Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
Affine transformationIn Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments.
Adaptive market hypothesisThe adaptive market hypothesis, as proposed by Andrew Lo, is an attempt to reconcile economic theories based on the efficient market hypothesis (which implies that markets are efficient) with behavioral economics, by applying the principles of evolution to financial interactions: competition, adaptation, and natural selection. This view is part of a larger school of thought known as Evolutionary Economics. Under this approach, the traditional models of modern financial economics can coexist with behavioral models.
ChatGPTChatGPT, which stands for Chat Generative Pre-trained Transformer, is a large language model-based chatbot developed by OpenAI and launched on November 30, 2022, notable for enabling users to refine and steer a conversation towards a desired length, format, style, level of detail, and language used. Successive prompts and replies, known as prompt engineering, are considered at each conversation stage as a context. ChatGPT is built upon GPT-3.
Ray KurzweilRaymond Kurzweil (ˈkɜrzwaɪl ; born February 12, 1948) is an American computer scientist, author, inventor, and futurist. He is involved in fields such as optical character recognition (OCR), text-to-speech synthesis, speech recognition technology, and electronic keyboard instruments. He has written books on health, artificial intelligence (AI), transhumanism, the technological singularity, and futurism.
