Feedforward Neuronal Network Research Articles

Controlling Algorithm of Reconfigurable Battery for State of Charge Balancing Using Amortized Q-Learning

In the context of the electrification of the mobility sector, smart algorithms have to be developed to control battery packs. Smart and reconfigurable batteries are a promising alternative to conventional battery packs and offer new possibilities for operation and condition monitoring. This work proposes a reinforcement learning (RL) algorithm to balance the State of Charge (SoC) of reconfigurable batteries based on the topologies half-bridge and battery modular multilevel management (BM3). As an RL algorithm, Amortized Q-learning (AQL) is implemented, which enables the control of enormous numbers of possible configurations of the reconfigurable battery as well as the combination of classical controlling approaches and machine learning methods. This enhances the safety mechanisms during control. As a neural network of the AQL, a Feedforward Neuronal Network (FNN) is implemented consisting of three hidden layers. The experimental evaluation using a 12-cell hybrid cascaded multilevel converter illustrates the applicability of the method to balance the SoC and maintain the balanced state during discharge. The evaluation shows a 20.3% slower balancing process compared to a conventional approach. Nevertheless, AQL shows great potential for multiobjective optimizations and can be applied as an RL algorithm for control in power electronics.

Chimera state in a feed-forward neuronal network.

Feed-forward effect gives rise to synchronization in neuron firing in deep layers of multiple neuronal network. But complete synchronization means the loss of encoding ability. In order to avoid the contradiction, we ask whether partial synchronization (coexistence of disordered and synchronized neuron firing emerges, also called chimera state) as a compromise strategy can achieve in the feed-forward multiple-layer network. The answer is YES. In order to manifest our argument, we design a multi-layer neuronal network in which neurons in every layer are arranged in a ring topology and neuron firing propagates within (intra-) and across (inter-) the multiply layers. Emergence of chimera state and other patterns highly depends on initial condition of neuronal network and strength of feed-forward effect. Chimera state, cluster and synchronization intra- and inter- layers are displayed by sequence through layers when initial values are elaborately chosen to guarantee emergence of chimera state in the first layer. All type of patterns except chimera state propagates down toward deeper layers in different speeds varying with strength of feed-forward effect. If chimera state already exists in every layer, feed-forward effect with strong and moderate strength spoils chimera states in deep layers and they can only survive in first few layers. When the effect is small enough, chimera states will propagate down toward deeper layers. Indeed, chimera states could exist and transit to deeper layers in a regular multiple network under very strict conditions. The results help understanding better the neuron firing propagating and encoding scheme in a feed-forward neuron network.

Inter-areal transmission of multiple neural signals through frequency-division-multiplexing communication.

Inter-areal information transmission in the brain cortex relates to cognitive functions. Researches used to pay attention to activity pattern transmission, signals gating, or routing in neuronal networks. However, the underlying mechanism of simultaneous transmission of multiple neural signals in the same channel across networks remains unclear. In this work, we construct a two-layer feedforward neuronal network (sender-receiver) with each layer's intrinsic rhythms consisting of slow- (low-frequency) and fast- gamma rhythms (high-frequency), investigating how to realize simultaneous transmission of multiple signals in neuronal systems. With the aid of resonance and frequency analysis, it is shown that low- and high-frequency signals can be transmitted simultaneously in such a feedforward network through frequency division multiplexing (FDM) communication. The transmission performance is related to the local resonance, connectivity, as well as background noise. Moreover, low- and high-frequency signals can also be gated or selected with appropriate adjustments of recurrent connection strength and delay, and background noise. Our model might provide a novel insight into the underlying mechanism of complex signals communication between different cortex areas.

Temperature-controlled propagation of spikes in neuronal networks

Temperature plays a vital role in the functioning of biological organisms and there often exists an optimal temperature for their best performance. In this work, we investigate the role of temperature on spike propagation in scale-free and small-world neuronal networks, where a single neuron is chosen randomly for receiving a stimulus current. Upon exploiting the dominant phase-advanced driving (DPAD) method, the complex neuronal network is seen as a regular feed-forward multilayer neuronal network. The propagation route is then clearly identified, and many traveling-like waves are formed along the propagation route. Interestingly, we find that temperature not only controls the shortest path of propagation but also regulates the response time of a single neuron. The propagation speed is also maximized for an optimal choice of temperature at which the spike rapidly propagates through the entire neuronal network. Our findings extend the current understanding of the neuronal networks functioning and provide new insights into the existence of an optimal temperature as seen in our experiments on several living biological systems.

Temperature-optimized propagation of synchronous firing rate in a feed-forward multilayer neuronal network

The environmental temperature plays a critical role in the system functioning. In biological organisms, there often exists an optimal temperature for the most effective functions. In this work, we investigate the effect of temperature on the propagation of firing rate in a feed-forward multilayer neural network in which neurons in the first layer are stimulated by stochastic noises. We then show that the firing rate can be transmitted through the network within a temperature range. We also show that the propagation of the firing rate by synchronization is optimized at an appropriate temperature. Our findings provide new insights and improve our understanding of the optimal temperature observed in the experiments in the living biological systems.

Information propagation in recurrent neuronal populations with mixed excitatory–inhibitory synaptic connections

Information propagation in the cortical neural network has attracted a large amount of attention. In this paper, a feedforward network is constructed with each subnetwork being a recurrent neuronal population, consisting of neurons coupled by excitatory and inhibitory synapses, in which neurons have both types of outgoing synapses. Namely, neurons in the constructed feedforward neuronal networks have mixed excitatory–inhibitory synapses. Here, propagation of population firing rate and pulse packets are investigated. For the propagation of population firing rate, it is found that proper feedforward connection probability and strength could promote the propagation of population firing rate. Properly larger feedforward synaptic time constant could considerably enhance the fidelity of the propagating population firing rate. For the propagation of pulse packet, we find suitably adjusting the relative strength, recurrent probability, and feedforward synaptic connection can promote propagation of pulse packet. Notably, different from each other, larger feedforward synaptic time constant can considerably promote the propagation of population firing rate while hindering the propagation of pulse packets.

Feed-forward neural networks using cerebral MR spectroscopy and DTI might predict neurodevelopmental outcome in preterm neonates

ObjectivesWe aimed to evaluate the ability of feed-forward neural networks (fNNs) to predict the neurodevelopmental outcome (NDO) of very preterm neonates (VPIs) at 12 months corrected age by using biomarkers of cerebral MR proton spectroscopy (1H-MRS) and diffusion tensor imaging (DTI) at term-equivalent age (TEA).MethodsIn this prospective study, 300 VPIs born before 32 gestational weeks received an MRI scan at TEA between September 2013 and December 2017. Due to missing or poor-quality spectroscopy data and missing neurodevelopmental tests, 173 VPIs were excluded. Data sets consisting of 103 and 115 VPIs were considered for prediction of motor and cognitive developmental delay, respectively. Five metabolite ratios and two DTI characteristics in six different areas of the brain were evaluated. A feature selection algorithm was developed for receiving a subset of characteristics prevalent for the VPIs with a developmental delay. Finally, the predictors were constructed employing multiple fNNs and fourfold cross-validation.ResultsBy employing the constructed fNN predictors, we were able to predict cognitive delays of VPIs with 85.7% sensitivity, 100% specificity, 100% positive predictive value (PPV) and 99.1% negative predictive value (NPV). For the prediction of motor delay, we achieved a sensitivity of 76.9%, a specificity of 98.9%, a PPV of 90.9% and an NPV of 96.7%.ConclusionFNNs might be able to predict motor and cognitive development of VPIs at 12 months corrected age when employing biomarkers of cerebral 1H-MRS and DTI quantified at TEA.Key Points• A feed-forward neuronal network is a promising tool for outcome prediction in premature infants.• Cerebral proton magnetic resonance spectroscopy and diffusion tensor imaging can be used for the construction of early prognostic biomarkers.• Premature infants that would most benefit from early intervention services can be spotted at the time of optimal neuroplasticity.

Feed-forward artificial neural network provides data-driven inference of functional connectivity.

We propose a new model-free method based on the feed-forward artificial neuronal network for detecting functional connectivity in coupled systems. The developed method which does not require large computational costs and which is able to work with short data trials can be used for analysis and reconstruction of connectivity in experimental multichannel data of different nature. We test this approach on the chaotic Rössler system and demonstrate good agreement with the previous well-known results. Then, we use our method to predict functional connectivity thalamo-cortical network of epileptic brain based on ECoG data set of WAG/Rij rats with genetic predisposition to absence epilepsy. We show the emergence of functional interdependence between cortical layers and thalamic nuclei after epileptic discharge onset.

Cusps enable line attractors for neural computation.

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.

Local excitation–inhibition ratio for synfire chain propagation in feed-forward neuronal networks

A leading hypothesis holds that spiking activity propagates along neuronal sub-populations which are connected in a feed-forward manner, and the propagation efficiency would be affected by the dynamics of sub-populations. In this paper, how the interaction between local excitation and inhibition effects on synfire chain propagation in feed-forward network (FFN) is investigated. The simulation results show that there is an appropriate excitation–inhibition (EI) ratio maximizing the performance of synfire chain propagation. The optimal EI ratio can significantly enhance the selectivity of FFN to synchronous signals, which thereby increases the stability to background noise. Moreover, the effect of network topology on synfire chain propagation is also investigated. It is found that synfire chain propagation can be maximized by an optimal interlayer linking probability. We also find that external noise is detrimental to synchrony propagation by inducing spiking jitter. The results presented in this paper may provide insights into the effects of network dynamics on neuronal computations.

Learning Precise Spike Train-to-Spike Train Transformations in Multilayer Feedforward Neuronal Networks.

We derive a synaptic weight update rule for learning temporally precise spike train-to-spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation to the deterministic spiking neuron setting, is based strictly on spike timing and avoids invoking concepts pertaining to spike rates or probabilistic models of spiking. The derivation is founded on two innovations. First, an error functional is proposed that compares the spike train emitted by the output neuron of the network to the desired spike train by way of their putative impact on a virtual postsynaptic neuron. This formulation sidesteps the need for spike alignment and leads to closed-form solutions for all quantities of interest. Second, virtual assignment of weights to spikes rather than synapses enables a perturbation analysis of individual spike times and synaptic weights of the output, as well as all intermediate neurons in the network, which yields the gradients of the error functional with respect to the said entities. Learning proceeds via a gradient descent mechanism that leverages these quantities. Simulation experiments demonstrate the efficacy of the proposed learning framework. The experiments also highlight asymmetries between synapses on excitatory and inhibitory neurons.

Prototipo de emulación de movimiento humano mediante una plataforma bípeda humanoide

En esta investigación se desarrolló una plataforma bípeda humanoide, cuya función es emular la marcha humana partiendo del principio de mantener el mínimo consumo energético minimizando el movimiento vertical de la pelvis. La plataforma se realizó utilizando herramientas de diseño y simulación como AutoCAD para la estructura mecánica, Solid-edge para el modelamiento tridimensional y Phyton para simular el movimiento de la plataforma. Estas herramientas suministraron las características físicas exactas de la plataforma, permitiendo generar el modelo cinemático. El modelo cinemático de la marcha se desarrolló utilizando MATLAB, así: a partir de una versión modificada de los parámetros de Denavit-Hartenberg se establece la cinemática directa, y la cinemática inversa se determina a partir de una red neuronal de tipo feedforward-backpropagation. Se obtuvo una plataforma bípeda humanoide con diez grados de libertad, capaz de realizar flexión - extensión en la cadera y rodilla, abducción - aducción en la cadera, flexión plantar-dorsal y pronación - supinación en el tobillo. La generación de trayectorias se obtiene en MATLAB mediante el ingreso del número de pasos, la longitud del paso, la altura del paso y una variable de tiempo que separará cada una de las secuencias o subpasos de la trayectoria. Como resultado se obtuvieron las trayectorias articulares en cadera, rodilla y tobillo en los tres planos, las cuales son acordes con la marcha humana y se evidenció con el robot bípedo humanoide.Con esta investigación se espera establecer nuevos modelos para emular la marcha humana normal y patológica. Asimismo, esta es desarrollada por el grupo de investigación DIGITI de la Universidad Distrital Francisco José de Caldas.

Oscillatorylike behavior in feedforward neuronal networks.

We demonstrate how rhythmic activity can arise in neural networks from feedforward rather than recurrent circuitry and, in so doing, we provide a mechanism capable of explaining the temporal decorrelation of γ-band oscillations. We compare the spiking activity of a delayed recurrent network of inhibitory neurons with that of a feedforward network with the same neural properties and axonal delays. Paradoxically, these very different connectivities can yield very similar spike-train statistics in response to correlated input. This happens when neurons are noisy and axonal delays are short. A Taylor expansion of the feedback network's susceptibility-or frequency-dependent gain function-can then be stopped at first order to a good approximation, thus matching the feedforward net's susceptibility. The feedback network is known to display oscillations; these oscillations imply that the spiking activity of the population is felt by all neurons within the network, leading to direct spike correlations in a given neuron. On the other hand, in the output layer of the feedforward net, the interaction between the external drive and the delayed feedforward projection of this drive by the input layer causes indirect spike correlations: spikes fired by a given output layer neuron are correlated only through the activity of the input layer neurons. High noise and short delays partially bridge the gap between these two types of correlation, yielding similar spike-train statistics for both networks. This similarity is even stronger when the delay is distributed, as confirmed by linear response theory.

Comparison of Arrhenius model and artificial neuronal network for the quality prediction of rainbow trout (Oncorhynchus mykiss) fillets during storage at different temperatures

Quality changes in total aerobic counts (TAC), electrical conductivity (EC), K-value and sensory assessment (SA) of rainbow trout (Oncorhynchus mykiss) fillets during storage at 282, 279, 276, 273 and 270 K were determined. Simultaneously, Arrhenius model and feed-forward artificial neuronal network (ANN) were established to predict changes of rainbow trout fillets during storage, and a comparative study between these two models was also performed. The relative error between predicted and experimental value was used as the comparative parameter. The results showed that TAC, EC and K-value increased with storage time, while SA decreased with time. The change rate of all indicators increased as a function of temperature. Arrhenius models based on EC and TAC were acceptable, while those based on SA and K-value showed poor performances in some days. By contrast, ANN was more effective to predict changes in TAC, EC, K-value and SA throughout the storage, with relative errors all below 10%. Therefore, ANN could be a potential tool in modeling quality changes of rainbow trout fillets within 270–282 K.

Vibrational resonance in feedforward neuronal network with unreliable synapses

In this paper, we investigate vibrational resonance in feedforward neuronal network coupled in an all-to-all fashion. In contrast to earlier most work, where only reliable synaptic connections are considered, we mainly examine the effects of unreliable synapses on signal propagation in this work. It is shown that the neurotransmitter release probability and excitatory synaptic strength largely influence the signal propagation, and better tuning of these synaptic parameters makes the feedforward neuronal network support stable signal propagation. Furthermore, it is found that high-frequency driving plays important roles in causing the response of the feedforward neuronal network to subthreshold low-frequency signal and strengthening the ability of the signal propagation between layers. In particular, the optimal amplitude of high-frequency driving is largely influenced by the stochastic effect of neurotransmitter release and the coupling strength. Finally, we compare our results with those obtained in corresponding feedforward neuronal networks connected with reliable synapses but in a random coupling fashion. It is demonstrated that unreliable synaptic coupling is more efficient than the random coupling for the transmission of local input signal. Considering that unreliable synapses are inevitable in neuronal communication, the presented results could have important implications for the weak signal detection and information propagation in neural systems.

The estimation of neurotransmitter release probability in feedforward neuronal network based on adaptive synchronization

In this paper, we proposed a new approach to estimate unknown parameters and topology of a neuronal network based on the adaptive synchronization control scheme. A virtual neuronal network is constructed as an observer to track the membrane potential of the corresponding neurons in the original network. When they achieve synchronization, the unknown parameters and topology of the original network are obtained. The method is applied to estimate the real-time status of the connection in the feedforward network and the neurotransmitter release probability of unreliable synapses is obtained by statistic computation. Numerical simulations are also performed to demonstrate the effectiveness of the proposed adaptive controller. The obtained results may have important implications in system identification in neural science.

Propagation of Spiking and Burst-Spiking Synchronous States in a Feed-Forward Neuronal Network

Neuronal firing that carries information can propagate stably in neuronal networks. One important feature of the stable states is their spatiotemporal correlation (STC) developed in the propagation. The propagation of synchronous states of spiking and burst-spiking neuronal activities in a feed-forward neuronal network with high STC is studied. Different dynamic regions and synchronous regions of the second layer are clarified for spiking and burst-spiking neuronal activities. By calculating correlation, it is found that five layers are needed for stable propagation. Synchronous regions of the 4th layer and the 10th layer are compared.

Specific Residues of a Conserved Domain in the N Terminus of the Human Cytomegalovirus pUL50 Protein Determine Its Intranuclear Interaction with pUL53

Herpesviral capsids are assembled in the host cell nucleus and are subsequently translocated to the cytoplasm. During this process it has been demonstrated that the human cytomegalovirus proteins pUL50 and pUL53 interact and form, together with other viral and cellular proteins, the nuclear egress complex at the nuclear envelope. In this study we provide evidence that specific residues of a conserved N-terminal region of pUL50 determine its intranuclear interaction with pUL53. In silico evaluation and biophysical analyses suggested that the conserved region forms a regular secondary structure adopting a globular fold. Importantly, site-directed replacement of individual amino acids by alanine indicated a strong functional influence of specific residues inside this globular domain. In particular, mutation of the widely conserved residues Glu-56 or Tyr-57 led to a loss of interaction with pUL53. Consistent with the loss of binding properties, mutants E56A and Y57A showed a defective function in the recruitment of pUL53 to the nuclear envelope in expression plasmid-transfected and human cytomegalovirus-infected cells. In addition, in silico analysis suggested that residues 3-20 form an amphipathic α-helix that appears to be conserved among Herpesviridae. Point mutants revealed a structural role of this N-terminal α-helix for pUL50 stability rather than a direct role in the binding of pUL53. In contrast, the central part of the globular domain including Glu-56 and Tyr-57 is directly responsible for the functional interaction with pUL53 and thus determines formation of the basic nuclear egress complex.

How attention and reinforcers jointly optimize the associations between sensory representations, working memory and motor programs

Almost all animal behaviors can be seen as sequences of actions towards achieving certain goals. How the association cortices learn to link sensory stimuli to a correct sequence of motor responses is not well understood, especially when only a correct sequence of responses is rewarding. We present a biologically plausible neuronal network model that can be trained to perform a large variety of tasks when only stimuli and reward contingencies are varied. The model’s aim is to learn action values in a feedforward neuronal network and we present mechanisms to overcome the structural and temporal credit assignment problems. The temporal credit assignment problem is solved by a form of Q-learning [1]. The structural credit assignment problem is solved by a form of ‘attentional’ feedback from motor cortex to association cortex that delineates the units that should change connectivity to improve behavior [2]. Moreover, the model has a new mechanism to store traces of relevant sensory stimuli in working memory. During learning, the sensory stimuli, in combination with traces of previous stimuli in working memory become associated with a unique set of action values. Learning in the model is biologically realistic as model units have Hebbian plasticity that is gated by two factors [2]. Firstly, reinforcers or increases in reward expectancy cause the global release of neuromodulatory signals that inform all synapses of the network if the outcome of a trial was better or worse than expected [3]. Selective attention is the second factor that gates plasticity. Attentional feedback highlights the chain of neurons between sensory and motor cortex responsible for the selected action. Only neurons that are causally linked to the action receive attentional feedback, and change the strength of their connections. Selective attention thereby solves the structural credit assignment problem. The resulting learning rule is a form of AGREL [2], which was previously shown to be on average equivalent to error-backpropagation in classification tasks with immediate reward. The present generalization of the learning scheme is based on temporal difference learning and it can train multilayer feedforward networks to perform delayed reward tasks with multiple epochs that require multiple behavioral responses. Importantly, the generalization MQ-AGREL learns to store in working memory information that is relevant at a later stage during a task. This memory is maintained by persistent activity of units at the intermediate network layers. We show that MQ-AGREL can be trained in many tasks that are in use in neurophysiology, including (1) (delayed) saccade-antisaccade tasks; (2) categorization tasks; and (3) probabilistic classification tasks. Neurons at intermediate levels of the network acquire visual responses and memory responses as the result of training that resemble the tuning of neurons in association areas of the cerebral cortex of animals that are trained in these same tasks. We conclude that MQ-AGREL is a powerful and biologically realistic learning rule that accounts for learning in delayed reward tasks that involve non-linear mappings from sensory stimuli and working memory onto motor responses.

Optimization of weak signal propagation in a feedforward network

The ability of weak signal detection and transduction of neurons is of great importance. Although the subject hotly debated in single neuron and complex networks [1], it has been partly addressed in feedforward networks [2,3]. In our previous work [2], we determined the conditions for weak rhythmic signal propagation through a feedforward network where the neurons are constructed with detailed biophysical modeling approaches. It is shown that the optimal propagation of weak rhythmic signals through feedforward neuronal networks depends significantly on the level of intrinsic noise, the forcing frequency and the inter-layer link density. Here, we used the same network structure in [2], which involves 10 layers with N=200 neurons in each one and 10% inter-layer link density (Fig1a). For synaptic transmission, alpha-synapse type is used to model the conductance variations in the post-synaptic neuron resulting from the binding of neurotransmitter released from the pre-synaptic neuron. Release time of neurotransmitters τsyn and coupling constant gsyn are critical parameters of this type of synapses. A measure Qi is chosen to quantify the signal transmission efficiency, which gives the existence of the input signal frequency at any layers’ output, similar to Signal to Noise Ratio (SNR). Model details and methods can be found in [2]. To extend our findings, we first investigated the role of fraction of forced neurons forming the first layer on the propagation of weak rhythmic activity. We consider different fractions of periodically forced neurons (chosen randomly) and compute Q10 (Fourier coefficients of output layer) over a broad frequency range (Fig 1b). Evidently, the larger the fraction of neurons subject to the weak forcing, the better the outreach of the signal through the network. This can be appreciated most clearly for the optimal angular forcing frequency, ω≈0.4ms–1[2]. Interestingly, the depicted curves show only marginal improvement in Q10 if more than 50% of the neurons forming the first layer are forced. This finding suggests that the propagation of weak signals across feedforward neuronal networks is rather robust to variations in the coverage of the initial input. We also examined how synaptic mechanisms effect the propagation of weak rhythmic activity through the network. For this purpose, a periodic sinusoidal force with the optimal angular frequency ω≈0.4ms–1 is introduced to all neurons in the first layer as shown in Fig​Fig1a,1a, then we computed Q10/Q1gain factor with respect to systematically changed values of synaptic parameters. Results are presented in Fig​Fig1c.1c. It is clearly seen that signal transmission can be modulated by the synaptic transmission parameters. There is an optimal τsyn range, i.e. 1.5 =1 for gsyn >0.4 nS, indicating the efficient transmission of the weak signal. The underlying mechanism can be understood by comparing synaptic and membrane time constants with respect to each other, because they together determine the operation mode of neurons, i.e. coincidence detector or temporal integrator [3]. Fig 1c also shows that weak signal can be transmitted to the output layer for the coupling constants of gsyn >0.4 nS regardless ofτsyn, implying that the synaptic coupling must be higher than a critical value. Figure 1 (a) Schematic illustration of a 10 layer feedforward network, (b) Fourier coefficient Q10 in dependence on ω for different fractions of forced neurons forming the first layer, (c) The dependence of the gain factor Q10 / Q1with respect to the synaptic ...