Quadratic fieldIn algebraic number theory, a quadratic field is an algebraic number field of degree two over , the rational numbers. Every such quadratic field is some where is a (uniquely defined) square-free integer different from and . If , the corresponding quadratic field is called a real quadratic field, and, if , it is called an imaginary quadratic field or a complex quadratic field, corresponding to whether or not it is a subfield of the field of the real numbers.
Systems neuroscienceSystems neuroscience is a subdiscipline of neuroscience and systems biology that studies the structure and function of neural circuits and systems. Systems neuroscience encompasses a number of areas of study concerned with how nerve cells behave when connected together to form neural pathways, neural circuits, and larger brain networks. At this level of analysis, neuroscientists study how different neural circuits analyze sensory information, form perceptions of the external world, make decisions, and execute movements.
Two-photon excitation microscopyTwo-photon excitation microscopy (TPEF or 2PEF) is a fluorescence imaging technique that is particularly well-suited to image scattering living tissue of up to about one millimeter in thickness. Unlike traditional fluorescence microscopy, where the excitation wavelength is shorter than the emission wavelength, two-photon excitation requires simultaneous excitation by two photons with longer wavelength than the emitted light. The laser is focused onto a specific location in the tissue and scanned across the sample to sequentially produce the image.
CytoarchitectureCytoarchitecture (Greek κύτος= "cell" + ἀρχιτεκτονική= "architecture"), also known as cytoarchitectonics, is the study of the cellular composition of the central nervous system's tissues under the microscope. Cytoarchitectonics is one of the ways to parse the brain, by obtaining sections of the brain using a microtome and staining them with chemical agents which reveal where different neurons are located. The study of the parcellation of nerve fibers (primarily axons) into layers forms the subject of myeloarchitectonics (
Degree of a field extensionIn mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently. Suppose that E/F is a field extension. Then E may be considered as a vector space over F (the field of scalars). The dimension of this vector space is called the degree of the field extension, and it is denoted by [E:F].
MicroscopyMicroscopy is the technical field of using microscopes to view objects and areas of objects that cannot be seen with the naked eye (objects that are not within the resolution range of the normal eye). There are three well-known branches of microscopy: optical, electron, and scanning probe microscopy, along with the emerging field of X-ray microscopy. Optical microscopy and electron microscopy involve the diffraction, reflection, or refraction of electromagnetic radiation/electron beams interacting with the specimen, and the collection of the scattered radiation or another signal in order to create an image.
Canny edge detectorThe Canny edge detector is an edge detection operator that uses a multi-stage algorithm to detect a wide range of edges in images. It was developed by John F. Canny in 1986. Canny also produced a computational theory of edge detection explaining why the technique works. Canny edge detection is a technique to extract useful structural information from different vision objects and dramatically reduce the amount of data to be processed. It has been widely applied in various computer vision systems.
Field (mathematics)In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers.
Feature (computer vision)In computer vision and , a feature is a piece of information about the content of an image; typically about whether a certain region of the image has certain properties. Features may be specific structures in the image such as points, edges or objects. Features may also be the result of a general neighborhood operation or feature detection applied to the image. Other examples of features are related to motion in image sequences, or to shapes defined in terms of curves or boundaries between different image regions.
Local fieldIn mathematics, a field K is called a (non-Archimedean) local field if it is complete with respect to a topology induced by a discrete valuation v and if its residue field k is finite. Equivalently, a local field is a locally compact topological field with respect to a non-discrete topology. Sometimes, real numbers R, and the complex numbers C (with their standard topologies) are also defined to be local fields; this is the convention we will adopt below.
