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The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and chance-constrained optimization problems based on a sample of the constraints. It also relates to inductive reasoning in modeling and decision-making.
The Oxford English Dictionary defines a paradigm as "a pattern or model, an exemplar; a typical instance of something, an example". [11] The historian of science Thomas Kuhn gave the word its contemporary meaning when he adopted the word to refer to the set of concepts and practices that define a scientific discipline at any particular period of time.
By time-reversal, it is a valid solution for the ball to rest at the top for a while and then roll down in any one direction. However, the same argument applied to the usual kinds of domes (e.g., a hemisphere) fails, because a ball launched with just the right energy to reach the top and stay there would actually take infinite time to do so.
Exemplar, a well-known science problem and its solution, from Thomas Kuhn's The Structure of Scientific Revolutions; Exemplar, the first name for the ship USS Dorothea L. Dix; Exemplar, in exemplification theory, an illustrative representation of information or an event
Furthermore, k-medoids can be used with arbitrary dissimilarity measures, whereas k-means generally requires Euclidean distance for efficient solutions. Because k -medoids minimizes a sum of pairwise dissimilarities instead of a sum of squared Euclidean distances , it is more robust to noise and outliers than k -means .
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.
Categorization is a type of cognition involving conceptual differentiation between characteristics of conscious experience, such as objects, events, or ideas.It involves the abstraction and differentiation of aspects of experience by sorting and distinguishing between groupings, through classification or typification [1] [2] on the basis of traits, features, similarities or other criteria that ...
The existence of a topological defect can be demonstrated whenever the boundary conditions entail the existence of homotopically distinct solutions. Typically, this occurs because the boundary on which the conditions are specified has a non-trivial homotopy group which is preserved in differential equations; the solutions to the differential equations are then topologically distinct, and are ...