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A digital current loop uses the absence of current for high (space or break), and the presence of current in the loop for low (mark). [1] This is done to ensure that on normal conditions there is always current flowing and in the event of a line being cut the flow stops indefinitely, immediately raising the alarm of the event usually as the heavy noise of the teleprinter not being synchronized ...
A major application of current loops is the industry de facto standard 4–20 mA current loop for process control applications, where they are extensively used to carry signals from process instrumentation to proportional–integral–derivative (PID) controllers, supervisory control and data acquisition (SCADA) systems, and programmable logic ...
The HART Communication Protocol (Highway Addressable Remote Transducer) is a hybrid analog+digital industrial automation open protocol. Its most notable advantage is that it can communicate over legacy 4–20 mA analog instrumentation current loops, sharing the pair of wires used by the analog-only host systems.
The polyhedral method treats each loop iteration within nested loops as lattice points inside mathematical objects called polyhedra, performs affine transformations or more general non-affine transformations such as tiling on the polytopes, and then converts the transformed polytopes into equivalent, but optimized (depending on targeted ...
The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. [5] FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in multicast.
In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions.
The simplex method is remarkably efficient in practice and was a great improvement over earlier methods such as Fourier–Motzkin elimination. However, in 1972, Klee and Minty [ 32 ] gave an example, the Klee–Minty cube , showing that the worst-case complexity of simplex method as formulated by Dantzig is exponential time .
The next step is to encode this ternary number using a fixed-point binary number of sufficient precision to recover it, such as 0.0010110001 2 – this is only 10 bits; 2 bits are saved in comparison with naïve block encoding. This is feasible for long sequences because there are efficient, in-place algorithms for converting the base of ...