The modular and hierarchical organization of the brain is believed to support the coexistence of segregated (specialization) and integrated (binding) information processes. A relevant question is yet to understand how such architecture naturally emerges and is sustained over time, given the plastic nature of the brain's wiring. Following evidences that the sensory cortices organize into assemblies under selective stimuli, it has been shown that stable neuronal assemblies can emerge due to targeted stimulation, embedding various forms of synaptic plasticity in presence of homeostatic and/or control mechanisms. Here, we show that simple spike-timing-dependent plasticity (STDP) rules, based only on pre- and post-synaptic spike times, can also lead to the stable encoding of memories in the absence of any control mechanism. We develop a model of spiking neurons, trained by stimuli targeting different sub-populations. The model satisfies some biologically plausible features: (i) it contains excitatory and inhibitory neurons with Hebbian and anti-Hebbian STDP; (ii) neither the neuronal activity nor the synaptic weights are frozen after the learning phase. Instead, the neurons are allowed to fire spontaneously while synaptic plasticity remains active. We find that only the combination of two inhibitory STDP sub-populations allows for the formation of stable modules in the network, with each sub-population playing a distinctive role. The Hebbian sub-population controls for the firing activity, while the anti-Hebbian neurons promote pattern selectivity. After the learning phase, the network settles into an asynchronous irregular resting-state. This post-learning activity is associated with spontaneous memory recalls which turn out to be fundamental for the long-term consolidation of the learned memories. Due to its simplicity, the introduced model can represent a test-bed for further investigations on the role played by STDP on memory storing and maintenance.

Assessing someone's level of consciousness is a complex matter, and attempts have been made to aid clinicians in these assessments through metrics based on neuroimaging data. Many studies have empirically investigated measures related to the complexity elicited after the brain is stimulated to quantify the level of consciousness across different states. Here we hypothesized that the level of non-equilibrium dynamics of the unperturbed brain already contains the information needed to know how the system will react to an external stimulus. We created personalized whole-brain models fitted to resting state fMRI data recorded in participants in altered states of consciousness (e.g., deep sleep, disorders of consciousness) to infer the effective connections underlying their brain dynamics. We then measured the out-of-equilibrium nature of the unperturbed brain by evaluating the level of asymmetry of the inferred connectivity, the time irreversibility in each model and compared this with the elicited complexity generated after in silico perturbations, using a simulated fMRI-based version of the Perturbational Complexity Index, a measure that has been shown to distinguish different levels of consciousness in in vivo settings. Crucially, we found that states of consciousness involving lower arousal and/or lower awareness had a lower level of asymmetry in their effective connectivities, a lower level of irreversibility in their simulated dynamics, and a lower complexity compared to control subjects. We show that the asymmetry in the underlying connections drives the nonequilibrium state of the system and in turn the differences in complexity as a response to the external stimuli.

The evolution from disturbed brain activity to physiological brain rhythms can precede recovery in patients with disorders of consciousness (DoC). Accordingly, intriguing questions arise: What are the pathophysiological factors associated to disrupted brain rhythms in patients with DoC, and are there potential pathways for individual patients with DoC to return to normal brain rhythms? We addressed these questions at the individual subject level using biophysical simulations based on electroencephalography (EEG). The main findings are that unconscious patients exhibit a loss of excitatory corticothalamic synaptic strength. Synaptic plasticity in this excitatory corticothalamic circuitry facilitates the return of physiological brain rhythms, characterized by the reappearance of spectral peaks and flattening of the aperiodic (1/f) component of the power spectrum, in the selection of patients with DoC, particularly in those who are minimally conscious. The extent to which this occurred was correlated with cerebral glucose uptake. The current findings emphasize the importance of excitatory thalamocortical activity in reestablishing normal brain rhythms after brain injury and show that biophysical modelling of the corticothalamic circuitry could help select patients who might be potentially receptive to treatment and undergo plasticity.

A fundamental challenge in neuroscience is accurately defining brain states and predicting how and where to perturb the brain to force a transition. Here, we investigated resting-state fMRI data of patients suffering from disorders of consciousness (DoC) after coma (minimally conscious and unresponsive wakefulness states) and healthy controls. We applied model-free and model-based approaches to help elucidate the underlying brain mechanisms of patients with DoC. The model-free approach allowed us to characterize brain states in DoC and healthy controls as a probabilistic metastable substate (PMS) space. The PMS of each group was defined by a repertoire of unique patterns (i.e., metastable substates) with different probabilities of occurrence. In the model-based approach, we adjusted the PMS of each DoC group to a causal whole-brain model. This allowed us to explore optimal strategies for promoting transitions by applying off-line in silico probing. Furthermore, this approach enabled us to evaluate the impact of local perturbations in terms of their global effects and sensitivity to stimulation, which is a model-based biomarker providing a deeper understanding of the mechanisms underlying DoC. Our results show that transitions were obtained in a synchronous protocol, in which the somatomotor network, thalamus, precuneus and insula were the most sensitive areas to perturbation. This motivates further work to continue understanding brain function and treatments of disorders of consciousness.

Brain signal irreversibility has been shown to be a promising approach to study neural dynamics. Nevertheless, the relation with cortical hierarchy and the influence of different electrophysiological features is not completely understood. In this study, we recorded local field potentials (LFPs) during spontaneous behavior, including awake and sleep periods, using custom micro-electrocorticographic (μECoG) arrays implanted in ferrets. In contrast to humans, ferrets remain less time in each state across the sleep-wake cycle. We deployed a diverse set of metrics in order to measure the levels of complexity of the different behavioral states. In particular, brain irreversibility, which is a signature of non-equilibrium dynamics, captured by the arrow of time of the signal, revealed the hierarchical organization of the ferret's cortex. We found different signatures of irreversibility and functional hierarchy of large-scale dynamics in three different brain states (active awake, quiet awake, and deep sleep), showing a lower level of irreversibility in the deep sleep stage, compared to the other. Irreversibility also allowed us to disentangle the influence of different cortical areas and frequency bands in this process, showing a predominance of the parietal cortex and the theta band. Furthermore, when inspecting the embedded dynamic through a Hidden Markov Model, the deep sleep stage was revealed to have a lower switching rate and lower entropy production. These results suggest functional hierarchies in organization that can be revealed through thermodynamic features and information theory metrics.

Spatiotemporal oscillations underlie all cognitive brain functions. Large-scale brain models, constrained by neuroimaging data, aim to trace the principles underlying such macroscopic neural activity from the intricate and multi-scale structure of the brain. Despite substantial progress in the field, many aspects about the mechanisms behind the onset of spatiotemporal neural dynamics are still unknown. In this work we establish a simple framework for the emergence of complex brain dynamics, including high-dimensional chaos and travelling waves. The model consists of a complex network of 90 brain regions, whose structural connectivity is obtained from tractography data. The activity of each brain area is governed by a Jansen neural mass model and we normalize the total input received by each node so it amounts the same across all brain areas. This assumption allows for the existence of an homogeneous invariant manifold, i.e., a set of different stationary and oscillatory states in which all nodes behave identically. Stability analysis of these homogeneous solutions unveils a transverse instability of the synchronized state, which gives rise to different types of spatiotemporal dynamics, such as chaotic alpha activity. Additionally, we illustrate the ubiquity of this route towards complex spatiotemporal activity in a network of next generation neural mass models. Altogehter, our results unveil the bifurcation landscape that underlies the emergence of function from structure in the brain.

A topic of growing interest in computational neuroscience is the discovery of fundamental principles underlying global dynamics and the self-organization of the brain. In particular, the notion that the brain operates near criticality has gained considerable support, and recent work has shown that the dynamics of different brain states may be modeled by pairwise maximum entropy Ising models at various distances from a phase transition, i.e., from criticality. Here we aim to characterize two brain states (psychedelics-induced and placebo) as captured by functional magnetic resonance imaging (fMRI), with features derived from the Ising spin model formalism (system temperature, critical point, susceptibility) and from algorithmic complexity. We hypothesized, along the lines of the entropic brain hypothesis, that psychedelics drive brain dynamics into a more disordered state at a higher Ising temperature and increased complexity. We analyze resting state blood-oxygen-level-dependent (BOLD) fMRI data collected in an earlier study from fifteen subjects in a control condition (placebo) and during ingestion of lysergic acid diethylamide (LSD). Working with the automated anatomical labeling (AAL) brain parcellation, we first create "archetype" Ising models representative of the entire dataset (global) and of the data in each condition. Remarkably, we find that such archetypes exhibit a strong correlation with an average structural connectome template obtained from dMRI (r = 0.6). We compare the archetypes from the two conditions and find that the Ising connectivity in the LSD condition is lower than in the placebo one, especially in homotopic links (interhemispheric connectivity), reflecting a significant decrease of homotopic functional connectivity in the LSD condition. The global archetype is then personalized for each individual and condition by adjusting the system temperature. The resulting temperatures are all near but above the critical point of the model in the paramagnetic (disordered) phase. The individualized Ising temperatures are higher in the LSD condition than in the placebo condition (p = 9 × 10-5). Next, we estimate the Lempel-Ziv-Welch (LZW) complexity of the binarized BOLD data and the synthetic data generated with the individualized model using the Metropolis algorithm for each participant and condition. The LZW complexity computed from experimental data reveals a weak statistical relationship with condition (p = 0.04 one-tailed Wilcoxon test) and none with Ising temperature (r(13) = 0.13, p = 0.65), presumably because of the limited length of the BOLD time series. Similarly, we explore complexity using the block decomposition method (BDM), a more advanced method for estimating algorithmic complexity. The BDM complexity of the experimental data displays a significant correlation with Ising temperature (r(13) = 0.56, p = 0.03) and a weak but significant correlation with condition (p = 0.04, one-tailed Wilcoxon test). This study suggests that the effects of LSD increase the complexity of brain dynamics by loosening interhemispheric connectivity-especially homotopic links. In agreement with earlier work using the Ising formalism with BOLD data, we find the brain state in the placebo condition is already above the critical point, with LSD resulting in a shift further away from criticality into a more disordered state.

Despite decades of research, there is still a lack of understanding of the role and generating mechanisms of the ubiquitous fluctuations and oscillations found in recordings of brain dynamics. Here, we used whole-brain computational models capable of presenting different dynamical regimes to reproduce empirical data's turbulence level. We showed that the model's fluctuations regime fitted to turbulence more faithfully reproduces the empirical functional connectivity compared to oscillatory and noise regimes. By applying global and local strength-dependent perturbations and subsequently measuring the responsiveness of the model, we revealed each regime's computational capacity demonstrating that brain dynamics is shifted towards fluctuations to provide much-needed flexibility. Importantly, fluctuation regime stimulation in a brain region within a given resting state network modulates that network, aligned with previous empirical and computational studies. Furthermore, this framework generates specific, testable empirical predictions for human stimulation studies using strength-dependent rather than constant perturbation. Overall, the whole-brain models fitted to the level of empirical turbulence together with functional connectivity unveil that the fluctuation regime best captures empirical data, and the strength-dependent perturbative framework demonstrates how this regime provides maximal flexibility to the human brain.

The self-organising global dynamics underlying brain states emerge from complex recursive nonlinear interactions between interconnected brain regions. Until now, most efforts of capturing the causal mechanistic generating principles have supposed underlying stationarity, being unable to describe the non-stationarity of brain dynamics, i.e. time-dependent changes. Here, we present a novel framework able to characterise brain states with high specificity, precisely by modelling the time-dependent dynamics. Through describing a topological structure associated to the brain state at each moment in time (its attractor or 'information structure'), we are able to classify different brain states by using the statistics across time of these structures hitherto hidden in the neuroimaging dynamics. Proving the strong potential of this framework, we were able to classify resting-state BOLD fMRI signals from two classes of post-comatose patients (minimally conscious state and unresponsive wakefulness syndrome) compared with healthy controls with very high precision.

We have extended the study of the Kuramoto model with additive Gaussian noise running on the KKI-18 large human connectome graph. We determined the dynamical behavior of this model by solving it numerically in an assumed homeostatic state, below the synchronization crossover point we determined previously. The de-synchronization duration distributions exhibit power-law tails, characterized by the exponent in the range 1.1<τt<2, overlapping the in vivo human brain activity experiments by Palva et al. We show that these scaling results remain valid, by a transformation of the ultra-slow eigen-frequencies to Gaussian with unit variance. We also compare the connectome results with those, obtained on a regular cube with N=106 nodes, related to the embedding space, and show that the quenched internal frequencies themselves can cause frustrated synchronization scaling in an extended coupling space.

Consciousness transiently fades away during deep sleep, more stably under anesthesia, and sometimes permanently due to brain injury. The development of an index to quantify the level of consciousness across these different states is regarded as a key problem both in basic and clinical neuroscience. We argue that this problem is ill-defined since such an index would not exhaust all the relevant information about a given state of consciousness. While the level of consciousness can be taken to describe the actual brain state, a complete characterization should also include its potential behavior against external perturbations. We developed and analyzed whole-brain computational models to show that the stability of conscious states provides information complementary to their similarity to conscious wakefulness. Our work leads to a novel methodological framework to sort out different brain states by their stability and reversibility, and illustrates its usefulness to dissociate between physiological (sleep), pathological (brain-injured patients), and pharmacologically-induced (anesthesia) loss of consciousness.

Axonal connections are widely regarded as faithful transmitters of neuronal signals with fixed delays. The reasoning behind this is that extracellular potentials caused by spikes travelling along axons are too small to have an effect on other axons. Here we devise a computational framework that allows us to study the effect of extracellular potentials generated by spike volleys in axonal fibre bundles on axonal transmission delays. We demonstrate that, although the extracellular potentials generated by single spikes are of the order of microvolts, the collective extracellular potential generated by spike volleys can reach several millivolts. As a consequence, the resulting depolarisation of the axonal membranes increases the velocity of spikes, and therefore reduces axonal delays between brain areas. Driving a neural mass model with such spike volleys, we further demonstrate that only ephaptic coupling can explain the reduction of stimulus latencies with increased stimulus intensities, as observed in many psychological experiments.

Brain activity displays a large repertoire of dynamics across the sleep-wake cycle and even during anesthesia. It was suggested that criticality could serve as a unifying principle underlying the diversity of dynamics. This view has been supported by the observation of spontaneous bursts of cortical activity with scale-invariant sizes and durations, known as neuronal avalanches, in recordings of mesoscopic cortical signals. However, the existence of neuronal avalanches in spiking activity has been equivocal with studies reporting both its presence and absence. Here, we show that signs of criticality in spiking activity can change between synchronized and desynchronized cortical states. We analyzed the spontaneous activity in the primary visual cortex of the anesthetized cat and the awake monkey, and found that neuronal avalanches and thermodynamic indicators of criticality strongly depend on collective synchrony among neurons, LFP fluctuations, and behavioral state. We found that synchronized states are associated to criticality, large dynamical repertoire and prolonged epochs of eye closure, while desynchronized states are associated to sub-criticality, reduced dynamical repertoire, and eyes open conditions. Our results show that criticality in cortical dynamics is not stationary, but fluctuates during anesthesia and between different vigilance states.

The uncertain option task has been recently adopted to investigate the neural systems underlying the decision confidence. Latterly single neurons activity has been recorded in lateral intraparietal cortex of monkeys performing an uncertain option task, where the subject is allowed to opt for a small but sure reward instead of making a risky perceptual decision. We propose a multiple choice model implemented in a discrete attractors network. This model is able to reproduce both behavioral and neurophysiological experimental data and therefore provides support to the numerous perspectives that interpret the uncertain option task as a sensory-motor association. The model explains the behavioral and neural data recorded in monkeys as the result of the multistable attractor landscape and produces several testable predictions. One of these predictions may help distinguish our model from a recently proposed continuous attractor model.

The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.

Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them has been variously recognized in previous works as expression of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of the determinant factors (dynamical and architectural) is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed 'quasi-orbits', which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network's firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.

Estimating the difficulty of a decision is a fundamental process to elaborate complex and adaptive behaviour. In this paper, we show that the movement time of behaving monkeys performing a decision-making task is correlated with decision difficulty and that the activity of a population of neurons in ventral Premotor cortex correlates with the movement time. Moreover, we found another population of neurons that encodes the discriminability of the stimulus, thereby supplying another source of information about the difficulty of the decision. The activity of neurons encoding the difficulty can be produced by very different computations. Therefore, we show that decision difficulty can be encoded through three different mechanisms: 1. Switch time coding, 2. rate coding and 3. binary coding. This rich representation reflects the basis of different functional aspects of difficulty in the making of a decision and the possible role of difficulty estimation in complex decision scenarios.

Spatial patterns of coherent activity across different brain areas have been identified during the resting-state fluctuations of the brain. However, recent studies indicate that resting-state activity is not stationary, but shows complex temporal dynamics. We were interested in the spatiotemporal dynamics of the phase interactions among resting-state fMRI BOLD signals from human subjects. We found that the global phase synchrony of the BOLD signals evolves on a characteristic ultra-slow (<0.01Hz) time scale, and that its temporal variations reflect the transient formation and dissolution of multiple communities of synchronized brain regions. Synchronized communities reoccurred intermittently in time and across scanning sessions. We found that the synchronization communities relate to previously defined functional networks known to be engaged in sensory-motor or cognitive function, called resting-state networks (RSNs), including the default mode network, the somato-motor network, the visual network, the auditory network, the cognitive control networks, the self-referential network, and combinations of these and other RSNs. We studied the mechanism originating the observed spatiotemporal synchronization dynamics by using a network model of phase oscillators connected through the brain's anatomical connectivity estimated using diffusion imaging human data. The model consistently approximates the temporal and spatial synchronization patterns of the empirical data, and reveals that multiple clusters that transiently synchronize and desynchronize emerge from the complex topology of anatomical connections, provided that oscillators are heterogeneous.

How a stimulus or a task alters the spontaneous dynamics of the brain remains a fundamental open question in neuroscience. One of the most robust hallmarks of task/stimulus-driven brain dynamics is the decrease of variability with respect to the spontaneous level, an effect seen across multiple experimental conditions and in brain signals observed at different spatiotemporal scales. Recently, it was observed that the trial-to-trial variability and temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here we examined the dynamics of a large-scale model of the human cortex to provide a mechanistic understanding of these observations. The model allows computing the statistics of synaptic activity in the spontaneous condition and in putative tasks determined by external inputs to a given subset of brain regions. We demonstrated that external inputs decrease the variance, increase the covariances, and decrease the autocovariance of synaptic activity as a consequence of single node and large-scale network dynamics. Altogether, these changes in network statistics imply a reduction of entropy, meaning that the spontaneous synaptic activity outlines a larger multidimensional activity space than does the task-driven activity. We tested this model's prediction on fMRI signals from healthy humans acquired during rest and task conditions and found a significant decrease of entropy in the stimulus-driven activity. Altogether, our study proposes a mechanism for increasing the information capacity of brain networks by enlarging the volume of possible activity configurations at rest and reliably settling into a confined stimulus-driven state to allow better transmission of stimulus-related information.

Decision making is a process of utmost importance in our daily lives, the study of which has been receiving notable attention for decades. Nevertheless, the neural mechanisms underlying decision making are still not fully understood. Computational modeling has revealed itself as a valuable asset to address some of the fundamental questions. Biophysically plausible models, in particular, are useful in bridging the different levels of description that experimental studies provide, from the neural spiking activity recorded at the cellular level to the performance reported at the behavioral level. In this article, we have reviewed some of the recent progress made in the understanding of the neural mechanisms that underlie decision making. We have performed a critical evaluation of the available results and address, from a computational perspective, aspects of both experimentation and modeling that so far have eluded comprehension. To guide the discussion, we have selected a central theme which revolves around the following question: how does the spatiotemporal structure of sensory stimuli affect the perceptual decision-making process? This question is a timely one as several issues that still remain unresolved stem from this central theme. These include: (i) the role of spatiotemporal input fluctuations in perceptual decision making, (ii) how to extend the current results and models derived from two-alternative choice studies to scenarios with multiple competing evidences, and (iii) to establish whether different types of spatiotemporal input fluctuations affect decision-making outcomes in distinctive ways. And although we have restricted our discussion mostly to visual decisions, our main conclusions are arguably generalizable; hence, their possible extension to other sensory modalities is one of the points in our discussion.

The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding general brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of (in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by deriving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely preserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only a small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the phase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked that of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous coupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived analytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct relationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be modified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit not a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical connectivity structure reported by Hagmann and others.

It is well established that the variability of the neural activity across trials, as measured by the Fano factor, is elevated. This fact poses limits on information encoding by the neural activity. However, a series of recent neurophysiological experiments have changed this traditional view. Single cell recordings across a variety of species, brain areas, brain states and stimulus conditions demonstrate a remarkable reduction of the neural variability when an external stimulation is applied and when attention is allocated towards a stimulus within a neuron's receptive field, suggesting an enhancement of information encoding. Using an heterogeneously connected neural network model whose dynamics exhibits multiple attractors, we demonstrate here how this variability reduction can arise from a network effect. In the spontaneous state, we show that the high degree of neural variability is mainly due to fluctuation-driven excursions from attractor to attractor. This occurs when, in the parameter space, the network working point is around the bifurcation allowing multistable attractors. The application of an external excitatory drive by stimulation or attention stabilizes one specific attractor, eliminating in this way the transitions between the different attractors and resulting in a net decrease in neural variability over trials. Importantly, non-responsive neurons also exhibit a reduction of variability. Finally, this reduced variability is found to arise from an increased regularity of the neural spike trains. In conclusion, these results suggest that the variability reduction under stimulation and attention is a property of neural circuits.

Attractor networks successfully account for psychophysical and neurophysiological data in various decision-making tasks. Especially their ability to model persistent activity, a property of many neurons involved in decision-making, distinguishes them from other approaches. Stable decision attractors are, however, counterintuitive to changes of mind. Here we demonstrate that a biophysically-realistic attractor network with spiking neurons, in its itinerant transients towards the choice attractors, can replicate changes of mind observed recently during a two-alternative random-dot motion (RDM) task. Based on the assumption that the brain continues to evaluate available evidence after the initiation of a decision, the network predicts neural activity during changes of mind and accurately simulates reaction times, performance and percentage of changes dependent on difficulty. Moreover, the model suggests a low decision threshold and high incoming activity that drives the brain region involved in the decision-making process into a dynamical regime close to a bifurcation, which up to now lacked evidence for physiological relevance. Thereby, we further affirmed the general conformance of attractor networks with higher level neural processes and offer experimental predictions to distinguish nonlinear attractor from linear diffusion models.

In recent experimental work it has been shown that neuronal interactions are modulated by neuronal synchronization and that this modulation depends on phase shifts in neuronal oscillations. This result suggests that connections in a network can be shaped through synchronization. Here, we test and expand this hypothesis using a model network. We use transfer entropy, an information theoretical measure, to quantify the exchanged information. We show that transferred information depends on the phase relation of the signal, that the amount of exchanged information increases as a function of oscillations in the signal and that the speed of the information transfer increases as a function of synchronization. This implies that synchronization makes information transport more efficient. In summary, our results reinforce the hypothesis that synchronization modulates neuronal interactions and provide further evidence that gamma band synchronization has behavioral relevance.

We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality of the data is first reduced to the first principal component, and then fitted by the stationary solution of a mean-field-like one-dimensional Langevin equation, which describes the motion of a Brownian particle in a potential. The advantage of such description is that the stationary probability density of the dynamical variable can be easily derived. We applied this method to the analysis of cortical network dynamics during up and down states in an anesthetized animal. During deep anesthesia, intracellularly recorded up and down states transitions occurred with high regularity and could not be adequately described by a one-dimensional diffusion equation. Under lighter anesthesia, however, the distributions of the times spent in the up and down states were better fitted by such a model, suggesting a role for noise in determining the time spent in a particular state.

The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

We propose a top-down approach to the symptoms of schizophrenia based on a statistical dynamical framework. We show that a reduced depth in the basins of attraction of cortical attractor states destabilizes the activity at the network level due to the constant statistical fluctuations caused by the stochastic spiking of neurons. In integrate-and-fire network simulations, a decrease in the NMDA receptor conductances, which reduces the depth of the attractor basins, decreases the stability of short-term memory states and increases distractibility. The cognitive symptoms of schizophrenia such as distractibility, working memory deficits, or poor attention could be caused by this instability of attractor states in prefrontal cortical networks. Lower firing rates are also produced, and in the orbitofrontal and anterior cingulate cortex could account for the negative symptoms, including a reduction of emotions. Decreasing the GABA as well as the NMDA conductances produces not only switches between the attractor states, but also jumps from spontaneous activity into one of the attractors. We relate this to the positive symptoms of schizophrenia, including delusions, paranoia, and hallucinations, which may arise because the basins of attraction are shallow and there is instability in temporal lobe semantic memory networks, leading thoughts to move too freely round the attractor energy landscape.

Recent advances in the technology of multiunit recordings make it possible to test Hebb's hypothesis that neurons do not function in isolation but are organized in assemblies. This has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data. We mention three possible measures for the presence of higher-order patterns of neural activation--coefficients of log-linear models, connected cumulants, and redundancies--and present arguments in favor of the coefficients of log-linear models. We present test statistics for detecting the presence of higher-order interactions in spike train data by parameterizing these interactions in terms of coefficients of log-linear models. We also present a Bayesian approach for inferring the existence or absence of interactions and estimating their strength. The two methods, the frequentist and the Bayesian one, are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other. A heuristic for the analysis of temporal patterns is also proposed. Finally, a Bayesian test is presented that establishes stochastic differences between recorded segments of data. The methods are applied to experimental data and synthetic data drawn from our statistical models. Our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys, the somatosensory cortex of anesthetized rats, and multiunit recordings in the visual cortex of behaving monkeys.

The hard problem of brain tumor detection based on rest ElectroEncephaloGraphic (EEG) analysis is investigated, relying on the hypothesis that the EEG signal contains more hidden useful information than what is clinically employed. A nonlinear analysis is applied to the pair (F3,F4) of EEG leads, that describe the electrical activity of the left and right brain hemisphere, respectively. The hidden dynamic of the pair (F3,F4) is tested against a hierarchy of null hypotheses, corresponding to one- and two-dimensional nonlinear Markov models of increasing order. An approximative measure of information flow, based on higher order cumulants, quantifies the hidden dynamic of each time series and is used as a discriminating statistic for testing the null hypotheses. The minimum order of the accepted Markov models represents a measure of the intrinsic nonlinearity of the underlying system. Rest EEG records of 6 patients with evidence of meningeoma or malignant glioma in lead F4, or without any pathology, are investigated. A high order hidden dynamic is detected in normal EEG records, confirming the very complex structure of the underlying system. Different inter-dependence degrees between the hidden dynamics of leads (F3,F4) discriminate meningeoma, malignant glioma, and no pathological status, while loss of structure in the hidden dynamic can represent a good hint for glioma/meningeoma localization.

We introduce a learning paradigm for networks of integrate-and-fire spiking neurons that is based on an information-theoretic criterion. This criterion can be viewed as a first principle that demonstrates the experimentally observed fact that cortical neurons display synchronous firing for some stimuli and not for others. The principle can be regarded as the postulation of a nonparametric reconstruction method as optimization criteria for learning the required functional connectivity that justifies and explains synchronous firing for binding of features as a mechanism for spatiotemporal coding. This can be expressed in an information-theoretic way by maximizing the discrimination ability between different sensory inputs in minimal time.

This article provides a detailed and rigorous analysis of the two commonly used methods for redundancy reduction: linear independent component analysis (ICA) posed as a direct minimization of a suitably chosen redundancy measure and information maximization (InfoMax) of a continuous stochastic signal transmitted through an appropriate nonlinear network. The article shows analytically that ICA based on the Kullback-Leibler information as a redundancy measure and InfoMax lead to the same solution if the parameterization of the output nonlinear functions in the latter method is sufficiently rich. Furthermore, this work discusses the alternative redundancy measures not based on the Kullback-Leibler information distance. The practical issues of applying ICA and InfoMax are also discussed and illustrated on the problem of extracting statistically independent factors from a linear, pixel-by-pixel mixture of images.

Characterizes a given dynamical system in the sense that the order of the Markov process which approximates its statistical dependencies appropriately, is determined. Our method measures the information flow of the dynamics indirectly via higher-order cumulants, considering linear and nonlinear correlations. The main point of the iterative procedure is that the raw data are tested against a hierarchy of nonlinear Markov processes, which correspond to the hypotheses in the surrogate mechanism. We extend the method of surrogate data in two ways to study the information flow in dynamical systems. First, we test the observable dynamics against a hierarchy of null hypotheses corresponding to nonlinear Markov processes of increasing order, the probability density function of which is estimated by neural networks. Second, the discriminating statistic is not a single number but a function of the look-ahead r. More precisely, we calculate a measure based on higher-order cumulants which quantifies the independence between the past values of the time series and the point r steps ahead. This procedure is iterative in the sense that whenever a null hypothesis is rejected new data sets can be generated corresponding to better approximations of the original process in terms of memory. We define cumulant-based measures of statistical independence which characterize the loss of information with the look-ahead. The iterative procedure for testing against nonlinear Markov processes is explained and our experiments with a DAX-time series are described.

This paper provides a detailed and rigorous analysis of the two commonly used methods for redundancy reduction: linear independent component analysis (ICA) and information maximization (InfoMax). The paper shows analytically that ICA based on the Kullback-Leibler information as a mutual information measure and InfoMax lead to the same solution if the parameterization of the output nonlinear functions in the latter method is sufficiently rich. Furthermore, this work discusses the alternative redundancy measures not based on the Kullback-Leibler information distance and nonlinear ICA. The practical issues of applying ICA and InfoMax are also discussed.

According to Barlow (1989), feature extraction can be understood as finding a statistically independent representation of the probability distribution underlying the measured signals. The search for a statistically independent representation can be formulated by the criterion of minimal mutual information, which reduces to decorrelation in the case of gaussian distributions. If nongaussian distributions are to be considered, minimal mutual information is the appropriate generalization of decorrelation as used in linear Principal Component Analyses (PCA). We also generalize to nonlinear transformations by only demanding perfect transmission of information. This leads to a general class of nonlinear transformations, namely symplectic maps. Conservation of information allows us to consider only the statistics of single coordinates. The resulting factorial representation of the joint probability distribution gives a density estimation. We apply this concept to the real world problem of electrical motor fault detection treated as a novelty detection task.

Controlling the network complexity in order to prevent overfitting is one of the major problems encountered when using neural network models to extract the structure from small data sets. In this paper we present a network architecture designed for use with a cost function that includes a novel complexity penalty term. In this architecture the outputs of the hidden units are strictly positive and sum to one, and their outputs are defined as the probability that the actual input belongs to a certain class formed during learning. The penalty term expresses the mutual information between the inputs and the extracted classes. This measure effectively describes the network complexity with respect to the given data in an unsupervised fashion. The efficiency of this architecture/penalty-term when combined with backpropagation training, is demonstrated on a real world economic time series forecasting problem. The model was also applied to the benchmark sunspot data and to a synthetic data set from the statistics community.

This paper presents a new learning paradigm that consists of a Hebbian and anti-Hebbian learning. A layer of radial basis functions is adapted in an unsupervised fashion by minimizing a two-element cost function. The first element maximizes the output of each gaussian neuron and it can be seen as an implementation of the traditional Hebbian learning law. The second element of the cost function reinforces the competitive learning by penalizing the correlation between the nodes. Consequently, the second term has an “anti-Hebbian” effect that is learned by the gaussian neurons without the implementation of lateral inhibition synapses. Therefore, the decorrelated Hebbian learning (DHL) performs clustering in the input space avoiding the “nonbiological” winner-take-all rule. In addition to the standard clustering problem, this paper also presents an application of the DHL in function approximation. A scaled piece-wise linear approximation of a function is obtained in the supervised fashion within the local regions of its domain determined by the DHL. For comparison, a standard single hidden-layer gaussian network is optimized with the initial centers corresponding to the DHL. The efficiency of the algorithm is demonstrated on the chaotic Mackey-Glass time series.

A neural network learning paradigm based on information theory is pro(cid:173) posed as a way to perform in an unsupervised fashion, redundancy reduction among the elements of the output layer without loss of infor(cid:173) mation from the sensory input. The model developed performs nonlin(cid:173) ear decorrelation up to higher orders of the cumulant tensors and results in probabilistic ally independent components of the output layer. This means that we don't need to assume Gaussian distribution neither at the input nor at the output. The theory presented is related to the unsuper(cid:173) vised-learning theory of Barlow, which proposes redundancy reduction as the goal of cognition. When nonlinear units are used nonlinear princi(cid:173) pal component analysis is obtained. In this case nonlinear manifolds can be reduced to minimum dimension manifolds. If such units are used the network performs a generalized principal component analysis in the sense that non-Gaussian distributions can be linearly decorrelated and higher orders of the correlation tensors are also taken into account. The basic structure of the architecture involves a general transfOlmation that is volume conserving and therefore the entropy, yielding a map without loss of infoIIDation. Minimization of the mutual infoIIDation among the output neurons eliminates the redundancy between the outputs and results in statistical decorrelation of the extracted features. This is known as factorialleaming. 248 Gustavo Deco, Wilfried Brauer

In recent years localized receptive fields have been the subject of intensive research, due to their learning speed and efficient reconstruction of hypersurfaces. A very efficient implementation for such a network was proposed recently by Platt (1991). This resource-allocating network (RAN) allocates a new neuron whenever an unknown pattern is presented at its input layer. In this paper we introduce a new network architecture and learning paradigm. The aim of our approach is to incorporate "coarse coding" to the resource-allocating network. The network presented here provides for each input coordinate a separate layer, which consists of one-dimensional, locally tuned gaussian neurons. In the following layer multidimensional receptive fields are built by using pi-neurons. Linear neurons aggregate the outputs of the pi-neurons in order to approximate the required input-output mapping. The learning process follows the ideas of the resource-allocating network of Platt but due to the extended architecture of our network other improvements of the learning process had to be defined. Compared to the resource-allocating network a more compact network with comparable accuracy is obtained.