioritize tasks, and to identify gaps/unmet requirements. The concept of a bipartite graph provides a mathematical framework for task-to-sensor mapping by establishing connectivity between various high-level tasks and the specific sensors and processes that must be invoked to fulfil those tasks and other mission requirements. The connectivity map embedded in the bipartite graph can change depending on the availability/unavailability of resources, the presence of constraints (physics, operational, sequencing), and the satisfaction of individual tasks. Changes can also occur according to the valuation, re-assignment and re-valuation of the perceived task benefit and how the completion of a specific task (or group of tasks) can contribute to the state of knowledge. We plan to study how machine learning can be used to perform bipartite learning for task-to-sensor planning.Naval Special Warfare Command (NAVSPECWARCOM)N9 - Warfare SystemsThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Bipartite Graph Learning for Autonomous Task-to-Sensor Optimization

NPS NRP Project PosterThis study addresses the question of how machine learning/artificial intelligence can be applied to identify the most appropriate 'sensor' for a task, to prioritize tasks, and to identify gaps/unmet requirements. The concept of a bipartite graph provides a mathematical framework for task-to-sensor mapping by establishing connectivity between various high-level tasks and the specific sensors and processes that must be invoked to fulfil those tasks and other mission requirements. The connectivity map embedded in the bipartite graph can change depending on the availability/unavailability of resources, the presence of constraints (physics, operational, sequencing), and the satisfaction of individual tasks. Changes can also occur according to the valuation, re-assignment and re-valuation of the perceived task benefit and how the completion of a specific task (or group of tasks) can contribute to the state of knowledge. We plan to study how machine learning can be used to perform bipartite learning for task-to-sensor planning.Naval Special Warfare Command (NAVSPECWARCOM)N9 - Warfare SystemsThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Network analysis identifies weak and strong links in a metapopulation system

The identification of key populations shaping the structure and connectivity of metapopulation systems is a major challenge in population ecology. The use of molecular markers in the theoretical framework of population genetics has allowed great advances in this field, but the prime question of quantifying the role of each population in the system remains unresolved. Furthermore, the use and interpretation of classical methods are still bounded by the need for a priori information and underlying assumptions that are seldom respected in natural systems. Network theory was applied to map the genetic structure in a metapopulation system by using microsatellite data from populations of a threatened seagrass, Posidonia oceanica, across its whole geographical range. The network approach, free from a priori assumptions and from the usual underlying hypotheses required for the interpretation of classical analyses, allows both the straightforward characterization of hierarchical population structure and the detection of populations acting as hubs critical for relaying gene flow or sustaining the metapopulation system. This development opens perspectives in ecology and evolution in general, particularly in areas such as conservation biology and epidemiology, where targeting specific populations is crucial

Introduction to the Special Issue on Individual Differences in Multisensory Perception: An Overview

The world is full of objects that can be perceived through multiple different senses to create an integrated understanding of our environment. Since each of us has different biological and psychological characteristics, different people may perceive the world in quite different ways. However, the questions of how and why our multisensory perceptions differ have not been explored in any great depth. This special issue, arising from a series of British Psychological Society-funded seminars, presents new research and opinions on the impacts of a variety of individual differences on multisensory perception. We hope that readers will enjoy this collection of eight papers on individual differences in multisensory perception arising from developmental changes, autism, Down syndrome, migraine, sensory loss and substitution, and personality

Stellar Collisions and Ultracompact X-ray Binary Formation

(abridged) We report the results of SPH calculations of parabolic collisions between a subgiant or slightly evolved red-giant star and a neutron star (NS). Such collisions are likely to form ultracompact X-ray binaries (UCXBs) observed today in old globular clusters. In particular, we compute collisions of a 1.4 Msun NS with realistically modelled parent stars of initial masses 0.8 and 0.9 Msun, each at three different evolutionary stages (corresponding to three different radii R). The distance of closest approach for the initial orbit varies from 0.04 R (nearly head-on) to 1.3 R (grazing). These collisions lead to the formation of a tight binary, composed of the NS and the subgiant or red-giant core, embedded in an extremely diffuse common envelope (CE) typically of mass ~0.1 to 0.3 Msun. Our calculations follow the binary for many hundreds of orbits, ensuring that the orbital parameters we determine at the end of the calculations are close to final. Some of the fluid initially in the envelope of the (sub)giant, from 0.003 to 0.023 Msun in the cases we considered, is left bound to the NS. The eccentricities of the resulting binaries range from about 0.2 for our most grazing collision to about 0.9 for the nearly head-on cases. In almost all the cases we consider, gravitational radiation alone will cause sufficiently fast orbital decay to form a UCXB within a Hubble time, and often on a much shorter timescale. Our hydrodynamics code implements the recent SPH equations of motion derived with a variational approach by Springel & Hernquist and by Monaghan. Numerical noise is reduced by enforcing an analytic constraint equation that relates the smoothing lengths and densities of SPH particles. We present tests of these new methods to help demonstrate their improved accuracy.Comment: 41 pages, 17 figures, accepted by Ap