21 research outputs found
Effective complexity: In which sense is it informative?
This work responds to a criticism of effective complexity made by James McAllister, according to which such a notion is not an appropriate measure for information content. Roughly, effective complexity is focused on the regularities of the data rather than on the whole data, as opposed to algorithmic complexity. McAllister’s argument shows that, because the set of relevant regularities for a given object is not unique, one cannot assign unique values of effective complexity to considered expressions and, therefore, that algorithmic complexity better serves as a measure of information than effective complexity. We accept that problem regarding uniqueness as McAllister presents it, but would not deny that if contexts could be defined appropriately, one could in principle find unique values of effective complexity. Considering this, effective complexity is informative not only regarding the entity being investigated but also regarding the context of investigation itself. Furthermore, we argue that effective complexity is an interesting epistemological concept that may be applied to better understand crucial issues related to context dependence such as theory choice and emergence. These applications are not available merely on the basis of algorithmic complexity
Effective complexity: In which sense is it informative?
This work responds to a criticism of effective complexity made by James McAllister, according to which such a notion is not an appropriate measure for information content. Roughly, effective complexity is focused on the regularities of the data rather than on the whole data, as opposed to algorithmic complexity. McAllister’s argument shows that, because the set of relevant regularities for a given object is not unique, one cannot assign unique values of effective complexity to considered expressions and, therefore, that algorithmic complexity better serves as a measure of information than effective complexity. We accept that problem regarding uniqueness as McAllister presents it, but would not deny that if contexts could be defined appropriately, one could in principle find unique values of effective complexity. Considering this, effective complexity is informative not only regarding the entity being investigated but also regarding the context of investigation itself. Furthermore, we argue that effective complexity is an interesting epistemological concept that may be applied to better understand crucial issues related to context dependence such as theory choice and emergence. These applications are not available merely on the basis of algorithmic complexity
Iowa State University, Courses and Programs Catalog 2014–2015
The Iowa State University Catalog is a one-year publication which lists all academic policies, and procedures. The catalog also includes the following: information for fees; curriculum requirements; first-year courses of study for over 100 undergraduate majors; course descriptions for nearly 5000 undergraduate and graduate courses; and a listing of faculty members at Iowa State University.https://lib.dr.iastate.edu/catalog/1025/thumbnail.jp
Quantum Reverse Shannon Theorem
Dual to the usual noisy channel coding problem, where a noisy (classical or
quantum) channel is used to simulate a noiseless one, reverse Shannon theorems
concern the use of noiseless channels to simulate noisy ones, and more
generally the use of one noisy channel to simulate another. For channels of
nonzero capacity, this simulation is always possible, but for it to be
efficient, auxiliary resources of the proper kind and amount are generally
required. In the classical case, shared randomness between sender and receiver
is a sufficient auxiliary resource, regardless of the nature of the source, but
in the quantum case the requisite auxiliary resources for efficient simulation
depend on both the channel being simulated, and the source from which the
channel inputs are coming. For tensor power sources (the quantum generalization
of classical IID sources), entanglement in the form of standard ebits
(maximally entangled pairs of qubits) is sufficient, but for general sources,
which may be arbitrarily correlated or entangled across channel inputs,
additional resources, such as entanglement-embezzling states or backward
communication, are generally needed. Combining existing and new results, we
establish the amounts of communication and auxiliary resources needed in both
the classical and quantum cases, the tradeoffs among them, and the loss of
simulation efficiency when auxiliary resources are absent or insufficient. In
particular we find a new single-letter expression for the excess forward
communication cost of coherent feedback simulations of quantum channels (i.e.
simulations in which the sender retains what would escape into the environment
in an ordinary simulation), on non-tensor-power sources in the presence of
unlimited ebits but no other auxiliary resource. Our results on tensor power
sources establish a strong converse to the entanglement-assisted capacity
theorem.Comment: 35 pages, to appear in IEEE-IT. v2 has a fixed proof of the Clueless
Eve result, a new single-letter formula for the "spread deficit", better
error scaling, and an improved strong converse. v3 and v4 each make small
improvements to the presentation and add references. v5 fixes broken
reference