One of the challenges in modern neuroscience is creating a brain-on-a-chip. Such a semiartificial device based on neural networks grown in vitro should interact with the environment when embodied in a robot. A crucial point in this endeavor is developing a neural network architecture capable of associative learning. This work proposes a mathematical model of a midscale modular spiking neural network (SNN) to study learning mechanisms within the brain-on-a-chip context. We show that besides spike-timing-dependent plasticity (STDP), synaptic and neuronal competitions are critical factors for successful learning. Moreover, the shortest pathway rule can implement the synaptic competition responsible for processing conditional stimuli coming from the environment. This solution is ready for testing in neuronal cultures. The neuronal competition can be implemented by lateral inhibition actuating over the SNN modulus responsible for unconditional responses. Empirical testing of this approach is challenging and requires the development of a technique for growing cultures with a given ratio of excitatory and inhibitory neurons. We test the modular SNN embedded in a mobile robot and show that it can establish the association between touch (unconditional) and ultrasonic (conditional) sensors. Then, the robot can avoid obstacles without hitting them, relying on ultrasonic sensors only.
Mathematical and computer simulation of learning in living neural networks have typically focused on changes in the efficiency of synaptic connections represented by synaptic weights in the models. Synaptic plasticity is believed to be the cellular basis for learning and memory. In spiking neural networks composed of dynamical spiking units, a biologically relevant learning rule is based on the so-called spike-timing-dependent plasticity or STDP. However, experimental data suggest that synaptic plasticity is only a part of brain circuit plasticity, which also includes homeostatic and structural plasticity. A model of structural plasticity proposed in this study is based on the activity-dependent appearance and disappearance of synaptic connections. The results of the research indicate that such adaptive rewiring enables the consolidation of the effects of STDP in response to a local external stimulation of a neural network. Subsequently, a vector field approach is used to demonstrate the successive “recording” of spike paths in both functional connectome and synaptic connectome, and finally in the anatomical connectome of the network. Moreover, the findings suggest that the adaptive rewiring could stabilize network dynamics over time in the context of activity patterns’ reproducibility. A universal measure of such reproducibility introduced in this article is based on similarity between time-consequent patterns of the special vector fields characterizing both functional and anatomical connectomes.
We propose simple agent-based mathematical model of epidemic development capable to generate various multi-peak dynamics typical to COVID-19 pandemic. Agents are supplied with very simple kind behavior moving in a homogeneous interaction space with a constant speed. There is a probability of infection transmission if the agents meet with at certain distance. Next we assume that our agents get three features of intelligences called here: (i) information induced feedback, (ii) delay reaction on danger and (iii) danger adaptation. All these features are accounted in the model by the infection probability that becomes dynamic variable driven by additional differential equation. The information feedback means that this probability decreases with growing number of infected cases. It reflects facts that in modern world information media monitor the pandemic situation and with progressing infection around people start to protect them carefully that finally leads to the decrease of infected cases. Characteristic timings accounted in our model by delay reaction on the information feedback and danger adaptation time are also important in the probability dynamics. Surprisingly, but within these simple assumptions that did not touch any molecular specificity of COVID-19, except quite long exposure time, we immediately get a multi-peak dynamics of the pandemic development. Here, we show different conceptual cases of how such rhythmicity evolves under different parametric conditions.
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