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An example of the quantum jump method being used to approximate the density matrix of a two-level atom undergoing damped Rabi oscillations.The random jumps can clearly be seen in the top subplot, and the bottom subplot compares the fully simulated density matrix to the approximation obtained using the quantum jump method.
The stationary wavelet transform (SWT) [1] is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). ). Translation-invariance is achieved by removing the downsamplers and upsamplers in the DWT and upsampling the filter coefficients by a factor of () in the th level of the alg
Force-directed graph drawing algorithms assign forces among the set of edges and the set of nodes of a graph drawing.Typically, spring-like attractive forces based on Hooke's law are used to attract pairs of endpoints of the graph's edges towards each other, while simultaneously repulsive forces like those of electrically charged particles based on Coulomb's law are used to separate all pairs ...
t-distributed stochastic neighbor embedding (t-SNE) is a statistical method for visualizing high-dimensional data by giving each datapoint a location in a two or three-dimensional map.
The example recursive algorithm outline below (MATLAB syntax) decomposes an array of 3-dimensional points into octree style bins. The implementation begins with a single bin surrounding all given points, which then recursively subdivides into its 8 octree regions.
Lagrange and other interpolation at equally spaced points, as in the example above, yield a polynomial oscillating above and below the true function. This behaviour tends to grow with the number of points, leading to a divergence known as Runge's phenomenon ; the problem may be eliminated by choosing interpolation points at Chebyshev nodes .
Matplotlib (portmanteau of MATLAB, plot, and library [3]) is a plotting library for the Python programming language and its numerical mathematics extension NumPy.It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK.
An example of a spider web projection of a trajectory on the graph of the logistic map, and the locations of the fixed points and on the graph. Graphs of maps, especially those of one variable such as the logistic map, are key to understanding the behavior of the map.