Modeling circuit mechanisms of opposing cortical responses to visual flow perturbations.

In an ever-changing visual world, animals' survival depends on their ability to perceive and respond to rapidly changing motion cues. The primary visual cortex (V1) is at the forefront of this sensory processing, orchestrating neural responses to perturbations in visual flow. However, the underlying neural mechanisms that lead to distinct cortical responses to such perturbations remain enigmatic. In this study, our objective was to uncover the neural dynamics that govern V1 neurons' responses to visual flow perturbations using a biologically realistic computational model. By subjecting the model to sudden changes in visual input, we observed opposing cortical responses in excitatory layer 2/3 (L2/3) neurons, namely, depolarizing and hyperpolarizing responses. We found that this segregation was primarily driven by the competition between external visual input and recurrent inhibition, particularly within L2/3 and L4. This division was not observed in excitatory L5/6 neurons, suggesting a more prominent role for inhibitory mechanisms in the visual processing of the upper cortical layers. Our findings share similarities with recent experimental studies focusing on the opposing influence of top-down and bottom-up inputs in the mouse primary visual cortex during visual flow perturbations.

Time delay reservoir computing with a silicon microring resonator and a fiber-based optical feedback loop.

Silicon microring resonators serve as critical components in integrated photonic neural network implementations, owing to their compact footprint, compatibility with CMOS technology, and passive nonlinear dynamics. Recent advancements have leveraged their filtering properties as weighting functions, and their nonlinear dynamics as activation functions with spiking capabilities. In this work, we investigate experimentally the linear and nonlinear dynamics of microring resonators for time delay reservoir computing, by introducing an external optical feedback loop. After effectively mitigating the impact of environmental noise on the fiber-based feedback phase dependencies, we evaluate the computational capacity of this system by assessing its performance across various benchmark tasks at a bit rate of few Mbps. We show that the additional memory provided by the optical feedback is necessary to achieve error-free operation in delayed-boolean tasks that require up to 3 bits of memory. In this case the microring was operated in the linear regime and the photodetection was the nonlinear activation function. We also show that the Santa Fe and Mackey Glass prediction tasks are solved when the microring nonlinearities are activated. Notably, our study reveals competitive outcomes even when employing only 7 virtual nodes within our photonic reservoir. Our findings illustrate the silicon microring's versatile performance in the presence of optical feedback, highlighting its ability to be tailored for various computing applications.

Exploiting oscillatory dynamics of delay systems for reservoir computing.

Nonlinear dynamical systems exhibiting inherent memory can process temporal information by exploiting their responses to input drives. Reservoir computing is a prominent approach to leverage this ability for time-series forecasting. The computational capabilities of analog computing systems often depend on both the dynamical regime of the system and the input drive. Most studies have focused on systems exhibiting a stable fixed-point solution in the absence of input. Here, we go beyond that limitation, investigating the computational capabilities of a paradigmatic delay system in three different dynamical regimes. The system we chose has an Ikeda-type nonlinearity and exhibits fixed point, bistable, and limit-cycle dynamics in the absence of input. When driving the system, new input-driven dynamics emerge from the autonomous ones featuring characteristic properties. Here, we show that it is feasible to attain consistent responses across all three regimes, which is an essential prerequisite for the successful execution of the tasks. Furthermore, we demonstrate that we can exploit all three regimes in two time-series forecasting tasks, showcasing the versatility of this paradigmatic delay system in an analog computing context. In all tasks, the lowest prediction errors were obtained in the regime that exhibits limit-cycle dynamics in the undriven reservoir. To gain further insights, we analyzed the diverse time-distributed node responses generated in the three regimes of the undriven system. An increase in the effective dimensionality of the reservoir response is shown to affect the prediction error, as also fine-tuning of the distribution of nonlinear responses. Finally, we demonstrate that a trade-off between prediction accuracy and computational speed is possible in our continuous delay systems. Our results not only provide valuable insights into the computational capabilities of complex dynamical systems but also open a new perspective on enhancing the potential of analog computing systems implemented on various hardware platforms.

Microring resonators with external optical feedback for time delay reservoir computing.

Microring resonators (MRRs) are a key photonic component in integrated devices, due to their small size, low insertion losses, and passive operation. While the MRRs have been established for optical filtering in wavelength-multiplexed systems, the nonlinear properties that they can exhibit give rise to new perspectives on their use. For instance, they have been recently considered for introducing optical nonlinearity in photonic reservoir computing systems. In this work, we present a detailed numerical investigation of a silicon MRR operation, in the presence of external optical feedback, in a time delay reservoir computing scheme. We demonstrate the versatility of this compact, passive device, by exploiting different operating regimes and solving computing tasks with diverse memory requirements. We show that when large memory is required, as it occurs in the Narma 10 task, the MRR nonlinearity does not play a significant role when the photodetection nonlinearity is involved, while the contribution of the external feedback is significant. On the contrary, for computing tasks such as the Mackey-Glass and the Santa Fe chaotic timeseries prediction, the MRR and the photodetection nonlinearities contribute both to efficient computation. The presence of optical feedback improves the prediction of the Mackey-Glass timeseries while it plays a minor role in the Santa Fe timeseries case.

Characterizing signal encoding and transmission in class I and class II neurons via ordinal time-series analysis.

Neurons encode and transmit information in spike sequences. However, despite the effort devoted to understand the encoding and transmission of information, the mechanisms underlying the neuronal encoding are not yet fully understood. Here, we use a nonlinear method of time-series analysis (known as ordinal analysis) to compare the statistics of spike sequences generated by applying an input signal to the neuronal model of Morris-Lecar. In particular, we consider two different regimes for the neurons which lead to two classes of excitability: class I, where the frequency-current curve is continuous and class II, where the frequency-current curve is discontinuous. By applying ordinal analysis to sequences of inter-spike-intervals (ISIs) our goals are (1) to investigate if different neuron types can generate spike sequences which have similar symbolic properties; (2) to get deeper understanding on the effects that electrical (diffusive) and excitatory chemical (i.e., excitatory synapse) couplings have; and (3) to compare, when a small-amplitude periodic signal is applied to one of the neurons, how the signal features (amplitude and frequency) are encoded and transmitted in the generated ISI sequences for both class I and class II type neurons and electrical or chemical couplings. We find that depending on the frequency, specific combinations of neuron/class and coupling-type allow a more effective encoding, or a more effective transmission of the signal.

Anticipation via canards in excitable systems.

Neurons can anticipate incoming signals by exploiting a physiological mechanism that is not well understood. This article offers a novel explanation on how a receiver neuron can predict the sender's dynamics in a unidirectionally-coupled configuration, in which both sender and receiver follow the evolution of a multi-scale excitable system. We present a novel theoretical viewpoint based on a mathematical object, called canard, to explain anticipation in excitable systems. We provide a numerical approach, which allows to determine the transient effects of canards. To demonstrate the general validity of canard-mediated anticipation in the context of excitable systems, we illustrate our framework in two examples, a multi-scale radio-wave circuit (the van der Pol model) that inspired a caricature neuronal model (the FitzHugh-Nagumo model) and a biophysical neuronal model (a 2-dimensional reduction of the Hodgkin-Huxley model), where canards act as messengers to the senders' prediction. We also propose an experimental paradigm that would enable experimental neuroscientists to validate our predictions. We conclude with an outlook to possible fascinating research avenues to further unfold the mechanisms underpinning anticipation. We envisage that our approach can be employed by a wider class of excitable systems with appropriate theoretical extensions.

High frequency neurons determine effective connectivity in neuronal networks.

The emergence of flexible information channels in brain networks is a fundamental question in neuroscience. Understanding the mechanisms of dynamic routing of information would have far-reaching implications in a number of disciplines ranging from biology and medicine to information technologies and engineering. In this work, we show that the presence of a node firing at a higher frequency in a network with local connections, leads to reliable transmission of signals and establishes a preferential direction of information flow. Thus, by raising the firing rate a low degree node can behave as a functional hub, spreading its activity patterns polysynaptically in the network. Therefore, in an otherwise homogeneous and undirected network, firing rate is a tunable parameter that introduces directionality and enhances the reliability of signal transmission. The intrinsic firing rate across neuronal populations may thus determine preferred routes for signal transmission that can be easily controlled by changing the firing rate in specific nodes. We show that the results are generic and the same mechanism works in the networks with more complex topology.

Anticipated and zero-lag synchronization in motifs of delay-coupled systems.

Anticipated and zero-lag synchronization have been observed in different scientific fields. In the brain, they might play a fundamental role in information processing, temporal coding and spatial attention. Recent numerical work on anticipated and zero-lag synchronization studied the role of delays. However, an analytical understanding of the conditions for these phenomena remains elusive. In this paper, we study both phenomena in systems with small delays. By performing a phase reduction and studying phase locked solutions, we uncover the functional relation between the delay, excitation and inhibition for the onset of anticipated synchronization in a sender-receiver-interneuron motif. In the case of zero-lag synchronization in a chain motif, we determine the stability conditions. These analytical solutions provide an excellent prediction of the phase-locked regimes of Hodgkin-Huxley models and Roessler oscillators.

On the role of the entorhinal cortex in the effective connectivity of the hippocampal formation.

Inferring effective connectivity from neurophysiological data is a challenging task. In particular, only a finite (and usually small) number of sites are simultaneously recorded, while the response of one of these sites can be influenced by other sites that are not being recorded. In the hippocampal formation, for instance, the connections between areas CA1-CA3, the dentate gyrus (DG), and the entorhinal cortex (EC) are well established. However, little is known about the relations within the EC layers, which might strongly affect the resulting effective connectivity estimations. In this work, we build excitatory/inhibitory neuronal populations representing the four areas CA1, CA3, the DG, and the EC and fix their connectivities. We model the EC by three layers (LII, LIII, and LV) and assume any possible connection between them. Our results, based on Granger Causality (GC) and Partial Transfer Entropy (PTE) measurements, reveal that the estimation of effective connectivity in the hippocampus strongly depends on the connectivities between EC layers. Moreover, we find, for certain EC configurations, very different results when comparing GC and PTE measurements. We further demonstrate that causal links can be robustly inferred regardless of the excitatory or inhibitory nature of the connection, adding complexity to their interpretation. Overall, our work highlights the importance of a careful analysis of the connectivity methods to prevent unrealistic conclusions when only partial information about the experimental system is available, as usually happens in brain networks. Our results suggest that the combination of causality measures with neuronal modeling based on precise neuroanatomical tracing may provide a powerful framework to disambiguate causal interactions in the brain.

Dynamics of brain networks in the aesthetic appreciation.

Neuroimage experiments have been essential for identifying active brain networks. During cognitive tasks as in, e.g., aesthetic appreciation, such networks include regions that belong to the default mode network (DMN). Theoretically, DMN activity should be interrupted during cognitive tasks demanding attention, as is the case for aesthetic appreciation. Analyzing the functional connectivity dynamics along three temporal windows and two conditions, beautiful and not beautiful stimuli, here we report experimental support for the hypothesis that aesthetic appreciation relies on the activation of two different networks, an initial aesthetic network and a delayed aesthetic network, engaged within distinct time frames. Activation of the DMN might correspond mainly to the delayed aesthetic network. We discuss adaptive and evolutionary explanations for the relationships existing between the DMN and aesthetic networks and offer unique inputs to debates on the mind/brain interaction.

A symbolic information approach to determine anticipated and delayed synchronization in neuronal circuit models.

The phenomenon of synchronization between two or more areas of the brain coupled asymmetrically is a relevant issue for understanding mechanisms and functions within the cerebral cortex. Anticipated synchronization (AS) refers to the situation in which the receiver system synchronizes to the future dynamics of the sender system while the intuitively expected delayed synchronization (DS) represents exactly the opposite case. AS and DS are investigated in the context of causal information formalism. More specifically, we use a multi-scale symbolic information-theory approach for discriminating the time delay displayed between two areas of the brain when they exchange information.

Modeling positive Granger causality and negative phase lag between cortical areas.

Different measures of directional influence have been employed to infer effective connectivity in the brain. When the connectivity between two regions is such that one of them (the sender) strongly influences the other (the receiver), a positive phase lag is often expected. The assumption is that the time difference implicit in the relative phase reflects the transmission time of neuronal activity. However, Brovelli et al. (2004) observed that, in monkeys engaged in processing a cognitive task, a dominant directional influence from one area of sensorimotor cortex to another may be accompanied by either a negative or a positive time delay. Here we present a model of two brain regions, coupled with a well-defined directional influence, that displays similar features to those observed in the experimental data. This model is inspired by the theoretical framework of Anticipated Synchronization developed in the field of dynamical systems. Anticipated Synchronization is a form of synchronization that occurs when a unidirectional influence is transmitted from a sender to a receiver, but the receiver leads the sender in time. This counterintuitive synchronization regime can be a stable solution of two dynamical systems coupled in a master-slave (sender-receiver) configuration when the slave receives a negative delayed self-feedback. Despite efforts to understand the dynamics of Anticipated Synchronization, experimental evidence for it in the brain has been lacking. By reproducing experimental delay times and coherence spectra, our results provide a theoretical basis for the underlying mechanisms of the observed dynamics, and suggest that the primate cortex could operate in a regime of Anticipated Synchronization as part of normal neurocognitive function.

Corrigendum: Understanding the effects of cortical gyrification in tACS: insights from experiments and computational models.

[This corrects the article DOI: 10.3389/fnins.2023.1223950.].

Understanding the effects of cortical gyrification in tACS: insights from experiments and computational models.

The alpha rhythm is often associated with relaxed wakefulness or idling and is altered by various factors. Abnormalities in the alpha rhythm have been linked to several neurological and psychiatric disorders, including Alzheimer's disease. Transcranial alternating current stimulation (tACS) has been proposed as a potential tool to restore a disrupted alpha rhythm in the brain by stimulating at the individual alpha frequency (IAF), although some research has produced contradictory results. In this study, we applied an IAF-tACS protocol over parieto-occipital areas to a sample of healthy subjects and measured its effects over the power spectra. Additionally, we used computational models to get a deeper understanding of the results observed in the experiment. Both experimental and numerical results showed an increase in alpha power of 8.02% with respect to the sham condition in a widespread set of regions in the cortex, excluding some expected parietal regions. This result could be partially explained by taking into account the orientation of the electric field with respect to the columnar structures of the cortex, showing that the gyrification in parietal regions could generate effects in opposite directions (hyper-/depolarization) at the same time in specific brain regions. Additionally, we used a network model of spiking neuronal populations to explore the effects that these opposite polarities could have on neural activity, and we found that the best predictor of alpha power was the average of the normal components of the electric field. To sum up, our study sheds light on the mechanisms underlying tACS brain activity modulation, using both empirical and computational approaches. Non-invasive brain stimulation techniques hold promise for treating brain disorders, but further research is needed to fully understand and control their effects on brain dynamics and cognition. Our findings contribute to this growing body of research and provide a foundation for future studies aimed at optimizing the use of non-invasive brain stimulation in clinical settings.

Synchronization in simple network motifs with negligible correlation and mutual information measures.

Can different or even identical coupled oscillators be completely uncorrelated and still be synchronized? What can be concluded from the absence of correlations or even mutual information in networks of dynamical elements about their connectivity? These are fundamental and far-reaching questions arising in many complex systems. In this Letter, we address these two questions and demonstrate in simple and generic network motifs that synchronized behavior in the generalized sense can be realized and constructed such that no correlations and even negligible mutual information remain. Our findings raise new questions, in particular, whether and to what extent indirect connections are being underestimated, since the related collective behavior and even synchronization are less likely to be detected.

Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatiotemporal systems using scalable neural networks.

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of delay-dynamical and spatiotemporal systems for a single size. Then, we drive the networks by their own predictions. We demonstrate that by scaling the size of the trained network, we can predict the complex dynamics for larger or smaller system sizes. Thus, the network learns from a single example and by exploiting symmetry properties infers entire bifurcation diagrams.

Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator.

In the dynamics of optical systems, one commonly needs to cope with the problem of coexisting deterministic and stochastic components. The separation of these components is an important, although difficult, task. Often the time scales at which determinism and noise dominate the system's dynamics differ. In this Letter we propose to use information-theory-derived quantifiers, more precisely, permutation entropy and statistical complexity, to distinguish between the two behaviors. Based on experiments of a paradigmatic opto-electronic oscillator, we demonstrate that the time scales at which deterministic or noisy behavior dominate can be identified. Supporting numerical simulations prove the accuracy of this identification.

Chaos-based communications at high bit rates using commercial fibre-optic links.

Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120 km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10(-7). The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.

Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays.

Multielectrode recordings have revealed zero time lag synchronization among remote cerebral cortical areas. However, the axonal conduction delays among such distant regions can amount to several tens of milliseconds. It is still unclear which mechanism is giving rise to isochronous discharge of widely distributed neurons, despite such latencies. Here, we investigate the synchronization properties of a simple network motif and found that, even in the presence of large axonal conduction delays, distant neuronal populations self-organize into lag-free oscillations. According to our results, cortico-cortical association fibers and certain cortico-thalamo-cortical loops represent ideal circuits to circumvent the phase shifts and time lags associated with conduction delays.

Information Transmission in Delay-Coupled Neuronal Circuits in the Presence of a Relay Population.

Synchronization between neuronal populations is hypothesized to play a crucial role in the communication between brain networks. The binding of features, or the association of computations occurring in spatially segregated areas, is supposed to take place when a stable synchronization between cortical areas occurs. While a direct cortico-cortical connection typically fails to support this mechanism, the participation of a third area, a relay element, mediating in the communication was proposed to overcome this limitation. Among the different structures that could play the role of coordination during the binding process, the thalamus is the best placed region to carry out this task. In this paper we study how information flows in a canonical motif that mimics a cortico-thalamo-cortical circuit composed by three mutually coupled neuronal populations (also called the V-motif). Through extensive numerical simulations, we found that the amount of information transferred between the oscillating neuronal populations is determined by the delay in their connections and the mismatch in their oscillation frequencies (detuning). While the transmission from a cortical population is mostly restricted to positive detuning, transmission from the relay (thalamic) population to the cortical populations is robust for a broad range of detuning values, including negative values, while permitting feedback communication from the cortex at high frequencies, thus supporting robust bottom up and top down interaction. In this case, a strong feedback transmission between the cortex to thalamus supports the possibility of robust bottom-up and top-down interactions in this motif. Interestingly, adding a cortico-cortical bidirectional connection to the V-motif (C-motif) expands the dynamics of the system with distinct operation modes. While overall transmission efficiency is decreased, new communication channels establish cortico-thalamo-cortical association loops. Switching between operation modes depends on the synaptic strength of the cortico-cortical connections. Our results support a role of the transthalamic V-motif in the binding of spatially segregated cortical computations, and suggest an important regulatory role of the direct cortico-cortical connection.