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The base diffusion model can only generate unconditionally from the whole distribution. For example, a diffusion model learned on ImageNet would generate images that look like a random image from ImageNet. To generate images from just one category, one would need to impose the condition, and then sample from the conditional distribution.
Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics , probability theory , information theory , neural networks , finance ...
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.
Expansion diffusion: an innovation or idea that develops in a source area and remains strong there, while also spreading outward to other areas. This can include hierarchical, stimulus, and contagious diffusion. Relocation diffusion: an idea or innovation that migrates into new areas, leaving behind its origin or source of the cultural trait.
Hierarchal diffusion occurs when a phenomenon spreads through an ordered sequence of classes or places. Network diffusion occurs when a disease spreads via transportation and social networks, "reflecting the geographical and social structuring of human interactions". [9] Mixed diffusion is a combination of contagious diffusion and hierarchal ...
Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.
Geography is subject to the laws of physics, and in studying things that occur in space, time must be considered. Time in geography is more than just the historical record of events that occurred at various discrete coordinates; but also includes modeling the dynamic movement of people, organisms, and things through space. [9]
The effects of networks and institutional environment on adoption of innovations can be explained using a social network theory model. In such a model, nodes represent agents (e.g. companies or organizations) and ties represent a connection between two entities (e.g. a company-client relationship or competitive relationship). Diffusion occurs ...