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Diffusion maps exploit the relationship between heat diffusion and random walk Markov chain.The basic observation is that if we take a random walk on the data, walking to a nearby data-point is more likely than walking to another that is far away.
When an orbital diagram is drawn for the logistic map, it is possible to see how the branch representing the stable periodic orbit splits, which represents a cascade of period-doubling bifurcations. Bifurcation diagram of the period-doubling bifurcation cascade occurring between parameters r 1 = 3 {\displaystyle r_{1}=3} and a ∞ = 3.56994 ...
Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. The generative artificial intelligence technology is the premier product of Stability AI and is considered to be a part of the ongoing artificial intelligence boom .
This functional equation arises in the study of one-dimensional maps that, as a function of a parameter, go through a period-doubling cascade. Discovered by Mitchell Feigenbaum and Predrag Cvitanović, [3] the equation is the mathematical expression of the universality of period doubling. It specifies a function g and a parameter α by the relation
A variant of diffusion weighted imaging, diffusion spectrum imaging (DSI), [4] was used in deriving the Connectome data sets; DSI is a variant of diffusion-weighted imaging that is sensitive to intra-voxel heterogeneities in diffusion directions caused by crossing fiber tracts and thus allows more accurate mapping of axonal trajectories than ...
A flow-based generative model is a generative model used in machine learning that explicitly models a probability distribution by leveraging normalizing flow, [1] [2] [3] which is a statistical method using the change-of-variable law of probabilities to transform a simple distribution into a complex one.
In 2009, Iraqi Prime Minister Nouri al-Maliki stood before lawmakers and experts at the U.S. Institute of Peace in Washington, D.C., and proclaimed, “Today, Iraq has become a peaceful, democratic country that relies on its democratic institutions.”
A period-doubling cascade is an infinite sequence of period-doubling bifurcations. Such cascades are a common route by which dynamical systems develop chaos. [ 1 ] In hydrodynamics , they are one of the possible routes to turbulence .