Interval jitter and spike resampling methods are used to analyze the time scale on which temporal correlations occur. They allow the computation of jitter corrected cross correlograms and the performance of an associated statistically robust hypothesis test to decide whether observed correlations at a given time scale are significant. Currently used Monte Carlo methods approximate the probability distribution of coincidences. They require generating $N_{\rm MC}$ simulated spike trains of length $T$ and calculating their correlation with another spike train up to lag $τ_{\max}$. This is computationally costly $O(N_{\rm MC} \times T \times τ_{\max})$ and it introduces errors in estimating the $p$ value. Instead, we propose to compute the distribution in closed form, with a complexity of $O(C_{\max} \log(C_{\max}) τ_{\max})$, where $C_{\max}$ is the maximum possible number of coincidences. All results are then exact rather than approximate, and as a consequence, the $p$-values obtained are the theoretically best possible for the available data and test statistic. In addition, simulations with realistic parameters predict a speed increase over Monte Carlo methods of two orders of magnitude for hypothesis testing, and four orders of magnitude for computing the full jitter-corrected cross correlogram.
We investigate the stimulus-dependent tuning properties of a noisy ionic conductance model for intrinsic subthreshold oscillations in membrane potential and associated spike generation. On depolarization by an applied current, the model exhibits subthreshold oscillatory activity with occasional spike generation when oscillations reach the spike threshold. We consider how the amount of applied current, the noise intensity, variation of maximum conductance values and scaling to different temperature ranges alter the responses of the model with respect to voltage traces, interspike intervals and …
A good understanding of how neurons use electrical pulses (i.e, spikes) to encode the signal information remains elusive. Analyzing spike sequences generated by individual neurons and by two coupled neurons (using the stochastic FitzHugh-Nagumo model), recent theoretical studies have found that the relative timing of the spikes can encode the signal information. Using a symbolic method to analyze the spike sequence, preferred and infrequent spike patterns were detected, whose probabilities vary with both, the amplitude and the frequency of the signal. To investigate if this encoding mechanism …
Reduced models of neuronal activity such as Integrate-and-Fire models allow a description of neuronal dynamics in simple, intuitive terms and are easy to simulate numerically. We present a method to fit an Integrate-and-Fire-type model of neuronal activity, namely a modified version of the Spike Response Model, to a detailed Hodgkin-Huxley-type neuron model driven by stochastic spike arrival. In the Hogkin-Huxley model, spike arrival at the synapse is modeled by a change of synaptic conductance. For such conductance spike input, more than 70% of the postsynaptic action potentials can be predic…
Our mysterious brain is believed to operate near a non-equilibrium point and generate critical self-organized avalanches in neuronal activity. Recent experimental evidence has revealed significant heterogeneity in both synaptic input and output connectivity, but whether the structural heterogeneity participates in the regulation of neuronal avalanches remains poorly understood. By computational modelling, we predict that different types of structural heterogeneity contribute distinct effects on avalanche neurodynamics. In particular, neuronal avalanches can be triggered at an intermediate leve…
One step in the conventional analysis of extracellularly recorded neuronal data is spike sorting, which separates electrical signal into action potentials from different neurons. Because spike sorting involves human judgment, it can be subjective and time intensive, particularly for large sets of neurons. Here we propose a simple, automated way to construct alternative representations of neuronal activity, called spectral representation (SR). In this approach, neuronal spikes are mapped to a discrete space of spike- waveform features and time. Spectral representation enables us to find single-…
The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations where analytic insight is lacking. A simple account for how fast spike time correlations affect both micro- and macroscopic network structure remains lacking. We develop a low-dimensional mean field theory showing how STDP gives rise to strongly coupled assemblies of neurons with shared stimulus preferences, with the connectivity actively reinforce…
Recent studies of cortical neurons driven by fluctuating currents revealed cutoff frequencies for action potential encoding of several hundred Hz. Theoretical studies of biophysical neuron models have predicted a much lower cutoff frequency of the order of average firing rate or the inverse membrane time constant. The biophysical origin of the observed high cutoff frequencies is thus not well understood. Here we introduce a neuron model with dynamical action potential generation, in which the linear response can be analytically calculated for uncorrelated synaptic noise. We find that the cutof…
Neuroprosthesis, as one type of precision medicine device, is aiming for manipulating neuronal signals of the brain in a closed-loop fashion, together with receiving stimulus from the environment and controlling some part of our brain/body. In terms of vision, incoming information can be processed by the brain in millisecond interval. The retina computes visual scenes and then sends its output as neuronal spikes to the cortex for further computation. Therefore, the neuronal signal of interest for retinal neuroprosthesis is spike. Closed-loop computation in neuroprosthesis includes two stages: …
We present a modified library-based method for simulating the Hodgkin-Huxley (HH) neuronal networks. By pre-computing a high resolution data library during the interval of an action potential (spike), we can avoid evolving the HH equations during the spike and can use a large time step to raise efficiency. The library method can stably achieve at most 10 times of speedup compared with the regular Runge-Kutta method while capturing most statistical properties of HH neurons like the distribution of spikes which data is widely used in the statistical analysis like transfer entropy and Granger cau…
A common way of studying the relationship between neural activity and behavior is through the analysis of neuronal spike trains that are recorded using one or more electrodes implanted in the brain. Each spike train typically contains spikes generated by multiple neurons. A natural question that arises is "what is the number of neurons $ν$ generating the spike train?"; This article proposes a method-of-moments technique for estimating $ν$. This technique estimates the noise nonparametrically using data from the silent region of the spike train and it applies to isolated spikes with a possibly …
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending …
Statistical similarities between neuronal spike trains could reveal significant information on complex underlying processing. In general, the similarity between synchronous spike trains is somewhat easy to identify. However, the similar patterns also potentially appear in an asynchronous manner. However, existing methods for their identification tend to converge slowly, and cannot be applied to short sequences. In response, we propose Hellinger distance measure based on empirical probabilities, which we show to be as accurate as existing techniques, yet faster to converge for synthetic as well…
Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow $\mathrm{K}^+$-currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in-vivo like fluctuating synaptic input, spike rate output and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current which primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold. A spike-dependent adap…
We investigated the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We found spike death phenomena, namely, the state of neurons transits from limit cycle to fixed point or transient state. The phenomena occur under the perturbation of excitatory synaptic interaction that has a high efficacy. We showed that the decrease of synaptic current results in spike death through depressing the feedback of sodium ionic current. In the networks with spike death property the degree of synchronization is lower and unsensitive to the heterogeneity of …
Chimera states are spatiotemporal patterns in which coherence and incoherence coexist. We observe the coexistence of synchronous (coherent) and desynchronous (incoherent) domains in a neuronal network. The network is composed of coupled adaptive exponential integrate-and-fire neurons that are connected by means of chemical synapses. In our neuronal network, the chimera states exhibit spatial structures both with spikes and bursts activities. Furthermore, those desynchronised domains not only have either spike or burst activity, but we show that the structures switch between spikes and bursts a…
Discovering the 'Neural Code' from multi-neuronal spike trains is an important task in neuroscience. For such an analysis, it is important to unearth interesting regularities in the spiking patterns. In this report, we present an efficient method for automatically discovering synchrony, synfire chains, and more general sequences of neuronal firings. We use the Frequent Episode Discovery framework of Laxman, Sastry, and Unnikrishnan (2005), in which the episodes are represented and recognized using finite-state automata. Many aspects of functional connectivity between neuronal populations can b…
The threshold voltage for action potential generation is a key regulator of neuronal signal transduction, yet the mechanism of its dynamic variation is still not well described. In this paper, we propose that threshold phenomena can be classified as parameter thresholds and state thresholds. Voltage thresholds which belong to the state threshold are determined by the `general separatrix' in state space. We demonstrate that the separatrix generally exists in the state space of neuron models. The general form of separatrix was assumed as the function of both states and stimuli and the previously…
In this paper, we study the effects of spike timing-dependent plasticity on synchronisation in a network of Hodgkin-Huxley neurons. Neuron plasticity is a flexible property of a neuron and its network to change temporarily or permanently their biochemical, physiological, and morphological characteristics, in order to adapt to the environment. Regarding the plasticity, we consider Hebbian rules, specifically for spike timing-dependent plasticity (STDP), and with regard to network, we consider that the connections are randomly distributed. We analyse the synchronisation and desynchronisation acc…
We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of the model over time, and to estimate the probability densities of neuronal membrane potentials using Gram-Charlier expansions. Our results are shown to provide a better alternative to Monte Carlo estimates via stochastic simulations, and computer codes based on combinatorial recursions are included…
With the increasing popularity of calcium imaging data in neuroscience research, methods for analyzing calcium trace data are critical to address various questions. The observed calcium traces are either analyzed directly or deconvolved to spike trains to infer neuronal activities. When both approaches are applicable, it is unclear whether deconvolving calcium traces is a necessary step. In this article, we compare the performance of using calcium traces or their deconvolved spike trains for three common analyses: clustering, principal component analysis (PCA), and population decoding. Our sim…
Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second-order motifs: diverging motifs, in which one cell provides in…
The role of synchronous firing in sensory coding and cognition remains controversial. While studies, focusing on its mechanistic consequences in attentional tasks, suggest that synchronization dynamically boosts sensory processing, others failed to find significant synchronization levels in such tasks. We attempt to understand both lines of evidence within a coherent theoretical framework. We conceptualize synchronization as an independent control parameter to study how the postsynaptic neuron transmits the average firing activity of a presynaptic population, in the presence of synchronization…
Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there …
Repeated occurrences of serial firing sequences of a group of neurons with fixed time delays between neurons are observed in many experiments involving simultaneous recordings from multiple neurons. Such temporal patterns are potentially indicative of underlying microcircuits and it is important to know when a repeatedly occurring pattern is statistically significant. These sequences are typically identified through correlation counts, such as in the two-tape algorithm of Abeles and Gerstein. In this paper we present a method for deciding on the significance of such correlations by characteriz…
We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the …
School of Electrical Engineering and Computer Science（电气工程与计算机科学学院）；The Pennsylvania State University（宾夕法尼亚州立大学）
Developing electrophysiological recordings of brain neuronal activity and their analysis provide a basis for exploring the structure of brain function and nervous system investigation. The recorded signals are typically a combination of spikes and noise. High amounts of background noise and possibility of electric signaling recording from several neurons adjacent to the recording site have led scientists to develop neuronal signal processing tools such as spike sorting to facilitate brain data analysis. Spike sorting plays a pivotal role in understanding the electrophysiological activity of ne…
Quantification of neuronal correlations in neuron populations helps us to understand neural coding rules. Such quantification could also reveal how neurons encode information in normal and disease conditions like Alzheimer's and Parkinson's. While neurons communicate with each other by transmitting spikes, there would be a change in calcium concentration within the neurons inherently. Accordingly, there would be correlations in calcium spike trains and they could have heterogeneous memory structures. In this context, estimation of mutual information rate in calcium spike trains assumes primary…
Measurements of electric potentials from neural activity have played a key role in neuroscience for almost a century, and simulations of neural activity is an important tool for understanding such measurements. Volume conductor (VC) theory is used to compute extracellular electric potentials such as extracellular spikes, MUA, LFP, ECoG and EEG surrounding neurons, and also inversely, to reconstruct neuronal current source distributions from recorded potentials through current source density methods. In this book chapter, we show how VC theory can be derived from a detailed electrodiffusive the…
Branching with immigration is one of the most common models for the stochastic processes observed in neuronal circuits. However, it is not observed directly and, in order to create branching-like processes, the observed spike time series is processed by attaching time bins to spikes. It has been shown that results such as criticality and size distributions depend on the chosen time bin. A different methodology whose results do not depend on the choice of time bin might therefore be useful and is proposed in this article. The new methodology circumvents using time bins altogether by replacing t…
The number of neurons that can be simultaneously recorded doubles every seven years. This ever increasing number of recorded neurons opens up the possibility to address new questions and extract higher dimensional stimuli from the recordings. Modeling neural spike trains as point processes, this task of extracting dynamical signals from spike trains is commonly set in the context of nonlinear filtering theory. Particle filter methods relying on importance weights are generic algorithms that solve the filtering task numerically, but exhibit a serious drawback when the problem dimensionality is …
Discovering frequent episodes in event sequences is an interesting data mining task. In this paper, we argue that this framework is very effective for analyzing multi-neuronal spike train data. Analyzing spike train data is an important problem in neuroscience though there are no data mining approaches reported for this. Motivated by this application, we introduce different temporal constraints on the occurrences of episodes. We present algorithms for discovering frequent episodes under temporal constraints. Through simulations, we show that our method is very effective for analyzing spike tra…
Biocomputing technologies exploit biological communication mechanisms involving cell-cell signal propagation to perform computations. Researchers recently worked toward realising logic gates made by neurons to develop novel devices such as organic neuroprostheses or brain implants made by cells, herein termed living implants. Several challenges arise from this approach, mainly associated with the stochastic nature and noise of neuronal communication. Since astrocytes play a crucial role in the regulation of neurons activity, there is a possibility whereby astrocytes can be engineered to contro…
Understanding the functioning of a neural system in terms of its underlying circuitry is an important problem in neuroscience. Recent developments in electrophysiology and imaging allow one to simultaneously record activities of hundreds of neurons. Inferring the underlying neuronal connectivity patterns from such multi-neuronal spike train data streams is a challenging statistical and computational problem. This task involves finding significant temporal patterns from vast amounts of symbolic time series data. In this paper we show that the frequent episode mining methods from the field of te…
Neuron is the most important building block in our brain, and information processing in individual neuron involves the transformation of input synaptic spike trains into an appropriate output spike train. Hardware implementation of neuron by individual ionic/electronic coupled device is of great importance for enhancing our understanding of the brain and solving sensory processing and complex recognition tasks. Here, we provide a proof-of-principle artificial neuron with multiple presynaptic inputs and one modulatory terminal based on a proton-coupled oxide-based electric-double-layer transist…
Extracellular recordings with multi-electrode arrays is one of the basic tools of contemporary neuroscience. These recordings are mostly used to monitor the activities, understood as sequences of emitted action potentials, of many individual neurons. But the raw data produced by extracellular recordings are most commonly a mixture of activities from several neurons. In order to get the activities of the individual contributing neurons, a pre-processing step called spike sorting is required. We present here a pure Python implementation of a well tested spike sorting procedure. The latter was de…
Neural coding is a field of study that concerns how sensory information is represented in the brain by networks of neurons. The link between external stimulus and neural response can be studied from two parallel points of view. The first, neural encoding refers to the mapping from stimulus to response, and primarily focuses on understanding how neurons respond to a wide variety of stimuli, and on constructing models that accurately describe the stimulus-response relationship. Neural decoding, on the other hand, refers to the reverse mapping, from response to stimulus, where the challenge is to…
Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies (from random to scale-free) have been simulated to study the effectiveness of the pattern-matching method in the reconstruction of network topology from network dynamics. Simulation results show that functional networks reconstructed from repeating spike patterns can be quite different from the original physical networks; even global properties, such as the deg…
Background: Spike trains of multiple neurons can be analyzed following the summed population (SP) or the labeled line (LL) hypothesis. Responses to external stimuli are generated by a neuronal population as a whole or the individual neurons have encoding capacities of their own. The SPIKE-distance estimated either for a single, pooled spike train over a population or for each neuron separately can serve to quantify these responses. New Method: For the SP case we compare three algorithms that search for the most discriminative subpopulation over all stimulus pairs. For the LL case we introduce …
Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects between noisy and nonlinear dynamics. Often, this is achieved by a simple noise term in the membrane equation (current noise). However, there are ongoing discussions whether such current noise is justified or whether rather conductance noise should be introduced because it is closer to the natural origin of noise. Therefore, we have compared the effects of cur…
The stiffness of the Hodgkin-Huxley (HH) equations during an action potential (spike) limits the use of large time steps. We observe that the neurons can be evolved independently between spikes, $i.e.,$ different neurons can be evolved with different methods and different time steps. This observation motivates us to design fast algorithms to raise efficiency. We present an adaptive method, an exponential time differencing (ETD) method and a library-based method to deal with the stiff period. All the methods can use time steps one order of magnitude larger than the regular Runge-Kutta methods t…
One of the main current issues in Neurobiology concerns the understanding of interrelated spiking activity among multineuronal ensembles and differences between stimulus-driven and spontaneous activity in neurophysiological experiments. Multi electrode array recordings that are now commonly used monitor neuronal activity in the form of spike trains from many well identified neurons. A basic question when analyzing such data is the identification of the directed graph describing "synaptic coupling" between neurons. In this article we deal with this matter working with a high quality multielectr…
Although recent neurophysiological experiments suggest that synchronous neural activity is involved in some perceptual and cognitive processes, the functional role of such coherent neuronal behavior is not well understood. As a first step in clarifying this role, we investigate how the temporal coherence of certain neuronal activity affects the activity pattern in a neural network. Using a simple network of leaky integrate-and-fire neurons, we study the effects of synchronized incoming spikes on the functioning of two mechanisms typically used in model neural systems, winner-take-all competiti…
Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For ini…
We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal c…
We show that for two identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony is an unstable attractor and arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity (mismatch in the intrinsic firing rate of the neurons) can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically conn…
We study the time delay in the synaptic conductance for suppression of spike synchronisation in a random network of Hodgkin Huxley neurons coupled by means of chemical synapses. In the first part, we examine in detail how the time delay acts over the network during the synchronised and desynchronised neuronal activities. We observe a relation between the neuronal dynamics and the syaptic conductance distributions. We find parameter values in which the time delay has high effectiveness in promoting the suppression of spike synchronisation. In the second part, we analyse how the delayed neuronal…
Brain-Computer Interfaces (BCI) arose as systems that merge computing systems with the human brain to facilitate recording, stimulation, and inhibition of neural activity. Over the years, the development of BCI technologies has shifted towards miniaturization of devices that can be seamlessly embedded into the brain and can target single neuron or small population sensing and control. We present a motivating example highlighting vulnerabilities of two promising micron-scale BCI technologies, demonstrating the lack of security and privacy principles in existing solutions. This situation opens t…
Weber's law is one of the basic laws in psychophysics, but the link between this psychophysical behavior and the neuronal response has not yet been established. In this paper, we carried out an analysis on the spike train statistics when Weber's law holds, and found that the efferent spike train of a single neuron is less variable than a Poisson process. For population neurons, Weber's law is satisfied only when the population size is small (< 10 neurons). However, if the population neurons share a weak correlation in their discharges and individual neuronal spike train is more regular than a …
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity, representative of a cortical column or hypercolumn with large proportion of inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics and it is interconnected randomly to other neurons. The network dynamics is investigated estimating Bandt and Pompe probability distribution f…
In this paper we consider the problem of detecting statistically significant sequential patterns in multi-neuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes. We have previously proposed a data mining scheme to efficiently discover such patterns which are frequent in the sense that the count of non-overlapping occurrences of the pattern in the data stream is above a threshold. Here we propose a method to determine the statistical significance of these repeating patterns and to set the thresholds autom…
Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at the macroscopic level. However the functional microscopic level, where the nodes of a network are composed of single neurons, is still poorly understood. At this level, although recent evidences suggest that functional connectivity maps exhibit small-world organization, it is not known whether and how these maps, distributed in multiple brain regions, change …
In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron. Our main contribution is to provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. The first step of the procedure is to select a subnetwork of neurons impacting the central neuro…
We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on classical random networks, we find critical phenomena accompanying the transitions and their dependence on the shot noise intensity. We show that a pattern of spontaneous neuronal activity near a critical point of a phase transition is a characteristic property that can be used to identify the bifurcation mechanism of the transition. We demonstrate that bursts …
Feedforward networks (FFN) are ubiquitous structures in neural systems and have been studied to understand mechanisms of reliable signal and information transmission. In many FFNs, neurons in one layer have intrinsic properties that are distinct from those in their pre-/postsynaptic layers, but how this affects network-level information processing remains unexplored. Here we show that layer-to-layer heterogeneity arising from lamina-specific cellular properties facilitates signal and information transmission in FFNs. Specifically, we found that signal transformations, made by each layer of neu…
