High-frequency oscillations in the ripple bands and amplitude information coding: Toward a biomarker of maximum entropy in the preictal signals.

Intracranial electroencephalography (iEEG) can directly record local field potentials (LFPs) from a large set of neurons in the vicinity of the electrode. To search for possible epileptic biomarkers and to determine the epileptogenic zone that gives rise to seizures, we investigated the dynamics of basal and preictal signals. For this purpose, we explored the dynamics of the recorded time series for different frequency bands considering high-frequency oscillations (HFO) up to 240 Hz. We apply a Hilbert transform to study the amplitude and phase of the signals. The dynamics of the different frequency bands in the time causal entropy-complexity plane, H × C, is characterized by comparing the dynamical evolution of the basal and preictal time series. As the preictal states evolve closer to the time in which the epileptic seizure starts, the, H × C, dynamics changes for the higher frequency bands. The complexity evolves to very low values and the entropy becomes nearer to its maximal value. These quasi-stable states converge to equiprobable states when the entropy is maximal, and the complexity is zero. We could, therefore, speculate that in this case, it corresponds to the minimization of Gibbs free energy. In this case, the maximum entropy is equivalent to the principle of minimum consumption of resources in the system. We can interpret this as the nature of the system evolving temporally in the preictal state in such a way that the consumption of resources by the system is minimal for the amplitude in frequencies between 220-230 and 230-240 Hz.

Pattern Separation Underpins Expectation-Modulated Memory.

Pattern separation and completion are fundamental hippocampal computations supporting memory encoding and retrieval. However, despite extensive exploration of these processes, it remains unclear whether and how top-down processes adaptively modulate the dynamics between these computations. Here we examine the role of expectation in shifting the hippocampus to perform pattern separation. In a behavioral task, 29 participants (7 males) learned a cue-object category contingency. Then, at encoding, one-third of the cues preceding the to-be-memorized objects, violated the studied rule. At test, participants performed a recognition task with old objects (targets) and a set of parametrically manipulated (very similar to dissimilar) foils for each object. Accuracy was found to be better for foils of high similarity to targets that were contextually unexpected at encoding compared with expected ones. Critically, there were no expectation-driven differences for targets and low similarity foils. To further explore these effects, we implemented a computational model of the hippocampus, performing the same task as the human participants. We used representational similarity analysis to examine how top-down expectation interacts with bottom-up perceptual input, in each layer. All subfields showed more dissimilar representations for unexpected items, with dentate gyrus (DG) and CA3 being more sensitive to expectation violation than CA1. Again, representational differences between expected and unexpected inputs were prominent for moderate to high levels of input similarity. This effect diminished when inputs from DG and CA3 into CA1 were lesioned. Overall, these novel findings strongly suggest that pattern separation in DG/CA3 underlies the effect that violation of expectation exerts on memory.SIGNIFICANCE STATEMENT What makes some events more memorable than others is a key question in cognitive neuroscience. Violation of expectation often leads to better memory performance, but the neural mechanism underlying this benefit remains elusive. In a behavioral study, we found that memory accuracy is enhanced selectively for unexpected highly similar foils, suggesting expectation violation does not enhance memory indiscriminately, but specifically aids the disambiguation of overlapping inputs. This is further supported by our subsequent investigation using a hippocampal computational model, revealing increased representational dissimilarity for unexpected highly similar foils in DG and CA3. These convergent results provide the first evidence that pattern separation plays an explicit role in supporting memory for unexpected information.

Evidence for frequency-dependent cortical plasticity in the human brain.

Frequency-dependent plasticity (FDP) describes adaptation at the synapse in response to stimulation at different frequencies. Its consequence on the structure and function of cortical networks is unknown. We tested whether cortical "resonance," favorable stimulation frequencies at which the sensory cortices respond maximally, influenced the impact of FDP on perception, functional topography, and connectivity of the primary somatosensory cortex using psychophysics and functional imaging (fMRI). We costimulated two digits on the hand synchronously at, above, or below the resonance frequency of the somatosensory cortex, and tested subjects' accuracy and speed on tactile localization before and after costimulation. More errors and slower response times followed costimulation at above- or below-resonance, respectively. Response times were faster after at-resonance costimulation. In the fMRI, the cortical representations of the two digits costimulated above-resonance shifted closer, potentially accounting for the poorer performance. Costimulation at-resonance did not shift the digit regions, but increased the functional coupling between them, potentially accounting for the improved response time. To relate these results to synaptic plasticity, we simulated a network of oscillators incorporating Hebbian learning. Two neighboring patches embedded in a cortical sheet, mimicking the two digit regions, were costimulated at different frequencies. Network activation outside the stimulated patches was greatest at above-resonance frequencies, reproducing the spread of digit representations seen with fMRI. Connection strengths within the patches increased following at-resonance costimulation, reproducing the increased fMRI connectivity. We show that FDP extends to the cortical level and is influenced by cortical resonance.

Melanopsin-driven increases in maintained activity enhance thalamic visual response reliability across a simulated dawn.

Twice a day, at dawn and dusk, we experience gradual but very high amplitude changes in background light intensity (irradiance). Although we perceive the associated change in environmental brightness, the representation of such very slow alterations in irradiance by the early visual system has been little studied. Here, we addressed this deficit by recording electrophysiological activity in the mouse dorsal lateral geniculate nucleus under exposure to a simulated dawn. As irradiance increased we found a widespread enhancement in baseline firing that extended to units with ON as well as OFF responses to fast luminance increments. This change in baseline firing was equally apparent when the slow irradiance ramp appeared alone or when a variety of higher-frequency artificial or natural visual stimuli were superimposed upon it. Using a combination of conventional knockout, chemogenetic, and receptor-silent substitution manipulations, we continued to show that, over higher irradiances, this increase in firing originates with inner-retinal melanopsin photoreception. At the single-unit level, irradiance-dependent increases in baseline firing were strongly correlated with improvements in the amplitude of responses to higher-frequency visual stimuli. This in turn results in an up to threefold increase in single-trial reliability of fast visual responses. In this way, our data indicate that melanopsin drives a generalized increase in dorsal lateral geniculate nucleus excitability as dawn progresses that both conveys information about changing background light intensity and increases the signal:noise for fast visual responses.

Cortical Resonance Frequencies Emerge from Network Size and Connectivity.

Neural oscillations occur within a wide frequency range with different brain regions exhibiting resonance-like characteristics at specific points in the spectrum. At the microscopic scale, single neurons possess intrinsic oscillatory properties, such that is not yet known whether cortical resonance is consequential to neural oscillations or an emergent property of the networks that interconnect them. Using a network model of loosely-coupled Wilson-Cowan oscillators to simulate a patch of cortical sheet, we demonstrate that the size of the activated network is inversely related to its resonance frequency. Further analysis of the parameter space indicated that the number of excitatory and inhibitory connections, as well as the average transmission delay between units, determined the resonance frequency. The model predicted that if an activated network within the visual cortex increased in size, the resonance frequency of the network would decrease. We tested this prediction experimentally using the steady-state visual evoked potential where we stimulated the visual cortex with different size stimuli at a range of driving frequencies. We demonstrate that the frequency corresponding to peak steady-state response inversely correlated with the size of the network. We conclude that although individual neurons possess resonance properties, oscillatory activity at the macroscopic level is strongly influenced by network interactions, and that the steady-state response can be used to investigate functional networks.

Information coding in a laminar computational model of cat primary visual cortex.

Neural populations across cortical layers perform different computational tasks. However, it is not known whether information in different layers is encoded using a common neural code or whether it depends on the specific layer. Here we studied the laminar distribution of information in a large-scale computational model of cat primary visual cortex. We analyzed the amount of information about the input stimulus conveyed by the different representations of the cortical responses. In particular, we compared the information encoded in four possible neural codes: (1) the information carried by the firing rate of individual neurons; (2) the information carried by spike patterns within a time window; (3) the rate-and-phase information carried by the firing rate labelled by the phase of the Local Field Potentials (LFP); (4) the pattern-and-phase information carried by the spike patterns tagged with the LFP phase. We found that there is substantially more information in the rate-and-phase code compared with the firing rate alone for low LFP frequency bands (less than 30 Hz). When comparing how information is encoded across layers, we found that the extra information contained in a rate-and-phase code may reach 90 % in Layer 4, while in other layers it reaches only 60 %, compared to the information carried by the firing rate alone. These results suggest that information processing in primary sensory cortices could rely on different coding strategies across different layers.

Linking dynamical and functional properties of intrinsically bursting neurons.

Several studies have shown that bursting neurons can encode information in the number of spikes per burst: As the stimulus varies, so does the length of individual bursts. There presented stimuli, however, vary substantially among different sensory modalities and different neurons.The goal of this paper is to determine which kind of stimulus features can be encoded in burst length, and how those features depend on the mathematical properties of the underlying dynamical system.We show that the initiation and termination of each burst is triggered by specific stimulus features whose temporal characteristsics are determined by the types of bifurcations that initiate and terminate firing in each burst. As only a few bifurcations are possible, only a restricted number of encoded features exists. Here we focus specifically on describing parabolic, square-wave and elliptic bursters. We find that parabolic bursters, whose firing is initiated and terminated by saddle-node bifurcations, behave as prototypical integrators: Firing is triggered by depolarizing stimuli, and lasts for as long as excitation is prolonged. Elliptic bursters, contrastingly, constitute prototypical resonators, since both the initiating and terminating bifurcations possess well-defined oscillation time scales. Firing is therefore triggered by stimulus stretches of matching frequency and terminated by a phase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they are triggered by a fold bifurcation of cycles of well-defined frequency but are terminated by a homoclinic bifurcation lacking an oscillating time scale. These correspondences show that stimulus selectivity is determined by the type of bifurcations. By testing several neuron models, we also demonstrate that additional biological properties that do not modify the bifurcation structure play a minor role in stimulus encoding. Moreover, we show that burst-length variability (and thereby, the capacity to transmit information) depends on a trade-off between the variance of the external signal driving the cell and the strength of the slow internal currents modulating bursts. Thus, our work explicitly links the computational properties of bursting neurons to the mathematical properties of the underlying dynamical systems.

Noise-modulated multistable synapses in a Wilson-Cowan-based model of plasticity.

Frequency-dependent plasticity refers to changes in synaptic strength in response to different stimulation frequencies. Resonance is a factor known to be of importance in such frequency dependence, however, the role of neural noise in the process remains elusive. Considering the brain is an inherently noisy system, understanding its effects may prove beneficial in shaping therapeutic interventions based on non-invasive brain stimulation protocols. The Wilson-Cowan (WC) model is a well-established model to describe the average dynamics of neural populations and has been shown to exhibit bistability in the presence of noise. However, the important question of how the different stable regimes in the WC model can affect synaptic plasticity when cortical populations interact has not yet been addressed. Therefore, we investigated plasticity dynamics in a WC-based model of interacting neural populations coupled with activity-dependent synapses in which a periodic stimulation was applied in the presence of noise of controlled intensity. The results indicate that for a narrow range of the noise variance, synaptic strength can be optimized. In particular, there is a regime of noise intensity for which synaptic strength presents a triple-stable state. Regulating noise intensity affects the probability that the system chooses one of the stable states, thereby controlling plasticity. These results suggest that noise is a highly influential factor in determining the outcome of plasticity induced by stimulation.

Phase-of-firing coding of natural visual stimuli in primary visual cortex.

We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts. The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.

GABA Modulates Frequency-Dependent Plasticity in Humans.

Frequency-dependent reorganization of the primary somatosensory cortex, together with perceptual changes, arises following repetitive sensory stimulation. Here, we investigate the role of GABA in this process. We co-stimulated two finger tips and measured GABA and Glx using magnetic resonance (MR) spectroscopy at the beginning and end of the stimulation. Participants performed a perceptual learning task before and after stimulation. There were 2 sessions with stimulation frequency either at or above the resonance frequency of the primary somatosensory cortex (23 and 39 Hz, respectively). Perceptual learning occurred following above resonance stimulation only, while GABA reduced during this condition. Lower levels of early GABA were associated with greater perceptual learning. One possible mechanism underlying this finding is that cortical disinhibition "unmasks" lateral connections within the cortex to permit adaptation to the sensory environment. These results provide evidence in humans for a frequency-dependent inhibitory mechanism underlying learning and suggest a mechanism-based approach for optimizing neurostimulation frequency.

Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information.

Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode rich naturalistic sensory stimuli. We addressed this question by recording LFPs and spikes from the primary visual cortex of anesthetized macaques while presenting a color movie. We then determined how the power of LFPs and spikes at different frequencies represents the visual features in the movie. We found that the most informative LFP frequency ranges were 1-8 and 60-100 Hz. LFPs in the range of 12-40 Hz carried little information about the stimulus, and may primarily reflect neuromodulatory inputs. Spike power was informative only at frequencies <12 Hz. We further quantified "signal correlations" (correlations in the trial-averaged power response to different stimuli) and "noise correlations" (trial-by-trial correlations in the fluctuations around the average) of LFPs and spikes recorded from the same electrode. We found positive signal correlation between high-gamma LFPs (60-100 Hz) and spikes, as well as strong positive signal correlation within high-gamma LFPs, suggesting that high-gamma LFPs and spikes are generated within the same network. LFPs <24 Hz shared strong positive noise correlations, indicating that they are influenced by a common source, such as a diffuse neuromodulatory input. LFPs <40 Hz showed very little signal and noise correlations with LFPs >40 Hz and with spikes, suggesting that low-frequency LFPs reflect neural processes that in natural conditions are fully decoupled from those giving rise to spikes and to high-gamma LFPs.

Comparable ecological dynamics underlie early cancer invasion and species dispersal, involving self-organizing processes.

Occupancy of new habitats through dispersion is a central process in nature. In particular, long-distance dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves cell spreading to tissues far away from the primary tumour. Using simulations and real data we show that the early spread of cancer cells is similar to the species individuals spread and we suggest that both processes are represented by a common spatio-temporal signature of long-distance dispersal and subsequent local proliferation. This signature is characterized by a particular fractal geometry of the boundaries of patches generated, and a power-law scaled, disrupted patch size distribution. In contrast, invasions involving only dispersal but not subsequent proliferation ("physiological invasions") like trophoblast cells invasion during normal human placentation did not show the patch size power-law pattern. Our results are consistent under different temporal and spatial scales, and under different resolution levels of analysis. We conclude that the scaling properties are a hallmark and a direct result of long-distance dispersal and proliferation, and that they could reflect homologous ecological processes of population self-organization during cancer and species spread. Our results are significant for the detection of processes involving long-range dispersal and proliferation like cancer local invasion and metastasis, biological invasions and epidemics, and for the formulation of new cancer therapeutical approaches.

Natural Language Statistical Features of LSTM-Generated Texts.

Long short-term memory (LSTM) networks have recently shown remarkable performance in several tasks that are dealing with natural language generation, such as image captioning or poetry composition. Yet, only few works have analyzed text generated by LSTMs in order to quantitatively evaluate to which extent such artificial texts resemble those generated by humans. We compared the statistical structure of LSTM-generated language to that of written natural language, and to those produced by Markov models of various orders. In particular, we characterized the statistical structure of language by assessing word-frequency statistics, long-range correlations, and entropy measures. Our main finding is that while both LSTM- and Markov-generated texts can exhibit features similar to real ones in their word-frequency statistics and entropy measures, LSTM-texts are shown to reproduce long-range correlations at scales comparable to those found in natural language. Moreover, for LSTM networks, a temperature-like parameter controlling the generation process shows an optimal value-for which the produced texts are closest to real language-consistent across different statistical features investigated.

Information-theoretic sensitivity analysis: a general method for credit assignment in complex networks.

Most systems can be represented as networks that couple a series of nodes to each other via one or more edges, with typically unknown equations governing their quantitative behaviour. A major question then pertains to the importance of each of the elements that act as system inputs in determining the output(s). We show that any such system can be treated as a 'communication channel' for which the associations between inputs and outputs can be quantified via a decomposition of their mutual information into different components characterizing the main effect of individual inputs and their interactions. Unlike variance-based approaches, our novel methodology can easily accommodate correlated inputs.

Modulation of Fast Narrowband Oscillations in the Mouse Retina and dLGN According to Background Light Intensity.

Background light intensity (irradiance) substantially impacts the visual code in the early visual system at synaptic and single-neuron levels, but its influence on population activity is largely unexplored. We show that fast narrowband oscillations, an important feature of population activity, systematically increase in amplitude as a function of irradiance in both anesthetized and awake, freely moving mice and at the level of the retina and dorsal lateral geniculate nucleus (dLGN). Narrowband coherence increases with irradiance across large areas of the dLGN, but especially for neighboring units. The spectral sensitivity of these effects and their substantial reduction in melanopsin knockout animals indicate a contribution from inner retinal photoreceptors. At bright backgrounds, narrowband coherence allows pooling of single-unit responses to become a viable strategy for enhancing visual signals within its frequency range.

Long range dispersal and spatial pattern formation in biological invasions.

In this paper we explore the consequences of long distance dispersal in biological invasion processes through simulations using a recently developed cellular automaton model. We show that long distance dispersal generate characteristic spatial patterns with several stationary scale-invariant properties. In particular, the patterns display a main patch around the focus of spread, with a fractal border structure whose fractal dimension contains information about the main statistical properties of the dispersal mechanism. Our results are in agreement with field data of spread of invaders with long distance dispersal mechanisms.

Bursting Neurons in the Hippocampal Formation Encode Features of LFP Rhythms.

Burst spike patterns are common in regions of the hippocampal formation such as the subiculum and medial entorhinal cortex (MEC). Neurons in these areas are immersed in extracellular electrical potential fluctuations often recorded as the local field potential (LFP). LFP rhythms within different frequency bands are linked to different behavioral states. For example, delta rhythms are often associated with slow-wave sleep, inactivity and anesthesia; whereas theta rhythms are prominent during awake exploratory behavior and REM sleep. Recent evidence suggests that bursting neurons in the hippocampal formation can encode LFP features. We explored this hypothesis using a two-compartment model of a bursting pyramidal neuron driven by time-varying input signals containing spectral peaks at either delta or theta rhythms. The model predicted a neural code in which bursts represented the instantaneous value, phase, slope and amplitude of the driving signal both in their timing and size (spike number). To verify whether this code is employed in vivo, we examined electrophysiological recordings from the subiculum of anesthetized rats and the MEC of a behaving rat containing prevalent delta or theta rhythms, respectively. In both areas, we found bursting cells that encoded information about the instantaneous voltage, phase, slope and/or amplitude of the dominant LFP rhythm with essentially the same neural code as the simulated neurons. A fraction of the cells encoded part of the information in burst size, in agreement with model predictions. These results provide in-vivo evidence that the output of bursting neurons in the mammalian brain is tuned to features of the LFP.

Thalamic neuron models encode stimulus information by burst-size modulation.

Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here, we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of thalamic neurons.

Phase-locking of bursting neuronal firing to dominant LFP frequency components.

Neuronal firing in the hippocampal formation relative to the phase of local field potentials (LFP) has a key role in memory processing and spatial navigation. Firing can be in either tonic or burst mode. Although bursting neurons are common in the hippocampal formation, the characteristics of their locking to LFP phase are not completely understood. We investigated phase-locking properties of bursting neurons using simulations generated by a dual compartmental model of a pyramidal neuron adapted to match the bursting activity in the subiculum of a rat. The model was driven with stochastic input signals containing a power spectral profile consistent with physiologically relevant frequencies observed in LFP. The single spikes and spike bursts fired by the model were locked to a preferred phase of the predominant frequency band where there was a peak in the power of the driving signal. Moreover, the preferred phase of locking shifted with increasing burst size, providing evidence that LFP phase can be encoded by burst size. We also provide initial support for the model results by analysing example data of spontaneous LFP and spiking activity recorded from the subiculum of a single urethane-anaesthetised rat. Subicular neurons fired single spikes, two-spike bursts and larger bursts that locked to a preferred phase of either dominant slow oscillations or theta rhythms within the LFP, according to the model prediction. Both power-modulated phase-locking and gradual shift in the preferred phase of locking as a function of burst size suggest that neurons can use bursts to encode timing information contained in LFP phase into a spike-count code.

Dynamics and nonequilibrium states in the Hamiltonian mean-field model: a closer look.

We critically revisit the evidence for the existence of quasistationary states in the globally coupled XY (or Hamiltonian mean-field) model. A slow-relaxation regime at long times is clearly revealed by numerical realizations of the model, but no traces of quasistationarity are found during the earlier stages of the evolution. We point out the nonergodic properties of this system in the short-time range, which makes a standard statistical description unsuitable. New aspects of the evolution during the nonergodic regime, and of the energy distribution function in the final approach to equilibrium, are disclosed.