Optimal stoppingIn mathematics, the theory of optimal stopping or early stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem. Optimal stopping problems can often be written in the form of a Bellman equation, and are therefore often solved using dynamic programming.
Topological manifoldIn topology, a branch of mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are formed by adding structure to a topological manifold (e.g. differentiable manifolds are topological manifolds equipped with a differential structure).
Differential evolutionIn evolutionary computation, differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as metaheuristics as they make few or no assumptions about the optimized problem and can search very large spaces of candidate solutions. However, metaheuristics such as DE do not guarantee an optimal solution is ever found.
Path (topology)In mathematics, a path in a topological space is a continuous function from the closed unit interval into Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there exists a path connecting any two points is said to be path-connected. Any space may be broken up into path-connected components. The set of path-connected components of a space is often denoted One can also define paths and loops in pointed spaces, which are important in homotopy theory.
Logical positivismLogical positivism, later called logical empiricism, and both of which together are also known as neopositivism, is a movement whose central thesis is the verification principle (also known as the verifiability criterion of meaning). This theory of knowledge asserted that only statements verifiable through direct observation or logical proof are meaningful in terms of conveying truth value, information or factual content.
Flat EarthFlat Earth is an archaic and scientifically disproven conception of the Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat-Earth cosmography. The idea of a spherical Earth appeared in ancient Greek philosophy with Pythagoras (6th century BC). However, most pre-Socratics (6th–5th century BC) retained the flat-Earth model. In the early 4th century BC, Plato wrote about a spherical Earth. By about 330 BC, his former student Aristotle had provided strong empirical evidence for a spherical Earth.
Myth of the flat EarthThe myth of the flat Earth, or the flat-Earth error, is a modern historical misconception that European scholars and educated people during the Middle Ages believed the Earth to be flat. The earliest clear documentation of the idea of a spherical Earth comes from the ancient Greeks (5th century BC). The belief was widespread in the Greek world when Eratosthenes calculated the circumference of Earth around 240 BC. This knowledge spread with Greek influence such that during the Early Middle Ages (~600–1000 AD), most European and Middle Eastern scholars espoused Earth's sphericity.
