Sleep disorderA sleep disorder, or somnipathy, is a medical disorder of an individual's sleep patterns. Some sleep disorders are severe enough to interfere with normal physical, mental, social and emotional functioning. Polysomnography and actigraphy are tests commonly ordered for diagnosing sleep disorders. Sleep disorders are broadly classified into dyssomnias, parasomnias, circadian rhythm sleep disorders involving the timing of sleep, and other disorders including ones caused by medical or psychological conditions.
Sleep studyA sleep study is a test that records the activity of the body during sleep. There are five main types of sleep studies that use different methods to test for different sleep characteristics and disorders. These include simple sleep studies, polysomnography, multiple sleep latency tests (MSLTs), maintenance of wakefulness tests (MWTs), and home sleep tests (HSTs). In medicine, sleep studies have been useful in identifying and ruling out various sleep disorders.
Quotient space (topology)In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes). In other words, a subset of a quotient space is open if and only if its under the canonical projection map is open in the original topological space.
Neuroscience of sleepThe neuroscience of sleep is the study of the neuroscientific and physiological basis of the nature of sleep and its functions. Traditionally, sleep has been studied as part of psychology and medicine. The study of sleep from a neuroscience perspective grew to prominence with advances in technology and the proliferation of neuroscience research from the second half of the twentieth century. The importance of sleep is demonstrated by the fact that organisms daily spend hours of their time in sleep, and that sleep deprivation can have disastrous effects ultimately leading to death in animals.
Polyphasic sleepPolyphasic sleep is the practice of sleeping during multiple periods over the course of 24 hours, in contrast to monophasic sleep, which is one period of sleep within 24 hours. Biphasic (or diphasic, bifurcated, or bimodal) sleep refers to two periods, while polyphasic usually means more than two. Segmented sleep and divided sleep may refer to polyphasic or biphasic sleep, but may also refer to interrupted sleep, where the sleep has one or several shorter periods of wakefulness, as was the norm for night sleep in pre-industrial societies.
Quotient space (linear algebra)In linear algebra, the quotient of a vector space by a subspace is a vector space obtained by "collapsing" to zero. The space obtained is called a quotient space and is denoted (read " mod " or " by "). Formally, the construction is as follows. Let be a vector space over a field , and let be a subspace of . We define an equivalence relation on by stating that if . That is, is related to if one can be obtained from the other by adding an element of .
Vertex (geometry)In geometry, a vertex (: vertices or vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments, and lines that result in two straight "sides" meeting at one place.
Vertex figureIn geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off. Take some corner or vertex of a polyhedron. Mark a point somewhere along each connected edge. Draw lines across the connected faces, joining adjacent points around the face. When done, these lines form a complete circuit, i.e. a polygon, around the vertex. This polygon is the vertex figure. More precise formal definitions can vary quite widely, according to circumstance.
Vertex coverIn graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it cannot be solved by a polynomial-time algorithm if P ≠ NP. Moreover, it is hard to approximate – it cannot be approximated up to a factor smaller than 2 if the unique games conjecture is true. On the other hand, it has several simple 2-factor approximations.
Vertex (graph theory)In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another.
