Strong asymptotics for Jacobi polynomials with varying nonstandard parameters

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$\lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B,$$ with $A$ and $B$ satisfying $A > -1$, $B>-1$, $A+B < -1$. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case the zeros distribute on the set of critical trajectories $\Gamma$ of a certain quadratic differential according to the equilibrium measure on $\Gamma$ in an external field. However, when either $\alpha_n$, $\beta_n$ or $\alpha_n+\beta_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential.Comment: 31 pages, 12 figures. Some references added. To appear in Journal D'Analyse Mathematiqu

Mathematics in Medical Diagnostics - 2022 Proceedings of the 4th International Conference on Trauma Surgery Technology

The 4th event of the Giessen International Conference Series on Trauma Surgery Technology took place on April, the 23rd 2022 in Warsaw, Poland. It aims to bring together practical application research, with a focus on medical imaging, and the TDA experts from Warsaw. This publication contains details of our presentations and discussions

Motor expertise modulates the unconscious processing of human body postures

Little is known about the cognitive background of unconscious visuomotor control of complex sports movements. Therefore, we investigated the extent to which novices and skilled high-jump athletes are able to identify visually presented body postures of the high jump unconsciously. We also asked whether or not the manner of processing differs (qualitatively or quantitatively) between these groups as a function of their motor expertise. A priming experiment with not consciously perceivable stimuli was designed to determine whether subliminal priming of movement phases (same vs. different movement phases) or temporal order (i.e. natural vs. reversed movement order) affects target processing. Participants had to decide which phase of the high jump (approach vs. flight phase) a target photograph was taken from. We found a main effect of temporal order for skilled athletes, that is, faster reaction times for prime-target pairs that reflected the natural movement order as opposed to the reversed movement order. This result indicates that temporal-order information pertaining to the domain of expertise plays a critical role in athletes’ perceptual capacities. For novices, data analyses revealed an interaction between temporal order and movement phases. That is, only the reversed movement order of flight-approach pictures increased processing time. Taken together, the results suggest that the structure of cognitive movement representation modulates unconscious processing of movement pictures and points to a functional role of motor representations in visual perception

Cognitive loading affects motor awareness and movement kinematics but not locomotor trajectories during goal-directed walking in a virtual reality environment.

The primary purpose of this study was to investigate the effects of cognitive loading on movement kinematics and trajectory formation during goal-directed walking in a virtual reality (VR) environment. The secondary objective was to measure how participants corrected their trajectories for perturbed feedback and how participants' awareness of such perturbations changed under cognitive loading. We asked 14 healthy young adults to walk towards four different target locations in a VR environment while their movements were tracked and played back in real-time on a large projection screen. In 75% of all trials we introduced angular deviations of ±5° to ±30° between the veridical walking trajectory and the visual feedback. Participants performed a second experimental block under cognitive load (serial-7 subtraction, counter-balanced across participants). We measured walking kinematics (joint-angles, velocity profiles) and motor performance (end-point-compensation, trajectory-deviations). Motor awareness was determined by asking participants to rate the veracity of the feedback after every trial. In-line with previous findings in natural settings, participants displayed stereotypical walking trajectories in a VR environment. Our results extend these findings as they demonstrate that taxing cognitive resources did not affect trajectory formation and deviations although it interfered with the participants' movement kinematics, in particular walking velocity. Additionally, we report that motor awareness was selectively impaired by the secondary task in trials with high perceptual uncertainty. Compared with data on eye and arm movements our findings lend support to the hypothesis that the central nervous system (CNS) uses common mechanisms to govern goal-directed movements, including locomotion. We discuss our results with respect to the use of VR methods in gait control and rehabilitation

The infuence of skin colour on the experience of ownership in the rubber hand illusion

Racial prejudice is associated with a fundamental distinction between "us" and "them"-a distinction linked to the perceived overlap between representations of the self and others. Implicit prejudice has been shown to reduce the intensity of White individuals' hand ownership sensation as induced by the Rubber Hand Illusion (RHI) with dark rubber hands. However, evidence for this link to implicit prejudice comes from self-report questionnaire data regarding the RHI. As an alternative, we assessed the onset time of the RHI. We hypothesized that onset time of the RHI would be higher for the black compared to the white RH, acting as the mediator between implicit prejudice and magnitude of the RH illusion and proprioceptive drift. As expected, participants took longer to incorporate the black RH and presented lower RH illusion magnitude and a smaller proprioceptive drift for the black RH. Mediation analysis revealed a significant indirect effect of implicit racial bias on proprioceptive drift and magnitude of illusion through onset time to illusion only for the black RH. These findings further illuminate the connection between implicit prejudice and embodied perception, suggesting new perspectives on how implicit biases operate.This work was supported by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq; grant numbers: 466922/2014-0 and 401143/2014-7).info:eu-repo/semantics/publishedVersio

The prediction of visual stimuli influences auditory loudness discrimination

The brain combines information from different senses to improve performance on perceptual tasks. For instance, auditory processing is enhanced by the mere fact that a visual input is processed simultaneously. However, the sensory processing of one modality is itself subject to diverse influences. Namely, perceptual processing depends on the degree to which a stimulus is predicted. The present study investigated the extent to which the influence of one processing pathway on another pathway depends on whether or not the stimulation in this pathway is predicted. We used an action–effect paradigm to vary the match between incoming and predicted visual stimulation. Participants triggered a bimodal stimulus composed of a Gabor and a tone. The Gabor was either congruent or incongruent compared to an action–effect association that participants learned in an acquisition phase.We tested the influence of action–effect congruency on the loudness perception of the tone. We observed that an incongruent–task-irrelevant Gabor stimulus increases participant’s sensitivity to loudness discrimination. An identical result was obtained for a second condition in which the visual stimulus was predicted by a cue instead of an action. Our results suggest that prediction error is a driving factor of the crossmodal interplay between vision and audition

First Person Experience of Body Transfer in Virtual Reality

Background: Altering the normal association between touch and its visual correlate can result in the illusory perception of a fake limb as part of our own body. Thus, when touch is seen to be applied to a rubber hand while felt synchronously on the corresponding hidden real hand, an illusion of ownership of the rubber hand usually occurs. The illusion has also been demonstrated using visuomotor correlation between the movements of the hidden real hand and the seen fake hand. This type of paradigm has been used with respect to the whole body generating out-of-the-body and body substitution illusions. However, such studies have only ever manipulated a single factor and although they used a form of virtual reality have not exploited the power of immersive virtual reality (IVR) to produce radical transformations in body ownership.Principal Findings: Here we show that a first person perspective of a life-sized virtual human female body that appears to substitute the male subjects' own bodies was sufficient to generate a body transfer illusion. This was demonstrated subjectively by questionnaire and physiologically through heart-rate deceleration in response to a threat to the virtual body. This finding is in contrast to earlier experimental studies that assume visuotactile synchrony to be the critical contributory factor in ownership illusions. Our finding was possible because IVR allowed us to use a novel experimental design for this type of problem with three independent binary factors: (i) perspective position (first or third), (ii) synchronous or asynchronous mirror reflections and (iii) synchrony or asynchrony between felt and seen touch.Conclusions: The results support the notion that bottom-up perceptual mechanisms can temporarily override top down knowledge resulting in a radical illusion of transfer of body ownership. The research also illustrates immersive virtual reality as a powerful tool in the study of body representation and experience, since it supports experimental manipulations that would otherwise be infeasible, with the technology being mature enough to represent human bodies and their motion

Dynamic Social Adaptation of Motion-Related Neurons in Primate Parietal Cortex

Social brain function, which allows us to adapt our behavior to social context, is poorly understood at the single-cell level due largely to technical limitations. But the questions involved are vital: How do neurons recognize and modulate their activity in response to social context? To probe the mechanisms involved, we developed a novel recording technique, called multi-dimensional recording, and applied it simultaneously in the left parietal cortices of two monkeys while they shared a common social space. When the monkeys sat near each other but did not interact, each monkey's parietal activity showed robust response preference to action by his own right arm and almost no response to action by the other's arm. But the preference was broken if social conflict emerged between the monkeys—specifically, if both were able to reach for the same food item placed on the table between them. Under these circumstances, parietal neurons started to show complex combinatorial responses to motion of self and other. Parietal cortex adapted its response properties in the social context by discarding and recruiting different neural populations. Our results suggest that parietal neurons can recognize social events in the environment linked with current social context and form part of a larger social brain network

Affective interoceptive inference: Evidence from heart-beat evoked brain potentials.

The perception of internal bodily signals (interoception) is central to many theories of emotion and embodied cognition. According to recent theoretical views, the sensory processing of visceral signals such as one's own heartbeat is determined by top-down predictions about the expected interoceptive state of the body (interoceptive inference). In this EEG study we examined neural responses to heartbeats following expected and unexpected emotional stimuli. We used a modified stimulus repetition task in which pairs of facial expressions were presented with repeating or alternating emotional content, and we manipulated the emotional valence and the likelihood of stimulus repetition. We found that affective predictions of external socially relevant information modulated the heartbeat-evoked potential, a marker of cardiac interoception. Crucially, the HEP changes highly relied on the expected emotional content of the facial expression. Thus, expected negative faces led to a decreased HEP amplitude, whereas such an effect was not observed after an expected neutral face. These results suggest that valence-specific affective predictions, and their uniquely associated predicted bodily sensory state, can reduce or amplify cardiac interoceptive responses. In addition, the affective repetition effects were dependent on repetition probability, highlighting the influence of top-down exteroceptive predictions on interoception. Our results are in line with recent models of interoception supporting the idea that predicted bodily states influence sensory processing of salient external information