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Event occurrence is not only subject to the environmental changes, but is also facilitated by the events that have occurred in a system. Here, we develop a method for estimating such extrinsic and intrinsic factors from a single series of event-occurrence times. The analysis is performed using a model that combines the inhomogeneous Poisson process and the Hawkes process, which represent exogenous fluctuations and endogenous chain-reaction mechanisms, respectively. The model is fit to a given dataset by minimizing the free energy, for which statistical physics and a path-integral method are utilized. Because the process of event occurrence is stochastic, parameter estimation is inevitably accompanied by errors, and it can ultimately occur that exogenous and endogenous factors cannot be captured even with the best estimator. We obtained four regimes categorized according to whether respective factors are detected. By applying the analytical method to real time series of debate in a social-networking service, we have observed that the estimated exogenous and endogenous factors are close to the first comments and the follow-up comments, respectively. This method is general and applicable to a variety of data, and we have provided an application program, by which anyone can analyze any series of event times., Comment: 17 pages, 7 figures

The recent increase in reliable, simultaneous high channel count extracellular recordings is exciting for physiologists and theoreticians because it offers the possibility of reconstructing the underlying neuronal circuits. We recently presented a method of inferring this circuit connectivity from neuronal spike trains by applying the generalized linear model to cross-correlograms. Although the algorithm can do a good job of circuit reconstruction, the parameters need to be carefully tuned for each individual dataset. Here we present another method using a Convolutional Neural Network for Estimating synaptic Connectivity from spike trains. After adaptation to huge amounts of simulated data, this method robustly captures the specific feature of monosynaptic impact in a noisy cross-correlogram. There are no user-adjustable parameters. With this new method, we have constructed diagrams of neuronal circuits recorded in several cortical areas of monkeys.

Oscillations often provide us with information of the origin. For instance, electrical oscillations measured by electroencephalograms and electrocardiograms afford clues to cognitive disorders and cardiac dysfunction, respectively. In particular, vibrations in air-pressure or sounds present rich information about circumstances. Here, we consider the problem of inferring types of coins from the sounds of their collision, and search for mechanisms that make such an inference possible. By devising a Bayesian learning algorithm and using a deep neural network, we reveal that optimizing the inference naturally leads the machines to select frequencies at which individual coins exhibit specific peaks in their sound spectra, indicating that inferences can be efficiently made by detecting the resonance sounds inherent in different coins. Both learning machines achieve high performances in correctly inferring coins. The developed methods are general and may be applicable to not only other sound identification tasks, but also various oscillatory phenomena, such as correlating brain activity to behavior as in the brain–computer interfaces.

SummaryTwo-photon imaging is a major recording technique in neuroscience, but it suffers from several limitations, including a low sampling rate, the nonlinearity of calcium responses, the slow dynamics of calcium dyes and a low signal-to-noise ratio, all of which impose a severe limitation on the application of two-photon imaging in elucidating neuronal dynamics with high temporal resolution. Here, we developed a hyperacuity algorithm (HA_time) based on an approach combining a generative model and machine learning to improve spike detection and the precision of spike time inference. First, Bayesian inference estimates the calcium spike model by assuming the constancy of the spike shape and size. A support vector machine employs this information and detects spikes with higher temporal precision than the sampling rate. Compared with conventional thresholding, HA_time improved the precision of spike time estimation up to 20-fold for simulated calcium data. Furthermore, the benchmark analysis of experimental data from different brain regions and simulation of a broader range of experimental conditions showed that our algorithm was among the best in a class of hyperacuity algorithms. We encourage experimenters to use the proposed algorithm to precisely estimate hyperacuity spike times from two-photon imaging.

State-of-the-art techniques allow researchers to record large numbers of spike trains in parallel for many hours. With enough such data, we should be able to infer the connectivity among neurons. Here we develop a method for reconstructing neuronal circuitry by applying a generalized linear model (GLM) to spike cross-correlations. Our method estimates connections between neurons in units of postsynaptic potentials and the amount of spike recordings needed to verify connections. The performance of inference is optimized by counting the estimation errors using synthetic data. This method is superior to other established methods in correctly estimating connectivity. By applying our method to rat hippocampal data, we show that the types of estimated connections match the results inferred from other physiological cues. Thus our method provides the means to build a circuit diagram from recorded spike trains, thereby providing a basis for elucidating the differences in information processing in different brain regions., Current techniques have enabled the simultaneous collection of spike train data from large numbers of neurons. Here, the authors report a method to infer the underlying neural circuit connectivity diagram based on a generalized linear model applied to spike cross-correlations between neurons.

The occurrence of new events in a system is typically driven by external causes and by previous events taking place inside the system. This is a general statement, applying to a range of situations including, more recently, to the activity of users in Online social networks (OSNs). Here we develop a method for extracting from a series of posting times the relative contributions of exogenous, e.g. news media, and endogenous, e.g. information cascade. The method is based on the fitting of a generalized linear model (GLM) equipped with a self-excitation mechanism. We test the method with synthetic data generated by a nonlinear Hawkes process, and apply it to a real time series of tweets with a given hashtag. In the empirical dataset, the estimated contributions of exogenous and endogenous volumes are close to the amounts of original tweets and retweets respectively. We conclude by discussing the possible applications of the method, for instance in online marketing., 5 figures

State-of-the-art techniques allow researchers to record large numbers of spike trains parallel for many hours. With enough such data, we should be able to infer the connectivity among neurons. Here we develop a computationally realizable method for reconstructing neuronal circuitry by applying a generalized linear model (GLM) to spike crosscorrelations. Our method estimates interneuronal connections in units of postsynaptic potentials and the amount of spike recording needed for verifying connections. The performance of inference is optimized by counting the estimation errors using synthetic data from a network of Hodgkin-Huxley type neurons. By applying our method to rat hippocampal data, we show that the numbers and types of connections estimated from our calculations match the results inferred from other physiological cues. Our method provides the means to build a circuit diagram from recorded spike trains, thereby providing a basis for elucidating the differences in information processing in different brain regions.

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm., National Science Foundation (U.S.) (Grant DMS-1127914), National Institute of Mental Health (U.S.) (Grant MH064537)

Recently, it has been suggested that certain neurons with Poissonian spiking statistics may communicate by discontinuously switching between two levels of firing intensity. Such a situation resembles in many ways the optimal information transmission protocol for the continuous-time Poisson channel known from information theory. In this contribution we employ the classical information-theoretic results to analyze the efficiency of such a transmission from different perspectives, emphasising the neurobiological viewpoint. We address both the ultimate limits, in terms of the information capacity under metabolic cost constraints, and the achievable bounds on performance at rates below capacity with fixed decoding error probability. In doing so we discuss optimal values of experimentally measurable quantities that can be compared with the actual neuronal recordings in a future effort.

There is a commonality among contagious diseases, tweets, urban crimes, nuclear reactions, and neuronal firings that past events facilitate the future occurrence of events. The spread of events has been extensively studied such that the systems exhibit catastrophic chain reactions if the interaction represented by the ratio of reproduction exceeds unity; however, their subthreshold states for the case of the weaker interaction are not fully understood. Here, we report that these systems are possessed by nonstationary cascades of event-occurrences already in the subthreshold regime. Event cascades can be harmful in some contexts, when the peak-demand causes vaccine shortages, heavy traffic on communication lines, frequent crimes, or large fluctuations in nuclear reactions, but may be beneficial in other contexts, such that spontaneous activity in neural networks may be used to generate motion or store memory. Thus it is important to comprehend the mechanism by which such cascades appear, and consider controlling a system to tame or facilitate fluctuations in the event-occurrences. The critical interaction for the emergence of cascades depends greatly on the network structure in which individuals are connected. We demonstrate that we can predict whether cascades may emerge in a network, given information about the interactions between individuals. Furthermore, we develop a method of reallocating connections among individuals so that event cascades may be either impeded or impelled in a network., 16 pages, 5 figures

Several methods and algorithms have recently been proposed that allow for the systematic evaluation of simple neuron models from intracellular or extracellular recordings. Models built in this way generate good quantitative predictions of the future activity of neurons under temporally structured current injection. It is, however, difficult to compare the advantages of various models and algorithms since each model is designed for a different set of data. Here, we report about one of the first attempts to establish a benchmark test that permits a systematic comparison of methods and performances in predicting the activity of rat cortical pyramidal neurons. We present early submissions to the benchmark test and discuss implications for the design of future tests and simple neurons models. (c) 2007 Elsevier B.V. All rights reserved.

People communicate with those who have the same background or share a common interest by using a social networking service (SNS). News or messages propagate through inhomogeneous connections in an SNS by sharing or facilitating additional comments. Such human activity is known to lead to endogenous bursting in the rate of message occurrences. We analyze a multi-dimensional self-exciting process to reveal dependence of the bursting activity on the topology of connections and the distribution of interaction strength on the connections. We determine the critical conditions for the cases where interaction strength is regulated at either the point of input or output for each person. In the input regulation condition, the network may exhibit bursting with infinitesimal interaction strength, if the dispersion of the degrees diverges as in the scale-free networks. In contrast, in the output regulation condition, the critical value of interaction strength, represented by the average number of events added by a single event, is a constant $1-1/\sqrt{2} \approx 0.3$, independent of the degree dispersion. Thus, the stability in human activity crucially depends on not only the topology of connections but also the manner in which interactions are distributed among the connections., 8 pages, 8 figures

Spike sequences of in-vivo cortical neurons are highly irregular. Recently, Softky and Koch addressed the question of the suitability of the integrate-and-fire model for the spiking mechanism in the light of spiking irregularity. We consider real neuronal spike sequences and examine whether this model is really unsatisfactory for explaining actual data. It is found that the leaky integrate-and-fire model is not completely inconsistent with the real data. Detailed analysis, however, shows a need for modifications of the model.

Because every spike of a neuron is determined by input signals, a train of spikes may contain information about the dynamics of unobserved neurons. A state-space method based on the leaky integrate-and-fire model, describing neuronal transformation from input signals to a spike train has been proposed for tracking input parameters represented by their mean and fluctuation [11]. In the present paper, we propose to make the estimation more realistic by adopting an LIF model augmented with an adaptive moving threshold. Moreover, because the direct state-space method is computationally infeasible for a data set comprising thousands of spikes, we further develop a practical method for transforming instantaneous firing characteristics back to input parameters. The instantaneous firing characteristics, represented by the firing rate and non-Poisson irregularity, can be estimated using a computationally feasible algorithm. We applied our proposed methods to synthetic data to clarify that they perform well.

Because neurons are integrating input signals and translating them into timed output spikes, examining spike timing may reveal information about inputs, such as population activities of excitatory and inhibitory presynaptic neurons. Here we construct a state-space method for estimating not only such extrinsic parameters, but also an intrinsic neuronal parameter such as the membrane time constant from a single spike train.

Neurons in vivo exhibit irregular firing, and some aspect of their firing pattern such as the degree of firing irregularity does not fluctuate greatly in time for individual neurons, while it differs among neurons [1]. By analyzing spike trains recorded from a variety of cortical areas, it has been revealed that neurons in motor-related cortical areas fire regularly while neurons in visual and prefrontal cortex fire randomly [2]. Here, the firing irregularity is defined as a variability of consecutive interspike intervals, independent of the firing rate. In those studies, the firing rate has been ignored, because it may fluctuate greatly in time depending on external stimuli or behavioral contexts of an animal. Though the neuronal firing rate may fluctuate with external stimuli, this does not necessarily mean that the rate is extrinsic and perfectly controllable; there could be some uncontrollable intrinsic aspect in the firing rate fluctuation. In this contribution, we go contrary to the above-mentioned studies, and attempt to characterize neuronal spike trains solely in terms of the firing rate, ignoring the firing irregularity. The key feature of neuronal spike trains we now pay attention to is dynamic mode of rate fluctuation, such that the rate either fluctuates smoothly in time or changes abruptly between several stationary states. We compare two different models of a fluctuating rate process for their goodness-of-fit with respect to spike trains recorded from single neurons in several cortical areas of rats. The first model is the state space model constructed under the Empirical Bayes method [3,4]. The generative inhomogeneous Poisson process is defined as the conditional distribution of the spike times ti≡t1,t2,...,tn given the rateλ(t), ptiλ(t)= ∏i=1nλ(ti)exp-∫ 0Tλ(t)dt. We give the prior distribution of λ(t) by incorporating the tendency of the rate to be flat, pλ(t)∝exp-β∫ 0Tdλ/dt2dt. The hyperparameter β is selected by the principle of maximizing the marginal likelihood, and then we obtain the maximum a posteriori (MAP) estimate for the rate λ⌢(t). The second alternative model is the Hidden Markov model (HMM) whose hidden states represent different rate states [5-7]. The number of states is selected with a variation Bayes method. In this way, two different estimations of the firing rate are obtained using the continuous state space model and the discrete HMM. We compare them for each spike train obtained from a neuron, and examine whether the continuous or discrete representation of the state transition is more plausible. Then, we examine how the different preferences are distributed in different cortical areas.

It has long been debated whether information in the brain is coded at the rate of neuronal spiking or at the precise timing of single spikes. Although this issue is essential to the understanding of neural signal processing, it is not easily resolved because the two mechanisms are not mutually exclusive. We suggest revising this coding issue so that one hypothesis is uniquely selected for a given spike train. To this end, we decide whether the spike train is likely to transmit a continuously varying analog signal or switching between active and inactive states. The coding hypothesis is selected by comparing the likelihood estimates yielded by empirical Bayes and hidden Markov models on individual data. The analysis method is applicable to generic event sequences, such as earthquakes, machine noises, human communications, and enhances the gain in decoding signals and infers underlying activities., Comment: 10 pages, 7 figures

In simulating realistic neuronal circuitry composed of diverse types of neurons, we need an elemental spiking neuron model that is capable of not only quantitatively reproducing spike times of biological neurons given in vivo-like fluctuating inputs, but also qualitatively representing a variety of firing responses to transient current inputs. Simplistic models based on leaky integrate-and-fire mechanisms have demonstrated the ability to adapt to biological neurons. In particular, the multi-timescale adaptive threshold (MAT) model reproduces and predicts precise spike times of regular-spiking, intrinsic-bursting, and fast-spiking neurons, under any fluctuating current; however, this model is incapable of reproducing such specific firing responses as inhibitory rebound spiking and resonate spiking. In this paper, we augment the MAT model by adding a voltage dependency term to the adaptive threshold so that the model can exhibit the full variety of firing responses to various transient current pulses while maintaining the high adaptability inherent in the original MAT model. Furthermore, with this addition, our model is actually able to better predict spike times. Despite the augmentation, the model has only four free parameters and is implementable in an efficient algorithm for large-scale simulation due to its linearity, serving as an element neuron model in the simulation of realistic neuronal circuitry.

Neuronal activity is measured by the number of stereotyped action potentials, called spikes, elicited in response to a stimulus or the behavioral conditions of an animal. Any nonparametric method for grasping the time-varying rate of spike firing contains a single parameter that controls the jaggedness of the estimated rate, such as the binsize of the time histogram or the bandwidth of the kernel smoother. In most neurophysiological studies, the parameter that determines the interpretation of neuronal activity has been selected subjectively by individual researchers. Recently, theories for objectively selecting the parameter have been developed. This chapter introduces the standard rate estimation tools, such as the peri-stimulus time histogram (PSTH), kernel density estimation, or Bayes estimation, and shows ways of selecting their parameters under the principles of minimizing the mean integrated squared error or maximizing the likelihood. We also sum up the methods in handy recipes that may be useful in practical data analysis.

or> Meeting abstracts - A single PDF containing all abstracts in this Supplement is available here . http://www. biomedcentral.co m/content/pdf/14 71-2202 -10-S1-info.pdf

Typical unsupervised learning, also called self-organisation, makes each neuron responsive to one of the input signals frequently presented. The prominent response of a neuron has been considered as a feature-detecting signal. It is found that a network organised under unsupervised learning has an information classification scheme rather than a mere ability to detect. Each bit of information is represented by an activity pattern of the set of neurons in the input layer and it is mapped into another activity pattern of the set of neurons in the output layer. Analysis of the activity pattern of multiple output neurons revealed the following tendencies beyond the feature detection by a single neuron. First, nearness and remoteness between pieces of information are emphasised by the mapping. Thus the neighbouring pieces are clustered. Secondly, the mapping emphasises the interrelationship implicit in the pieces of information and tends to categorise them. The point is discussed from a viewpoint of ultrametricity.

It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are distributed in time. Here, a neuron is modeled as a discrete-time threshold element that responds in an all-or-nothing manner to a linear sum of signals that arrive after delays assigned to individual transmission lines. Even though transmission delays are distributed in time, a whole network exhibits a single collective oscillation with a period close to the average transmission delay. The collective oscillation can not only be a simple alternation of the consecutive firing and resting, but also nontrivially sequenced series of firing and resting, reverberating in a certain period of time. Moreover, the system dynamics can be made quasiperiodic or chaotic by changing the distribution of delays., 8pages, 9figures

The apparent irregularity of in vivo spike sequences could be read as being derived either irregularly in time from a constant rate or regularly from a fluctuating rate. We recently proposed the Empirical Bayes method that selects one out of the alternative interpretations (J. Phys. A: Math. Gen. 2005; 38:L531-L537). In this paper, we demonstrate that this method may also give a solution to the controversy between rate and temporal coding. For a given single sequence of spikes, the method may indicate two potential hypothetical rate processes, nearly constant and highly fluctuating, and selects one according to the statistical plausibility. As the rate fluctuation of a spike sequence is increased, the Bayesian interpretation exhibits a discontinuous transition from one to the other. In this way, a sequence of spikes can be distinctly categorized as either rate or temporal coding, according to the estimated degree of rate fluctuation.

When a person tracks a small moving object, the visual images in the background of the visual scene move across his/her retina. It, however, is possible to estimate the actual motion of the images despite the eye-movement-induced motion. To understand the neural mechanism that reconstructs a stable visual world independent of eye movements, we explored areas MT (middle temporal) and MST (medial superior temporal) in the monkey cortex, both of which are known to be essential for visual motion analysis. We recorded the responses of neurons to a moving textured image that appeared briefly on the screen while the monkeys were performing smooth pursuit or stationary fixation tasks. Although neurons in both areas exhibited significant responses to the motion of the textured image with directional selectivity, the responses of MST neurons were mostly correlated with the motion of the image on the screen independent of pursuit eye movement, whereas the responses of MT neurons were mostly correlated with the motion of the image on the retina. Thus these MST neurons were more likely than MT neurons to distinguish between external and self-induced motion. The results are consistent with the idea that MST neurons code for visual motion in the external world while compensating for the counter-rotation of retinal images due to pursuit eye movements.

It has been established that a biological neuron reproduces the precise spike response to identical fluctuating input currents. We wish to predict the firing times of a given neuron for any input current. For this purpose, a mathematical model is introduced for mimicking the voltage response of the neuron to an input current. In predicting the firing times of a target neuron for a novel input current, we propose here the method of estimating the probability of spike occurrence, instead of naively thresholding an instantaneous value of the model voltage. The assessment is carried out maximally utilizing the information about the state space of the voltage and its time derivative(s) of the model, in advance of a possible spike, with a time lag that is determined by maximizing the mutual information. The prediction is significantly improved by the present method in comparison to the naive thresholding method.

Synchrony emerges in a population of oscillators interacting through in-phase couplings. We addressed a question of whether inhibitory neurons simply hinder the emergence of the synchronous activity among excitatory neurons, or facilitate it. An analysis of a simple phase model revealed that both cases may take place. Numerical simulations of the more realistic models revealed that inhibitory neurons rather facilitate rhythmic activity.

There has been an on-going controversy on whether the standard neuro-spiking models can reproduce the spiking statistics of cortical neurons. The past discussions have focused solely on spiking irregularity and many issues remain unsettled. We attempt here to solve the problem by taking account of three kinds of spiking statistics: the coefficient of variation and the skewness coefficient of inter-spike intervals, and the correlation coefficients of the consecutive inter-spike intervals. It was found that the standard neuro-spiking models incorporating the assumption of temporally uncorrelated inputs are not able to account for the spiking data recorded from a monkey prefrontal cortex.

In a self-organization process of a neural network, each neuron becomes responsive to one of the input signals frequently presented. Prominent response of a neuron has been considered as a feature detecting signal. It is found that the activity pattern of the set of neurons shows a structurized information classification scheme rather than a mere ability in feature detection. Kinship among the pieces of information is emphasized by the mapping of the activity pattern.

A rule of synaptic modification in neural networks is proposed under a principle which minimises 'free energy' with synaptic strength roughly bounded. The rule does not allow the overloading of memories which can be a cause of failure in the memory process and it stabilises the synaptic connection, provided that memories are properly stored.

The cognition is based on classification processes. In every stage of computation or information processing, a sub-unit in each site of the brain will also classify whether or not the input signal to that unit is identifiable in its part.

Receptive properties of neurons in visual pathways of mammalian brains have become clarified as a result of physiological and anatomical research. There are a number of neurons with rather simple receptive functions, which respond to different types of spatial differentiation of the lightness field. The significance of each function, however, is not yet understood in terms of visual perception. For instance, although the neurons for early stage visual processing participate in spatial differentiation, we are not particularly conscious of the spatial derivatives of images, but are able to recover the general images.