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.
Node of RanvierIn neuroscience and anatomy, nodes of Ranvier (ˈrɑːnvieɪ ), also known as myelin-sheath gaps, occur along a myelinated axon where the axolemma is exposed to the extracellular space. Nodes of Ranvier are uninsulated and highly enriched in ion channels, allowing them to participate in the exchange of ions required to regenerate the action potential. Nerve conduction in myelinated axons is referred to as saltatory conduction () due to the manner in which the action potential seems to "jump" from one node to the next along the axon.
Split-brainSplit-brain or callosal syndrome is a type of disconnection syndrome when the corpus callosum connecting the two hemispheres of the brain is severed to some degree. It is an association of symptoms produced by disruption of, or interference with, the connection between the hemispheres of the brain. The surgical operation to produce this condition (corpus callosotomy) involves transection of the corpus callosum, and is usually a last resort to treat refractory epilepsy.
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.
Nervous tissueNervous tissue, also called neural tissue, is the main tissue component of the nervous system. The nervous system regulates and controls body functions and activity. It consists of two parts: the central nervous system (CNS) comprising the brain and spinal cord, and the peripheral nervous system (PNS) comprising the branching peripheral nerves. It is composed of neurons, also known as nerve cells, which receive and transmit impulses, and neuroglia, also known as glial cells or glia, which assist the propagation of the nerve impulse as well as provide nutrients to the neurons.
Tautological bundleIn mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of -dimensional subspaces of , given a point in the Grassmannian corresponding to a -dimensional vector subspace , the fiber over is the subspace itself. In the case of projective space the tautological bundle is known as the tautological line bundle. The tautological bundle is also called the universal bundle since any vector bundle (over a compact space) is a pullback of the tautological bundle; this is to say a Grassmannian is a classifying space for vector bundles.
MyelinIn most vertebrates (including humans), myelin is a lipid-rich material that surrounds nerve cell axons (the nervous system's "wires") to insulate them and increase the rate at which electrical impulses (called action potentials) are passed along the axon. The myelinated axon can be likened to an electrical wire (the axon) with insulating material (myelin) around it. However, unlike the plastic covering on an electrical wire, myelin does not form a single long sheath over the entire length of the axon.
Robust statisticsRobust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution.
ConnectogramConnectograms are graphical representations of connectomics, the field of study dedicated to mapping and interpreting all of the white matter fiber connections in the human brain. These circular graphs based on diffusion MRI data utilize graph theory to demonstrate the white matter connections and cortical characteristics for single structures, single subjects, or populations. The connectogram, as a graphical representation of brain connectomics, was proposed in 2012.
Line bundleIn mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example, a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology, a line bundle is defined as a vector bundle of rank 1. Line bundles are specified by choosing a one-dimensional vector space for each point of the space in a continuous manner.
Development of the nervous system in humansThe development of the nervous system in humans, or neural development or neurodevelopment involves the studies of embryology, developmental biology, and neuroscience to describe the cellular and molecular mechanisms by which the complex nervous system forms in humans, develops during prenatal development, and continues to develop postnatally.
Projective bundleIn mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle if it is locally a projective n-space; i.e., and transition automorphisms are linear. Over a regular scheme S such as a smooth variety, every projective bundle is of the form for some vector bundle (locally free sheaf) E. Every vector bundle over a variety X gives a projective bundle by taking the projective spaces of the fibers, but not all projective bundles arise in this way: there is an obstruction in the cohomology group H2(X,O*).
