Search results
Results From The WOW.Com Content Network
Especially for chaotic systems, the Kaplan–Yorke conjecture is a useful tool in order to estimate the fractal dimension and the Hausdorff dimension of the corresponding attractor. [4] [3] In this case, we find j = 1 and the dimension formula reduces to. The resulting Lyapunov exponents are {2.16, 0.00, −32.4}. Noting that j = 2, we find.
In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a set in a Euclidean space , or more generally in a metric space . It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand .
Definition. Like approximate entropy (ApEn), Sample entropy (SampEn) is a measure of complexity. But it does not include self-similar patterns as ApEn does. For a given embedding dimension, tolerance and number of data points, SampEn is the negative natural logarithm of the probability that if two sets of simultaneous data points of length have distance < then two sets of simultaneous data ...
The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller, [1] is a random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a source of uniformly distributed random numbers. The method was first mentioned explicitly by Raymond ...
The multivariate normal distribution is said to be "non-degenerate" when the symmetric covariance matrix is positive definite. In this case the distribution has density [5] where is a real k -dimensional column vector and is the determinant of , also known as the generalized variance.
Multivariate kernel density estimation. Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties.
IB2d: Immersed Boundary Method for MATLAB and Python in 2D with 60+ examples, N.A. Battista, TCNJ; ESPResSo: Immersed Boundary Method for soft elastic objects; CFD IBM code based on OpenFoam; sdfibm: Another CFD IBM code based on OpenFoam; SimScale: Immersed Boundary Method for fluid mechanics and conjugate heat transfer simulation in the cloud ...
Further nonlinear dimensions are then added, produced by combining the original dimensions. The enlarged latent space is then projected back into the 1D data space. The probability of a given projection is, as before, given by the product of the likelihood of the data under the Gaussian noise model with the prior on the deformation parameter.