Statistical coding and decoding of heartbeat intervals

The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.     

A numerical simulation of muscle spindle ensemble encoding during planar movement of the human arm: correlation sensitivity and parameter dependence

We extend the analysis developed in the preceding paper in which we correlated kinematic parameters of planar movements of the human arm made by subjects moving to a visual target with numerical estimates of the ensemble encoding of muscle spindles within some of the muscles of this limb. Three possible models for the inclusion of noise in the calculations of the ensemble encodings are considered: (i) random errors in the angular coordinates from which muscle fascicle, and hence spindle length are calculated, (ii) variability of spindle discharge rates, and (iii) variability in the calculation of the ensemble encoding. In each case the correlations between kinematic variables of the movements and the resultant ensemble encodings decrease as the contribution of the noise term to the calculation of the encodings increases. Subject to the constraint that the magnitude of the noise term remains within physiologically realistic limits, however, the observed correlations persist at statistically significant levels. We also investigate the dependence of the observed correlations on the choice of model parameters, namely (i) the absolute and relative contributions made by simulated spindle primary and secondary afferents to the ensemble encoding, (ii) the inclusion of explicit length-related terms in the model of muscle spindle discharge, and (iii) the fractional power of velocity experienced by the model spindles during movement. The resulting correlations are approximately independent of both the fractional power of velocity and absolute firing levels of both the primary and secondary afferents of the spindle model. The inclusion of explicit length-dependent terms in the model does result in differences in the observed correlation coefficients. In this case, however, the magnitudes of the differences are small. On the basis of these findings we conclude that the correlations between kinematic variables of movement and the associated ensemble encodings are robust with regard to both the choice of model parameters and noise inherent at all stages of the transduction and processing of proprioceptive information. The findings of the present study provide further evidence, therefore, to support the hypothesis that motor structures capable of deriving such an ensemble encoding would be provided with information regarding ongoing movements in both intrinsic (body-centered) and extrinsic (Cartesian) coordinate systems. Received: 17 November 1995 / Accepted in revised form: 17 June 1996     

An information theoretic characterisation of auditory encoding

The entropy metric derived from information theory provides a means to quantify the amount of information transmitted in acoustic streams like speech or music. By systematically varying the entropy of pitch sequences, we sought brain areas where neural activity and energetic demands increase as a function of entropy. Such a relationship is predicted to occur in an efficient encoding mechanism that uses less computational resource when less information is present in the signal: we specifically tested the hypothesis that such a relationship is present in the planum temporale (PT). In two convergent functional MRI studies, we demonstrated this relationship in PT for encoding, while furthermore showing that a distributed fronto-parietal network for retrieval of acoustic information is independent of entropy. The results establish PT as an efficient neural engine that demands less computational resource to encode redundant signals than those with high information content.     

Modelling simultaneous echo waveform reconstruction and localization in bats

Echolocating bats perceive the world through sound signals reflecting from the objects around them. In these signals, information is contained about reflector location and reflector identity. Bats are able to extract and separate the cues for location from those that carry identification information. We propose a model based on Wiener deconvolution that also performs this separation for a virtual system mimicking the echolocation system of the lesser spearnosed bat, Phyllostomus discolor. In particular, the model simultaneously reconstructs the reflected echo signal and localizes the reflector from which the echo originates. The proposed technique is based on a model that performs a similar task based on information from the frog’s lateral line system. We show that direct application of the frog model to the bat sonar system is not feasible. However, we suggest a technique that does apply to the bat biosonar and indicate its performance in the presence of noise.     

A neural mechanism for detecting the distance of a selected target by modulating the FM sweep rate of biosonar in echolocation of bat

Most species of bats making echolocation use frequency modulated (FM) ultrasonic pulses to measure the distance to targets. These bats detect with a high accuracy the arrival time differences between emitted pulses and their echoes generated by targets. In order to clarify the neural mechanism for echolocation, we present neural model of inferior colliculus (IC), medial geniculate body (MGB) and auditory cortex (AC) along which information of echo delay times is processed. The bats increase the downward frequency sweep rate of emitted FM pulse as they approach the target. The functional role of this modulation of sweep rate is not yet clear. In order to investigate the role, we calculated the response properties of our models of IC, MGB, and AC changing the target distance and the sweep rate. We found based on the simulations that the distance of a target in various ranges may be encoded the most clearly into the activity pattern of delay time map network in AC, when the sweep rate of FM pulse used is coincided with the observed value which the bats adopt for each range of target distance.     

Balanced input allows optimal encoding in a stochastic binary neural network model: an analytical study

Recent neurophysiological experiments have demonstrated a remarkable effect of attention on the underlying neural activity that suggests for the first time that information encoding is indeed actively influenced by attention. Single cell recordings show that attention reduces both the neural variability and correlations in the attended condition with respect to the non-attended one. This reduction of variability and redundancy enhances the information associated with the detection and further processing of the attended stimulus. Beyond the attentional paradigm, the local activity in a neural circuit can be modulated in a number of ways, leading to the general question of understanding how the activity of such circuits is sensitive to these relatively small modulations. Here, using an analytically tractable neural network model, we demonstrate how this enhancement of information emerges when excitatory and inhibitory synaptic currents are balanced. In particular, we show that the network encoding sensitivity--as measured by the Fisher information--is maximized at the exact balance. Furthermore, we find a similar result for a more realistic spiking neural network model. As the regime of balanced inputs has been experimentally observed, these results suggest that this regime is functionally important from an information encoding standpoint.     

Plant classification from bat-like echolocation signals

Classification of plants according to their echoes is an elementary component of bat behavior that plays an important role in spatial orientation and food acquisition. Vegetation echoes are, however, highly complex stochastic signals: from an acoustical point of view, a plant can be thought of as a three-dimensional array of leaves reflecting the emitted bat call. The received echo is therefore a superposition of many reflections. In this work we suggest that the classification of these echoes might not be such a troublesome routine for bats as formerly thought. We present a rather simple approach to classifying signals from a large database of plant echoes that were created by ensonifying plants with a frequency-modulated bat-like ultrasonic pulse. Our algorithm uses the spectrogram of a single echo from which it only uses features that are undoubtedly accessible to bats. We used a standard machine learning algorithm (SVM) to automatically extract suitable linear combinations of time and frequency cues from the spectrograms such that classification with high accuracy is enabled. This demonstrates that ultrasonic echoes are highly informative about the species membership of an ensonified plant, and that this information can be extracted with rather simple, biologically plausible analysis. Thus, our findings provide a new explanatory basis for the poorly understood observed abilities of bats in classifying vegetation and other complex objects.     

Stimulus and network dynamics collide in a ratiometric model of the antennal lobe macroglomerular complex

Time is considered to be an important encoding dimension in olfaction, as neural populations generate odour-specific spatiotemporal responses to constant stimuli. However, during pheromone mediated anemotactic search insects must discriminate specific ratios of blend components from rapidly time varying input. The dynamics intrinsic to olfactory processing and those of naturalistic stimuli can therefore potentially collide, thereby confounding ratiometric information. In this paper we use a computational model of the macroglomerular complex of the insect antennal lobe to study the impact on ratiometric information of this potential collision between network and stimulus dynamics. We show that the model exhibits two different dynamical regimes depending upon the connectivity pattern between inhibitory interneurons (that we refer to as fixed point attractor and limit cycle attractor), which both generate ratio-specific trajectories in the projection neuron output population that are reminiscent of temporal patterning and periodic hyperpolarisation observed in olfactory antennal lobe neurons. We compare the performance of the two corresponding population codes for reporting ratiometric blend information to higher centres of the insect brain. Our key finding is that whilst the dynamically rich limit cycle attractor spatiotemporal code is faster and more efficient in transmitting blend information under certain conditions it is also more prone to interference between network and stimulus dynamics, thus degrading ratiometric information under naturalistic input conditions. Our results suggest that rich intrinsically generated network dynamics can provide a powerful means of encoding multidimensional stimuli with high accuracy and efficiency, but only when isolated from stimulus dynamics. This interference between temporal dynamics of the stimulus and temporal patterns of neural activity constitutes a real challenge that must be successfully solved by the nervous system when faced with naturalistic input.     

Some comments on the proposed perception of phase and nanosecond time disparities by echolocating bats

In a series of recent reports, Simmons and his colleagues propose that bats are able to accurately encode the spectral, temporal and phase information of their emitted calls and echoes. The information so encoded is then extracted by the networks of the auditory system with specialized processing. They propose that bats use this information to determine the distance to their target by crosscorrelating the entire structure of the emitted call with the structure of the echo. The idea is that slight deviations in the correlation function can be detected by the bat and the degree of mismatch provides an accurate measure of temporal disparity and hence range. The data in the reports purport to show that bats perceive the phase of ultrasonic signals and that they can resolve temporal disparities of about 10 ns, and thus can distinguish range differences as small as 2 m.The hypothesis also attempts to explain how a variety of acoustic cues are processed and represented in the auditory system and how they are combined to form a unitary percept of space and fine structure. The theory incorporates some time honored processes of extracting information, such as crosscorrelations. The implications of. the hypothesis, however, go far beyond a theory of neural processing and representation of information by ensembles of cells. The hypothesis requires some remarkable abilities, such as the phase coding of ultrasonic signals and a temporal acuity on the order of 10 ns. These features have never been seen in any neurophysiological study of any animal nor has its existence been implied in behavioral studies of other animals. If bats, in fact, detect and process those signals in the manner proposed by Simmons and his colleagues, it would suggest that bats are supermammals whose auditory systems have evolved new and extraordinary mechanisms not possessed by other animals.In view of the extraordinary implications of the hypothesis, it seems prudent to critically evaluate the data upon which the hypothesis is based. The purpose of this review is to point out a number of technical problems and deficiencies in those experiments which undermine the veracity of the purported demonstration of phase perception and nanosecond time resolution by bats.     

Redundant information encoding in primary motor cortex during natural and prosthetic motor control

Redundant encoding of information facilitates reliable distributed information processing. To explore this hypothesis in the motor system, we applied concepts from information theory to quantify the redundancy of movement-related information encoded in the macaque primary motor cortex (M1) during natural and neuroprosthetic control. Two macaque monkeys were trained to perform a delay center-out reaching task controlling a computer cursor under natural arm movement (manual control, ‘MC’), and using a brain-machine interface (BMI) via volitional control of neural ensemble activity (brain control, ‘BC’). During MC, we found neurons in contralateral M1 to contain higher and more redundant information about target direction than ipsilateral M1 neurons, consistent with the laterality of movement control. During BC, we found that the M1 neurons directly incorporated into the BMI (‘direct’ neurons) contained the highest and most redundant target information compared to neurons that were not incorporated into the BMI (‘indirect’ neurons). This effect was even more significant when comparing to M1 neurons of the opposite hemisphere. Interestingly, when we retrained the BMI to use ipsilateral M1 activity, we found that these neurons were more redundant and contained higher information than contralateral M1 neurons, even though ensembles from this hemisphere were previously less redundant during natural arm movement. These results indicate that ensembles most associated to movement contain highest redundancy and information encoding, which suggests a role for redundancy in proficient natural and prosthetic motor control.     

Echo SPL influences the ranging performance of the big brown bat,Eptesicus fuscus

Four bats of the species Eptesicus fuscus were trained in a two-alternative forced-choice procedure to discriminate between two phantom targets that differed in range. The rewarded stimulus was located at a distance of 52.7 cm, while the other unrewarded stimulus was further away. Only one target was presented at a time.In the first experiment we measured the range discrimination performance at an echo SPL of –28 dB relative to the bat's sonar transmission. A 75% correct performance level was arbitrarily defined as threshold and was obtained at a delay difference of 80 s, corresponding to a range difference of 13.8 mm.In the second experiment the delay difference was fixed at 150 s and the echo SPL varied between –8 and –48 dB relative to sonar emissions. The performance of the bats depended on the relative echo SPL. At –28 dB the bats showed the best performance. It deteriorated at an increase of the relative echo SPL to –18 dB and –8 dB. The performance also deteriorated when the relative echo SPL was reduced to –38 dB and –48 dB. Only at low relative echo SPLs did the bats partially compensate for the reduction in echo SPL and increased the SPL of their emitted signals by a few dB.Our results support the hypothesis that neurons exhibiting paradoxical latency shift may be involved in encoding target range. This hypothesis predicts a decrease in performance at high echo SPLs as we found it in our experiments. The observed reduction in performance at very low echo SPLs may be due to a decrease in S/N ratio.     

Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli

Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.     

Subspace projection approaches to classification and visualization of neural network-level encoding patterns

Recent advances in large-scale ensemble recordings allow monitoring of activity patterns of several hundreds of neurons in freely behaving animals. The emergence of such high-dimensional datasets poses challenges for the identification and analysis of dynamical network patterns. While several types of multivariate statistical methods have been used for integrating responses from multiple neurons, their effectiveness in pattern classification and predictive power has not been compared in a direct and systematic manner. Here we systematically employed a series of projection methods, such as Multiple Discriminant Analysis (MDA), Principal Components Analysis (PCA) and Artificial Neural Networks (ANN), and compared them with non-projection multivariate statistical methods such as Multivariate Gaussian Distributions (MGD). Our analyses of hippocampal data recorded during episodic memory events and cortical data simulated during face perception or arm movements illustrate how low-dimensional encoding subspaces can reveal the existence of network-level ensemble representations. We show how the use of regularization methods can prevent these statistical methods from over-fitting of training data sets when the trial numbers are much smaller than the number of recorded units. Moreover, we investigated the extent to which the computations implemented by the projection methods reflect the underlying hierarchical properties of the neural populations. Based on their ability to extract the essential features for pattern classification, we conclude that the typical performance ranking of these methods on under-sampled neural data of large dimension is MDA>PCA>ANN>MGD.     

Complex sound analysis in the FM bat Eptesicus fuscus,correlated with structural parameters of frequency modulated signals

Big brown bats, Eptesicus fuscus, were presented with artificial frequency modulated (FM) echoes that simulated an object becoming progressively closer to the bat. A stereotyped approach phase behavioral response of the bat to the virtual approaching target was used to determine the ability of the bat to analyze FM signals for target distance information. The degree to which the bats responded with approach phase behavior to a virtual approaching target was similar when they were presented with either a naturally structured artificial FM echo or an artificial FM echo constructed from a series of brief pure tone steps. The ability of the bats to respond to an FM signal structured from a sequence of pure tone elements depended on the number of pure tone steps in the series; the bats required the presentation of tone-step FM signals containing about 83 or greater pure tone elements. Moreover, the duration of the individual tone steps of the tone-step FM signals could not exceed a specific upper limit of about 0.05 ms. Finally, it appears that the bats were able to independently resolve individual tone steps within the tone-step FM signals that were separated by about 450 Hz or more.Abbreviations CF constant frequency - FM frequency modulation     

On the Relationships between Generative Encodings,Regularity, and Learning Abilities when Evolving Plastic Artificial Neural Networks

A major goal of bio-inspired artificial intelligence is to design artificial neural networks with abilities that resemble those of animal nervous systems. It is commonly believed that two keys for evolving nature-like artificial neural networks are (1) the developmental process that links genes to nervous systems, which enables the evolution of large, regular neural networks, and (2) synaptic plasticity, which allows neural networks to change during their lifetime. So far, these two topics have been mainly studied separately. The present paper shows that they are actually deeply connected. Using a simple operant conditioning task and a classic evolutionary algorithm, we compare three ways to encode plastic neural networks: a direct encoding, a developmental encoding inspired by computational neuroscience models, and a developmental encoding inspired by morphogen gradients (similar to HyperNEAT). Our results suggest that using a developmental encoding could improve the learning abilities of evolved, plastic neural networks. Complementary experiments reveal that this result is likely the consequence of the bias of developmental encodings towards regular structures: (1) in our experimental setup, encodings that tend to produce more regular networks yield networks with better general learning abilities; (2) whatever the encoding is, networks that are the more regular are statistically those that have the best learning abilities.     

Ion channel noise can explain firing correlation in auditory nerves

Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.     

Dominant glint based prey localization in horseshoe bats: a possible strategy for noise rejection

Rhinolophidae or Horseshoe bats emit long and narrowband calls. Fluttering insect prey generates echoes in which amplitude and frequency shifts are present, i.e. glints. These glints are reliable cues about the presence of prey and also encode certain properties of the prey. In this paper, we propose that these glints, i.e. the dominant glints, are also reliable signals upon which to base prey localization. In contrast to the spectral cues used by many other bats, the localization cues in Rhinolophidae are most likely provided by self-induced amplitude modulations generated by pinnae movement. Amplitude variations in the echo not introduced by the moving pinnae can be considered as noise interfering with the localization process. The amplitude of the dominant glints is very stable. Therefore, these parts of the echoes contain very little noise. However, using only the dominant glints potentially comes at a cost. Depending on the flutter rate of the insect, a limited number of dominant glints will be present in each echo giving the bat a limited number of sample points on which to base localization. We evaluate the feasibility of a strategy under which Rhinolophidae use only dominant glints. We use a computational model of the echolocation task faced by Rhinolophidae. Our model includes the spatial filtering of the echoes by the morphology of the sonar apparatus of Rhinolophus rouxii as well as the amplitude modulations introduced by pinnae movements. Using this model, we evaluate whether the dominant glints provide Rhinolophidae with enough information to perform localization. Our simulations show that Rhinolophidae can use dominant glints in the echoes as carriers for self-induced amplitude modulations serving as localization cues. In particular, it is shown that the reduction in noise achieved by using only the dominant glints outweighs the information loss that occurs by sampling the echo.     

关于耦合神经元活动时的能量原理

最近美国耶鲁大学的神经科学家们用实验数据表明,哺乳动物大脑皮层中神经信号的传递是一个代价昂贵的能量支出过程,而神经信号的编码是与能量代谢紧密地耦合在一起的,但是到目前为止还无法定量给出神经元活动时的能量函数。在这篇文章中,能量原理被用于神经活动和神经信息处理机制的研究,在电生理实验数据的基础上,建立神经元活动的用能量函数表示的运动方程。结果表明用能量函数表达耦合神经元的阈下电活动和动作电位,数值计算结果与用Hodgkin-Huxley方程所描述的动作电位一致。从而有可能依据能量原理从脑信息处理的角度揭示和理解大脑神经网络系统的信息表现规律。     

From sensors to spikes: evolving receptive fields to enhance sensorimotor information in a robot-arm

In biological systems, instead of actual encoders at different joints, proprioception signals are acquired through distributed receptive fields. In robotics, a single and accurate sensor output per link (encoder) is commonly used to track the position and the velocity. Interfacing bio-inspired control systems with spiking neural networks emulating the cerebellum with conventional robots is not a straight forward task. Therefore, it is necessary to adapt this one-dimensional measure (encoder output) into a multidimensional space (inputs for a spiking neural network) to connect, for instance, the spiking cerebellar architecture; i.e. a translation from an analog space into a distributed population coding in terms of spikes. This paper analyzes how evolved receptive fields (optimized towards information transmission) can efficiently generate a sensorimotor representation that facilitates its discrimination from other "sensorimotor states". This can be seen as an abstraction of the Cuneate Nucleus (CN) functionality in a robot-arm scenario. We model the CN as a spiking neuron population coding in time according to the response of mechanoreceptors during a multi-joint movement in a robot joint space. An encoding scheme that takes into account the relative spiking time of the signals propagating from peripheral nerve fibers to second-order somatosensory neurons is proposed. Due to the enormous number of possible encodings, we have applied an evolutionary algorithm to evolve the sensory receptive field representation from random to optimized encoding. Following the nature-inspired analogy, evolved configurations have shown to outperform simple hand-tuned configurations and other homogenized configurations based on the solution provided by the optimization engine (evolutionary algorithm). We have used artificial evolutionary engines as the optimization tool to circumvent nonlinearity responses in receptive fields.     

Spectral selectivity of FM-FM neurons in the auditory cortex of the echolocating bat,Myotis lucifugus

1. Spectral sensitivity was examined in delay-sensitive neurons in the auditory cortex of the awake FM bat, Myotis lucifugus. FM stimuli sweeping 60 kHz downward in 4 ms were used as simulated pulse-echo pairs to measure delay-dependent responses. At each neuron's best delay, the pulse and/or echo were divided into 4 FM quarters (Ist, IInd, IIIrd, and IVth), each sweeping 15 kHz in 1 ms, and quarters essential for delay sensitivity were determined for both pulse and echo. 2. For the pulse, the IVth quarter was essential for delay sensitivity in the majority of neurons. For the echo, the essential quarter for most neurons was the IInd, IIIrd, or IVth. 3. Different quarters of the pulse and echo were essential for delay sensitivity in 68% of the neurons examined. 4. This study provides neurophysiological evidence linking both spectral and temporal processing in delay-sensitive neurons of Myotis. Since spectral cues can provide target-shape information, sensitivity to both spectral and temporal parameters in single neurons may endow these neurons in FM bats with the potential for target analysis other than echo-ranging.