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.

The influence of a transport process on the epidemic threshold.

By generating transient encounters between individuals beyond their immediate social environment, transport can have a profound impact on the spreading of an epidemic. In this work, we consider epidemic dynamics in the presence of the transport process that gives rise to a multiplex network model. In addition to a static layer, the (multiplex) epidemic network consists of a second dynamic layer in which any two individuals are connected for the time they occupy the same site during a random walk they perform on a separate transport network. We develop a mean-field description of the stochastic network model and study the influence the transport process has on the epidemic threshold. We show that any transport process generally lowers the epidemic threshold because of the additional connections it generates. In contrast, considering also random walks of fractional order that in some sense are a more realistic model of human mobility, we find that these non-local transport dynamics raise the epidemic threshold in comparison to a classical local random walk. We also test our model on a realistic transport network (the Munich U-Bahn network), and carefully compare mean-field solutions with stochastic trajectories in a range of scenarios.

Spontaneous and evoked activity patterns diverge over development.

The immature brain is highly spontaneously active. Over development this activity must be integrated with emerging patterns of stimulus-evoked activity, but little is known about how this occurs. Here we investigated this question by recording spontaneous and evoked neural activity in the larval zebrafish tectum from 4 to 15 days post-fertilisation. Correlations within spontaneous and evoked activity epochs were comparable over development, and their neural assemblies refined in similar ways. However, both the similarity between evoked and spontaneous assemblies, and also the geometric distance between spontaneous and evoked patterns, decreased over development. At all stages of development, evoked activity was of higher dimension than spontaneous activity. Thus, spontaneous and evoked activity do not converge over development in this system, and these results do not support the hypothesis that spontaneous activity evolves to form a Bayesian prior for evoked activity.

Limitations to Estimating Mutual Information in Large Neural Populations.

Information theory provides a powerful framework to analyse the representation of sensory stimuli in neural population activity. However, estimating the quantities involved such as entropy and mutual information from finite samples is notoriously hard and any direct estimate is known to be heavily biased. This is especially true when considering large neural populations. We study a simple model of sensory processing and show through a combinatorial argument that, with high probability, for large neural populations any finite number of samples of neural activity in response to a set of stimuli is mutually distinct. As a consequence, the mutual information when estimated directly from empirical histograms will be equal to the stimulus entropy. Importantly, this is the case irrespective of the precise relation between stimulus and neural activity and corresponds to a maximal bias. This argument is general and applies to any application of information theory, where the state space is large and one relies on empirical histograms. Overall, this work highlights the need for alternative approaches for an information theoretic analysis when dealing with large neural populations.

Behavioral Signatures of a Developing Neural Code.

During early life, neural codes must develop to appropriately transform sensory inputs into behavioral outputs. Here, we demonstrate a link between the maturity of neural coding in the visual brain and developmental changes in visually guided behavior. In zebrafish larvae, we show that visually driven hunting behavior improves from 4 to 15 days post-fertilization, becoming faster and more accurate. During the same period, population activity in parts of the optic tectum refines, improving decoding and information transmission for particular spatial positions. Remarkably, individual differences in decoding can predict each fish's hunting success. Together, these results help reveal how the neural codes required for a natural behavior emerge during development.

Co-expression of synaptic genes in the sponge Amphimedon queenslandica uncovers ancient neural submodules.

The synapse is a complex cellular module crucial to the functioning of neurons. It evolved largely through the exaptation of pre-existing smaller submodules, each of which are comprised of ancient sets of proteins that are conserved in modern animals and other eukaryotes. Although these ancient submodules themselves have non-neural roles, it has been hypothesized that they may mediate environmental sensing behaviors in aneural animals, such as sponges. Here we identify orthologues in the sponge Amphimedon queenslandica of genes encoding synaptic submodules in neural animals, and analyse their cell-type specific and developmental expression to determine their potential to be co-regulated. We find that genes comprising certain synaptic submodules, including those involved in vesicle trafficking, calcium-regulation and scaffolding of postsynaptic receptor clusters, are co-expressed in adult choanocytes and during metamorphosis. Although these submodules may contribute to sensory roles in this cell type and this life cycle stage, total synaptic gene co-expression profiles do not support the existence of a functional synapse in A. queenslandica. The lack of evidence for the co-regulation of genes necessary for pre- and post-synaptic functioning in A. queenslandica suggests that sponges, and perhaps the last common ancestor of sponges and other extant animals, had the ability to promulgate sensory inputs without complete synapse-like functionalities. The differential co-expression of multiple synaptic submodule genes in sponge choanocytes, which have sensory and feeding roles, however, is consistent with the metazoan ancestor minimally being able to undergo exo- and endocytosis in a controlled and localized manner.

Correction to: Detecting neural assemblies in calcium imaging data.

Upon publication of the original article, [1], the authors noticed that the first authors' affiliation contained an error.

Detecting neural assemblies in calcium imaging data.

BACKGROUND: Activity in populations of neurons often takes the form of assemblies, where specific groups of neurons tend to activate at the same time. However, in calcium imaging data, reliably identifying these assemblies is a challenging problem, and the relative performance of different assembly-detection algorithms is unknown. RESULTS: To test the performance of several recently proposed assembly-detection algorithms, we first generated large surrogate datasets of calcium imaging data with predefined assembly structures and characterised the ability of the algorithms to recover known assemblies. The algorithms we tested are based on independent component analysis (ICA), principal component analysis (Promax), similarity analysis (CORE), singular value decomposition (SVD), graph theory (SGC), and frequent item set mining (FIM-X). When applied to the simulated data and tested against parameters such as array size, number of assemblies, assembly size and overlap, and signal strength, the SGC and ICA algorithms and a modified form of the Promax algorithm performed well, while PCA-Promax and FIM-X did less well, for instance, showing a strong dependence on the size of the neural array. Notably, we identified additional analyses that can improve their importance. Next, we applied the same algorithms to a dataset of activity in the zebrafish optic tectum evoked by simple visual stimuli, and found that the SGC algorithm recovered assemblies closest to the averaged responses. CONCLUSIONS: Our findings suggest that the neural assemblies recovered from calcium imaging data can vary considerably with the choice of algorithm, but that some algorithms reliably perform better than others. This suggests that previous results using these algorithms may need to be reevaluated in this light.

Spontaneous Activity in the Zebrafish Tectum Reorganizes over Development and Is Influenced by Visual Experience.

Spontaneous patterns of activity in the developing visual system may play an important role in shaping the brain for function. During the period 4-9 dpf (days post-fertilization), larval zebrafish learn to hunt prey, a behavior that is critically dependent on the optic tectum. However, how spontaneous activity develops in the tectum over this period and the effect of visual experience are unknown. Here we performed two-photon calcium imaging of GCaMP6s zebrafish larvae at all days from 4 to 9 dpf. Using recently developed graph theoretic techniques, we found significant changes in both single-cell and population activity characteristics over development. In particular, we identified days 5-6 as a critical moment in the reorganization of the underlying functional network. Altering visual experience early in development altered the statistics of tectal activity, and dark rearing also caused a long-lasting deficit in the ability to capture prey. Thus, tectal development is shaped by both intrinsic factors and visual experience.