Convex setIn geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve.
Clinical trialClinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietary choices, dietary supplements, and medical devices) and known interventions that warrant further study and comparison. Clinical trials generate data on dosage, safety and efficacy. They are conducted only after they have received health authority/ethics committee approval in the country where approval of the therapy is sought.
DecussationDecussation is used in biological contexts to describe a crossing (due to the shape of the Roman numeral for ten, an uppercase 'X' (decussis), ). In Latin anatomical terms, the form decussatio is used, e.g. decussatio pyramidum. Similarly, the anatomical term chiasma is named after the Greek uppercase 'Χ' (chi). Whereas a decussation refers to a crossing within the central nervous system, various kinds of crossings in the peripheral nervous system are called chiasma.
Duality (optimization)In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.
Convex functionIn mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain.
Convex hullIn geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact.
Head injuryA head injury is any injury that results in trauma to the skull or brain. The terms traumatic brain injury and head injury are often used interchangeably in the medical literature. Because head injuries cover such a broad scope of injuries, there are many causes—including accidents, falls, physical assault, or traffic accidents—that can cause head injuries. The number of new cases is 1.7 million in the United States each year, with about 3% of these incidents leading to death.
Nerve compression syndromeNerve compression syndrome, or compression neuropathy, or nerve entrapment syndrome, is a medical condition caused by chronic, direct pressure on a peripheral nerve. It is known colloquially as a trapped nerve, though this may also refer to nerve root compression (by a herniated disc, for example). Its symptoms include pain, tingling, numbness and muscle weakness. The symptoms affect just one particular part of the body, depending on which nerve is affected. The diagnosis is largely clinical and can be confirmed with diagnostic nerve blocks.
Brachial plexus injuryA brachial plexus injury (BPI), also known as brachial plexus lesion, is an injury to the brachial plexus, the network of nerves that conducts signals from the spinal cord to the shoulder, arm and hand. These nerves originate in the fifth, sixth, seventh and eighth cervical (C5–C8), and first thoracic (T1) spinal nerves, and innervate the muscles and skin of the chest, shoulder, arm and hand. Brachial plexus injuries can occur as a result of shoulder trauma (e.g. dislocation), tumours, or inflammation, or obstetric.
Action potentialAn action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and in some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells.
