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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 .
The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. [ 1 ] [ 2 ] Of the four parameters defining the family, most attention has been focused on the stability parameter, α {\displaystyle \alpha } (see panel).
The importance in probability theory of "stability" and of the stable family of probability distributions is that they are "attractors" for properly normed sums of independent and identically distributed random variables. Important special cases of stable distributions are the normal distribution, the Cauchy distribution and the Lévy distribution.
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.
Stable Diffusion Mohammad Emad Mostaque ( Bengali : মোহম্মদ ইমাদ মোশতাক ; born 17 April 1983) is a British-Bangladeshi business executive , mathematician , and former hedge fund manager. [ 3 ]
where : + is a Lebesgue measurable essentially bounded external input and is a Lipschitz continuous function w.r.t. the first argument uniformly w.r.t. the second one. This ensures that there exists a unique absolutely continuous solution of the system ().
Typically, dementia is associated with classic symptoms like confusion and memory loss. But new research finds that there could be a less obvious risk factor out there: your cholesterol levels ...
A Lyapunov function for an autonomous dynamical system {: ˙ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative ˙ = is non positive (these conditions are required on some region containing the origin).