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Capacity of the two-way channel: The capacity of the two-way channel (a channel in which information is sent in both directions simultaneously) is unknown. [ 5 ] [ 6 ] Capacity of Aloha : The ALOHAnet used a very simple access scheme for which the capacity is still unknown, though it is known in a few special cases.
information bottleneck method; information theoretic security; information theory; joint entropy; Kullback–Leibler divergence; lossless compression; negentropy; noisy-channel coding theorem (Shannon's theorem) principle of maximum entropy; quantum information science; range encoding; redundancy (information theory) Rényi entropy; self ...
One early commercial application of information theory was in the field of seismic oil exploration. Work in this field made it possible to strip off and separate the unwanted noise from the desired seismic signal. Information theory and digital signal processing offer a major improvement of resolution and image clarity over previous analog methods.
In information theory, the typical set is a set of sequences whose probability is close to two raised to the negative power of the entropy of their source distribution. That this set has total probability close to one is a consequence of the asymptotic equipartition property (AEP) which is a kind of law of large numbers .
Information flow (information theory) Information fluctuation complexity; Information–action ratio; Information projection; Information source (mathematics) Information theory and measure theory; Integrated information theory; Interaction information; Interactions of actors theory; Interference channel
Skolem–Mahler–Lech theorem (number theory) Solutions to Pell's equation (number theory) Sophie Germain's theorem (number theory) Sphere packing theorems in dimensions 8 and 24 (geometry, modular forms) Stark–Heegner theorem (number theory) Subspace theorem (Diophantine approximation) Sylvester's theorem (number theory)
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [5] [6] [7] Chrystal's equation: 1 + + + = Generalization of Clairaut's equation with a singular solution [8] Clairaut's equation: 1
Many of the concepts in information theory have separate definitions and formulas for continuous and discrete cases. For example, entropy is usually defined for discrete random variables, whereas for continuous random variables the related concept of differential entropy, written (), is used (see Cover and Thomas, 2006, chapter 8).