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Now, there’s an AI generator for that. Justin Pinkney, a machine learning researcher at Lambda Labs, created a “text to Pokémon” generator by fine-tuning Stable Diffusion, an AI image ...
To do so technically would require a more sophisticated grammar, like a Chomsky Type 1 grammar, also termed a context-sensitive grammar. However, parser generators for context-free grammars often support the ability for user-written code to introduce limited amounts of context-sensitivity. (For example, upon encountering a variable declaration ...
Meanwhile, two-hour deliveries otherwise will include a service fee of $6.95 for orders ranging from $50-$100, and $9.95 for deliveries under $50, for Prime members. Non-members will be charged ...
Random permutation. A random permutation is a random ordering of a set of objects, that is, a permutation -valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation. A good example of a random permutation is the shuffling of a deck of ...
A free group of rank k clearly has subgroups of every rank less than k. Less obviously, a (nonabelian!) free group of rank at least 2 has subgroups of all countable ranks. The commutator subgroup of a free group of rank k > 1 has infinite rank; for example for F(a,b), it is freely generated by the commutators [a m, b n] for non-zero m and n.
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