Perspectives on adaptive dynamical systems.

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

Auditory cortex modelled as a dynamical network of oscillators: understanding event-related fields and their adaptation.

Adaptation, the reduction of neuronal responses by repetitive stimulation, is a ubiquitous feature of auditory cortex (AC). It is not clear what causes adaptation, but short-term synaptic depression (STSD) is a potential candidate for the underlying mechanism. In such a case, adaptation can be directly linked with the way AC produces context-sensitive responses such as mismatch negativity and stimulus-specific adaptation observed on the single-unit level. We examined this hypothesis via a computational model based on AC anatomy, which includes serially connected core, belt, and parabelt areas. The model replicates the event-related field (ERF) of the magnetoencephalogram as well as ERF adaptation. The model dynamics are described by excitatory and inhibitory state variables of cell populations, with the excitatory connections modulated by STSD. We analysed the system dynamics by linearising the firing rates and solving the STSD equation using time-scale separation. This allows for characterisation of AC dynamics as a superposition of damped harmonic oscillators, so-called normal modes. We show that repetition suppression of the N1m is due to a mixture of causes, with stimulus repetition modifying both the amplitudes and the frequencies of the normal modes. In this view, adaptation results from a complete reorganisation of AC dynamics rather than a reduction of activity in discrete sources. Further, both the network structure and the balance between excitation and inhibition contribute significantly to the rate with which AC recovers from adaptation. This lifetime of adaptation is longer in the belt and parabelt than in the core area, despite the time constants of STSD being spatially homogeneous. Finally, we critically evaluate the use of a single exponential function to describe recovery from adaptation.

Why do humans have unique auditory event-related fields? Evidence from computational modeling and MEG experiments.

Auditory event-related fields (ERFs) measured with magnetoencephalography (MEG) are useful for studying the neuronal underpinnings of auditory cognition in human cortex. They have a highly subject-specific morphology, albeit certain characteristic deflections (e.g., P1m, N1m, and P2m) can be identified in most subjects. Here, we explore the reason for this subject-specificity through a combination of MEG measurements and computational modeling of auditory cortex. We test whether ERF subject-specificity can predominantly be explained in terms of each subject having an individual cortical gross anatomy, which modulates the MEG signal, or whether individual cortical dynamics is also at play. To our knowledge, this is the first time that tools to address this question are being presented. The effects of anatomical and dynamical variation on the MEG signal is simulated in a model describing the core-belt-parabelt structure of the auditory cortex, and with the dynamics based on the leaky-integrator neuron model. The experimental and simulated ERFs are characterized in terms of the N1m amplitude, latency, and width. Also, we examine the waveform grand-averaged across subjects, and the standard deviation of this grand average. The results show that the intersubject variability of the ERF arises out of both the anatomy and the dynamics of auditory cortex being specific to each subject. Moreover, our results suggest that the latency variation of the N1m is largely related to subject-specific dynamics. The findings are discussed in terms of how learning, plasticity, and sound detection are reflected in the auditory ERFs. The notion of the grand-averaged ERF is critically evaluated.

Explaining event-related fields by a mechanistic model encapsulating the anatomical structure of auditory cortex.

Event-related fields of the magnetoencephalogram are triggered by sensory stimuli and appear as a series of waves extending hundreds of milliseconds after stimulus onset. They reflect the processing of the stimulus in cortex and have a highly subject-specific morphology. However, we still have an incomplete picture of how event-related fields are generated, what the various waves signify, and why they are so subject-specific. Here, we focus on this problem through the lens of a computational model which describes auditory cortex in terms of interconnected cortical columns as part of hierarchically placed fields of the core, belt, and parabelt areas. We develop an analytical approach arriving at solutions to the system dynamics in terms of normal modes: damped harmonic oscillators emerging out of the coupled excitation and inhibition in the system. Each normal mode is a global feature which depends on the anatomical structure of the entire auditory cortex. Further, normal modes are fundamental dynamical building blocks, in that the activity of each cortical column represents a combination of all normal modes. This approach allows us to replicate a typical auditory event-related response as a weighted sum of the single-column activities. Our work offers an alternative to the view that the event-related field arises out of spatially discrete, local generators. Rather, there is only a single generator process distributed over the entire network of the auditory cortex. We present predictions for testing to what degree subject-specificity is due to cross-subject variations in dynamical parameters rather than in the cortical surface morphology.