Common inputs in subthreshold membrane potential: the role of quiescent states in neuronal activity

Experiments in certain regions of the cerebral cortex suggest that the spiking activity of neuronalpopulations is regulated by common non-Gaussian inputs across neurons. We model these deviations from random walk processes with q-Gaussian distributions into simple threshold neurons, and investigate the scaling properties in large neural populations. We show that deviations from the Gaussian statistics provide a natural framework to regulate population statistics such as sparsity, entropy and specific heat. This type of description allows us to provide an adequate strategy to explain the information encoding in the case of low neuronal activity and its possible implications on information transmission.Instituto de Física de Líquidos y Sistemas Biológico

Higher-order cumulants drive neuronal activity patterns, inducing UP-DOWN states in neural populations

A major challenge in neuroscience is to understand the role of the higher-order correlations structure of neuronal populations. The dichotomized Gaussian model (DG) generates spike trains by means of thresholding a multivariate Gaussian random variable. The DG inputs are Gaussian distributed, and thus have no interactions beyond the second order in their inputs; however, they can induce higher-order correlations in the outputs. We propose a combination of analytical and numerical techniques to estimate higher-order, above the second, cumulants of the firing probability distributions. Our findings show that a large amount of pairwise interactions in the inputs can induce the system into two possible regimes, one with low activity (“DOWN state”) and another one with high activity (“UP state”), and the appearance of these states is due to a combination between the third- and fourth-order cumulant. This could be part of a mechanism that would help the neural code to upgrade specific information about the stimuli, motivating us to examine the behavior of the critical fluctuations through the Binder cumulant close to the critical point. We show, using the Binder cumulant, that higher-order correlations in the outputs generate a critical neural system that portrays a second-order phase transition.Fil: Baravalle, Román. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; ArgentinaFil: Montani, Fernando Fabián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentin

Common inputs in subthreshold membrane potential: The role of quiescent states in neuronal activity

Experiments in certain regions of the cerebral cortex suggest that the spiking activity of neuronalpopulations is regulated by common non-Gaussian inputs across neurons. We model these deviations from random walk processes with q-Gaussian distributions into simple threshold neurons, and investigate the scaling properties in large neural populations. We show that deviations from theGaussian statistics provide a natural framework to regulate population statistics such as sparsity, entropy and specific heat. This type of description allows us to provide an adequate strategy to explain the information encoding in the case of low neuronal activity and its possible implications on information transmission.Fil: Montangie, Lisandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Montani, Fernando Fabián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin

Information theoretic measures and their applications

The concept of entropy, an ever-growing physical magnitude that measured the degree of decay of order in a physical system, was introduced by Rudolf Clausius in 1865 through an elegant formulation of the second law of thermodynamics. Seven years later, in 1872, Ludwig Boltzmann proved the famous H-theorem, showing that the quantity H always decreases in time, and in the case of perfect gas in equilibrium, the quantity H was related to Clausius’ entropyS. The dynamical approach of Boltzmann, together with the elegant theory of statistical ensembles at equilibrium proposed by Josiah Willard Gibbs, led to the Boltzmann–Gibbs theory of statistical mechanics, which represents one of the most successful theoretical frameworks of physics. In fact, with the introduction of entropy, thermodynamics became a model of theoretical science.Fil: Rosso, Osvaldo Anibal. Universidade Federal de Alagoas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Montani, Fernando Fabián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

An information-theoretic study of neuronal spike correlations in the mammalian cerebral cortex

In chapter I of this thesis we present a review of the historical background of the previousspike correlation studies and current state of the problem. In the chapters II, III and IV ofthis thesis we have applied an information theoretic approach to study the role of correlationsin the neuronal code, using the responses of pairs of neurons to drifting sinusoidal gratingsof different orientations and contrasts recorded in the primary visual cortex of anesthetizedmacaque monkeys. In chapter V we investigate the effects of a focal stroke in a populationof neurons on information transmission using a computational and analytical approach tothe problem. Finally, in chapter VI we use a novel analytical approach to study effects ofhigher order correlations in a population of neurons.It has been proposed in neuroscientific literature that pooling can lead to a significant improvementin signal reliability, provided that the neurons being pooled are at most weaklycross-correlated. We have computed mutual information, and compared the informationavailable from pairs of cells with the sum of the single cell information values. This allowedus to assess the degree of synergy (or conversely, redundancy) in the coding. In chapter IIof this thesis, we show that due to a loss of information encoded in the neuronal identity ofthe cells, pooling spikes across neurons leads to a loss of a large fraction of the informationpresent in their spike trains.We have used information theory to examine whether stimulus-dependent correlation couldcontribute to the neural coding of orientation and contrast by pairs of V1 cells. To this end,in chapter III, we have used a modified version of the method of information components.This analysis revealed that although synchrony is prevalent and informative, the additionalinformation it provides is frequently offset by the redundancy arising from the similar tuningproperties of the two cells. Thus, coding is roughly independent with weak synergy orredundancy arising depending on the similarity in tuning and the temporal precision of theanalysis. Our findings suggest that this would allow cortical circuits to enjoy the stabilityprovided by having similarly tuned neurons without suffering the penalty of redundancyas the associated information transmission deficit is compensated by stimulus dependentsynchrony.In chapter IV, we present a discussion about different measures of correlations and in particularwe propose the Jensen-Shannon Divergence as a measure of the distance between thecorresponding probability distribution functions associated with each spikes fired observedpatterns. We applied this Divergence for fixed stimuli as a measure of discrimination betweencorrelated and independent firing of pairs of cells in the primary visual cortex. Thisprovides a new, information-theoretic measure of the strength of correlation. We found thatthe relative Jensen-Shannon Divergence (measured in relation to the case in which all cellsfired completely independently) decreases with respect to the difference in orientation preferencebetween the receptive field from each pair of cells. Our finding indicates that theJensen-Shannon Divergence can be used for characterizing the effective circuitry network ina population of neurons.The underlying origins of synchronized firing between cortical neurons are still under discussion.Inter-cellular communication through chemically mediated synaptic transmissionis considered a major contributor to the formation of neuronal synchrony. GABAergic inhibitoryneurons may be involved in the generation of oscillatory activity in the cortex andits synchronization. Specifically, reduction of GABAergic inhibition may favour corticalplasticity producing functional recovery following focal brain lesions. Research into neurotransmittersystems is therefore of paramount importance to understand the origins ofsynchronized spiking. However, it is necessary to understand first how simple focal abnormalitiesin GABAergic modulators can affect the information transmission in an impairedbrain tissue. In chapter V, we present a computational and analytical model of a topographicallymapped population code which includes a focal lesion as well as a process for receptivefield enlargement (plasticity). The model simulates the recovery processes in the brain, andallows us to investigate mechanisms which increase the ability of the cortex to restore lostbrain functions. We have estimated the Fisher Information carried by the topographic mapbefore and after the stroke. Our finding shows that by tuning the receptive field plasticity toa certain value, the information transfer through the cortex after stroke can be optimized.A widespread distribution of neuronal activity can generate higher-order stochastic interactions.In this case, pair-wise correlations do not uniquely determine synchronizing spiking ina population of neurons, and higher order interactions across neurons cannot be disregarded.We present a new statistical approach, using the information geometry framework, for analyzingthe probability distribution function (PDF) of spike firing patterns by consideringhigher order correlations in a neuronal pool. In chapter VI, we have studied the limit ofa large population of neurons and associated a deformation parameter to the higher ordercorrelations in the PDF. We have also performed an analytical estimation of the Fisher informationin order to evaluate the implications of higher order correlations between spikeson information transmission. This leads to a new procedure to study higher order stochasticinteractions.The overall findings of this thesis warn about making any extensive statement about therole of neuronal spike correlations without considering the general case inclusive of higherorder correlations, and suggest a need to reshape the current debate about the role of spikecorrelations across neurons.Imperial College Londo

Rhythmic activities of the brain: quantifying the high complexity of beta and gamma oscillations during visuomotor tasks

Electroencephalography (EEG) signals depict the electrical activity that take place at the surface of the brain, and provide an important tool for understanding a variety of cognitive processes. The EEG are the product of synchronized activity of the brain and variations in EEG oscillations patterns reflect the underlying changes in neuronal synchrony. Our aim is to characterize the complexity of the EEG rhythmic oscillations bands when the subjects performs a visuomotor or imagined cognitive tasks (imagined movement), providing a causal mapping of the dynamical rhythmic activities of the brain as a measure of attentional investment. We estimate the intrinsic correlational structure of the signals within the causality entropy-complexity plane H x C, where the enhanced complexity in the gamma 1, gamma 2 and beta 1 bands allow us to distinguish motor-visual memory tasks from control conditions. We identify the dynamics of the gamma 1, gamma 2 and beta 1 rhythmic oscillations within the zone of a chaotic dissipative behavior, while in contrast the beta 2 band shows a much higher level of entropy and a significant low level of complexity that corresponds to a non-invertible cubic map. Our findings enhance the importance of the gamma band during attention in perceptual feature binding during the visuomotor/imagery tasks.Instituto de Física de Líquidos y Sistemas Biológico

Causal Shannon-Fisher Characterization of Motor/Imagery Movements in EEG

The electroencephalogram (EEG) is an electrophysiological monitoring method that allows us to glimpse the electrical activity of the brain. Neural oscillations patterns are perhaps the best salient feature of EEG as they are rhythmic activities of the brain that can be generated by interactions across neurons. Large-scale oscillations can be measured by EEG as the different oscillation patterns reflected within the different frequency bands, and can provide us with new insights into brain functions. In order to understand how information about the rhythmic activity of the brain during visuomotor/imagined cognitive tasks is encoded in the brain we precisely quantify the different features of the oscillatory patterns considering the Shannon-Fisher plane H × F. This allows us to distinguish the dynamics of rhythmic activities of the brain showing that the Beta band facilitate information transmission during visuomotor/imagined tasks.Facultad de Ciencias ExactasInstituto de Física de Líquidos y Sistemas Biológico

Rhythmic activities of the brain: quantifying the high complexity of beta and gamma oscillations during visuomotor tasks

Electroencephalography (EEG) signals depict the electrical activity that take place at the surface of the brain, and provide an important tool for understanding a variety of cognitive processes. The EEG are the product of synchronized activity of the brain and variations in EEG oscillations patterns reflect the underlying changes in neuronal synchrony. Our aim is to characterize the complexity of the EEG rhythmic oscillations bands when the subjects performs a visuomotor or imagined cognitive tasks (imagined movement), providing a causal mapping of the dynamical rhythmic activities of the brain as a measure of attentional investment. We estimate the intrinsic correlational structure of the signals within the causality entropy-complexity plane H x C, where the enhanced complexity in the gamma 1, gamma 2 and beta 1 bands allow us to distinguish motor-visual memory tasks from control conditions. We identify the dynamics of the gamma 1, gamma 2 and beta 1 rhythmic oscillations within the zone of a chaotic dissipative behavior, while in contrast the beta 2 band shows a much higher level of entropy and a significant low level of complexity that corresponds to a non-invertible cubic map. Our findings enhance the importance of the gamma band during attention in perceptual feature binding during the visuomotor/imagery tasks.Fil: Baravalle, Román. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Rosso, Osvaldo Aníbal. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Montani, Fernando Fabián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin

Quantifying higher-order correlations in a neuronal pool

Recent experiments involving a relatively large population of neurons have shown a very significant amount of higher-order correlations. However, little is known of how these affect the integration and firing behavior of a population of neurons beyond the second order statistics. To investigate how higher-order inputs statistics can shape beyond pairwise spike correlations and affect information coding in the brain, we consider a neuronal pool where each neuron fires stochastically. We develop a simple mathematically tractable model that makes it feasible to account for higher-order spike correlations in a neuronal pool with highly interconnected common inputs beyond second order statistics. In our model, correlations between neurons appear from q-Gaussian inputs into threshold neurons. The approach constitutes the natural extension of the Dichotomized Gaussian model, where the inputs to the model are just Gaussian distributed and therefore have no input interactions beyond second order. We obtain an exact analytical expression for the joint distribution of firing, quantifying the degree of higher-order spike correlations, truly emphasizing the functional aspects of higher-order statistics, as we account for beyond second order inputs correlations seen by each neuron within the pool. We determine how higherorder correlations depend on the interaction structure of the input, showing that the joint distribution of firing is skewed as the parameter q increases inducing larger excursions of synchronized spikes. We show how input nonlinearities can shape higher-order correlations and enhance coding performance by neural populations.Instituto de Física de Líquidos y Sistemas Biológico

Effect of interacting second- and third-order stimulus-dependent correlations on population-coding asymmetries

Spike correlations among neurons are widely encountered in the brain. Although models accounting for pairwise interactions have proved able to capture some of the most important features of population activity at the level of the retina, the evidence shows that pairwise neuronal correlation analysis does not resolve cooperative population dynamics by itself. By means of a series expansion for short time scales of the mutual information conveyed by a population of neurons, the information transmission can be broken down into firing rate and correlational components. In a proposed extension of this framework, we investigate the information components considering both second- and higher-order correlations.We showthat the existence of a mixed stimulus-dependent correlation term defines a new scenario for the interplay between pairwise and higher-than-pairwise interactions in noise and signal correlations that would lead either to redundancy or synergy in the information-theoretic sense.Instituto de Física de Líquidos y Sistemas Biológico