Computational neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous. The term mathematical neuroscience is also used sometimes, to stress the quantitative nature of the field. Computational neuroscience focuses on the description of biologically plausible neurons (and neural systems) and their physiology and dynamics, and it is therefore not directly concerned with biologically unrealistic models used in connectionism, control theory, cybernetics, quantitative psychology, machine learning, artificial neural networks, artificial intelligence and computational learning theory; although mutual inspiration exists and sometimes there is no strict limit between fields, with model abstraction in computational neuroscience depending on research scope and the granularity at which biological entities are analyzed. Models in theoretical neuroscience are aimed at capturing the essential features of the biological system at multiple spatial-temporal scales, from membrane currents, and chemical coupling via network oscillations, columnar and topographic architecture, nuclei, all the way up to psychological faculties like memory, learning and behavior. These computational models frame hypotheses that can be directly tested by biological or psychological experiments. The term 'computational neuroscience' was introduced by Eric L. Schwartz, who organized a conference, held in 1985 in Carmel, California, at the request of the Systems Development Foundation to provide a summary of the current status of a field which until that point was referred to by a variety of names, such as neural modeling, brain theory and neural networks.

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Artificial neural network Spiking neural networks (SNNs) are artificial neural networks 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 (as it happens with typical multi-layer perceptron networks), 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.

Morphometrics (from Greek μορφή morphe, "shape, form", and -μετρία metria, "measurement") or morphometry refers to the quantitative analysis of form, a concept that encompasses size and shape. Morphometric analyses are commonly performed on organisms, and are useful in analyzing their fossil record, the impact of mutations on shape, developmental changes in form, covariances between ecological factors and shape, as well for estimating quantitative-genetic parameters of shape.

Biological 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.

The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.

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In this course we study mathematical models of neurons and neuronal networks in the context of biology and establish links to models of cognition. The focus is on brain dynamics approximated by determ

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Neuroanatomy is the study of the structure and organization of the nervous system. In contrast to animals with radial symmetry, whose nervous system consists of a distributed network of cells, animals with bilateral symmetry have segregated, defined nervous systems. Their neuroanatomy is therefore better understood. In vertebrates, the nervous system is segregated into the internal structure of the brain and spinal cord (together called the central nervous system, or CNS) and the routes of the nerves that connect to the rest of the body (known as the peripheral nervous system, or PNS).

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

Neurology (from νεῦρον (neûron), "string, nerve" and the suffix -logia, "study of") is the branch of medicine dealing with the diagnosis and treatment of all categories of conditions and disease involving the nervous system, which comprises the brain, the spinal cord and the peripheral nerves. Neurological practice relies heavily on the field of neuroscience, the scientific study of the nervous system. A neurologist is a physician specializing in neurology and trained to investigate, diagnose and treat neurological disorders.