A Primal-Dual Augmented Lagrangian

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual $\ell$1 linearly constrained Lagrangian (pd$\ell$1-LCL) method

Accurate numerical potential and field in razor-thin axisymmetric discs

We demonstrate the high accuracy of the density splitting method to compute the gravitational potential and field in the plane of razor-thin, axially symmetric discs, as preliminarily outlined in Pierens & Hure (2004). Because residual kernels in Poisson integrals are not C^infinity-class functions, we use a dynamical space mapping in order to increase the efficiency of advanced quadrature schemes. In terms of accuracy, results are better by orders of magnitude than for the classical FFT-methods.Comment: 11 pages, 5 color figures, 2 table

There and Back Again: The Study of Mental Disorder and Terrorist Involvement

For the past forty years, researchers studied the relationship between mental disorder and terrorist involvement. The literature developed in four paradigms, each of which differs in terms of their empirical evidence, the specific mental disorders studied, and their conceptualizations of terrorist involvement. These paradigms have not, however, witnessed linear and incremental improvements upon one another. Although one paradigm has generally tended to dominate a temporal period, many false assumptions and incorrect interpretations of earlier work permeate into today’s discourse. This paper provides a history of the study of mental disorders and the terrorist. First, we briefly outline the core fundamental principles of the first two paradigms, The paper then outlines the core arguments produced by the seminal reviews conducted in paradigm three. We highlight how these findings were consistently misinterpreted in subsequent citations. We then highlight recent innovations in the study of terrorism and mental disorder since the various influential literature reviews of 1997-2005. We conclude by outlining how future research in this area may improve in the coming years by broadening our understanding of both terrorist involvement and psychopathology away from simple dichotomous thinking

A False Dichotomy? Mental Illness and Lone-Actor Terrorism

We test whether significant differences in mental illness exist in a matched sample of lone- and group-based terrorists. We then test whether there are distinct behavioral differences between lone-actor terrorists with and without mental illness. We then stratify our sample across a range of diagnoses and again test whether significant differences exist. We conduct a series of bivariate, multivariate, and multinomial statistical tests using a unique dataset of 119 lone-actor terrorists and a matched sample of group-based terrorists. The odds of a lone-actor terrorist having a mental illness is 13.49 times higher than the odds of a group actor having a mental illness. Lone actors who were mentally ill were 18.07 times more likely to have a spouse or partner who was involved in a wider movement than those without a history of mental illness. Those with a mental illness were more likely to have a proximate upcoming life change, more likely to have been a recent victim of prejudice, and experienced proximate and chronic stress. The results identify behaviors and traits that security agencies can utilize to monitor and prevent lone-actor terrorism events. The correlated behaviors provide an image of how risk can crystalize within the individual offender and that our understanding of lone-actor terrorism should be multivariate in nature

Is There a Nexus Between Terrorist Involvement and Mental Health in the Age of the Islamic State?

The wave of Islamic State-linked terrorism experienced in the West over the past couple of years has rekindled debates surrounding mental disorders and terrorist engagement. A very preliminary survey by the authors found that out of 55 attacks in the West where the 76 individuals involved were possibly influenced by the Islamic State, according to media reports, 27.6% had a history of apparent psychological instability, a percentage comparable to that found in the general population. This figure is driven largely by individuals inspired by the Islamic State, as opposed to those directed by it, however. The percentage is likely overinflated for several noteworthy reasons, including poor reporting, low benchmarks, and the tendency to overuse mental health problems as a ‘silver-bullet’ explanation for terrorist involvement. The relationship is, in fact, far more complex than typically presented

Psychological distress and terrorist engagement: Measuring, correlating, and sequencing its onset with negative life events, social factors, and protective factors

This article employs probability-based modelling to unpack the complex and multifaceted individual, social, and psychological processes that may provide psychological protection for individuals engaged with terrorist groups. We outline the predictors of the onset of psychological distress across two phases of terrorist involvement (pre-engagement and engagement). Using a dataset of 96 terrorist autobiographies, we conduct sequence analyses to pinpoint the onset of psychological problems and the experiences that preceded and followed this onset. The results demonstrate a complexity in the relationship between mental disorders and terrorist engagement, as well as the heterogeneity of the lived experience of “being” a terrorist. The experience of psychological distress was mediated by numerous factors and the combination of these factors. The evidence suggests that, in certain cases, individual and group resilience may be a protective factor when an individual faces negative experiences. The presence of protective factors may not be sufficient to explain why group-actor terrorists present with a lower than expected prevalence of mental disorder. Future work should examine whether experiences commonly viewed as risk factors may be more useful in examining the occurrence of psychopathology in terrorists

Hybrid Superconductor-Quantum Point Contact Devices using InSb Nanowires

Proposals for studying topological superconductivity and Majorana bound states in nanowires proximity coupled to superconductors require that transport in the nanowire is ballistic. Previous work on hybrid nanowire-superconductor systems has shown evidence for Majorana bound states, but these experiments were also marked by disorder, which disrupts ballistic transport. In this letter, we demonstrate ballistic transport in InSb nanowires interfaced directly with superconducting Al by observing quantized conductance at zero-magnetic field. Additionally, we demonstrate that the nanowire is proximity coupled to the superconducting contacts by observing Andreev reflection. These results are important steps for robustly establishing topological superconductivity in InSb nanowires

Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140440/1/6.2014-2594.pd