Fiber bundleIn mathematics, and particularly topology, a fiber bundle (or, in Commonwealth English: fibre bundle) is a space that is a product space, but may have a different topological structure. Specifically, the similarity between a space and a product space is defined using a continuous surjective map, that in small regions of behaves just like a projection from corresponding regions of to The map called the projection or submersion of the bundle, is regarded as part of the structure of the bundle.
Corpus callosumThe corpus callosum (Latin for "tough body"), also callosal commissure, is a wide, thick nerve tract, consisting of a flat bundle of commissural fibers, beneath the cerebral cortex in the brain. The corpus callosum is only found in placental mammals. It spans part of the longitudinal fissure, connecting the left and right cerebral hemispheres, enabling communication between them. It is the largest white matter structure in the human brain, about in length and consisting of 200–300 million axonal projections.
Arcuate fasciculusIn neuroanatomy, the arcuate fasciculus (AF; ) is a bundle of axons that generally connects the Broca's area and the Wernicke's area in the brain. It is an association fiber tract connecting caudal temporal cortex and inferior frontal lobe. The arcuate fasciculus is a white matter tract that runs parallel to the superior longitudinal fasciculus. Due to their proximity, some researchers refer to them interchangeably. They can be distinguished by the location and function of their endpoints in the frontal cortex.
Section (fiber bundle)In the mathematical field of topology, a section (or cross section) of a fiber bundle is a continuous right inverse of the projection function . In other words, if is a fiber bundle over a base space, : then a section of that fiber bundle is a continuous map, such that for all . A section is an abstract characterization of what it means to be a graph. The graph of a function can be identified with a function taking its values in the Cartesian product , of and : Let be the projection onto the first factor: .
Corticobulbar tractIn neuroanatomy, the corticobulbar (or corticonuclear) tract is a two-neuron white matter motor pathway connecting the motor cortex in the cerebral cortex to the medullary pyramids, which are part of the brainstem's medulla oblongata (also called "bulbar") region, and are primarily involved in carrying the motor function of the non-oculomotor cranial nerves. The corticobulbar tract is one of the pyramidal tracts, the other being the corticospinal tract.
Principal bundleIn mathematics, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product of a space with a group . In the same way as with the Cartesian product, a principal bundle is equipped with An action of on , analogous to for a product space. A projection onto . For a product space, this is just the projection onto the first factor, . Unlike a product space, principal bundles lack a preferred choice of identity cross-section; they have no preferred analog of .
Vector bundleIn mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space (for example could be a topological space, a manifold, or an algebraic variety): to every point of the space we associate (or "attach") a vector space in such a way that these vector spaces fit together to form another space of the same kind as (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over .
Agenesis of the corpus callosumAgenesis of the corpus callosum (ACC) is a rare birth defect in which there is a complete or partial absence of the corpus callosum. It occurs when the development of the corpus callosum, the band of white matter connecting the two hemispheres in the brain, in the embryo is disrupted. The result of this is that the fibers that would otherwise form the corpus callosum are instead longitudinally oriented along the ipsilateral ventricular wall and form structures called Probst bundles.
Spinal cordThe spinal cord is a long, thin, tubular structure made up of nervous tissue, which extends from the medulla oblongata in the brainstem to the lumbar region of the vertebral column (backbone). The backbone encloses the central canal of the spinal cord, which contains cerebrospinal fluid. The brain and spinal cord together make up the central nervous system (CNS). In humans, the spinal cord begins at the occipital bone, passing through the foramen magnum and then enters the spinal canal at the beginning of the cervical vertebrae.
Dorsal column–medial lemniscus pathwayThe dorsal column–medial lemniscus pathway (DCML) (also known as the posterior column-medial lemniscus pathway, PCML) is a sensory pathway of the central nervous system that conveys sensations of fine touch, vibration, two-point discrimination, and proprioception (body position) from the skin and joints. It transmits information from the body to the primary somatosensory cortex in the postcentral gyrus of the parietal lobe of the brain.
Bundle mapIn mathematics, a bundle map (or bundle morphism) is a morphism in the of fiber bundles. There are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space. There are also several variations on the basic theme, depending on precisely which category of fiber bundles is under consideration. In the first three sections, we will consider general fiber bundles in the . Then in the fourth section, some other examples will be given.
Associated bundleIn mathematics, the theory of fiber bundles with a structure group (a topological group) allows an operation of creating an associated bundle, in which the typical fiber of a bundle changes from to , which are both topological spaces with a group action of . For a fiber bundle F with structure group G, the transition functions of the fiber (i.e., the cocycle) in an overlap of two coordinate systems Uα and Uβ are given as a G-valued function gαβ on Uα∩Uβ.
Frame bundleIn mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex. The general linear group acts naturally on F(E) via a change of basis, giving the frame bundle the structure of a principal GL(k, R)-bundle (where k is the rank of E). The frame bundle of a smooth manifold is the one associated to its tangent bundle. For this reason it is sometimes called the tangent frame bundle.
Magnetic resonance imagingMagnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from computed tomography (CT) and positron emission tomography (PET) scans.
Spinocerebellar tractThe spinocerebellar tract is a nerve tract originating in the spinal cord and terminating in the same side (ipsilateral) of the cerebellum. Proprioceptive information is obtained by Golgi tendon organs and muscle spindles. Golgi tendon organs consist of a fibrous capsule enclosing tendon fascicles and bare nerve endings that respond to tension in the tendon by causing action potentials in type Ib afferents. These fibers are relatively large, myelinated, and quickly conducting.
Human brainThe human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. The brain consists of the cerebrum, the brainstem and the cerebellum. It controls most of the activities of the body, processing, integrating, and coordinating the information it receives from the sense organs, and making decisions as to the instructions sent to the rest of the body. The brain is contained in, and protected by, the skull bones of the head.
Sensory decussationIn neuroanatomy, the sensory decussation or decussation of the lemnisci is a decussation (i.e. crossover) of axons from the gracile nucleus and cuneate nucleus, which are responsible for fine touch, vibration, proprioception and two-point discrimination of the body. The fibres of this decussation are called the internal arcuate fibres and are found at the superior aspect of the closed medulla superior to the motor decussation. It is part of the second neuron in the posterior column–medial lemniscus pathway.
Fiber bundle construction theoremIn mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle from a given base space, fiber and a suitable set of transition functions. The theorem also gives conditions under which two such bundles are isomorphic. The theorem is important in the associated bundle construction where one starts with a given bundle and surgically replaces the fiber with a new space while keeping all other data the same. Let X and F be topological spaces and let G be a topological group with a continuous left action on F.
White matterWhite matter refers to areas of the central nervous system (CNS) that are mainly made up of myelinated axons, also called tracts. Long thought to be passive tissue, white matter affects learning and brain functions, modulating the distribution of action potentials, acting as a relay and coordinating communication between different brain regions. White matter is named for its relatively light appearance resulting from the lipid content of myelin.
Dorsal column nucleiIn neuroanatomy, the dorsal column nuclei are a pair of nuclei in the dorsal columns in the brainstem. The name refers collectively to the cuneate nucleus and gracile nucleus, which are situated at the lower end of the medulla oblongata. Both nuclei contain second-order neurons of the dorsal column–medial lemniscus pathway, which convey fine touch and proprioceptive information from the body to the brain. The dorsal column nuclei project to the thalamus.
