kernel density estimation

If your data is continuous, you can integrate over the entire dataset and normalize it to be able

\begin{equation} NP = \bigcup_{k \in N} \text{NTIME}\qty(n^{k}) \end{equation}

Meaning, these are problems with the property that once you “have” the solution, its “easy” to verify the solution.

verifier formulation of NP

\(L \in \text{NP}\), if there exists a Polynomial Time turing machine named \(V\) (called a “verifier”) such that:

\begin{equation} X \in L \Leftrightarrow \exists\ w \in \qty {0,1}^{\text{poly}\qty(|x|)} V(x,w) = 1 \end{equation}

that is, “yes instances have efficiently checkable certificates/“proofs”

The nonviolence movement a method of protest which is developed by Mahatma Ghandi and leveraged by Martin Luther King in the civil rights movement.

The idea is to achieve civil disobedience and allowing oneself to be punished so egregiously without inciting violence so at to elicit sympathy across the nation.

The civil rights movement leveraged training tactics and training to ensure its participants would be completely nonviolent and so elicit the correct response.