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In mathematics, the capacity of a set in Euclidean space is a measure of the "size" of that set. Unlike, say, Lebesgue measure , which measures a set's volume or physical extent, capacity is a mathematical analogue of a set's ability to hold electrical charge .
11,520,000 bits – capacity of a lower-resolution computer monitor (as of 2006), 800 × 600 pixels, 24 bpp: 11,796,480 bits – capacity of a 3.5 in floppy disk, colloquially known as 1.44 megabyte but actually 1.44 × 1000 × 1024 bytes 2 24: 16,777,216 bits (2 mebibytes) 25,000,000 bits – amount of data in a typical color slide
the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem; the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; as well as; the bit—a new way of seeing the most fundamental unit of information.
Due to the need to work with data sizes that range from very small to very large, units of information cover a wide range of data sizes. Units are defined as multiples of a smaller unit except for the smallest unit which is based on convention and hardware design. Multiplier prefixes are used to describe relatively large sizes.
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
According to computer scientist Eric Brewer of the University of California, Berkeley, the theorem first appeared in autumn 1998. [9] It was published as the CAP principle in 1999 [10] and presented as a conjecture by Brewer at the 2000 Symposium on Principles of Distributed Computing (PODC). [11]
This method, later known as Hartley's law, became an important precursor for Shannon's more sophisticated notion of channel capacity. Hartley argued that the maximum number of distinguishable pulse levels that can be transmitted and received reliably over a communications channel is limited by the dynamic range of the signal amplitude and the ...
The feedback capacity is known as a closed-form expression only for several examples such as the trapdoor channel, [14] Ising channel, [15] [16]. For some other channels, it is characterized through constant-size optimization problems such as the binary erasure channel with a no-consecutive-ones input constraint [ 17 ] , NOST channel [ 18 ] .