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

Sexual Violence against Girls in Schools: Addressing the Gaps between Policy and Practice in Awaso, Ghana

Despite the established relationship between girls\u27 education and several social development outcomes, gender disparities in education remain particularly concerning. Among the many obstacles that still hinder girls’ access to quality education, sexual violence against girls in schools (SVAGS) is one of the most worrying but also one that has received the least attention in light of recent efforts to increase girls’ attendance in school. This article explores the interface between the seemingly solid Ghanaian legal and policy framework to protect children in educational institutions and the high incidence of SVAGS in such institutions. Its purpose is twofold: to identify the major barriers to fighting SVAGS in Awaso, a rural Ghanaian town, and to highlight strategies for lifting those barriers. Using classroom observation, focus group discussions and interviews with students, teachers, parents, NGO staff and government representatives, it explains how lack of knowledge, lack of financial resources, deep-set values and popular perceptions of masculinity, femininity and violence against women and girls contribute to SVAGS

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

The expectancy bias: Expectancy-violating faces evoke earlier pupillary dilation than neutral or negative faces

Humans maintain a negativity bias, whereby they perceive threatening stimuli to be more salient than rewarding or neutral stimuli. Across 6 within-subject experimental comparisons, we tested the hypothesis that humans maintain an even stronger expectancy bias, preferentially processing stimuli that violate mental representations of expected associations. To assess this bias, we measured variations in pupillary dilation as a means of determin- ing attentional arousal in response to neutral, negative and expectancy-violating versions of the same social stimuli: human faces. We conducted three baseline manipulation checks that directly compared neutral faces with threatening (angry) and expectancy-violating (upside-down and Thatcherized) faces, and three bias comparisons that directly compared threatening and expectancy-violating faces with one another. Across these experiments, we found evidence for a dominant expectancy bias in pupillary arousal for social stimuli, whereby expectancy-violating faces produced pupillary dilation earlier than neutral and threatening faces, with Thatcherized faces producing the greatest magnitude of dilation

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

Separation and identification of dominant mechanisms in double photoionization

Double photoionization by a single photon is often discussed in terms of two contributing mechanisms, {\it knock-out} (two-step-one) and {\it shake-off} with the latter being a pure quantum effect. It is shown that a quasi-classical description of knock-out and a simple quantum calculation of shake-off provides a clear separation of the mechanisms and facilitates their calculation considerably. The relevance of each mechanism at different photon energies is quantified for helium. Photoionization ratios, integral and singly differential cross sections obtained by us are in excellent agreement with benchmark experimental data and recent theoretical results.Comment: 4 pages, 5 figure

Iron Bioavailability of Maize Hemoglobin in a Caco-2 Cell Culture Model

: Maize (Zea mays) is an important staple crop in many parts of the world but has low iron bioavailability, in part due to its high phytate content. Hemoglobin is a form of iron that is highly bioavailable, and its bioavailability is not inhibited by phytate. It was hypothesized that maize hemoglobin is a highly bioavailable iron source and that biofortification of maize with iron can be accomplished by overexpression of maize globin in the endosperm. Maize was transformed with a gene construct encoding a translational fusion of maize globin and green fluorescent protein under transcriptional control of the maize 27 kDa γ- zein promoter. Iron bioavailability of maize hemoglobin produced in Escherichia coli and of stably transformed seeds expressing the maize globin−GFP fusion was determined using an in vitro Caco-2 cell culture model. Maize flour fortified with maize hemoglobin was found to have iron bioavailability that is not significantly different from that of flour fortified with ferrous sulfate or bovine hemoglobin but is significantly higher than unfortified flour. Transformed maize grain expressing maize globin was found to have iron bioavailability similar to that of untransformed seeds. These results suggest that maize globin produced in E. coli may be an effective iron fortificant, but overexpressing maize globin in maize endosperm may require a different strategy to increase bioavailable iron content in maiz