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Different from linear dimensionality reduction methods such as principal component analysis (PCA), diffusion maps are part of the family of nonlinear dimensionality reduction methods which focus on discovering the underlying manifold that the data has been sampled from. By integrating local similarities at different scales, diffusion maps give ...
The six stability classes are referred to: A-extremely unstable B-moderately unstable C-slightly unstable D-neutral E-slightly stable F-moderately stable The resulting calculations for air pollutant concentrations are often expressed as an air pollutant concentration contour map in order to show the spatial variation in contaminant levels over ...
Diffusion curves are vector graphic primitives for creating smooth-shaded images. Each diffusion curve partitions the 2D graphics space through which it is drawn, defining different colors on either side. When rendered, these colors then spread into the regions on either side of the curve in a way analogous to diffusion. The colors may also be ...
It is used heavily in statistical physics, statistical analysis, information theory, data science, neural networks, finance and marketing. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion.
An image conditioned on the prompt an astronaut riding a horse, by Hiroshige, generated by Stable Diffusion 3.5, a large-scale text-to-image model first released in 2022. A text-to-image model is a machine learning model which takes an input natural language description and produces an image matching that description.
For most infinite lattice graphs, p c cannot be calculated exactly, though in some cases p c there is an exact value. For example: For example: for the square lattice ℤ 2 in two dimensions, p c = 1 / 2 for bond percolation, a fact which was an open question for more than 20 years and was finally resolved by Harry Kesten in the early ...
Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
Since diffusion goes as the Laplacian of velocity, the dissipation rate may be written in terms of the energy spectrum as: = (), with ν the kinematic viscosity of the fluid. From this equation, it may again be observed that dissipation is mainly associated with high wavenumbers (small eddies) even though kinetic energy is associated mainly ...