Σ-finite measureIn mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.
Locally compact groupIn mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are locally compact and such groups have a natural measure called the Haar measure. This allows one to define integrals of Borel measurable functions on G so that standard analysis notions such as the Fourier transform and spaces can be generalized.
Borel measureIn mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors require additional restrictions on the measure, as described below. Let be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of ; this is known as the σ-algebra of Borel sets. A Borel measure is any measure defined on the σ-algebra of Borel sets.
Orbitofrontal cortexThe orbitofrontal cortex (OFC) is a prefrontal cortex region in the frontal lobes of the brain which is involved in the cognitive process of decision-making. In non-human primates it consists of the association cortex areas Brodmann area 11, 12 and 13; in humans it consists of Brodmann area 10, 11 and 47. The OFC is functionally related to the ventromedial prefrontal cortex. Therefore, the region is distinguished due to the distinct neural connections and the distinct functions it performs.
Cerebral cortexThe cerebral cortex, also known as the cerebral mantle, is the outer layer of neural tissue of the cerebrum of the brain in humans and other mammals. The cerebral cortex mostly consists of the six-layered neocortex, with just 10% consisting of allocortex. It is separated into two cortices, by the longitudinal fissure that divides the cerebrum into the left and right cerebral hemispheres. The two hemispheres are joined beneath the cortex by the corpus callosum. The cerebral cortex is the largest site of neural integration in the central nervous system.
Fluorodeoxyglucose (18F)DISPLAYTITLE:Fluorodeoxyglucose (18F) [18F]Fluorodeoxyglucose (INN), or fluorodeoxyglucose F 18 (USAN and USP), also commonly called fluorodeoxyglucose and abbreviated [18F]FDG, 2-[18F]FDG or FDG, is a radiopharmaceutical, specifically a radiotracer, used in the medical imaging modality positron emission tomography (PET). Chemically, it is 2-deoxy-2-[18F]fluoro-D-glucose, a glucose analog, with the positron-emitting radionuclide fluorine-18 substituted for the normal hydroxyl group at the C-2 position in the glucose molecule.
Glucose tolerance testThe glucose tolerance test (GTT, not to be confused with GGT test) is a medical test in which glucose is given and blood samples taken afterward to determine how quickly it is cleared from the blood. The test is usually used to test for diabetes, insulin resistance, impaired beta cell function, and sometimes reactive hypoglycemia and acromegaly, or rarer disorders of carbohydrate metabolism. In the most commonly performed version of the test, an oral glucose tolerance test (OGTT), a standard dose of glucose is ingested by mouth and blood levels are checked two hours later.
Ex vivoEx vivo (Latin: "out of the living") literally means that which takes place outside an organism. In science, ex vivo refers to experimentation or measurements done in or on tissue from an organism in an external environment with minimal alteration of natural conditions. A primary advantage of using ex vivo tissues is the ability to perform tests or measurements that would otherwise not be possible or ethical in living subjects. Tissues may be removed in many ways, including in part, as whole organs, or as larger organ systems.
Locally compact spaceIn topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely, it is a topological space in which every point has a compact neighborhood. In mathematical analysis locally compact spaces that are Hausdorff are of particular interest; they are abbreviated as LCH spaces. Let X be a topological space. Most commonly X is called locally compact if every point x of X has a compact neighbourhood, i.
Dorsolateral prefrontal cortexThe dorsolateral prefrontal cortex (DLPFC or DL-PFC) is an area in the prefrontal cortex of the primate brain. It is one of the most recently derived parts of the human brain. It undergoes a prolonged period of maturation which lasts into adulthood. The DLPFC is not an anatomical structure, but rather a functional one. It lies in the middle frontal gyrus of humans (i.e., lateral part of Brodmann's area (BA) 9 and 46). In macaque monkeys, it is around the principal sulcus (i.e., in Brodmann's area 46).
