Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems

We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with two Hermitian Hamilitonians the latter form a quadruple of Hamiltonians that are related by two time-dependent Dyson equations and two intertwining relations in form of a commutative diagram. Our construction is extended to the entire hierarchy of Hamiltonians obtained from time-dependent Darboux-Crum transformations. 
 As an alternative approach we also discuss the intertwining relations for Lewis-Riesenfeld invariants for Hermitian as well as non-Hermitian Hamiltonians that reduce the time-dependent equations to auxiliary eigenvalue equations. The working of our proposals is discussed for a hierarchy of explicitly time-dependent rational, hyperbolic, Airy function and nonlocal potentials

Extended Limber Approximation

We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in 1/(\ell+1/2). This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large \ell's. We show that the error in ordinary Limber approximation is O(1/\ell^2). We also provide a simple expression for the second order correction to the Limber formula, which improves the accuracy to O(1/\ell^4). This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the zeroth order Limber formula has a large error. We also point out that using \ell instead of (\ell+1/2), as is often done in the literature, spoils the accuracy of the approximation to O(1/\ell).Comment: 7 pages, 6 figure

Development during adolescence of the neural processing of social emotion

In this fMRI study, we investigated the development between adolescence and adulthood of the neural processing of social emotions. Unlike basic emotions (such as disgust and fear), social emotions (such as guilt and embarrassment) require the representation of another's mental states. Nineteen adolescents (10–18 years) and 10 adults (22–32 years) were scanned while thinking about scenarios featuring either social or basic emotions. In both age groups, the anterior rostral medial prefrontal cortex (MPFC) was activated during social versus basic emotion. However, adolescents activated a lateral part of the MPFC for social versus basic emotions, whereas adults did not. Relative to adolescents, adults showed higher activity in the left temporal pole for social versus basic emotions. These results show that, although the MPFC is activated during social emotion in both adults and adolescents, adolescents recruit anterior (MPFC) regions more than do adults, and adults recruit posterior (temporal) regions more than do adolescents

The perception of self-produced sensory stimuli in patients with auditory hallucinations and passivity experiences: evidence for a breakdown in self-monitoring

BACKGROUND: To test the hypothesis that certain psychotic symptomatology is due to a defect in self-monitoring, we investigated the ability of groups of psychiatric patients to differentiate perceptually between self-produced and externally produced tactile stimuli. METHODS: Responses to tactile stimulation were assessed in three groups of subjects: schizophrenic patients; patients with bipolar affective disorder or depression; and normal control subjects. Within the psychiatric groups subjects were divided on the basis of the presence or absence of auditory hallucinations and/or passivity experiences. The subjects were asked to rate the perception of a tactile sensation on the palm of their left hand. The tactile stimulation was either self-produced by movement of the subject's right hand or externally produced by the experimenter. RESULTS: Normal control subjects and those psychiatric patients with neither auditory hallucinations nor passivity phenomena experienced self-produced stimuli as less intense, tickly and pleasant than identical, externally produced tactile stimuli. In contrast, psychiatric patients with these symptoms did not show a decrease in their perceptual ratings for tactile stimuli produced by themselves as compared with those produced by the experimenter. This failure to show a difference in perception between self-produced and externally produced stimuli appears to relate to the presence of auditory hallucinations and/or passivity experiences rather than to the diagnosis of schizophrenia. CONCLUSIONS: We propose that auditory hallucinations and passivity experiences are associated with an abnormality in the self-monitoring mechanism that normally allows us to distinguish self-produced from externally produced sensations

Dam site selection in the north-eastern wheatbelt

Western Australia\u27s wheatbelt farm dams are dug three to eight metres deep and are generally sited in soils which either are inherently impermeable or can be made so during construction. In the eastern and north-eastern wheatbelt, however, only a small proportion of the soils meets these criteria. Dam site selection in these areas therefore depends on a good knowledge ofwhich soils aresuitable and on our being able to locate them efficiently by using surface indications such as surface soil, natural vegetation or topographic features

Mobile Virtual Realities and Portable Magic Circles

Hybrid reality games such as Pokémon GO enable new approaches to embodied space that problematise traditional understandings of play. More recently, smartphones have again become involved in the provision of a new kind of relationship with space: the space of virtual reality. It is the intention of this exploratory chapter to examine mobile virtual reality as part of the continuum of mobile media in the context of two related themes: (1) physical distraction and (2) embodied space. The chapter will consider how this reassessment might provide new understandings of play’s connection to the ordinary space of daily life before expanding upon these issues within the broader context of the “smartphone movement” and concluding with suggested directions for future research within the field