Neural closure models for dynamical systems

Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened or aggregated. As the neglected and unresolved terms become important, the utility of model predictions diminishes. We develop a novel, versatile and rigorous methodology to learn non-Markovian closure parametrizations for known-physics/low-fidelity models using data from high-fidelity simulations. The new neural closure models augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori–Zwanzig formulation and the inherent delays in complex dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgrid-scale processes in coarse models and augment the simplification of complex biological and physical–biogeochemical models. We find that using non-Markovian over Markovian closures improves long-term prediction accuracy and requires smaller networks. We derive adjoint equations and network architectures needed to efficiently implement the new discrete and distributed nDDEs, for any time-integration schemes and allowing non-uniformly spaced temporal training data. The performance of discrete over distributed delays in closure models is explained using information theory, and we find an optimal amount of past information for a specified architecture. Finally, we analyse computational complexity and explain the limited additional cost due to neural closure models.

Greater Visual Working Memory Capacity for Visually Matched Stimuli When They Are Perceived as Meaningful

Almost all models of visual working memory—the cognitive system that holds visual information in an active state—assume it has a fixed capacity: Some models propose a limit of three to four objects, where others propose there is a fixed pool of resources for each basic visual feature. Recent findings, however, suggest that memory performance is improved for real-world objects. What supports these increases in capacity? Here, we test whether the meaningfulness of a stimulus alone influences working memory capacity while controlling for visual complexity and directly assessing the active component of working memory using EEG. Participants remembered ambiguous stimuli that could either be perceived as a face or as meaningless shapes. Participants had higher performance and increased neural delay activity when the memory display consisted of more meaningful stimuli. Critically, by asking participants whether they perceived the stimuli as a face or not, we also show that these increases in visual working memory capacity and recruitment of additional neural resources are because of the subjective perception of the stimulus and thus cannot be driven by physical properties of the stimulus. Broadly, this suggests that the capacity for active storage in visual working memory is not fixed but that more meaningful stimuli recruit additional working memory resources, allowing them to be better remembered.

Middle Latency Responses to Optimized Chirps in Adult Cochlear Implant Users

Cochlear implant (CI) outcomes can be assessed using objective measures that reflect the integrity of the auditory pathway. One such measure is the middle latency response (MLR), which can provide valuable information for clinicians.Traditional stimuli for evoking MLRs, that is, clicks or tone bursts, do not stimulate all parts of the cochlea simultaneously, whereas chirp stimuli compensate for the cochlear neural delay and, therefore, produce more synchronous responses from the different neural elements of the cochlea. The purpose of the present study was to determine whether chirp stimuli can elicit reliable MLRs in CI users and whether those responses correlate with clinical outcomes and with deprivation-related factors.We presented 2,000 free-field optimized chirp stimuli to CI and control participants while their electroencephalography (EEG) was being recorded.Twenty-four adult CI users and 24 matched normal-hearing (NH) individuals (age range from 18 to 63 years) participated in this study.The EEG was recorded from 64 active electrodes placed on the scalp. EEG signals were processed using EEGLAB and ERPLAB toolboxes. We characterized the latencies and amplitudes of the different MLR components in both groups.Chirp stimuli reliably evoked qualitatively similar MLRs across all NH and CI participants with a couple of differences observed between the NH and CI group. Among the different MLR components, the Na latency was significantly shorter for the CI group. A significant amplitude difference was also found between groups for the Pa–Nb complex, with higher amplitudes observed in the NH group. Finally, there were no significant correlations between MLR latencies (or amplitudes) and clinical outcomes or deprivation-related measures.Free-field–presented optimized chirp stimuli were shown to evoke measurable and reliable MLRs in CI users. In this experiment, the MLR morphology in CI users was similar to those observed in NH participants. Even though we did not replicate here a significant relationship between MLR and speech perception measures, we were able to successfully collect acoustically evoked MLRs, which could constitute an important supplemental measure to the standard behavioral tests presently being used in postoperative clinical evaluation settings.

Greater visual working memory capacity for visually-matched stimuli when they are recognized as meaningful

Almost all models of visual working memory assume it has a fixed capacity: some models propose a limit of 3-4 objects, where others propose there is a fixed pool of resources for each basic visual feature. Recent findings, however, suggest that memory performance is improved for real-world objects. What supports these increases in capacity? Here, we test whether the meaningfulness of a stimulus alone influences working memory capacity while controlling for visual complexity and directly assessing the active component of working memory using EEG. Participants remembered ambiguous stimuli that could either be perceived as a face or as meaningless shapes. Participants had higher performance and increased neural delay activity when the memory display consisted of more meaningful stimuli and when they subjectively perceived the stimuli as meaningful. Thus, there are genuine increases in working memory capacity that arise from the subjective perception of the stimulus as meaningful.

Anticipatory coadaptation of ankle stiffness and sensorimotor gain for standing balance

External perturbation forces may compromise standing balance. The nervous system can intervene only after a delay greater than 100 ms, during which the body falls freely. With ageing, sensorimotor delays are prolonged, posing a critical threat to balance. We study a generic model of stabilisation with neural delays to understand how the organism should adapt to challenging balance conditions. The model suggests that ankle stiffness should be increased in anticipation of perturbations, for example by muscle co-contraction, so as to slow down body fall during the neural response delay. Increased ankle muscle co-contraction is indeed observed in young adults when standing in challenging balance conditions, and in older relative to young adults during normal stance. In parallel, the analysis of the model shows that increases in either stiffness or neural delay must be coordinated with decreases in spinal sensorimotor gains, otherwise the feedback itself becomes destabilizing. Accordingly, a decrease in spinal feedback is observed in challenging conditions, and with age-related increases in neural delay. These observations have been previously interpreted as indicating an increased reliance on cortical rather than spinal control of balance, despite the fact that cortical responses have a longer latency. Our analysis challenges this interpretation by showing that these observations are consistent with a functional coadaptation of spinal feedback gains to functional changes in stiffness and neural delay.Author summaryBeing able to stand still can be difficult when faced with an unexpected push. It takes the nervous system more than a tenth of a second to respond to such a perturbation, and during this delay the body falls under the influence of its own weight. By co-contracting their ankle muscles in anticipation of a perturbation, subjects can increase their ankle stiffness, which slows down their fall during the neural delay. Young subjects indeed adopt this strategy when they need to remain particularly still (for example when they stand in front of a cliff). Older subjects adopt this strategy even during normal standing. We present a model of standing balance that shows that this postural strategy provides partial compensation for the increase in neural delays with ageing. According to our model, increasing ankle stiffness only improves balance if it is accompanied by a decrease in sensorimotor gain. This provides a novel and functional interpretation for the decrease in spinal feedback observed during ageing, and observed in young subjects when they stand in challenging balance conditions.

Telling the time with audiovisual speech and non-speech: Does the brain use multiple clocks?

It has often been claimed that there is mutual dependence between the perceived synchrony of auditory and visual sources, and the extent to which they perceptually integrate (‘unity assumption’: Vroomen and Keetels, 2010; Welsh and Warren, 1980). However subjective audiovisual synchrony can vary widely between subjects (Stone, 2001) and between paradigms (van Eijk, 2008). Do such individual differences in subjective synchrony correlate positively with individual differences in optimal timing for integration, as expected under the unity assumption? In separate experiments we measured the optimal audiovisual asynchrony for the McGurk illusion (McGurk and MacDonald, 1976), and the stream-bounce illusion (Sekuler et al., 1997). We concurrently elicited either temporal order judgements (TOJ) or simultaneity judgements (SJ), in counterbalanced sessions, from which we derived the point of subjective simultaneity (PSS). For both experiments, the asynchrony for maximum illusion showed a significant positive correlation with PSS derived from SJ, following the unity assumption. But surprisingly, the analogous correlation with PSS derived from TOJ was significantly negative. The temporal mechanisms for this pairing of tasks seem neither unitary nor fully independent, but apparently antagonistic. A tentative temporal renormalisation mechanism explains these paradoxical results as follows: (1) subjective timing in our different tasks can depend on independent mechanisms subject to their own neural delays; (2) inter-modal synchronization is achieved by first discounting the mean neural delay within each modality; and (3) apparent antagonism between estimates of subjective timing emerges as the mean is attracted towards deviants in the unimodal temporal distribution.