Migration-selection balance at multiple loci and selection on dominance and recombination

A steady influx of a single deleterious multilocus genotype will impose genetic load on the resident population and leave multiple descendants carrying various numbers of the foreign alleles. Provided that the foreign types are rare at equilibrium, and that all immigrant genes will eventually be eliminated by selection, the population structure can be inferred explicitly from the deterministic branching process taking place within a single immigrant lineage. Unless the migration and recombination rates were high, this simple method was a very close approximation to the simulated migration-selection balance with all possible multilocus genotypes considered.Comment: includes 6 figures and a Supporting Information. Mathematica notebook where the numerical results were obtained is available upon reques

An Optimal Control Theory for the Traveling Salesman Problem and Its Variants

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.Comment: 24 pages, 8 figure

Polarimetric modeling of corotating interaction regions (CIRs) threading massive-star winds

Massive star winds are complex radiation-hydrodynamic (sometimes magnetohydrodynamic) outflows that are propelled by their enormously strong luminosities. The winds are often found to be structured and variable, but can also display periodic or quasi-periodic behavior in a variety of wind diagnostics. The regular variations observed in putatively single stars, especially in UV wind lines, have often been attributed to corotating interaction regions (CIRs) like those seen in the solar wind. We present light curves for variable polarization from winds with CIR structures. We develop a model for a time-independent CIR based on a kinematical description. Assuming optically thin electron scattering, we explore the range of polarimetric light curves that result as the curvature, latitude, and number of CIRs are varied. We find that a diverse array of variable polarizations result from an exploration of cases. The net polarization from an unresolved source is weighted more toward the inner radii of the wind. Given that most massive stars have relatively fast winds compared to their rotation speeds, CIRs tend to be conical at inner radii, transitioning to a spiral shape at a few to several stellar radii in the wind. Winds with a single CIR structure lead to easily identifiable polarization signatures. By contrast allowing for multiple CIRs, all emerging from a range of azimuth and latitude positions at the star, can yield complex polarimetric behavior. Although our model is based on some simplifying assumptions, it produces qualitative behavior that we expect to be robust, and this has allowed us to explore a wide range of CIR configurations that will prove useful for interpreting polarimetric data.Comment: accepted to A&

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

Implementations of the Universal Birkhoff Theory for Fast Trajectory Optimization

This is part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computational grid is selected from any one of the Legendre and Chebyshev family of node points, be it Lobatto, Radau or Gauss, then, the resulting collection of trajectory optimization methods satisfy the hypotheses required for the universal Birkhoff theory to hold. All of these grid points can be generated at an $\mathcal{O}(1)$ computational speed. Furthermore, all Birkhoff-generated solutions can be tested for optimality by a joint application of Pontryagin's- and Covector-Mapping Principles, where the latter was developed in Part~I. More importantly, the optimality checks can be performed without resorting to an indirect method or even explicitly producing the full differential-algebraic boundary value problem that results from an application of Pontryagin's Principle. Numerical problems are solved to illustrate all these ideas. The examples are chosen to particularly highlight three practically useful features of Birkhoff methods: (1) bang-bang optimal controls can be produced without suffering any Gibbs phenomenon, (2) discontinuous and even Dirac delta covector trajectories can be well approximated, and (3) extremal solutions over dense grids can be computed in a stable and efficient manner

The transition of GTDS to the Unix workstation environment

Future Flight Dynamics systems should take advantage of the possibilities provided by current and future generations of low-cost, high performance workstation computing environments with Graphical User Interface. The port of the existing mainframe Flight Dynamics systems to the workstation environment offers an economic approach for combining the tremendous engineering heritage that has been encapsulated in these systems with the advantages of the new computing environments. This paper will describe the successful transition of the Draper Laboratory R&D version of GTDS (Goddard Trajectory Determination System) from the IBM Mainframe to the Unix workstation environment. The approach will be a mix of historical timeline notes, descriptions of the technical problems overcome, and descriptions of associated SQA (software quality assurance) issues

Size Matters: Large Objects Capture Attention in Visual Search

Can objects or events ever capture one's attention in a purely stimulus-driven manner? A recent review of the literature set out the criteria required to find stimulus-driven attentional capture independent of goal-directed influences, and concluded that no published study has satisfied that criteria. Here visual search experiments assessed whether an irrelevantly large object can capture attention. Capture of attention by this static visual feature was found. The results suggest that a large object can indeed capture attention in a stimulus-driven manner and independent of displaywide features of the task that might encourage a goal-directed bias for large items. It is concluded that these results are either consistent with the stimulus-driven criteria published previously or alternatively consistent with a flexible, goal-directed mechanism of saliency detection

The role of plant functional trade-offs for biodiversity changes and biome shifts under scenarios of global climatic change

The global geographic distribution of biodiversity and biomes is determined by species-specific physiological tolerances to climatic constraints. Current vegetation models employ empirical bioclimatic relationships to predict present-day vegetation patterns and to forecast biodiversity changes and biome shifts under climatic change. In this paper, we consider trade-offs in plant functioning and their responses under climatic changes to forecast and explain changes in plant functional richness and shifts in biome geographic distributions. <br><br> The Jena Diversity model (JeDi) simulates plant survival according to essential plant functional trade-offs, including ecophysiological processes such as water uptake, photosynthesis, allocation, reproduction and phenology. We use JeDi to quantify changes in plant functional richness and biome shifts between present-day and a range of possible future climates from two SRES emission scenarios (A2 and B1) and seven global climate models using metrics of plant functional richness and functional identity. <br><br> Our results show (i) a significant loss of plant functional richness in the tropics, (ii) an increase in plant functional richness at mid and high latitudes, and (iii) a pole-ward shift of biomes. While these results are consistent with the findings of empirical approaches, we are able to explain them in terms of the plant functional trade-offs involved in the allocation, metabolic and reproduction strategies of plants. We conclude that general aspects of plant physiological tolerances can be derived from functional trade-offs, which may provide a useful process- and trait-based alternative to bioclimatic relationships. Such a mechanistic approach may be particularly relevant when addressing vegetation responses to climatic changes that encounter novel combinations of climate parameters that do not exist under contemporary climate