This article has multiple issues. Please help improve it or discuss these issues on the talk page . (Learn how and when to remove these template messages)
|
Synthetic Nervous System (SNS) is a computational neuroscience model that may be developed with the Functional Subnetwork Approach (FSA) to create biologically plausible models of circuits in a nervous system. [1] The FSA enables the direct analytical tuning of dynamical networks that perform specific operations within the nervous system without the need for global optimization methods like genetic algorithms and reinforcement learning. The primary use case for a SNS is system control, where the system is most often a simulated biomechanical model or a physical robotic platform. [2] [3] [4] [5] [6] [7] [8] An SNS is a form of a neural network much like artificial neural networks (ANNs), convolutional neural networks (CNN), and recurrent neural networks (RNN). The building blocks for each of these neural networks is a series of nodes and connections denoted as neurons and synapses. More conventional artificial neural networks rely on training phases where they use large data sets to form correlations and thus “learn” to identify a given object or pattern. When done properly this training results in systems that can produce a desired result, sometimes with impressive accuracy. However, the systems themselves are typically “black boxes” meaning there is no readily distinguishable mapping between structure and function of the network. This makes it difficult to alter the function, without simply starting over, or extract biological meaning except in specialized cases. [9] [10] The SNS method differentiates itself by using details of both structure and function of biological nervous systems. The neurons and synapse connections are intentionally designed rather than iteratively changed as part of a learning algorithm.
As in many other computational neuroscience models (Rybak, [11] Eliasmith [12] ), the details of a neural model are informed by experimental data wherever possible. Not every study can measure every parameter of the network under investigation, requiring the modeler to make assumptions regarding plausible parameter values. Rybak uses a sampling method where each node is composed of many neurons and each particular neuron’s parameters are pulled from a probability distribution. [11] Eliasmith uses what they call the Neural Engineering Framework (NEF) in which the user specifies the functions of the network and the synaptic and neural properties are learned over time. [12] SNS follows a similar approach via the Functional Subnetwork Approach (FSA). FSA allows parameters within the network (e.g., membrane conductances, synaptic conductances) to be designed analytically based on their intended function. As a result, it is possible to use this approach to directly assemble networks that perform basic functions, like addition or subtraction, as well as dynamical operations like differentiation and integration.
The details of the underlying control networks for many biological systems are not very well understood. However, recent advancements in neuroscience tools and techniques have clarified the cellular and biophysical mechanisms of these networks, and their operation during behavior in complex environments. [13] [14] [15] [16] Although there is a long-standing interest in biologically-inspired robots and robotic platforms, there is a recent interest in incorporating features of biomechanics and neural control, e.g., biomimicry. The SNS method uses data from neuroscience in control systems for neuromechanical simulations and robots. Designing both a robot’s mechanics and controller to capture key aspects of a particular animal may lead to more flexible functionality while suggesting new hypotheses for how the animal’s nervous system works. [1] [17] [18]
Keeping neural models simple facilitates analysis, real time operation, and tuning. To this end, SNSs primarily model neurons as leaky integrators, which are reasonable approximations of sub-threshold passive membrane dynamics. The leaky integrator also models non-spiking interneurons which contribute to motor control in some invertebrates (locust, [19] stick insect, [20] C. elegans [21] ). If spiking needs to be incorporated into the model, nodes may be represented using the leaky integrate-and-fire models. [2] [22] In addition, other conductances like those of the Hodgkin-Huxley model can be incorporated into the model. [3] A model may be initialized with simple components (e.g., leaky integrators), and then details added to incorporate additional biological details. The modeler may then increase or decrease the level of biological detail depending upon the intended application. Keeping models simple in this way offers:
While the neuroscientific models are typically simplified for SNS, the method is flexible enough that more features can be incorporated. Consequently, the SNS method can accommodate demand driven complexity, only adding features specifically where they are needed. For example, persistent sodium channels can be added to just two neurons in a neural circuit to create a half- center oscillator pattern generator without changing the other neurons in the circuit. While these additions may increase computational cost, they grant the system the ability to perform a wider array of interesting behaviors.
The term “synthetic nervous system” (SNS) has appeared in the literature since the year 2000 to describe several different computational frameworks for mimicking the functionality of biological nervous systems.
Cynthia Breazeal developed a social robot named “Kismet” while at MIT in the early 2000s. [23] She used the term SNS to refer to her biologically-inspired hierarchical model of cognition, which included systems for low-level sensory feature extraction, attention, perception, motivation, behavior, and motor output. Using this framework, Kismet could respond to people by abstracting its sensory information into motivation for responsive behaviors and the corresponding motor output.
In 2005, Inman Harvey used the term in a review article on his field, Evolutionary Robotics. [24] In his article, Harvey uses the term SNS to refer to the evolved neural controller for a simulated agent. He does not explicitly define the term SNS; instead, he uses the term to differentiate the evolved neural controller from one created via alternative approaches, e.g., multi-layer perceptron (MLP) networks.
In 2008, Thomas R. Insel, MD, the director of the National Institute of Mental Health, was quoted in an American Academy of Neurology interview calling for a “clear moon shot…[to motivate] a decade of new discovery [and] basic research on brain anatomy”. [25] As part of that interview, Dr. Insel suggested building a “synthetic nervous system” as one such motivational moon shot to drive ongoing and future research. The technical details of what such a SNS would entail were not described.
An article published as part of the International Work-Conference on Artificial Neural Networks (IWANN) proposes a “synthetic nervous system” as an alternative to artificial neural networks (ANNs) based in machine learning. In particular, SNS should be able to include or learn new information without forgetting what it has already learned. [26] However, the authors do not propose a computational neuroscience framework for constructing such networks. Instead, they propose a homeostatic network of the robot’s “needs”, in which the robot takes actions to satisfy its needs and return to homeostasis. Over time, the robot learns which actions to take in response to its needs.
A dissertation from Prof. Joseph Ayer’s lab at Northeastern University uses a similar term in its title but never explicitly defines it. The topic of the dissertation is “RoboLobster, a biomimetic robot controlled by an electronic nervous system simulation”. [27] Other publications from Prof. Ayers use the term “electronic nervous system” (ENS) to describe similar work. [28] [29] [30] In each of these studies, Prof. Ayers uses a robot that is controlled by a network of simplified dynamical neural models whose structure mimic specific networks from the model organism. [31] The choice of neural model reflects a balance between simulating the dynamics of the nervous system, which motivates mathematical complexity, while ensuring the simulation runs in real time, which motivates mathematical simplicity.
A 2017 research article from Prof. Alexander Hunt, Dr. Nicholas Szczecinski, and Prof. Roger Quinn use the term SNS and implicitly define it as “neural [or] neuro-mechanical models…composed of non-spiking leaky integrator neuron models”. [5] Similar to work by Ayers et al., Hunt et al. apply the term SNS to refer to a simplified dynamical simulation of neurons and synapses used in the closed-loop control of robotic hardware. Subsequent articles by these authors present the Functional Subnetwork Approach for tuning SNS constructed from these and other simplified dynamical neural models [1] [2] (i.e., leaky integrate-and-fire), as well as further SNS models of the nervous system [7] [32] [33] [34]
Comparing the diversity of works that use the term SNS produces an implicit definition of SNS:
SNSs share some features with machine learning networks like Artificial Neural Networks (ANN), Convolutional Neural Networks (CNN), and Recurrent Neural Networks (RNN). All of these networks are composed of neurons and synapses inspired in some way by biological nervous systems. These components are used to build neural circuits with the express purpose of accomplishing a specific task. ANN simply refers to a collection of nodes (neurons) connected such that they loosely model a biological brain. This is a rather broad definition and as a consequence there are many subcategories of ANN, two of which are CNN and RNN. CNNs are primarily used for image recognition and classification. Their layer-to-layer connections implement convolutional kernels across small areas of the image, which map the input to the system (typically an image) onto a collection of features. ANNs and CNNs are only loosely associated with SNS in that they share the same general building blocks of neurons and synapses, though the methods used to model each component varies between the networks. Of the three, RNNs are the most closely related to SNS. SNSs use the same leaky-integrator neuron models utilized in RNNs. This is advantageous as neurons inherently act as low pass filters, which is useful for robotic applications where such filtering is often applied to reduce noise for both sensing and control purposes. Both models also exhibit dynamic responses to inputs. While predicting the responses of a complicated network can be difficult, the dynamics of each node are relatively simple in that each is a system of first order differential equations (as opposed to fractional derivatives). The key difference that distinguishes SNS from these neural networks are the synaptic connections and the general architecture of the neural circuit.
RNN structures generally present as large, highly connected or even all-to- all connected layers of neurons. Instead of these layers, SNS relies on functional subnetworks which are tuned to perform specific operations and then assembled into larger networks with explainable functions. These are significantly more tractable than a typical machine learning network. The tradeoff of SNS is that it typically takes more time to design and tune the network but it does not require a training phase involving large amounts of computing power and training data. The other key difference is that SNS synapses are conductance based rather than current based which makes the dynamics non-linear, unlike an RNN. This allows for the modelling of modulatory neural pathways since the synapses can alter the net membrane conductance of a postsynaptic neuron without injecting current. It also enables the functional subnetwork approach to encompass addition, subtraction, multiplication, division, differentiation, and integration operations using the same family of functions.
SNS networks are composed mainly of non-spiking leaky integrator nodes to which complexity may be added if needed. Such dynamics model non-spiking neurons like those studied extensively in invertebrates (e.g., nematode, [35] locust, [19] cockroach [36] ) or may represent the mean activity of a population of spiking neurons. [37] The dynamics of the membrane voltage of a non-spiking neuron are governed by the differential equation
where is the membrane capacitance, is an arbitrary current injected into the cell e.g., via a current clamp, and and are the leak and synaptic currents, respectively. The leak current
where is the conductance of the cell membrane and is the rest potential across the cell membrane. The synaptic current
where is the number of synapses that impinge on the cell, is the instantaneous synaptic conductance of the incoming synapse, and is the reversal potential of the incoming synapse.
Non-spiking neurons communicate via graded chemical synapses:. [38] Typically, synaptic conductances are modeled with a continuous function like a sigmoid but in an SNS this conductance is approximated by the following piecewise-linear function [1]
As shown in the corresponding figure this allows the conductance to vary between 0 and a prescribed or designed maximum value () depending on the presynaptic potential (). A piecewise approach is used to ensure exactly 0 conductance, and therefore current, at low activation potentials. This approximates a feature of spiking neuron activity in that no information is transmitted when the neuron isn’t spiking/active. Furthermore, this approximation eliminates transcendental functions enabling analytical calculations of dynamical properties. While this does prevent the network activity from being differentiable, since no gradient-based learning methods are employed (like backpropagation) this is not a drawback.
It was previously mentioned that additional ion channels could be incorporated to elicit more interesting behaviors from non-spiking neuron models. The persistent sodium current is one such addition. A persistent sodium current can depolarize a membrane enough to induce action potential firings at sub-threshold membrane potentials while also being slow to inactivate. In the context of neuroscientific models, this is useful for applications such as pattern generators where it is desired that a neuron’s potential can be rapidly increased and remain elevated until inhibited by another neural signal or applied current. [3] [4]
The model for the behavior of this channel is based on the m and h gating present in the full Hodgkin-Huxley model. The main difference is that this model only uses one m gate instead of three. The equations governing this behavior can be found here and in this paper. [3]
Unless explicitly studying or utilizing the Hodgkin-Huxley model for action potentials, spiking neurons can be modeled via the integrate-and-fire method. This is significantly more computationally efficient than Hodgkin-Huxley making it easier to simulate much larger networks. In particular, leaky integrate-and-fire (LIF) neurons are used for SNS. [2] As the name suggests, this model accounts for membrane potential leak behavior representing ion diffusion across the membrane. This integrate-and-fire model is very similar to the non-spiking neuron described above with the key addition of a firing threshold parameter. When the neuron potential depolarizes to this threshold the neuron “spikes” by instantaneously resetting to its resting potential [2]
While these do not provide the same diversity of dynamical responses as Hodgkin-Huxley, they are usually sufficient for SNS applications and can be analyzed mathematically which is crucial for network tractability. Please refer to the linked Wikipedia article and paper for the equations associated with the LIF neuron model.
Spiking neurons can also be modeled in a computationally efficient manner without sacrificing the rich behaviors exhibited in biological neural activity. [39] The Izhikevich model can produce spiking behaviors approximately as plausible as Hodgkin-Huxley but with comparable computational efficiency to the integrate-and-fire method. To accomplish this, Izhikevich reduces the Hodgkin-Huxley model to a two-dimensional set of ordinary differential equations via bifurcation methods. [40] These can be seen here:
Where the membrane potential resets after spiking as described by:
is a dimensionless variable representing the membrane potential. is a dimensionless variable representing membrane recovery which accounts for the ion current behaviors, specifically those of and . , , , and are dimensionless parameters that can be altered to shape the signal into different neuronal response patterns. This enables chattering, bursting, and continuous spiking with frequency adaptation which constitute a richer array of behaviors than the basic integrate-and-fire method can produce.
The coefficients in the equation were acquired via data fitting to a particular neuron’s spiking patterns (a cortical neuron in this case) to get the potentials in the mV range and time on the scale of ms. It is possible to use other neurons to fit the spike initiation dynamics, they will simply produce different coefficients.
For more information on the Izhikevich model and the bifurcation methods used to develop it please read the following. [39] [40]
The Rulkov map forgoes complex ion channel-based models composed of many non-linear differential equations in favor of a two-dimensional map. [31] This map expresses slow and fast dynamics which is vital for representing both slow oscillations and fast spikes and bursts. The model is shown below:
is the fast dynamical variable and represents the membrane potential while is the slow dynamical variable and does not have explicit biological meaning. and are used to describe external influences and help model the dynamics of stimuli like injected/synaptic and tonic/bias currents. Small values of result in slow changes in that account for its slower behavior. Assuming a constant external influence () the function can be written as the following discontinuous function:
In this case is the map control parameter and can be used, along with , to shape the output behavior of the neuron.
You can read more about the Rulkov map on the Wikipedia page hyperlinked here and in. [31]
Functional Subnetworks are the building blocks of SNSs. [1] They are composed of neurons and synapses modeled from the equations described above as well as other neuroscience models. When tuned properly, as shown in the following section, they are capable of performing mathematical calculations as well as dynamical operations. This process is different from other artificial neural networks in that the tuning exploits the network structure. The artificial neural networks mentioned previously utilize all-to-all connectivity between layers but in a SNS there are no distinct layers. Rather the synaptic connections are methodically designed with an express function in mind. This results in fewer synaptic connections without sacrificing network effectiveness. Tuned subnetworks can be assembled into larger networks to form the SNS itself. Assembly can be done in series or in parallel, much like adding components to an electrical circuit. The resulting neural network is reminiscent of a peripheral nervous system, rather than a brain-like network (ANN).
The leaky-integrator model above can be converted into a tuning-friendly equation by normalizing the membrane potential to read 0 when at rest () and by introducing the parameter. is the potential operating range of the graded chemical synapse and is equal to . Making these changes and then solving for the steady-state activation () of the neuron (when ) gives the following equation: [1]
is determined by the difference between cell resting potential () and the synaptic reversal potential (). This equation can be used to tune synapse conductances for specific points in the network’s operation where the neurons are in a steady state or have a known/designed membrane potential (). In this way it is possible to intentionally and directly set the state of the network during key moments in its operation sequence so that it produces a desired action or behavior.
Tuning a subnetwork requires the use of signal transmission and/or modulation pathways. Signal transmission pathways make a postsynaptic neuron’s potential proportional to that of the presynaptic neuron(s). The ratio of the synaptic proportionality is referred to as . This can be used to calculate the maximum conductance value for a synapse () via the equation: [1]
is used in the graded chemical synapse model discussed previously. Tuning a synapse using instead of the steady-state activation equation is practical when a specific relationship between a small subset of neurons is desired. For example, if a network requires that the postsynaptic neuron membrane potential be half that of the presynaptic neuron, can be set to and plugged into the equation.
The signal modulation pathway is used to modulate neuron sensitivity This allows for adaptive responses to various inputs. In this pathway is used instead of . Technically both are defined as the steady state postsynaptic potential () divided by the presynaptic potential (), the ratio mentioned above, for a given applied current. The letter is used for modulation to indicate that the neuron sensitivity is changing and is therefore not the same as which represents a static relationship. For a modulation pathway, can be calculated as: [1]
In order to minimize hyperpolarization of the postsynaptic neuron should be kept negative and as close to 0 as possible (or zeroed entirely).
All arithmetic subnetwork tuning methods were taken from. [1]
Addition subnetworks are composed of one postsynaptic neuron connected to presynaptic neurons via excitatory transmission pathways. The purpose of the network is to enable an approximation of linear addition of the incoming presynaptic signals. The subnetwork can be tuned using either of the methods outlined previously. The addition behavior can be weighted using . This type of network may represent positive feedback mechanisms in biology. To capture the addition properly must be small but it cannot be 0 or the synapse will effectively be severed. Instead, is maximized which results in small values of .
Subtraction subnetworks are similar to addition networks except the presynaptic potentials being subtracted travel to the postsynaptic cell via inhibitory transmission pathways. This may approximate negative feedback mechanisms in the nervous system. Unlike with depolarizing ions, hyperpolarizing ion potentials tend to be much closer to the membrane resting potential. This results in smaller values so it is difficult to minimize like in the addition subnetwork. The easiest way to properly tune a subtraction network is to design the parameters to fit a specific scenario. This process was already described using the steady state activation equation. can also be used as in the addition subnetwork but since cannot be minimized to the same degree the effect is not as precise. The equation to solve the inhibitory pathway in this manner is as follows:
The excitation pathway synaptic potential difference () must first be determined. It is vital that for the inhibitory pathway be negative or solving the equation will produce a negative conductance which is biologically impossible.
The physical structure of a division subnetwork is the same as a subtraction subnetwork except the inhibitory synapse is modulatory, rather than transmission. The division performed in this network follows the form below where the transmitted signal is divided by the modulating signal :
The excitatory transmission synapse is tuned as described previously. The modulatory reversal potential is right around 0 so the from before is cancelled out (set to 0). Setting equal to and applying these to the steady-state activation equation gives the division equation above once simplified. From here the equation can be used as before and can be set such that the network produces the desired division behavior. For example, if it were desired that when then could be set to (example from [1] ). values closer to 0 more strongly reduce the postsynaptic neuron’s sensitivity to inputs.
Multiplication networks are somewhat similar to division networks but rather than having the modulatory synaptic connection directly between the presynaptic and postsynaptic neuron there is an interneuron in the way. The presynaptic neuron connects to the interneuron via a modulatory pathway and the interneuron connects to the postsynaptic neuron with another modulatory synapse (please see the figure in this section for clarification). This modulation in series results in a network that essentially divides by the inverse which turns out to be multiplication. The parameter between the interneuron and the postsynaptic neuron is 0. This ensures that when its potential () is at the maximum value allowed () the postsynaptic neuron potential () is 0 regardless of the applied current. This makes sense since dividing by a maximum allowed number for a system should result in the lowest possible output. Plugging this into the steady-state activation equation gives the following solution for the synaptic conductance:
cannot be greater than or equal to 0 here as division by zero is undefined and dividing by a positive number gives a negative conductance which is impossible. The less negative is, the larger is. This means must determine so as to stay within the confines of biological plausibility. With this synapse designed the rest can be determined using the methods outlined in. [1] The process is rather involved and better suited for an in-depth reading.
All dynamic subnetwork tuning methods were taken from. [1]
Differentiation networks are nearly the same as subtraction networks with an added dynamical component. The presynaptic neuron that inhibits the postsynaptic neuron is modelled as a physically larger neuron which means it has a greater capacitance than the excitatory synapsing neuron. This increased capacitance results in a neuron that is slower to reach its fully excited state (ie. ). Subtracting the slow responding neuron signal (with the inhibitory synapse) from the fast responding signal is basically a biological version of numerical differentiation whereby a previous time-“step” is subtracted from the current time-“step”. This network is good for identifying changes in applied current to a network or applied stimulus to a sensory neuron. The equations that detail this behavior are presented in. [1]
The neuron model used for SNS has leak dynamics meaning a current is always leaking out of the neuron to return it to resting potential. This means a single neuron modelled in this fashion is incapable of storing data. A system of two neurons, however, are capable of this if linked via mutually inhibitory transmission synapses with a marginally stable equilibrium curve. The mutual inhibition means that the activation levels are maintained instead of leaking away and the system state changes continuously for the duration of an applied stimulus (integration). Integration subnetworks, while not necessarily complicated in structure, are the most complex to define and prove. As such the derivation and proof of marginal stability are worth an in-depth read here [1] as a cursory overview would be insufficient.
As mentioned previously, the primary application of the Synthetic Nervous System method is robotic control. Within this field, SNSs have largely been used to control the locomotion of legged robots. Many examples of both simulated and physical robots which incorporate SNSs exist in the literature:
Synthetic Nervous Systems have also been used to model higher functions in the nervous system than the peripheral networks responsible for locomotion. Some examples of these kinds of SNS are listed here:
Within a nervous system, a neuron, neurone, or nerve cell is an electrically excitable cell that fires electric signals called action potentials across a neural network. Neurons communicate with other cells via synapses, which are specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap.
The development of the nervous system, or neural development (neurodevelopment), refers to the processes that generate, shape, and reshape the nervous system of animals, from the earliest stages of embryonic development to adulthood. The field of neural development draws on both neuroscience and developmental biology to describe and provide insight into the cellular and molecular mechanisms by which complex nervous systems develop, from nematodes and fruit flies to mammals.
An artificial neuron is a mathematical function conceived as a model of biological neurons in a neural network. Artificial neurons are the elementary units of artificial neural networks. The artificial neuron receives one or more inputs and sums them to produce an output. Usually, each input is separately weighted, and the sum is often added to a term known as a bias, before being passed through a non-linear function known as an activation function or transfer function. The transfer functions usually have a sigmoid shape, but they may also take the form of other non-linear functions, piecewise linear functions, or step functions. They are also often monotonically increasing, continuous, differentiable and bounded. Non-monotonic, unbounded and oscillating activation functions with multiple zeros that outperform sigmoidal and ReLU-like activation functions on many tasks have also been recently explored. The thresholding function has inspired building logic gates referred to as threshold logic; applicable to building logic circuits resembling brain processing. For example, new devices such as memristors have been extensively used to develop such logic in recent times.
Hebbian theory is a neuropsychological theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptation of brain neurons during the learning process. It was introduced by Donald Hebb in his 1949 book The Organization of Behavior. The theory is also called Hebb's rule, Hebb's postulate, and cell assembly theory. Hebb states it as follows:
Let us assume that the persistence or repetition of a reverberatory activity tends to induce lasting cellular changes that add to its stability. ... When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased.
In neuroscience, synaptic plasticity is the ability of synapses to strengthen or weaken over time, in response to increases or decreases in their activity. Since memories are postulated to be represented by vastly interconnected neural circuits in the brain, synaptic plasticity is one of the important neurochemical foundations of learning and memory.
An electrical synapse is a mechanical and electrically conductive synapse, a functional junction between two neighboring neurons. The synapse is formed at a narrow gap between the pre- and postsynaptic neurons known as a gap junction. At gap junctions, such cells approach within about 3.8 nm of each other, a much shorter distance than the 20- to 40-nanometer distance that separates cells at a chemical synapse. In many animals, electrical synapse-based systems co-exist with chemical synapses.
Neuromorphic computing is an approach to computing that is inspired by the structure and function of the human brain. A neuromorphic computer/chip is any device that uses physical artificial neurons to do computations. In recent times, the term neuromorphic has been used to describe analog, digital, mixed-mode analog/digital VLSI, and software systems that implement models of neural systems. The implementation of neuromorphic computing on the hardware level can be realized by oxide-based memristors, spintronic memories, threshold switches, transistors, among others. Training software-based neuromorphic systems of spiking neural networks can be achieved using error backpropagation, e.g., using Python based frameworks such as snnTorch, or using canonical learning rules from the biological learning literature, e.g., using BindsNet.
A Hopfield network is a form of recurrent artificial neural network and a type of spin glass system popularised by John Hopfield in 1982 as described by Shun'ichi Amari in 1972 and by Little in 1974 based on Ernst Ising's work with Wilhelm Lenz on the Ising model. Hopfield networks serve as content-addressable ("associative") memory systems with binary threshold nodes, or with continuous variables. Hopfield networks also provide a model for understanding human memory.
A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Multiple neural circuits interconnect with one another to form large scale brain networks.
Neuromodulation is the physiological process by which a given neuron uses one or more chemicals to regulate diverse populations of neurons. Neuromodulators typically bind to metabotropic, G-protein coupled receptors (GPCRs) to initiate a second messenger signaling cascade that induces a broad, long-lasting signal. This modulation can last for hundreds of milliseconds to several minutes. Some of the effects of neuromodulators include: altering intrinsic firing activity, increasing or decreasing voltage-dependent currents, altering synaptic efficacy, increasing bursting activity and reconfigurating synaptic connectivity.
Computational neurogenetic modeling (CNGM) is concerned with the study and development of dynamic neuronal models for modeling brain functions with respect to genes and dynamic interactions between genes. These include neural network models and their integration with gene network models. This area brings together knowledge from various scientific disciplines, such as computer and information science, neuroscience and cognitive science, genetics and molecular biology, as well as engineering.
In computational neuroscience, the Wilson–Cowan model describes the dynamics of interactions between populations of very simple excitatory and inhibitory model neurons. It was developed by Hugh R. Wilson and Jack D. Cowan and extensions of the model have been widely used in modeling neuronal populations. The model is important historically because it uses phase plane methods and numerical solutions to describe the responses of neuronal populations to stimuli. Because the model neurons are simple, only elementary limit cycle behavior, i.e. neural oscillations, and stimulus-dependent evoked responses are predicted. The key findings include the existence of multiple stable states, and hysteresis, in the population response.
In neuroscience and computer science, synaptic weight refers to the strength or amplitude of a connection between two nodes, corresponding in biology to the amount of influence the firing of one neuron has on another. The term is typically used in artificial and biological neural network research.
Biological neuron models, also known as spiking neuron models, are mathematical descriptions of neurons. In particular, these models describe how the voltage potential across the cell membrane changes over time. In an experimental setting, stimulating neurons with an electrical current generates an action potential, that propagates down the neuron's axon. This axon can branch out and connect to a large number of downstream neurons at sites called synapses. At these synapses, the spike can cause release of a biochemical substance (neurotransmitter), which in turn can change the voltage potential of downstream neurons, potentially leading to spikes in those downstream neurons, thus propagating the signal. As many as 85% of neurons in the neocortex, the outermost layer of the mammalian brain, consists of excitatory pyramidal neurons, and each pyramidal neuron receives tens of thousands of inputs from other neurons. Thus, spiking neurons are a major information processing unit of the nervous system.
Models of neural computation are attempts to elucidate, in an abstract and mathematical fashion, the core principles that underlie information processing in biological nervous systems, or functional components thereof. This article aims to provide an overview of the most definitive models of neuro-biological computation as well as the tools commonly used to construct and analyze them.
The dynamical systems approach to neuroscience is a branch of mathematical biology that utilizes nonlinear dynamics to understand and model the nervous system and its functions. In a dynamical system, all possible states are expressed by a phase space. Such systems can experience bifurcation as a function of its bifurcation parameters and often exhibit chaos. Dynamical neuroscience describes the non-linear dynamics at many levels of the brain from single neural cells to cognitive processes, sleep states and the behavior of neurons in large-scale neuronal simulation.
Sparse distributed memory (SDM) is a mathematical model of human long-term memory introduced by Pentti Kanerva in 1988 while he was at NASA Ames Research Center.
An autapse is a chemical or electrical synapse from a neuron onto itself. It can also be described as a synapse formed by the axon of a neuron on its own dendrites, in vivo or in vitro.
AnimatLab is an open-source neuromechanical simulation tool that allows authors to easily build and test biomechanical models and the neural networks that control them to produce behaviors. Users can construct neural models of varied level of details, 3D mechanical models of triangle meshes, and use muscles, motors, receptive fields, stretch sensors and other transducers to interface the two systems. Experiments can be run in which various stimuli are applied and data is recorded, making it a useful tool for computational neuroscience. The software can also be used to model biomimetic robotic systems.
The Galves–Löcherbach model is a mathematical model for a network of neurons with intrinsic stochasticity.
This article needs additional or more specific categories .(November 2023) |