Temporal encoding in a nervous system

We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.     

The Essential Complexity of Auditory Receptive Fields

Encoding properties of sensory neurons are commonly modeled using linear finite impulse response (FIR) filters. For the auditory system, the FIR filter is instantiated in the spectro-temporal receptive field (STRF), often in the framework of the generalized linear model. Despite widespread use of the FIR STRF, numerous formulations for linear filters are possible that require many fewer parameters, potentially permitting more efficient and accurate model estimates. To explore these alternative STRF architectures, we recorded single-unit neural activity from auditory cortex of awake ferrets during presentation of natural sound stimuli. We compared performance of > 1000 linear STRF architectures, evaluating their ability to predict neural responses to a novel natural stimulus. Many were able to outperform the FIR filter. Two basic constraints on the architecture lead to the improved performance: (1) factorization of the STRF matrix into a small number of spectral and temporal filters and (2) low-dimensional parameterization of the factorized filters. The best parameterized model was able to outperform the full FIR filter in both primary and secondary auditory cortex, despite requiring fewer than 30 parameters, about 10% of the number required by the FIR filter. After accounting for noise from finite data sampling, these STRFs were able to explain an average of 40% of A1 response variance. The simpler models permitted more straightforward interpretation of sensory tuning properties. They also showed greater benefit from incorporating nonlinear terms, such as short term plasticity, that provide theoretical advances over the linear model. Architectures that minimize parameter count while maintaining maximum predictive power provide insight into the essential degrees of freedom governing auditory cortical function. They also maximize statistical power available for characterizing additional nonlinear properties that limit current auditory models.     

Assessing Movement Factors in Upper Limb Kinematics Decoding from EEG Signals

The past decades have seen the rapid development of upper limb kinematics decoding techniques by performing intracortical recordings of brain signals. However, the use of non-invasive approaches to perform similar decoding procedures is still in its early stages. Recent studies show that there is a correlation between electroencephalographic (EEG) signals and hand-reaching kinematic parameters. From these studies, it could be concluded that the accuracy of upper limb kinematics decoding depends, at least partially, on the characteristics of the performed movement. In this paper, we have studied upper limb movements with different speeds and trajectories in a controlled environment to analyze the influence of movement variability in the decoding performance. To that end, low frequency components of the EEG signals have been decoded with linear models to obtain the position of the volunteer’s hand during performed trajectories grasping the end effector of a planar manipulandum. The results confirm that it is possible to obtain kinematic information from low frequency EEG signals and show that decoding performance is significantly influenced by movement variability and tracking accuracy as continuous and slower movements improve the accuracy of the decoder. This is a key factor that should be taken into account in future experimental designs.     

Neuron selection by relative importance for neural decoding of dexterous finger prosthesis control application

Future generations of upper limb prosthesis will have dexterous hand with individual fingers and will be controlled directly by neural signals. Neurons from the primary motor (M1) cortex code for finger movements and provide the source for neural control of dexterous prosthesis. Each neuron's activation can be quantified by the change in firing rate before and after finger movement, and the quantified value is then represented by the neural activity over each trial for the intended movement. Since this neural activity varies with the intended movement, we define the relative importance of each neuron independent of specific intended movements. The relative importance of each neuron is determined by the inter-movement variance of the neural activities for respective intended movements. Neurons are ranked by the relative importance and then a subpopulation of rank-ordered neurons is selected for the neural decoding. The use of the proposed neuron selection method in individual finger movements improved decoding accuracy by 21.5% in the case of decoding with only 5 neurons and by 9.2% in the case of decoding with only 10 neurons. With only 15 highly ranked neurons, a decoding accuracy of 99.5% was achieved. The performance improvement is still maintained when combined movements of two fingers were included though the decoding accuracy fell to 95.7%. Since the proposed neuron selection method can achieve the targeting accuracy of decoding algorithms with less number of input neurons, it can be significant for developing brain–machine interfaces for direct neural control of hand prostheses.     

Validation of a mathematical approach to estimate dynamic scapular orientation

The goal of this study was to develop and validate a non-invasive approach to estimate scapular kinematics in individual patients. We hypothesized that individualized mathematical algorithms can be developed using motion capture data to accurately estimate dynamic scapula orientation based on measured humeral orientations and acromion process positions. The accuracy of the mathematical algorithms was evaluated against a gold standard of biplane fluoroscopy using a 2D to 3D fluoroscopy/model matching process. Individualized linear models were developed for nine healthy adult shoulders. These models were used to predict scapulothoracic kinematics, and the predicted kinematics were compared to kinematics obtained using biplane fluoroscopy to determine the accuracy of the algorithms. Results showed strong correlations between mathematically predicted kinematics and validation kinematics. Estimated kinematics were within 8° of validation kinematics. We concluded that individualized linear models show promise for providing accurate, non-invasive measurements of scapulothoracic kinematics in a clinical environment.     

Unscented Kalman Filter for Brain-Machine Interfaces

Brain machine interfaces (BMIs) are devices that convert neural signals into commands to directly control artificial actuators, such as limb prostheses. Previous real-time methods applied to decoding behavioral commands from the activity of populations of neurons have generally relied upon linear models of neural tuning and were limited in the way they used the abundant statistical information contained in the movement profiles of motor tasks. Here, we propose an n-th order unscented Kalman filter which implements two key features: (1) use of a non-linear (quadratic) model of neural tuning which describes neural activity significantly better than commonly-used linear tuning models, and (2) augmentation of the movement state variables with a history of n-1 recent states, which improves prediction of the desired command even before incorporating neural activity information and allows the tuning model to capture relationships between neural activity and movement at multiple time offsets simultaneously. This new filter was tested in BMI experiments in which rhesus monkeys used their cortical activity, recorded through chronically implanted multielectrode arrays, to directly control computer cursors. The 10th order unscented Kalman filter outperformed the standard Kalman filter and the Wiener filter in both off-line reconstruction of movement trajectories and real-time, closed-loop BMI operation.     

Dynamics of population code for working memory in the prefrontal cortex

Some neurons (delay cells) in the prefrontal cortex elevate their activities throughout the time period during which the animal is required to remember past events and prepare future behavior, suggesting that working memory is mediated by continuous neural activity. It is unknown, however, how working memory is represented within a population of prefrontal cortical neurons. We recorded from neuronal ensembles in the prefrontal cortex as rats learned a new delayed alternation task. Ensemble activities changed in parallel with behavioral learning so that they increasingly allowed correct decoding of previous and future goal choices. In well-trained rats, considerable decoding was possible based on only a few neurons and after removing continuously active delay cells. These results show that neural activity in the prefrontal cortex changes dynamically during new task learning so that working memory is robustly represented and that working memory can be mediated by sequential activation of different neural populations.     

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate versus current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.     

人工神经网络模型在水稻群体分蘖动态模拟中外推能力的测试

研究利用人工神经网络模型 ,以水稻群体分蘖动态为例 ,采用交互验证和独立验证的方式 ,对水稻生长 BP网络模型进行了训练与模拟 ,其结果与水稻群体分蘖的积温统计模型、基本动力学模型和复合分蘖模型进行了比较。研究结果表明 ,神经网络模型具有一定的外推能力 ,但其外推能力依赖于大量的训练样本。神经网络模型具有较好的拟合能力 ,是因为有较多的模型参数 ,因此对神经网络模型的训练需要大量的参数来保证其参数不致过度吻合。具有外推能力神经网络模型的最少训练样本数应大于 6 .75倍于神经网络参数数目 ,小于 13.5倍于神经网络参数数目。因此在应用神经网络模型时 ,如果神经网络模型包括较多的输入变量时 ,可考虑采用主成分分析、对应分析等技术对输入变量进行信息综合 ,相应地减少网络模型的参数。另一方面 ,当训练样本不足时 ,最好只用神经网络模型对同一系统的情况进行模拟 ,应谨慎使用神经网络模型进行外推。神经网络模型给作物模拟研究的科学工作者提供了一个“傻瓜”式工具 ,对数学建模不熟悉的农业研究人员 ,人工神经网络可以替代数学建模进行仿真实验 ;对于精通数学建模的研究人员来说 ,它至少是一种补充和可作为比较的非线性数据处理方法     

Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs, especially as models of brain processing, is undisputed, it is also widely acknowledged that the computations in standard RNN models may be an over-simplification of what real neuronal networks compute. Here, we suggest that the RNN approach may be made computationally more powerful by its fusion with Bayesian inference techniques for nonlinear dynamical systems. In this scheme, we use an RNN as a generative model of dynamic input caused by the environment, e.g. of speech or kinematics. Given this generative RNN model, we derive Bayesian update equations that can decode its output. Critically, these updates define a 'recognizing RNN' (rRNN), in which neurons compute and exchange prediction and prediction error messages. The rRNN has several desirable features that a conventional RNN does not have, e.g. fast decoding of dynamic stimuli and robustness to initial conditions and noise. Furthermore, it implements a predictive coding scheme for dynamic inputs. We suggest that the Bayesian inversion of RNNs may be useful both as a model of brain function and as a machine learning tool. We illustrate the use of the rRNN by an application to the online decoding (i.e. recognition) of human kinematics.     

Grasp Detection from Human ECoG during Natural Reach-to-Grasp Movements

Various movement parameters of grasping movements, like velocity or type of the grasp, have been successfully decoded from neural activity. However, the question of movement event detection from brain activity, that is, decoding the time at which an event occurred (e.g. movement onset), has been addressed less often. Yet, this may be a topic of key importance, as a brain-machine interface (BMI) that controls a grasping prosthesis could be realized by detecting the time of grasp, together with an optional decoding of which type of grasp to apply. We, therefore, studied the detection of time of grasps from human ECoG recordings during a sequence of natural and continuous reach-to-grasp movements. Using signals recorded from the motor cortex, a detector based on regularized linear discriminant analysis was able to retrieve the time-point of grasp with high reliability and only few false detections. Best performance was achieved using a combination of signal components from time and frequency domains. Sensitivity, measured by the amount of correct detections, and specificity, represented by the amount of false detections, depended strongly on the imposed restrictions on temporal precision of detection and on the delay between event detection and the time the event occurred. Including neural data from after the event into the decoding analysis, slightly increased accuracy, however, reasonable performance could also be obtained when grasping events were detected 125 ms in advance. In summary, our results provide a good basis for using detection of grasping movements from ECoG to control a grasping prosthesis.     

High-Resolution,Non-Invasive Imaging of Upper Vocal Tract Articulators Compatible with Human Brain Recordings

A complete neurobiological understanding of speech motor control requires determination of the relationship between simultaneously recorded neural activity and the kinematics of the lips, jaw, tongue, and larynx. Many speech articulators are internal to the vocal tract, and therefore simultaneously tracking the kinematics of all articulators is nontrivial—especially in the context of human electrophysiology recordings. Here, we describe a noninvasive, multi-modal imaging system to monitor vocal tract kinematics, demonstrate this system in six speakers during production of nine American English vowels, and provide new analysis of such data. Classification and regression analysis revealed considerable variability in the articulator-to-acoustic relationship across speakers. Non-negative matrix factorization extracted basis sets capturing vocal tract shapes allowing for higher vowel classification accuracy than traditional methods. Statistical speech synthesis generated speech from vocal tract measurements, and we demonstrate perceptual identification. We demonstrate the capacity to predict lip kinematics from ventral sensorimotor cortical activity. These results demonstrate a multi-modal system to non-invasively monitor articulator kinematics during speech production, describe novel analytic methods for relating kinematic data to speech acoustics, and provide the first decoding of speech kinematics from electrocorticography. These advances will be critical for understanding the cortical basis of speech production and the creation of vocal prosthetics.     

Fading memory and kernel properties of generic cortical microcircuit models

It is quite difficult to construct circuits of spiking neurons that can carry out complex computational tasks. On the other hand even randomly connected circuits of spiking neurons can in principle be used for complex computational tasks such as time-warp invariant speech recognition. This is possible because such circuits have an inherent tendency to integrate incoming information in such a way that simple linear readouts can be trained to transform the current circuit activity into the target output for a very large number of computational tasks. Consequently we propose to analyze circuits of spiking neurons in terms of their roles as analog fading memory and non-linear kernels, rather than as implementations of specific computational operations and algorithms. This article is a sequel to [W. Maass, T. Natschl?ger, H. Markram, Real-time computing without stable states: a new framework for neural computation based on perturbations, Neural Comput. 14 (11) (2002) 2531-2560, Online available as #130 from: ], and contains new results about the performance of generic neural microcircuit models for the recognition of speech that is subject to linear and non-linear time-warps, as well as for computations on time-varying firing rates. These computations rely, apart from general properties of generic neural microcircuit models, just on capabilities of simple linear readouts trained by linear regression. This article also provides detailed data on the fading memory property of generic neural microcircuit models, and a quick review of other new results on the computational power of such circuits of spiking neurons.     

Encoding and decoding amplitude-modulated cochlear implant stimuli—a point process analysis

Cochlear implant speech processors stimulate the auditory nerve by delivering amplitude-modulated electrical pulse trains to intracochlear electrodes. Studying how auditory nerve cells encode modulation information is of fundamental importance, therefore, to understanding cochlear implant function and improving speech perception in cochlear implant users. In this paper, we analyze simulated responses of the auditory nerve to amplitude-modulated cochlear implant stimuli using a point process model. First, we quantify the information encoded in the spike trains by testing an ideal observer’s ability to detect amplitude modulation in a two-alternative forced-choice task. We vary the amount of information available to the observer to probe how spike timing and averaged firing rate encode modulation. Second, we construct a neural decoding method that predicts several qualitative trends observed in psychophysical tests of amplitude modulation detection in cochlear implant listeners. We find that modulation information is primarily available in the sequence of spike times. The performance of an ideal observer, however, is inconsistent with observed trends in psychophysical data. Using a neural decoding method that jitters spike times to degrade its temporal resolution and then computes a common measure of phase locking from spike trains of a heterogeneous population of model nerve cells, we predict the correct qualitative dependence of modulation detection thresholds on modulation frequency and stimulus level. The decoder does not predict the observed loss of modulation sensitivity at high carrier pulse rates, but this framework can be applied to future models that better represent auditory nerve responses to high carrier pulse rate stimuli. The supplemental material of this article contains the article’s data in an active, re-usable format.     

Experimental analysis of neuronal dynamics in cultured cortical networks and transitions between different patterns of activity

A general method for developing data-based, stochastic nonlinear models of neurons by means of extended functional series expansions was applied to neural activities of pigeon auditory nerve fibers responding to Gaussian white noise stimuli. To determine Wiener series representations of the investigated neurons the fast orthogonal search algorithm was used. The results suggest that nonlinearities are only instantaneous and that the signal transduction of the investigated sensory system can be described by cascades of dynamic linear and static nonlinear devices. However, only slight improvements result from the nonlinear terms. Considerable improvements are, nevertheless, possible by generalizing the ordinary Wiener series, so that prior neural activity can be taken into account. These extended series were used to develop stochastic models of spiking neurons. The models are able to generate realistic interspike interval distributions and rate-intensity functions. Finally, it will be shown that the irregularity in real and modeled action potential trains has advantages concerning the decoding of neural responses. Received: 16 April 1996 / Accepted in revised form: 23 October 1996     

人工神经网络模型及其在农业和生态学研究中的应用

对于一些复杂的农业生态系统,人们对其生态过程了解较少,且这些系统的不确定性和模糊性较大,用传统的方法难以模拟这些系统的行为,神经网络模型因为能较精确地模拟这些系统的行为,而引起生态学者们的广泛兴趣。该文着重介绍了误差逆传神经网络模型的结构、算法及其在农业和生态学中的应用研究。误差逆传神经网络模型一般采用三层神经网络模型结构,三层的神经网络模型能模拟任意复杂程度的连续函数,而且因为它的结构小而不容易产生与训练数据的过度吻合。误差逆传神经网络模型算法的主要特征是:利用当前的输入误差对权值进行调整。在生态学和农业研究中,误差逆传神经网络模型通常作为非线性函数模拟器用于预测作物产量、生物生产量、生物与环境之间的关系等。已有的研究表明:误差逆传神经网络模型的模拟精度要远远高于多元线性方程,类似于非线性方程,而在样本量足够的情况下,有一定的外推能力。但是误差逆传神经网络模型需要大量的样本量来保证所求取参数的可靠性,但这在实际研究中很难做到,因而限制了误差逆传神经网络模型的应用。近年来人们提出了强制训练停止、复合模型等多种技术来提高误差逆传神经网络模型的外推能力,也提出了Garson算法、敏感性分析以及随机化检验等技术对误差逆传神经网络模型的机理进行解释。误差逆传神经网络模型的真正优势在于模拟人们了解较少或不确定性和模糊性较大系统的行为,这些是传统模型所无法实现的,因而是对传统机理模型的重要补充。     

Factors Predicting Difficulty of Laparoscopic Low Anterior Resection for Rectal Cancer with Total Mesorectal Excision and Double Stapling Technique

Background

Laparoscopic sphincter-preserving low anterior resection for rectal cancer is a surgery demanding great skill. Immense efforts have been devoted to identifying factors that can predict operative difficulty, but the results are inconsistent.

Objective

Our study was conducted to screen patients’ factors to build models for predicting the operative difficulty using well controlled data.

Method

We retrospectively reviewed records of 199 consecutive patients who had rectal cancers 5–8 cm from the anal verge. All underwent laparoscopic sphincter-preserving low anterior resections with total mesorectal excision (TME) and double stapling technique (DST). Data of 155 patients from one surgeon were utilized to build models to predict standardized endpoints (operative time, blood loss) and postoperative morbidity. Data of 44 patients from other surgeons were used to test the predictability of the built models.

Results

Our results showed prior abdominal surgery, preoperative chemoradiotherapy, tumor distance to anal verge, interspinous distance, and BMI were predictors for the standardized operative times. Gender and tumor maximum diameter were related to the standardized blood loss. Temporary diversion and tumor diameter were predictors for postoperative morbidity. The model constructed for the operative time demonstrated excellent predictability for patients from different surgeons.

Conclusions

With a well-controlled patient population, we have built a predictable model to estimate operative difficulty. The standardized operative time will make it possible to significantly increase sample size and build more reliable models to predict operative difficulty for clinical use.     

Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics. Received: 8 August 1997 / Accepted in revised form: 18 June 1998     

Use of Neural Networks to Correlate Spine and Rib Deformity in Scoliosis

Artificial neural networks (ANN's) recognize patterns relating input and output data in a manner analogous to the function of biological neurons. Here, we show that ANN's can predict rib deformity in scoliosis more accurately than regression analysis. ANN's and linear regression models were developed to predict rib rotation from several combinations of input spinal indices including Cobb angle, vertebral rotation, apex location and orientation of the plane of maximal curvature. ANN's averaged 60% correct predictions compared to 34% for regression analysis. This study provides evidence for the utility of artificial neural networks in scoliosis research. These data lend credence to the use of ANN's in future work on the prediction of scoliotic spinal deformity from torso surface data, which would permit assessment of scoliosis severity with minimal use of harmful X-rays.