Computational neuroscience is a branch of neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system.
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.
Spike-timing-dependent plasticity (STDP) is a biological process that adjusts the strength of connections between neurons in the brain. The process adjusts the connection strengths based on the relative timing of a particular neuron's output and input action potentials. The STDP process partially explains the activity-dependent development of nervous systems, especially with regard to long-term potentiation and long-term depression.
A neural network, also called a neuronal network, is an interconnected population of neurons. Biological neural networks are studied to understand the organization and functioning of nervous systems.
Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in an electroencephalogram. Oscillatory activity in groups of neurons generally arises from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macroscopic neural oscillations is alpha activity.
Bursting, or burst firing, is an extremely diverse general phenomenon of the activation patterns of neurons in the central nervous system and spinal cord where periods of rapid action potential spiking are followed by quiescent periods much longer than typical inter-spike intervals. Bursting is thought to be important in the operation of robust central pattern generators, the transmission of neural codes, and some neuropathologies such as epilepsy. The study of bursting both directly and in how it takes part in other neural phenomena has been very popular since the beginnings of cellular neuroscience and is closely tied to the fields of neural synchronization, neural coding, plasticity, and attention.
Neural coding is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the neuronal responses, and the relationship among the electrical activities of the neurons in the ensemble. Based on the theory that sensory and other information is represented in the brain by networks of neurons, it is believed that neurons can encode both digital and analog information.
Spiking neural networks (SNNs) are artificial neural networks (ANN) that more closely mimic natural neural networks. In addition to neuronal and synaptic state, SNNs incorporate the concept of time into their operating model. The idea is that neurons in the SNN do not transmit information at each propagation cycle, but rather transmit information only when a membrane potential—an intrinsic quality of the neuron related to its membrane electrical charge—reaches a specific value, called the threshold. When the membrane potential reaches the threshold, the neuron fires, and generates a signal that travels to other neurons which, in turn, increase or decrease their potentials in response to this signal. A neuron model that fires at the moment of threshold crossing is also called a spiking neuron model.
Henry John Markram is a South African-born Israeli neuroscientist, professor at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland and director of the Blue Brain Project and founder of the Human Brain Project.
BCM theory, BCM synaptic modification, or the BCM rule, named for Elie Bienenstock, Leon Cooper, and Paul Munro, is a physical theory of learning in the visual cortex developed in 1981. The BCM model proposes a sliding threshold for long-term potentiation (LTP) or long-term depression (LTD) induction, and states that synaptic plasticity is stabilized by a dynamic adaptation of the time-averaged postsynaptic activity. According to the BCM model, when a pre-synaptic neuron fires, the post-synaptic neurons will tend to undergo LTP if it is in a high-activity state, or LTD if it is in a lower-activity state. This theory is often used to explain how cortical neurons can undergo both LTP or LTD depending on different conditioning stimulus protocols applied to pre-synaptic neurons.
Biological neuron models, also known as spiking neuron models, are mathematical descriptions of the conduction of electrical signals in neurons. Neurons are electrically excitable cells within the nervous system, able to fire electric signals, called action potentials, across a neural network. These mathematical models describe the role of the biophysical and geometrical characteristics of neurons on the conduction of electrical activity.
Neurophysics is the branch of biophysics dealing with the development and use of physical methods to gain information about the nervous system. Neurophysics is an interdisciplinary science using physics and combining it with other neurosciences to better understand neural processes. The methods used include the techniques of experimental biophysics and other physical measurements such as EEG mostly to study electrical, mechanical or fluidic properties, as well as theoretical and computational approaches. The term "neurophysics" is a portmanteau of "neuron" and "physics".
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.
The network of the human nervous system is composed of nodes that are connected by links. The connectivity may be viewed anatomically, functionally, or electrophysiologically. These are presented in several Wikipedia articles that include Connectionism, Biological neural network, Artificial neural network, Computational neuroscience, as well as in several books by Ascoli, G. A. (2002), Sterratt, D., Graham, B., Gillies, A., & Willshaw, D. (2011), Gerstner, W., & Kistler, W. (2002), and David Rumelhart, McClelland, J. L., and PDP Research Group (1986) among others. The focus of this article is a comprehensive view of modeling a neural network. Once an approach based on the perspective and connectivity is chosen, the models are developed at microscopic, mesoscopic, or macroscopic (system) levels. Computational modeling refers to models that are developed using computing tools.
In biology exponential integrate-and-fire models are compact and computationally efficient nonlinear spiking neuron models with one or two variables. The exponential integrate-and-fire model was first proposed as a one-dimensional model. The most prominent two-dimensional examples are the adaptive exponential integrate-and-fire model and the generalized exponential integrate-and-fire model. Exponential integrate-and-fire models are widely used in the field of computational neuroscience and spiking neural networks because of (i) a solid grounding of the neuron model in the field of experimental neuroscience, (ii) computational efficiency in simulations and hardware implementations, and (iii) mathematical transparency.
Claudia Clopath is a Professor of Computational Neuroscience at Imperial College London and research leader at the Sainsbury Wellcome Centre for Neural Circuits and Behaviour. She develops mathematical models to predict synaptic plasticity for both medical applications and the design of human-like machines.
Tim P. Vogels is a professor of theoretical neuroscience and research leader at the Institute of Science and Technology Austria. He is primarily known for his scholarly contributions to the study of neuronal plasticity related to learning and memory in the brain.
Ila Fiete is an Indian–American physicist and computational neuroscientist as well as a Professor in the Department of Brain and Cognitive Sciences within the McGovern Institute for Brain Research at the Massachusetts Institute of Technology. Fiete builds theoretical models and analyses neural data and to uncover how neural circuits perform computations and how the brain represents and manipulates information involved in memory and reasoning.
The spike response model (SRM) is a spiking neuron model in which spikes are generated by either a deterministic or a stochastic threshold process. In the SRM, the membrane voltage V is described as a linear sum of the postsynaptic potentials (PSPs) caused by spike arrivals to which the effects of refractoriness and adaptation are added. The threshold is either fixed or dynamic. In the latter case it increases after each spike. The SRM is flexible enough to account for a variety of neuronal firing pattern in response to step current input. The SRM has also been used in the theory of computation to quantify the capacity of spiking neural networks; and in the neurosciences to predict the subthreshold voltage and the firing times of cortical neurons during stimulation with a time-dependent current stimulation. The name Spike Response Model points to the property that the two important filters and of the model can be interpreted as the response of the membrane potential to an incoming spike (response kernel , the PSP) and to an outgoing spike (response kernel , also called refractory kernel). The SRM has been formulated in continuous time and in discrete time. The SRM can be viewed as a generalized linear model (GLM) or as an (integrated version of) a generalized integrate-and-fire model with adaptation.
Panayiota Poirazi is a neuroscientist known for her work in modelling dendritic computations. She is an elected member of the European Molecular Biology Organization (EMBO).
