2010/04/23 by Emanuel Gluskin, Gluskin, Emanuel · 1 citation
Computer Science · Engineering · #Advanced Memory and Neural Computing #FOS: Computer and information sciences #Neural Networks and Applications #Other Computer Science (cs.OH) #Quantum Computing Algorithms and Architecture #cs.OH
paper · pdf · doi:10.48550/arxiv.1004.4128
This is my old (2005-6) Ms.. The "f-connection" is new and thus the work seems to be too detailed, but some central proofs were difficult for me, and having to be sure in good precision of the "analytical superposition", I calculated different cases. See in http://www.ee.bgu.ac.il/~gluskin/ Article no 50 and the Conference Presentation of 2008. 25 pages, 7 figures, 1 table.
openalex publication_date 2010/04/23 · arxiv created 2010/04/26 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One-ports named "f-circuits", composed of similar conductors described by a monotonic polynomial, or quasi-polynomial (i.e. with positive but not necessarily integer, powers) characteristic i = f(v) are studied, focusing on the algebraic map f --> F. Here F(.) is the input conductivity characteristic; i.e., iin = F(vin) is the input current. The "power-law" "alfa-circuit" introduced in [1], for which f(v) ~ v^"alfa", is an important particular case. By means of a generalization of a parallel connection, the f-circuits are constructed from the alfa-circuits of the same topology, with different "alfa", so that the given topology is kept, and 'f' is an additive function of the connection. We observe and consider an associated, generally approximated, but, in all of the cases studied, always high-precision, specific superposition. This superposition is in terms of f --> F, and it means that F(.) of the connection is close to the sum of the input currents of the independent "alfa"-circuits, all connected in parallel to the same source. In other words, F(.) is well approximated by a linear combination of the same degrees of the independent variable as in f(.), i.e. the map of the characteristics f --> F is close to a linear one. This unexpected result is useful for understanding nonlinear algebraic circuits, and is missed in the classical theory. The cases of f(v) = D1v + D2v2 and f(v) = D1v + D3v3, are analyzed in examples. Special topologies when the superposition must be ideal, are also considered. In the second part [2] of the work the "circuit mechanism" that is responsible for the high precision of the superposition, in the most general case, will be explained.