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The Gaussian function is the archetypal example of a bell shaped function. A bell-shaped function or simply 'bell curve' is a mathematical function having a characteristic "bell"-shaped curve. These functions are typically continuous or smooth, asymptotically approach zero for large negative/positive x, and have a single, unimodal maximum at ...
The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".
In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve). Main article: Central limit theorem The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution.
The Bell test has its origins in the debate between Einstein and other pioneers of quantum physics, principally Niels Bohr.One feature of the theory of quantum mechanics under debate was the meaning of Heisenberg's uncertainty principle.
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function , which is defined by the formula: [ 1 ]
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement.
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
To the right is a molecular dynamics (MD) simulation in which 900 hard sphere particles are constrained to move in a rectangle. They interact via perfectly elastic collisions . The system is initialized out of equilibrium, but the velocity distribution (in blue) quickly converges to the 2D Maxwell–Boltzmann distribution (in orange).