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tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Let (s n) be a real sequence, let (σ n) denote the sequence of averages of its first n partial sums. Let lim sup n σ n = β and lim inf n σ n = α, where β = α. We prove… (More)
The number L(a, b) = a−b ln a−ln b for a 6= b and L(a, a) = a, is said to be the logarithmic mean of the positive numbers a, b. We shall say that a sequence (an) ∞ n=1 with positive terms is a logarithmic sequence if an = L(an−1, an+1). In the present paper some basic estimations of the terms of logarithmic sequences are investigated.
We use computational simulations to analyse the behavior of the recently proposed Bidirectional Activation-based Learning algorithm (BAL) which was inspired by the Generalized Recirculation algorithm (GeneRec). Both algorithms avoid biologically implausible backpropagation of the error signal, and instead use propagation of neuron activations, which drive… (More)