Reduction in social learning and increased policy uncertainty about harmful intent is associated with pre-existing paranoid beliefs: evidence from modelling a modified serial dictator game.

Current computational models suggest that paranoia may be explained by stronger higher-order beliefs about others and increased sensitivity to environments. However, it is unclear whether this applies to social contexts, and whether it is specific to harmful intent attributions, the live expression of paranoia. We sought to fill this gap this by fitting a computational model to data (n = 1754) from a modified serial dictator game, to explore whether pre-existing paranoia could be accounted by specific alterations to cognitive parameters characterising harmful intent attributions. We constructed a ‘Bayesian brain’ model of others’ intent, which we fitted to harmful intent and self-interest attributions made over 18 trials, across three different partners. We found that pre-existing paranoia was associated with greater uncertainty about other’s actions. It moderated the relationship between learning rates and harmful intent attributions, making harmful intent attributions less reliant on prior interactions. Overall, the magnitude of harmful intent attributions was directly related to their uncertainty, and importantly, the opposite was true for self-interest attributions. Our results explain how pre-existing paranoia may be the result of an increased need to attend to immediate experiences in determining intentional threat, at the expense of what is already known, and more broadly, they suggest that environments that induce greater probabilities of harmful intent attributions may also induce states of uncertainty, potentially as an adaptive mechanism to better detect threatening others. Importantly, we suggest that if paranoia were able to be explained exclusively by core domain-general alterations we wouldn’t observe differential parameter estimates underlying harmful-intent and self-interest attributions.

S197. PAVLOVIAN CONDITIONED HALLUCINATIONS TASKS AND PSYCHOMETRIC THRESHOLDING IN ENRICHED ONLINE SAMPLE

Background The predictive coding framework of perception postulates that we automatically infer what is around us by combining our sensory input with our prior beliefs. Mathematical models based in Bayesian statistics can describe this process, elucidating both typical as well as atypical brain processes, such as emergence of hallucinations. A previous study using a Pavlovian conditioning task showed that hallucinations are a result of over-weighting of prior beliefs over incoming sensory evidence. Participants with Auditory Verbal Hallucinations (AVH) were more susceptible to auditory conditioned hallucinations (ACH) than individuals without AVH, regardless of a diagnosis of psychosis. This suggests a common underlying mechanism for the emergence of hallucinations irrespective of functional status. To further investigate these mechanisms, we developed a visual conditioned hallucinations (VCH) task, modeled after the original ACH task. Together, these tasks can elucidate the specificity of conditioned hallucinations with regards to sensory modality. In addition to the deployment of the VCH, we also tested the feasibility of the first known online deployment of QUEST, an adaptive psychometric thresholding method, in a targeted population. Methods Task Methodology. Individual trials of the task consist of simultaneous presentation of a faintly-presented (low-contrast) visual stimulus (Gaussian stripes embedded in visual white noise) and a salient auditory stimulus (loud tone). An association between visual and auditory stimuli is established, followed by testing of the strength of this association by presenting the auditory stimulus alone. Trials where the visual stimulus is not presented, but nevertheless reported to be perceived are considered as CH trials. Data Collection and Analysis. Subjects were recruited on two platforms, the Amazon-powered Mechanical Turk (MTurk) and the COPE Project an initiative targeted at individuals with unusual experiences. Analyses were conducted by pooling across the four groups and grouping based on presence of visual or auditory hallucinations, creating four groups: AH+/VH+, AH+/VH-, AH-/VH+, AH-/VH-. Between-group differences were analyzed using two-sample t-tests. Results The responses of participants across the board, both in the control sample and in those with perceptual experiences, validates the efficacy of using the QUEST thresholding paradigm to predict response to threshold levels. Participants who were assigned VH+ groups showed a significantly higher rate of reporting CHs, compared to the control group with no hallucinatory experiences (p < 0.01). Similarly, participants assigned to AH+ groups also showed a significantly higher rate of reporting CHs (p < 0.01). Differential parameter values for a computational model assessing perceptual inference were computational signatures of CH were also examined between groups, as were neural signatures encoding visual versus auditory-mediated conditioned hallucinations. Discussion In this study, we show the feasibility of psychometric experiments in a targeted online sample of individuals with unusual experiences. We also demonstrate that the differential parameter values of the computational modeling of visually conditioned hallucinations differentiate between individuals with and without hallucinations, leading to better understanding of the neural signatures of hallucinations and potential therapeutic targets in clinical populations.

Catastrophes in Optimal Control

System optimization over a parameter space produces optimal solutions which lie on the bifurcation set of the ambient space. As such, the optimality (quality) metric (as a function of the parameters) is highly sensitive to the parameters, to the point of inducing instability for differential parameter variations. Singularities in this function diffeomorphically induce corresponding degenerate singularities in the optimal closed-loop characteristic polynomials, which serves as a signature for potential catastrophic loss of quality that is most easily exhibited by the resulting dynamic instability. In this paper, we examine the loss of quality in H∞ and related optimal systems via these diffeomorphic degenerate closed-loop poles.

The differential parameter method for multifrequency airborne resistivity mapping

Helicopter EM resistivity mapping began to be accepted as a means of geologic mapping in the late 1970s. The data were first displayed as plan maps and images. Some 10 years later, sectional resistivity displays became available using the same “pseudolayer” half‐space resistivity algorithm developed by Fraser and the new centroid depth algorithm developed by Sengpiel. Known as Sengpiel resistivity sections, these resistivity/depth images proved to be popular for the display of helicopter electromagnetic (EM) data in conductive environments. A limitation of the above resistivity and depth algorithms is that the resulting Sengpiel section may imply that the depth of exploration of the EM system is substantially less than is actually the case. For example, a target at depth may be expressed in the raw data, but its appearance on the Sengpiel section may be too shallow (which is a problem with the depth algorithm), or it may not even appear at all (which is a problem with the resistivity algorithm). An algorithm has been adapted from a ground EM analytic method that yields a parameter called the differential resistivity, which is plotted at the differential depth. The technique yields the true resistivity when the half‐space is homogeneous. It also tracks a dipping target with greater sensitivity and to greater depth than does the Sengpiel display method. The input parameters are the apparent resistivity and apparent depth from the pseudolayer half‐space algorithm and the skin depth for the various frequencies. The output parameters are differential resistivity and differential depth, which are computed from pairs of adjacent frequencies.

Direct Determination of Stresses in Plane Elasticity Problems Based on the Properties of Isostatics

An experimental method is developed for the calculation of stresses in plane elasticity problems. The method consists substantially in determining a function of the complex variable representing the field of isostatics. This function has a convenient form so that the boundary conditions can be expressed by simple relations. From the isostatics, which are traced experimentally, the differential parameter of first order h can be calculated all over the field. The components of stresses are expressed by relations depending on boundary conditions and the parameter h. The method is applied to two particular problems of plane elasticity and a comparison of the results obtained by this method and by analytic methods is provided.

IX.—Harmonic Riemannian Spaces

In this paper we consider a new class of Riemannian spaces which arise in the theory of the solution of the tensor generalisation of Laplace's equation ∇2V = o. To obtain this generalisation Beltrami's second differential parameter is defined in terms of the metricof the associated n-dimensional Riemannian space by the usual formulæwhere denotes the Christoffel symbol . The generalised Laplace's equation is then Δ2V = o. For simplicity the quadratic differential form (1.1) is taken to be positive definite, which involves no essential loss of generality.