In case of a min-sum BP decoding failure, let x m = { β 1 m, β 2 m, …, β I BP m } denote the m th sample sequence having for each coordinate the number of errors in the corresponding BP iteration.
Therefore in this case, in a joint stationary point all state values are equal, which was also found above by more specific methods for the special cases of a scaled sum and an advanced logistic sum combination function, which indeed both are symmetric and monotonic combination functions.
For example, considering the case of a numerical array, sum and max are reduce functions whereas internal product is a map function.
The auto-covariance function Rtot in this case is a sum of N c auto-covariance functions of individual one-cluster problems (due to linearity of the Fourier transform operation): R tot = ∑ k = 1 N c P k exp j 2 π f D k τ sinc Δ f D k τ. (7).
Closer observation reveals that of 42 angiogenic carcinomas only 14 (group A) fulfil the theoretical criteria of a sum of 100% (that is about one third of the data set) whereas the majority of the cases have a sum of 81% or less (groups B and C).
In our work, a use case is a sum of activities in a domain that allows answering product requirements.
In a recent report, Senior Auto Analyst Michael Bruynesteyn at Prudential Equity Group notes, "It has long been the case that a sum of the parts valuation for General Motors yielded a value far in excess of its market value.
The merit of this newly proposed method arises from the fact that the neuronal spiking duration in this case is a sum of nanosecond-scale alert, nanosecond to microsecond delay, and nanosecond to microsecond gating pulses, resulting in a total duration on the order of a few microsecond that exceeds the biological synaptic rate at the same delay level of 100 ms.
However, we provide the proof, since we deal with more general case involving a sum of two subdifferentials.
And the above noted phenomenon is based on the fact that in the considering case the G-limit of a sum is not equal to the sum of G-limits.
