Optimal tuning widths in population coding of periodic variables

We study the relationship between the accuracy of a large neuronal population in encoding periodic sensory stimuli and the width of the tuning curves of individual neurons in the population. By using general simple models of population activity, we show that when considering one or two periodic stimulus features, a narrow tuning width provides better population encoding accuracy. When encoding more than two periodic stimulus features, the information conveyed by the population is instead maximal for finite values of the tuning width. These optimal values are only weakly dependent on model parameters and are similar to the width of tuning to orientation or motion direction of real visual cortical neurons. A very large tuning width leads to poor encoding accuracy, whatever the number of stimulus features encoded. Thus, optimal coding of periodic stimuli is different from that of nonperiodic stimuli, which, as shown in previous studies, would require infinitely large tuning widths when coding more than two stimulus features.     

Testing for and estimating latency effects for poisson and non-poisson spike trains

Determining the variations in response latency of one or several neurons to a stimulus is of interest in different contexts. Two common problems concern correlating latency with a particular behavior, for example, the reaction time to a stimulus, and adjusting tools for detecting synchronization between two neurons. We use two such problems to illustrate the latency testing and estimation methods developed in this article. Our test for latencies is a formal statistical test that produces a p-value. It is applicable for Poisson and non-Poisson spike trains via use of the bootstrap. Our estimation method is model free, it is fast and easy to implement, and its performance compares favorably to other methods currently available.     

Investigation of possible neural architectures underlying information-geometric measures

A novel analytical method based on information geometry was recently proposed, and this method may provide useful insights into the statistical interactions within neural groups. The link between informationgeometric measures and the structure of neural interactions has not yet been elucidated, however, because of the ill-posed nature of the problem. Here, possible neural architectures underlying information-geometric measures are investigated using an isolated pair and an isolated triplet of model neurons. By assuming the existence of equilibrium states, we derive analytically the relationship between the information-geometric parameters and these simple neural architectures. For symmetric networks, the first- and second-order information-geometric parameters represent, respectively, the external input and the underlying connections between the neurons provided that the number of neurons used in the parameter estimation in the log-linear model and the number of neurons in the network are the same. For asymmetric networks, however, these parameters are dependent on both the intrinsic connections and the external inputs to each neuron. In addition, we derive the relation between the information-geometric parameter corresponding to the two-neuron interaction and a conventional cross-correlation measure. We also show that the information-geometric parameters vary depending on the number of neurons assumed for parameter estimation in the log-linear model. This finding suggests a need to examine the information-geometric method carefully. A possible criterion for choosing an appropriate orthogonal coordinate is also discussed. This article points out the importance of a model-based approach and sheds light on the possible neural structure underlying the application of information geometry to neural network analysis.     

A coarse-to-fine disparity energy model with both phase-shift and position-shift receptive field mechanisms

Numerous studies suggest that the visual system uses both phase- and position-shift receptive field (RF) mechanisms for the processing of binocular disparity. Although the difference between these two mechanisms has been analyzed before, previous work mainly focused on disparity tuning curves instead of population responses. However, tuning curve and population response can exhibit different characteristics, and it is the latter that determines disparity estimation. Here we demonstrate, in the framework of the disparity energy model, that for relatively small disparities, the population response generated by the phase-shift mechanism is more reliable than that generated by the position-shift mechanism. This is true over a wide range of parameters, including the RF orientation. Since the phase model has its own drawbacks of underestimating large stimulus disparity and covering only a restricted range of disparity at a given scale, we propose a coarse-to-fine algorithm for disparity computation with a hybrid of phase-shift and position-shift components. In this algorithm, disparity at each scale is always estimated by the phase-shift mechanism to take advantage of its higher reliability. Since the phase-based estimation is most accurate at the smallest scale when the disparity is correspondingly small, the algorithm iteratively reduces the input disparity from coarse to fine scales by introducing a constant position-shift component to all cells for a given location in order to offset the stimulus disparity at that location. The model also incorporates orientation pooling and spatial pooling to further enhance reliability. We have tested the algorithm on both synthetic and natural stereo images and found that it often performs better than a simple scale-averaging procedure.     

关于视觉注意力选择的神经编码

本文提出了一种改进的注意力选择模型,在这个模型中,周边神经元代表初级视觉皮层的神经元,中心神经元代表更高级视觉皮层中的神经元.生理实验发现方向选择性是初级视觉皮层神经元的重要特性之一,所以模型除了考虑外部刺激的强度,也考虑了初级视觉皮层中的神经元的方向选择性.仿真结果显示改进后的模型能够选择具有不同方向选择性的目标,并且能从一个目标转移到另一个目标.和原模型相比,改进后的模型更符合生理背景.该模型的动力学分析结果,对于理解视觉神经系统的编码有一定的帮助.     

Common-input models for multiple neural spike-train data

Recent developments in multi-electrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenge in computational neuroscience today. In this work, we develop a multivariate point-process model in which the observed activity of a network of neurons depends on three terms: (1) the experimentally-controlled stimulus; (2) the spiking history of the observed neurons; and (3) a hidden term that corresponds, for example, to common input from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We consider two models for the network firing-rates, one of which is computationally and analytically tractable but can lead to unrealistically high firing-rates, while the other with reasonable firing-rates imposes a greater computational burden. We develop an expectation-maximization algorithm for fitting the parameters of both the models. For the analytically tractable model the expectation step is based on a continuous-time implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The other model that we consider necessitates the use of Monte Carlo methods for the expectation as well as maximization step. We discuss the trade-off involved in choosing between the two models and the associated methods. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron's ring rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach.     

Enhanced sound perception by widespread-onset neuronal responses in auditory cortex

Accumulating evidence suggests that auditory cortical neurons exhibit widespread-onset responses and restricted sustained responses to sound stimuli. When a sound stimulus is presented to a subject, the auditory cortex first responds with transient discharges across a relatively large population of neurons, showing widespread-onset responses. As time passes, the activation becomes restricted to a small population of neurons that are preferentially driven by the stimulus, showing restricted sustained responses. The sustained responses are considered to have a role in expressing information about the stimulus, but it remains to be seen what roles the widespread-onset responses have in auditory information processing. We carried out numerical simulations of a neural network model for a lateral belt area of auditory cortex. In the network, dynamic cell assemblies expressed information about auditory sounds. Lateral excitatory and inhibitory connections were made between cell assemblies, respectively, by direct and indirect projections via interneurons. Widespread-onset neuronal responses to sound stimuli (bandpassed noises) took place over the network if lateral excitation preceded lateral inhibition, making a time widow for the onset responses. The widespread-onset responses contributed to the accelerating reaction time of neurons to sensory stimulation. Lateral interaction among dynamic cell assemblies was essential for maintaining ongoing membrane potentials near thresholds for action potential generation, thereby accelerating reaction time to subsequent sensory input as well. We suggest that the widespread-onset neuronal responses and the ongoing subthreshold cortical state, for which the coordination of lateral synaptic interaction among dissimilar cell assemblies is essential, may work together in order for the auditory cortex to quickly detect the sudden occurrence of sounds from the external environment.     

An improved selective attention model considering orientation preferences

An improved selective attention model is proposed in this paper, which is designed as a network of spiking neurons of Hodgkin--Huxley type with star-like connections between the central units and peripheral neurons. In this model, peripheral neurons represent the neurons located in the primary visual cortex. Since orientation preference is an important property of neurons in primary visual cortex, it should be considered except for external stimuli intensity. Simulation results show that the improved model can sequentially select objects with different orientation preferences and has a reliable shift of attention from one object to another, which are consistent with the experimental results that the neurons with different orientation preferences are laid out in pinwheel patterns.     

Faithful representation of stimuli with a population of integrate-and-fire neurons

We consider a formal model of stimulus encoding with a circuit consisting of a bank of filters and an ensemble of integrate-and-fire neurons. Such models arise in olfactory systems, vision, and hearing. We demonstrate that bandlimited stimuli can be faithfully represented with spike trains generated by the ensemble of neurons. We provide a stimulus reconstruction scheme based on the spike times of the ensemble of neurons and derive conditions for perfect recovery. The key result calls for the spike density of the neural population to be above the Nyquist rate. We also show that recovery is perfect if the number of neurons in the population is larger than a threshold value. Increasing the number of neurons to achieve a faithful representation of the sensory world is consistent with basic neurobiological thought. Finally we demonstrate that in general, the problem of faithful recovery of stimuli from the spike train of single neurons is ill posed. The stimulus can be recovered, however, from the information contained in the spike train of a population of neurons.     

Contextual modulation of orientation tuning contributes to efficient processing of natural stimuli

It has been proposed that sensory neurons are adapted to the statistical structure of the natural environment in order to encode natural stimuli efficiently. While spatiotemporal correlations in luminance signals may be decorrelated by neurons in early visual processing stages, higher-order correlations, such as those in the orientation domain, are likely to persist in the input representation until the cortical level. In this study, we first examine orientation correlations in natural stimuli across brief time intervals and across nearby regions of space, and find strong correlations in both domains. We then examine contextual modulation of orientation tuning. We find that both temporal and spatial contexts exert a common influence on orientation tuning, shifting tuning away from the orientation of either the adapting (temporal) or surrounding (spatial) grating. Finally, we incorporate this context-mediated repulsive shift in orientation tuning into a model of cortical responses. We find that a direct result of the shift is a reduction of the redundancy in the population responses evoked by the orientation configurations that are most common in natural stimuli. Thus, cortical neurons may be adapted to the statistics of orientation in natural stimuli in order to increase the efficiency of natural stimulus representation.     

Noise spectrum and signal transmission through a population of spiking neurons.

How reliably can a population of spiking neurons transmit a continuous-time signal? We study the noise spectrum of a fully connected population of spiking neurons with relative and absolute refractoriness. Spikes are generated stochastically with a rate that depends on the postsynaptic potential. The analytical solution of the noise spectrum of the population activity is compared with simulations. We find that strong inhibitory couplings can considerably reduce the noise level in a certain frequency band. This allows the population to reliably transmit signals at frequencies close to or even above the single-neuron firing rate.     

Replicating receptive fields of simple and complex cells in primary visual cortex in a neuronal network model with temporal and population sparseness and reliability

We propose a new principle for replicating receptive field properties of neurons in the primary visual cortex. We derive a learning rule for a feedforward network, which maintains a low firing rate for the output neurons (resulting in temporal sparseness) and allows only a small subset of the neurons in the network to fire at any given time (resulting in population sparseness). Our learning rule also sets the firing rates of the output neurons at each time step to near-maximum or near-minimum levels, resulting in neuronal reliability. The learning rule is simple enough to be written in spatially and temporally local forms. After the learning stage is performed using input image patches of natural scenes, output neurons in the model network are found to exhibit simple-cell-like receptive field properties. When the output of these simple-cell-like neurons are input to another model layer using the same learning rule, the second-layer output neurons after learning become less sensitive to the phase of gratings than the simple-cell-like input neurons. In particular, some of the second-layer output neurons become completely phase invariant, owing to the convergence of the connections from first-layer neurons with similar orientation selectivity to second-layer neurons in the model network. We examine the parameter dependencies of the receptive field properties of the model neurons after learning and discuss their biological implications. We also show that the localized learning rule is consistent with experimental results concerning neuronal plasticity and can replicate the receptive fields of simple and complex cells.     

A model of the response of visual area V2 to combinations of orientations

The role of the V2 area in visual processing is still almost entirely unexplored. Recently, several studies revealed the tuning of V2 neurons in the macaque to stimuli consisting of two segments with different orientations. By measuring orientation tuning inside subunits of the overall receptive field, units with non uniform orientation selectivity have been found. In this work, the emergence of a computational organization supporting similar responses is explored, using an artificial model of cortical maps. This model, called LISSOM (Laterally Interconnected Synergetically Self-Organizing Map) includes excitatory and inhibitory lateral connections. In this simulation two LISSOM maps are arranged as V1 and V2 areas. In the first area, the classical domains of orientation selectivity develop, while in V2 most neurons become sensitive to pairs of orientations. The overall activation of these units depend on the presence of oriented segments at a finer grain than the whole receptive fields, with complex nonlinear interactions.     

Feedback and Surround Modulated Boundary Detection

Edges are key components of any visual scene to the extent that we can recognise objects merely by their silhouettes. The human visual system captures edge information through neurons in the visual cortex that are sensitive to both intensity discontinuities and particular orientations. The “classical approach” assumes that these cells are only responsive to the stimulus present within their receptive fields, however, recent studies demonstrate that surrounding regions and inter-areal feedback connections influence their responses significantly. In this work we propose a biologically-inspired edge detection model in which orientation selective neurons are represented through the first derivative of a Gaussian function resembling double-opponent cells in the primary visual cortex (V1). In our model we account for four kinds of receptive field surround, i.e. full, far, iso- and orthogonal-orientation, whose contributions are contrast-dependant. The output signal from V1 is pooled in its perpendicular direction by larger V2 neurons employing a contrast-variant centre-surround kernel. We further introduce a feedback connection from higher-level visual areas to the lower ones. The results of our model on three benchmark datasets show a big improvement compared to the current non-learning and biologically-inspired state-of-the-art algorithms while being competitive to the learning-based methods.     

Self-organizing continuous attractor networks and path integration: one-dimensional models of head direction cells

Some neurons encode information about the orientation or position of an animal, and can maintain their response properties in the absence of visual input. Examples include head direction cells in rats and primates, place cells in rats and spatial view cells in primates. 'Continuous attractor' neural networks model these continuous physical spaces by using recurrent collateral connections between the neurons which reflect the distance between the neurons in the state space (e.g. head direction space) of the animal. These networks maintain a localized packet of neuronal activity representing the current state of the animal. We show how the synaptic connections in a one-dimensional continuous attractor network (of for example head direction cells) could be self-organized by associative learning. We also show how the activity packet could be moved from one location to another by idiothetic (self-motion) inputs, for example vestibular or proprioceptive, and how the synaptic connections could self-organize to implement this. The models described use 'trace' associative synaptic learning rules that utilize a form of temporal average of recent cell activity to associate the firing of rotation cells with the recent change in the representation of the head direction in the continuous attractor. We also show how a nonlinear neuronal activation function that could be implemented by NMDA receptors could contribute to the stability of the activity packet that represents the current state of the animal.     

MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test

Insulin sensitivity and pancreatic responsivity are the two main factors controlling glucose tolerance. We have proposed a method for measuring these two factors, using computer analysis of a frequently-sampled intravenous glucose tolerance test (FSIGT). This 'minimal modelling approach' fits two mathematical models with FSIGT glucose and insulin data: one of glucose disappearance and one of insulin kinetics. MINMOD is the computer program which identifies the model parameters for each individual. A nonlinear least squares estimation technique is used, employing a gradient-type of estimation algorithm, and the first derivatives (not known analytically) are computed according to the 'sensitivity approach'. The program yields the parameter estimates and the precision of their estimation. From the model parameters, it is possible to extract four indices: SG, the ability of glucose per se to enhance its own disappearance at basal insulin, SI, the tissue insulin sensitivity index, phi 1, first phase pancreatic responsivity, and phi 2, second phase pancreatic responsivity. These four characteristic parameters have been shown to represent an integrated metabolic portrait of a single individual.     

How optimal stimuli for sensory neurons are constrained by network architecture

Identifying the optimal stimuli for a sensory neuron is often a difficult process involving trial and error. By analyzing the relationship between stimuli and responses in feedforward and stable recurrent neural network models, we find that the stimulus yielding the maximum firing rate response always lies on the topological boundary of the collection of all allowable stimuli, provided that individual neurons have increasing input-output relations or gain functions and that the synaptic connections are convergent between layers with nondegenerate weight matrices. This result suggests that in neurophysiological experiments under these conditions, only stimuli on the boundary need to be tested in order to maximize the response, thereby potentially reducing the number of trials needed for finding the most effective stimuli. Even when the gain functions allow firing rate cutoff or saturation, a peak still cannot exist in the stimulus-response relation in the sense that moving away from the optimum stimulus always reduces the response. We further demonstrate that the condition for nondegenerate synaptic connections also implies that proper stimuli can independently perturb the activities of all neurons in the same layer. One example of this type of manipulation is changing the activity of a single neuron in a given processing layer while keeping that of all others constant. Such stimulus perturbations might help experimentally isolate the interactions of selected neurons within a network.     

Stationary bumps in networks of spiking neurons.

We examine the existence and stability of spatially localized "bumps" of neuronal activity in a network of spiking neurons. Bumps have been proposed in mechanisms of visual orientation tuning, the rat head direction system, and working memory. We show that a bump solution can exist in a spiking network provided the neurons fire asynchronously within the bump. We consider a parameter regime where the bump solution is bistable with an all-off state and can be initiated with a transient excitatory stimulus. We show that the activity profile matches that of a corresponding population rate model. The bump in a spiking network can lose stability through partial synchronization to either a traveling wave or the all-off state. This can occur if the synaptic timescale is too fast through a dynamical effect or if a transient excitatory pulse is applied to the network. A bump can thus be activated and deactivated with excitatory inputs that may have physiological relevance.     

Selectivity and stability via dendritic nonlinearity

Inspired by recent studies regarding dendritic computation, we constructed a recurrent neural network model incorporating dendritic lateral inhibition. Our model consists of an input layer and a neuron layer that includes excitatory cells and an inhibitory cell; this inhibitory cell is activated by the pooled activities of all the excitatory cells, and it in turn inhibits each dendritic branch of the excitatory cells that receive excitations from the input layer. Dendritic nonlinear operation consisting of branch-specifically rectified inhibition and saturation is described by imposing nonlinear transfer functions before summation over the branches. In this model with sufficiently strong recurrent excitation, on transiently presenting a stimulus that has a high correlation with feed- forward connections of one of the excitatory cells, the corresponding cell becomes highly active, and the activity is sustained after the stimulus is turned off, whereas all the other excitatory cells continue to have low activities. But on transiently presenting a stimulus that does not have high correlations with feedforward connections of any of the excitatory cells, all the excitatory cells continue to have low activities. Interestingly, such stimulus-selective sustained response is preserved for a wide range of stimulus intensity. We derive an analytical formulation of the model in the limit where individual excitatory cells have an infinite number of dendritic branches and prove the existence of an equilibrium point corresponding to such a balanced low-level activity state as observed in the simulations, whose stability depends solely on the signal-to-noise ratio of the stimulus. We propose this model as a model of stimulus selectivity equipped with self-sustainability and intensity-invariance simultaneously, which was difficult in the conventional competitive neural networks with a similar degree of complexity in their network architecture. We discuss the biological relevance of the model in a general framework of computational neuroscience.