Biological neuron modelBiological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system.
NeuronWithin 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 - 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 neuron is the main component of nervous tissue in all animals except sponges and placozoa.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Single-unit recordingIn neuroscience, single-unit recordings (also, single-neuron recordings) provide a method of measuring the electro-physiological responses of a single neuron using a microelectrode system. When a neuron generates an action potential, the signal propagates down the neuron as a current which flows in and out of the cell through excitable membrane regions in the soma and axon. A microelectrode is inserted into the brain, where it can record the rate of change in voltage with respect to time.
Long-term depressionIn neurophysiology, long-term depression (LTD) is an activity-dependent reduction in the efficacy of neuronal synapses lasting hours or longer following a long patterned stimulus. LTD occurs in many areas of the CNS with varying mechanisms depending upon brain region and developmental progress. As the opposing process to long-term potentiation (LTP), LTD is one of several processes that serves to selectively weaken specific synapses in order to make constructive use of synaptic strengthening caused by LTP.
Stochastic partial differential equationStochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations. They have relevance to quantum field theory, statistical mechanics, and spatial modeling. One of the most studied SPDEs is the stochastic heat equation, which may formally be written as where is the Laplacian and denotes space-time white noise.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Artificial neuronAn artificial neuron is a mathematical function conceived as a model of biological neurons, a neural network. Artificial neurons are elementary units in an artificial neural network. The artificial neuron receives one or more inputs (representing excitatory postsynaptic potentials and inhibitory postsynaptic potentials at neural dendrites) and sums them to produce an output (or , representing a neuron's action potential which is transmitted along its axon).
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
Pyramidal cellPyramidal cells, or pyramidal neurons, are a type of multipolar neuron found in areas of the brain including the cerebral cortex, the hippocampus, and the amygdala. Pyramidal cells are the primary excitation units of the mammalian prefrontal cortex and the corticospinal tract. Pyramidal neurons are also one of two cell types where the characteristic sign, Negri bodies, are found in post-mortem rabies infection. Pyramidal neurons were first discovered and studied by Santiago Ramón y Cajal.
Motor neuronA motor neuron (or motoneuron or efferent neuron) is a neuron whose cell body is located in the motor cortex, brainstem or the spinal cord, and whose axon (fiber) projects to the spinal cord or outside of the spinal cord to directly or indirectly control effector organs, mainly muscles and glands. There are two types of motor neuron – upper motor neurons and lower motor neurons. Axons from upper motor neurons synapse onto interneurons in the spinal cord and occasionally directly onto lower motor neurons.
Mirror neuronA mirror neuron is a neuron that fires both when an organism acts and when the organism observes the same action performed by another. Thus, the neuron "mirrors" the behavior of the other, as though the observer were itself acting. Mirror neurons are not always physiologically distinct from other types of neurons in the brain; their main differentiating factor is their response patterns. By this definition, such neurons have been directly observed in humans and primate species, and in birds.
SimulationA simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.
Hebbian theoryHebbian 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.
DendriteA dendrite (from Greek δένδρον déndron, "tree") or dendron is a branched protoplasmic extension of a nerve cell that propagates the electrochemical stimulation received from other neural cells to the cell body, or soma, of the neuron from which the dendrites project. Electrical stimulation is transmitted onto dendrites by upstream neurons (usually via their axons) via synapses which are located at various points throughout the dendritic tree.
Models of neural computationModels 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.
Action potentialAn action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and in some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells.
