Connection (mathematics)In geometry, the notion of a connection makes precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for parallel transport of tangent vectors on a manifold from one point to another along a curve.
NeuroinformaticsNeuroinformatics is the field that combines informatics and neuroscience. Neuroinformatics is related with neuroscience data and information processing by artificial neural networks. There are three main directions where neuroinformatics has to be applied: the development of computational models of the nervous system and neural processes.
Student's t-distributionIn probability and statistics, Student's t-distribution (or simply the t-distribution) is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, has heavier tails and the amount of probability mass in the tails is controlled by the parameter . For the Student's t distribution becomes the standard Cauchy distribution, whereas for it becomes the standard normal distribution .
Neuronal ensembleA neuronal ensemble is a population of nervous system cells (or cultured neurons) involved in a particular neural computation. The concept of neuronal ensemble dates back to the work of Charles Sherrington who described the functioning of the CNS as the system of reflex arcs, each composed of interconnected excitatory and inhibitory neurons. In Sherrington's scheme, α-motoneurons are the final common path of a number of neural circuits of different complexity: motoneurons integrate a large number of inputs and send their final output to muscles.
Processor (computing)In computing and computer science, a processor or processing unit is an electrical component (digital circuit) that performs operations on an external data source, usually memory or some other data stream. It typically takes the form of a microprocessor, which can be implemented on a single metal–oxide–semiconductor integrated circuit chip. In the past, processors were constructed using multiple individual vacuum tubes, multiple individual transistors, or multiple integrated circuits. Today, processors use built-in transistors.
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.
Levi-Civita connectionIn Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection.
SpeedupIn computer architecture, speedup is a number that measures the relative performance of two systems processing the same problem. More technically, it is the improvement in speed of execution of a task executed on two similar architectures with different resources. The notion of speedup was established by Amdahl's law, which was particularly focused on parallel processing. However, speedup can be used more generally to show the effect on performance after any resource enhancement.
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.
Affine connectionIn differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space. Connections are among the simplest methods of defining differentiation of the sections of vector bundles.
