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Matrix-tree theorem for cohomological electrical networks
Pavlo Pylyavskyy, Svetlana Shirokovskikh, Mikhail Skopenkov
We introduce a new type of boundary condition for electrical networks by specifying a cohomology class on the underlying cell complex. As special and limiting cases, we recover the…
Superport networks
Pavlo Pylyavskyy, Svetlana Shirokovskikh, Mikhail Skopenkov
We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the…
Transformations of 2-port networks and tiling by rectangles
Svetlana Shirokovskikh
In this paper, we study 2-port networks and introduce new concepts of voltage drop and -equivalence. The main result is that each planar network is -equivalent to a network w…