For wavelets on the interval (when > 1 and the number of vanishing moments is N = de), there are never more than 2N wavelets that overlap (for a given j). Indeed, in the above sums we have for each j and each x: 0 2 j x 0 k 2N 0 1. (Other values of k would place the argument 2 j x 0 k of the wavelet functions outside of the support and would hence only produce zero-terms in the sums.) Hence, k only needs to range from d2 j xe02N +1 through d2 j xe, which corresponds to 2N values of k. Therefore, the same calculation as for Haar wavelets applies, except that the constants C1, C2, C3, c 0 1 , and c 0 2 need to be multiplied by 2N. ACKNOWLEDGMENT D. Hong wishes to thank Ronald DeVore for his advice and Shushuang Man for helpful discussions while writing this correspondence.
In individuals with chronic pain harmless bodily sensations can elicit anticipatory fear of pain resulting in maladaptive responses such as taking pain medication. Here, we aim to broaden the perspective taking into account recent evidence that suggests that interoceptive perception is largely a construction of beliefs, which are based on past experience and that are kept in check by the actual state of the body. Taking a Bayesian perspective, we propose that individuals with chronic pain display a heightened prediction of pain [prior probability p(pain)], which results in heightened pain perception [posterior probability p(pain|sensation)] due to an assumed link between pain and a harmless bodily sensation [p(sensation|pain)]. This pain perception emerges because their mind infers pain as the most likely cause for the sensation. When confronted with a mismatch between predicted pain and a (harmless bodily) sensation, individuals with chronic pain try to minimize the mismatch most likely by active inference of pain or alternatively by an attentional shift away from the sensation. The active inference results in activities that produce a stronger sensation that will match with the prediction, allowing subsequent perceptual inference of pain. Here, we depict heightened pain perception in individuals with chronic pain by reformulating and extending the assumptions of the interoceptive predictive coding model from a Bayesian perspective. The review concludes with a research agenda and clinical considerations.
In everyday life, the motivational value of faces is bound to the contexts in which faces are perceived. Electrophysiological studies have demonstrated that inherent negatively valent contexts modulate cortical face processing as assessed with ERP components. However, it is not well understood whether learned (rather than inherent) and three‐dimensional aversive contexts similarly modulate the neural processing of faces. Using full immersive virtual reality (VR) and mobile EEG techniques, 25 participants underwent a differential fear conditioning paradigm, in which one virtual room was paired with an aversive noise burst (threat context) and another with a nonaversive noise burst (safe context). Subsequently, avatars with neutral or angry facial expressions were presented in the threat and safe contexts while EEG was recorded. Analysis of the late positive potential (LPP), which presumably indicates motivational salience, revealed a significant interaction of context (threat vs. safe) and face type (neutral vs. angry). Neutral faces evoked increased LPP amplitudes in threat versus safe contexts, while angry faces evoked increased early LPP amplitudes regardless of context. In addition to indicating that threat‐conditioned contexts alter the processing of ambiguous faces, the present study demonstrates the successful integration of EEG and VR with particular relevance for affective neuroscience research.
Decoding the rich temporal dynamics of complex sounds such as speech is constrained by the underlying neuronal-processing mechanisms. Oscillatory theories suggest the existence of one optimal perceptual performance regime at auditory stimulation rates in the delta to theta range (< 10 Hz), but reduced performance in the alpha range (10–14 Hz) is controversial. Additionally, the widely discussed motor system contribution to timing remains unclear. We measured rate discrimination thresholds between 4 and 15 Hz, and auditory-motor coupling strength was estimated through a behavioral auditory-motor synchronization task. In a Bayesian model comparison, high auditory-motor synchronizers showed a larger range of constant optimal temporal judgments than low synchronizers, with performance decreasing in the alpha range. This evidence for optimal processing in the theta range is consistent with preferred oscillatory regimes in auditory cortex that compartmentalize stimulus encoding and processing. The findings suggest, remarkably, that increased auditory-motor synchronization might extend such an optimal range towards faster rates.
Expectations are probabilistic beliefs about the future that shape and influence our perception, affect, cognition, and behavior in many contexts. This makes expectations a highly relevant concept across basic and applied psychological disciplines. When expectations are confirmed or violated, individuals can respond by either updating or maintaining their prior expectations in light of the new evidence. Moreover, proactive and reactive behavior can change the probability with which individuals encounter expectation confirmations or violations. The investigation of predictors and mechanisms underlying expectation update and maintenance has been approached from many research perspectives. However, in many instances there has been little exchange between different research fields. To further advance research on expectations and expectation violations, collaborative efforts across different disciplines in psychology, cognitive (neuro)science, and other life sciences are warranted. For fostering and facilitating such efforts, we introduce the ViolEx 2.0 model, a revised framework for interdisciplinary research on cognitive and behavioral mechanisms of expectation update and maintenance in the context of expectation violations. To support different goals and stages in interdisciplinary exchange, the ViolEx 2.0 model features three model levels with varying degrees of specificity in order to address questions about the research synopsis, central concepts, or functional processes and relationships, respectively. The framework can be applied to different research fields and has high potential for guiding collaborative research efforts in expectation research.
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