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Neurons and Cognition

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preprint2016arXiv

Complete coverage of space favors modularity of the grid system in the brain

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e. there are groups of neurons which have grids with similar periodicity, orientation and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e. without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed co-modularity of grid cell periodicity, orientation and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at l

preprint2015arXiv

Intracellular impedance measurements reveal non-ohmic properties of the extracellular medium around neurons

The electrical properties of extracellular space around neurons are important to understand the genesis of extracellular potentials, as well as for localizing neuronal activity from extracellular recordings. However, the exact nature of these extracellular properties is still uncertain. We introduce a method to measure the impedance of the tissue, and which preserves the intact cell-medium interface, using whole-cell patch-clamp recordings in vivo and in vitro. We find that neural tissue has marked non-ohmic and frequency-filtering properties, which are not consistent with a resistive (ohmic) medium, as often assumed. In contrast, using traditional metal electrodes provides very different results, more consistent with a resistive medium. The amplitude and phase profiles of the measured impedance are consistent with the contribution of ionic diffusion. We also show that the impact of such frequency-filtering properties is possibly important on the genesis of local field potentials, as well as on the cable properties of neurons. The present results show non-ohmic properties of the extracellular medium around neurons, and suggest that source estimation methods, as well as the cable pr

preprint2016arXiv

A computational investigation of the relationships between single-neuron and network dynamics in the cerebral cortex

Functions of brain areas in complex animals are believed to rely on the dynamics of networks of neurons rather than on single neurons. On the other hand, the network dynamics reflect and arise from the integration and coordination of the activity of populations of single neurons. Understanding how single-neurons and neural-circuits dynamics complement each other to produce brain functions is thus of paramount importance. LFPs and EEGs are good indicators of the dynamics of mesoscopic and macroscopic populations of neurons, while microscopic-level activities can be documented by measuring the membrane potential, the synaptic currents or the spiking activity of individual neurons. In this thesis we develop mathematical modelling and mathematical analysis tools that can help the interpretation of joint measures of neural activity at microscopic and mesoscopic or macroscopic scales. In particular, we develop network models of recurrent cortical circuits that can clarify the impact of several aspects of single-neuron (i.e., microscopic-level) dynamics on the activity of the whole neural population (as measured by LFP). We then develop statistical tools to characterize the relationship b

preprint2017arXiv

Collective Stochastic Coherence in Recurrent Neuronal Networks

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behavior in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscill

preprint2016arXiv

The Hamiltonian brain: efficient probabilistic inference with excitatory-inhibitory neural circuit dynamics

Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference: neural activity displays prominent oscillations in response to constant input, and large transient changes in response to stimulus onset. Here we show that these dynamical behaviours may in fact be understood as hallmarks of the specific representation and algorithm that the cortex employs to perform probabilistic inference. We demonstrate that a particular family of probabilistic inference algorithms, Hamiltonian Monte Carlo (HMC), naturally maps onto the dynamics of excitatory-inhibitory neural networks. Specifically, we constructed a model of an excitatory-inhibitory circuit in primary visual cortex that performed HMC inference, and thus inherently gave rise to oscillations and transients. These oscillations were not mere epiphenomena but served an important functional role: speeding up inference by rapidly spanning a large volume of state space. Inference thus became an order of magnitude more efficient than in a non-oscillatory variant of the

preprint2016arXiv

The ontogeny of discourse structure mimics the development of literature

Discourse varies with age, education, psychiatric state and historical epoch, but the ontogenetic and cultural dynamics of discourse structure remain to be quantitatively characterized. To this end we investigated word graphs obtained from verbal reports of 200 subjects ages 2-58, and 676 literary texts spanning ~5,000 years. In healthy subjects, lexical diversity, graph size, and long-range recurrence departed from initial near-random levels through a monotonic asymptotic increase across ages, while short-range recurrence showed a corresponding decrease. These changes were explained by education and suggest a hierarchical development of discourse structure: short-range recurrence and lexical diversity stabilize after elementary school, but graph size and long-range recurrence only stabilize after high school. This gradual maturation was blurred in psychotic subjects, who maintained in adulthood a near-random structure. In literature, monotonic asymptotic changes over time were remarkable: While lexical diversity, long-range recurrence and graph size increased away from near-randomness, short-range recurrence declined, from above to below random levels. Bronze Age texts are structu

preprint2016arXiv

EEG in the classroom: Synchronised neural recordings during video presentation

We performed simultaneous recordings of electroencephalography (EEG) from multiple students in a classroom, and measured the inter-subject correlation (ISC) of activity evoked by a common video stimulus. The neural reliability, as quantified by ISC, has been linked to engagement and attentional modulation in earlier studies that used high-grade equipment in laboratory settings. Here we reproduce many of the results from these studies using portable low-cost equipment, focusing on the robustness of using ISC for subjects experiencing naturalistic stimuli. The present data shows that stimulus-evoked neural responses, known to be modulated by attention, can be tracked in for groups of students with synchronized EEG acquisition. This is a step towards real-time inference of engagement in the classroom.

preprint2016arXiv

An FFT-based Synchronization Approach to Recognize Human Behaviors using STN-LFP Signal

Classification of human behavior is key to developing closed-loop Deep Brain Stimulation (DBS) systems, which may be able to decrease the power consumption and side effects of the existing systems. Recent studies have shown that the Local Field Potential (LFP) signals from both Subthalamic Nuclei (STN) of the brain can be used to recognize human behavior. Since the DBS leads implanted in each STN can collect three bipolar signals, the selection of a suitable pair of LFPs that achieves optimal recognition performance is still an open problem to address. Considering the presence of synchronized aggregate activity in the basal ganglia, this paper presents an FFT-based synchronization approach to automatically select a relevant pair of LFPs and use the pair together with an SVM-based MKL classifier for behavior recognition purposes. Our experiments on five subjects show the superiority of the proposed approach compared to other methods used for behavior classification.

preprint2016arXiv

Multi-Region Neural Representation: A novel model for decoding visual stimuli in human brains

Multivariate Pattern (MVP) classification holds enormous potential for decoding visual stimuli in the human brain by employing task-based fMRI data sets. There is a wide range of challenges in the MVP techniques, i.e. decreasing noise and sparsity, defining effective regions of interest (ROIs), visualizing results, and the cost of brain studies. In overcoming these challenges, this paper proposes a novel model of neural representation, which can automatically detect the active regions for each visual stimulus and then utilize these anatomical regions for visualizing and analyzing the functional activities. Therefore, this model provides an opportunity for neuroscientists to ask this question: what is the effect of a stimulus on each of the detected regions instead of just study the fluctuation of voxels in the manually selected ROIs. Moreover, our method introduces analyzing snapshots of brain image for decreasing sparsity rather than using the whole of fMRI time series. Further, a new Gaussian smoothing method is proposed for removing noise of voxels in the level of ROIs. The proposed method enables us to combine different fMRI data sets for reducing the cost of brain studies. Exp

preprint2016arXiv

Bayesian Nonparametric Models for Synchronous Brain-Computer Interfaces

A brain-computer interface (BCI) is a system that aims for establishing a non-muscular communication path for subjects who had suffer from a neurodegenerative disease. Many BCI systems make use of the phenomena of event-related synchronization and de-synchronization of brain waves as a main feature for classification of different cognitive tasks. However, the temporal dynamics of the electroencephalographic (EEG) signals contain additional information that can be incorporated into the inference engine in order to improve the performance of the BCIs. This information about the dynamics of the signals have been exploited previously in BCIs by means of generative and discriminative methods. In particular, hidden Markov models (HMMs) have been used in previous works. These methods have the disadvantage that the model parameters such as the number of hidden states and the number of Gaussian mixtures need to be fix "a priori". In this work, we propose a Bayesian nonparametric model for brain signal classification that does not require "a priori" selection of the number of hidden states and the number of Gaussian mixtures of a HMM. The results show that the proposed model

preprint2016arXiv

Critical dynamics on a large human Open Connectome network

Extended numerical simulations of threshold models have been performed on a human brain network with N=836733 connected nodes available from the Open Connectome project. While in case of simple threshold models a sharp discontinuous phase transition without any critical dynamics arises, variable thresholds models exhibit extended power-law scaling regions. This is attributed to fact that Griffiths effects, stemming from the topological/interaction heterogeneity of the network, can become relevant if the input sensitivity of nodes is equalized. I have studied the effects effects of link directness, as well as the consequence of inhibitory connections. Non-universal power-law avalanche size and time distributions have been found with exponents agreeing with the values obtained in electrode experiments of the human brain. The dynamical critical region occurs in an extended control parameter space without the assumption of self organized criticality.

preprint2016arXiv

Optical magnetic detection of single-neuron action potentials using quantum defects in diamond

A key challenge for neuroscience is noninvasive, label-free sensing of action potential (AP) dynamics in whole organisms with single-neuron resolution. Here, we present a new approach to this problem: using nitrogen-vacancy (NV) quantum defects in diamond to measure the time-dependent magnetic fields produced by single-neuron APs. Our technique has a unique combination of features: (i) it is noninvasive, as the light that probes the NV sensors stays within the biocompatible diamond chip and does not enter the organism, enabling activity monitoring over extended periods; (ii) it is label-free and should be widely applicable to most organisms; (iii) it provides high spatial and temporal resolution, allowing precise measurement of the AP waveforms and conduction velocities of individual neurons; (iv) it directly determines AP propagation direction through the inherent sensitivity of NVs to the associated AP magnetic field vector; (v) it is applicable to neurons located within optically opaque tissue or whole organisms, through which magnetic fields pass largely unperturbed; and (vi) it is easy-to-use, scalable, and can be integrated with existing techniques such as wide-field and supe

preprint2016arXiv

Functional Hypergraph Uncovers Novel Covariant Structures over Neurodevelopment

Brain development during adolescence is marked by substantial changes in brain structure and function, leading to a stable network topology in adulthood. However, most prior work has examined the data through the lens of brain areas connected to one another in large-scale functional networks. Here, we apply a recently-developed hypergraph approach that treats network connections (edges) rather than brain regions as the unit of interest, allowing us to describe functional network topology from a fundamentally different perspective. Capitalizing on a sample of 780 youth imaged as part of the Philadelphia Neurodevelopmental Cohort, this hypergraph representation of resting-state functional MRI data reveals three distinct classes of sub-networks (hyperedges): clusters, bridges, and stars, which represent spatially distributed, bipartite, and focal architectures, respectively. Cluster hyperedges show a strong resemblance to the functional modules of the brain including somatomotor, visual, default mode, and salience systems. In contrast, star hyperedges represent highly localized subnetworks centered on a small set of regions, and are distributed across the entire cortex. Finally, bridg

preprint2016arXiv

Pattern completion in symmetric threshold-linear networks

Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically possess multiple stable fixed points (steady states), making them viable candidates for memory encoding and retrieval. In this work, we characterize stable fixed points of general threshold-linear networks with constant external drive, and discover constraints on the co-existence of fixed points involving different subsets of active neurons. In the case of symmetric networks, we prove the following antichain property: if a set of neurons $τ$ is the support of a stable fixed point, then no proper subset or superset of $τ$ can support a stable fixed point. Symmetric threshold-linear networks thus appear to be well suited for pattern completion, since the dynamics are guaranteed not to get "stuck" in a subset or superset of a stored pattern. We also show that for any graph G, we can construct a network whose stable fixed points correspond precisely to the maximal cliques of G. As an application, we design network decoders for place field codes, and demonstrate their efficacy for error correction and

preprint2016arXiv

A Point-process Response Model for Spike Trains from Single Neurons in Neural Circuits under Optogenetic Stimulation

Optogenetics is a new tool to study neuronal circuits that have been genetically modified to allow stimulation by flashes of light. We study recordings from single neurons within neural circuits under optogenetic stimulation. The data from these experiments present a statistical challenge of modeling a high frequency point process (neuronal spikes) while the input is another high frequency point process (light flashes). We further develop a generalized linear model approach to model the relationships between two point processes, employing additive point-process response functions. The resulting model, Point-process Responses for Optogenetics (PRO), provides explicit nonlinear transformations to link the input point process with the output one. Such response functions may provide important and interpretable scientific insights into the properties of the biophysical process that governs neural spiking in response to optogenetic stimulation. We validate and compare the PRO model using a real dataset and simulations, and our model yields a superior area-under-the- curve value as high as 93% for predicting every future spike. For our experiment on the recurrent layer V circuit in the pr

preprint2016arXiv

What makes a neural code convex?

Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information via the collective behavior of populations of neurons. A code is called convex if its codewords correspond to regions defined by an arrangement of convex open sets in Euclidean space. Convex codes have been observed experimentally in many brain areas, including sensory cortices and the hippocampus, where neurons exhibit convex receptive fields. What makes a neural code convex? That is, how can we tell from the intrinsic structure of a code if there exists a corresponding arrangement of convex open sets? In this work, we provide a complete characterization of local obstructions to convexity. This motivates us to define max intersection-complete codes, a family guaranteed to have no local obstructions. We then show how our characterization enables one to use free resolutions of Stanley-Reisner ideals in order to detect violations of convexity. Taken together, these results provide a significant advance in understanding the intrinsic combinatorial properties of convex codes.

preprint2016arXiv

Neural Signal Multiplexing via Compressed Sensing

Transport of neural signals in the brain is challenging, owing to neural interference and neural noise. There is experimental evidence of multiplexing of sensory information across population of neurons, particularly in the vertebrate visual and olfactory systems. Recently, it has been discovered that in lateral intraparietal cortex of the brain, decision signals are multiplexed with decision-irrelevant visual signals. Furthermore, it is well known that several cortical neurons exhibit chaotic spiking patterns. Multiplexing of chaotic neural signals and their successful demultiplexing in the neurons amidst interference and noise, is difficult to explain. In this work, a novel compressed sensing model for efficient multiplexing of chaotic neural signals constructed using the Hindmarsh-Rose spiking model is proposed. The signals are multiplexed from a pre-synaptic neuron to its neighbouring post-synaptic neuron, in the presence of $10^4$ interfering noisy neural signals and demultiplexed using compressed sensing techniques.

preprint2016arXiv

Unsupervised feature learning from finite data by message passing: discontinuous versus continuous phase transition

Unsupervised neural network learning extracts hidden features from unlabeled training data. This is used as a pretraining step for further supervised learning in deep networks. Hence, understanding unsupervised learning is of fundamental importance. Here, we study the unsupervised learning from a finite number of data, based on the restricted Boltzmann machine learning. Our study inspires an efficient message passing algorithm to infer the hidden feature, and estimate the entropy of candidate features consistent with the data. Our analysis reveals that the learning requires only a few data if the feature is salient and extensively many if the feature is weak. Moreover, the entropy of candidate features monotonically decreases with data size and becomes negative (i.e., entropy crisis) before the message passing becomes unstable, suggesting a discontinuous phase transition. In terms of convergence time of the message passing algorithm, the unsupervised learning exhibits an easy-hard-easy phenomenon as the training data size increases. All these properties are reproduced in an approximate Hopfield model, with an exception that the entropy crisis is absent, and only continuous phase tr

preprint2016arXiv

What can topology tell us about the neural code?

Neuroscience is undergoing a period of rapid experimental progress and expansion. New mathematical tools, previously unknown in the neuroscience community, are now being used to tackle fundamental questions and analyze emerging data sets. Consistent with this trend, the last decade has seen an uptick in the use of topological ideas and methods in neuroscience. In this talk I will survey recent applications of topology in neuroscience, and explain why topology is an especially natural tool for understanding neural codes. Note: This is a write-up of my talk for the Current Events Bulletin, held at the 2016 Joint Math Meetings in Seattle, WA.

preprint2016arXiv

A tractable method for describing complex couplings between neurons and population rate

Neurons within a population are strongly correlated, but how to simply capture these correlations is still a matter of debate. Recent studies have shown that the activity of each cell is influenced by the population rate, defined as the summed activity of all neurons in the population. However, an explicit, tractable model for these interactions is still lacking. Here we build a probabilistic model of population activity that reproduces the firing rate of each cell, the distribution of the population rate, and the linear coupling between them. This model is tractable, meaning that its parameters can be learned in a few seconds on a standard computer even for large population recordings. We inferred our model for a population of 160 neurons in the salamander retina. In this population, single-cell firing rates depended in unexpected ways on the population rate. In particular, some cells had a preferred population rate at which they were most likely to fire. These complex dependencies could not be explained by a linear coupling between the cell and the population rate. We designed a more general, still tractable model that could fully account for these non-linear dependencies. We thu

preprint2016arXiv

Automatic Neuron Detection in Calcium Imaging Data Using Convolutional Networks

Calcium imaging is an important technique for monitoring the activity of thousands of neurons simultaneously. As calcium imaging datasets grow in size, automated detection of individual neurons is becoming important. Here we apply a supervised learning approach to this problem and show that convolutional networks can achieve near-human accuracy and superhuman speed. Accuracy is superior to the popular PCA/ICA method based on precision and recall relative to ground truth annotation by a human expert. These results suggest that convolutional networks are an efficient and flexible tool for the analysis of large-scale calcium imaging data.

preprint2016arXiv

Emerging Frontiers of Neuroengineering: A Network Science of Brain Connectivity

Neuroengineering is faced with unique challenges in repairing or replacing complex neural systems that are composed of many interacting parts. These interactions form intricate patterns over large spatiotemporal scales, and produce emergent behaviors that are difficult to predict from individual elements. Network science provides a particularly appropriate framework in which to study and intervene in such systems, by treating neural elements (cells, volumes) as nodes in a graph and neural interactions (synapses, white matter tracts) as edges in that graph. Here, we review the emerging discipline of network neuroscience, which uses and develops tools from graph theory to better understand and manipulate neural systems, from micro- to macroscales. We present examples of how human brain imaging data is being modeled with network analysis and underscore potential pitfalls. We then highlight current computational and theoretical frontiers, and emphasize their utility in informing diagnosis and monitoring, brain-machine interfaces, and brain stimulation. A flexible and rapidly evolving enterprise, network neuroscience provides a set of powerful approaches and fundamental insights critica

preprint2016arXiv

Instability to a heterogeneous oscillatory state in randomly connected recurrent networks with delayed interactions

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks consisting of randomly coupled rate units. We identify a novel type of bifurcation in which a continuous part of the eigenvalue spectrum of the linear stability matrix crosses the instability line at non-zero-frequency. This bifurcation occurs when the interactions are delayed and partially anti-symmetric, and leads to a heterogeneous oscillatory state in which oscillations are apparent in the activity of individual units, but not on the population-average level.

preprint2016arXiv

Similarities and differences between stimulus tuning in the inferotemporal visual cortex and convolutional networks

Deep convolutional neural networks (CNNs) trained for object classification have a number of striking similarities with the primate ventral visual stream. In particular, activity in early, intermediate, and late layers is closely related to activity in V1, V4, and the inferotemporal cortex (IT). This study further compares activity in late layers of object-classification CNNs to activity patterns reported in the IT electrophysiology literature. There are a number of close similarities, including the distributions of population response sparseness across stimuli, and the distribution of size tuning bandwidth. Statisics of scale invariance, responses to clutter and occlusion, and orientation tuning are less similar. Statistics of object selectivity are quite different. These results agree with recent studies that highlight strong parallels between object-categorization CNNs and the ventral stream, and also highlight differences that could perhaps be reduced in future CNNs.

498 works