Statistical and computational phase transitions in group testing

  • What is the difference between adaptive and non adaptive group testing?

    In group testing, each test involves a subset of the given samples.
    The result of a test is negative if and only if all the involved samples are negative.
    The group testing is called adaptive if one can choose samples to be tested after one sees the result of the previous test and is called non-adaptive otherwise..

  • A familiar example of group testing involves a string of light bulbs connected in series, where exactly one of the bulbs is known to be broken.
    The objective is to find the broken bulb using the smallest number of tests (where a test is when some of the bulbs are connected to a power supply).

Generalized learning mechanism

Statistical learning is the ability for humans and other animals to extract statistical regularities from the world around them to learn about the environment.
Although statistical learning is now thought to be a generalized learning mechanism, the phenomenon was first identified in human infant language acquisition.
The Wang and Landau algorithm, proposed by Fugao Wang and David P.
Landau, is a Monte Carlo method designed to estimate the density of states of a system.
The method performs a non-Markovian random walk to build the density of states by quickly visiting all the available energy spectrum.
The Wang and Landau algorithm is an important method to obtain the density of states required to perform a multicanonical simulation.

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