We present a set of algorithms for automated simplification of symbolic constants of the form ∑iαixi with αi rational and xi complex. The included algorithms, called SimplifySum2 and implemented in Mathematica, remove redundant terms, attempt to make terms and the full expression real, and remove terms using repeated application of the multipair PSLQ integer relation detection algorithm. Also included are facilities for making substitutions according to user-specified identities. We illustrate this toolset by giving some real-world examples of its usage, including (...) one, for instance, where the tool reduced a symbolic expression of approximately 100 000 characters in size enough to enable manual manipulation to one with just four simple terms.2Available from https://github.com/alexkaiser/SimplifySum. (shrink)

This comment focuses on part III of the book, ‘Carl Schmitt’s 21st Century’, by William Scheuerman. It raises two points. The first point concerns the author’s continuity thesis. According to Scheu...

Unilateral spatial neglect is a disorder characterized by the failure to report, respond to, or orient toward the contralateral side of space to a brain lesion. Current assessment methods often fail to discover milder forms, cannot differentiate between unilateral spatial neglect subtypes and lack ecological validity. There is also a need for treatment methods that target subtypes. Immersive virtual reality systems in combination with eye-tracking have the potential to overcome these shortcomings, by providing more naturalistic environments and tasks, with sensitive (...) and detailed measures. This systematic review examines the state of the art of research on these technologies as applied in the assessment and treatment of USN. As we found no studies that combined immersive VR and ET, we reviewed these approaches individually. The review of VR included seven articles, the ET review twelve. The reviews revealed promising results. All included studies found significant group-level differences for several USN measures. In addition, several studies found asymmetric behavior in VR and ET tasks for patients who did not show signs of USN in conventional tests. Particularly promising features were multitasking in complex VR environments and detailed eye-movement analysis. No VR and only a few ET studies attempted to differentiate USN subtypes, although the technologies appeared appropriate. One ET study grouped USN participants using individual heatmaps, and another differentiated between subtypes on drawing tasks. Regarding ecological validity, although no studies tested the prognostic validity of their assessment methods, VR and ET studies utilized naturalistic tasks and stimuli reflecting everyday situations. Technological characteristics, such as the field of view and refresh rate of the head-mounted displays, could be improved, though, to improve ecological validity. We found no studies that utilized VR or ET technologies for USN treatment up until the search date of the 26th of February 2020. In conclusion, VR-ET-based systems show great potential for USN assessment. VR-ET holds great promise for treatment, for example, by monitoring behavior and adapting and tailoring to the individual person’s needs and abilities. Future research should consider developing methods for individual subtypes and differential diagnostics to inform individual treatment programs. (shrink)

The management of an infant after a decision to withdraw active treatment creates dilemmas. Both lingering death and active killing are undesirable, but palliative interventions can hasten death. We investigated what staff on our neonatal unit thought were the limits of acceptable practice and why. We administered a structured interview to elucidate their views, and asked them to justify their answers. The interviews were analysed quantitatively and qualitatively. A total of 25 participants (15 nurses and 10 doctors) were recruited. 80% (...) emphasized the importance of pain relief following withdrawal, 60% mentioned meeting parental needs at that time. 76% agreed that death can be a desired consequence of withdrawal, yet 52% felt that death should never be hastened. 96% felt that morphine is acceptable after withdrawal, and 72% would give a higher than normal dose if necessary. 56% would stop paralysis at extubation but not reverse it, while 24% would continue paralysis. 16% would consider a drug that ended life instantly in some cases. A wide variety of views emerged, but there were two main positions, a cautious majority, and a more proactive minority. Apparent contradictions within the majority position could be explained using the doctrine of double effect and the acts and omissions distinction. (shrink)