Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as theta3) and van der Pol (involving terms such as theta2theta), and the nonlinear elastic functions identified by Duffing (involving terms such as theta3), constitute elementary nonlinear components for the assembling of self-sustained oscillators, Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as theta2theta3 and thetatheta2, and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.
Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as theta3) and van der Pol (involving terms such as theta2theta), and the nonlinear elastic functions identified by Duffing (involving terms such as theta3), constitute elementary nonlinear components for the assembling of self-sustained oscillators, Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as theta2theta3 and thetatheta2, and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.
When comparing alternative courses of action, modern military decision makers often must consider both the military effectiveness and the ethical consequences of the available alternatives. The basis, design, calibration, and performance of a principles-based computational model of ethical considerations in military decision making are reported in this article. The relative ethical violation (REV) model comparatively evaluates alternative military actions based upon the degree to which they violate contextually relevant ethical principles. It is based on a set of specific ethical principles deemed by philosophers and ethicists to be relevant to military courses of action. A survey of expert and non-expert human decision makers regarding the relative ethical violation of alternative actions for a set of specially designed calibration scenarios was conducted to collect data that was used to calibrate the REV model. Perhaps unsurprisingly, the survey showed that people, even experts, disagreed greatly amongst themselves regarding the scenarios' ethical considerations. Despite this disagreement, two significant results emerged. First, after calibration the REV model performed very well in terms of replicating the ethical assessments of human experts for the calibration scenarios. The REV model outperformed an earlier model that was based on tangible consequences rather than ethical principles, that earlier model performed comparably to human experts, the experts outperformed human non-experts, and the non-experts outperformed random selection of actions. All of these performance comparisons were measured quantitatively and confirmed with suitable statistical tests. Second, although humans tended to value some principles over others, none of the ethical principles involved-even the principle of not harming civilians-completely overshadowed all of the other principles.
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