Bootstrapping (statistics)Bootstrapping is any test or metric that uses random sampling with replacement (e.g. mimicking the sampling process), and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an estimand (such as its variance) by measuring those properties when sampling from an approximating distribution.
Mirror neuronA mirror neuron is a neuron that fires both when an organism acts and when the organism observes the same action performed by another. Thus, the neuron "mirrors" the behavior of the other, as though the observer were itself acting. Mirror neurons are not always physiologically distinct from other types of neurons in the brain; their main differentiating factor is their response patterns. By this definition, such neurons have been directly observed in humans and primate species, and in birds.
Topological ringIn mathematics, a topological ring is a ring that is also a topological space such that both the addition and the multiplication are continuous as maps: where carries the product topology. That means is an additive topological group and a multiplicative topological semigroup. Topological rings are fundamentally related to topological fields and arise naturally while studying them, since for example completion of a topological field may be a topological ring which is not a field.
Raising and lowering indicesIn mathematics and mathematical physics, raising and lowering indices are operations on tensors which change their type. Raising and lowering indices are a form of index manipulation in tensor expressions. Mathematically vectors are elements of a vector space over a field , and for use in physics is usually defined with or . Concretely, if the dimension of is finite, then, after making a choice of basis, we can view such vector spaces as or . The dual space is the space of linear functionals mapping .
