# Permutation-based parallel-by-serial calculation of resistance in a circuit

We have employed a computational method for identifying order of receipt of signals from senders based on a telecommunications and/or EE technique. However, we would like to find out which permutation-based technique in EE this stems from.

The technical report states the following:

“The approach is similar to computing resistance in a circuit, which is a parallel-by-serial procedure. The parallel conductivities from all preceding components to a target component are all summed, within a permuted ordering of components, to determine the phase conductivity of the permutation, and then the order conductivity is formulated by cascading all the phase conductivities.”

Note, all the components have to be the same type, maybe resistors or capacitors, but differ by varying rating of their units (10 Ohms, 20 Ohms, 30 Ohms, ..., 500 Ohms). However, you don't know their ratings, but rather, only a label like 1,2,3,4,5. During the calculation, the order of all of the components in the circuit are permuted(shuffled), and all the resistance up to a target is calculated – but each component is once the target.

The application of this calculation would be employed for numerous e.g. circuit boards, where the goal for each board would be to determine if order 7-->3-->1-->2-->5-->6-->4 resulted in the greatest resistance. Another board might have components with labels 12, 3, 55, 13, 92, and 105 (which in truth have different ratings, but you don't know what the ratings are). Overall, you are trying to determine for each board what order of labels results in the greatest resistance. Then over several hundred boards you can develop a picture of what the order is for labels which results in the greatest resistance (on average).

Is there a standard permutation-based technique in EE to find resistance in a circuit that is both serial and parallel?

• I think the answer is probably "no"... Assuming you have no EE experience: Basic lumped-constant circuit analysis does not use any of the kind of stochastic random rearrangement of components you seem to be implying. In CompE/math terminology, a circuit is a graph of nodes (where each node has a voltage and KCL applies) and each edge is a component (e.g. resistor). KVL applies around each complete loop/mesh. Ohm's Law constrains the relation of current and voltage. Solving this system of equations yields all node voltages and mesh currents. No need to perform any permutation. – MarkU Jul 23 '16 at 3:44
• The first part of your question and the text you're quoting from are pure technobabble -- they use a lot of technical terms without saying anything specific. They're equivalent to saying, "I created this fancy turkey dinner with all of the trimmings by 'cooking'." Well, duh! You need to be a lot more specific about the system(s) you are describing. – Dave Tweed Jul 23 '16 at 12:23
• Thanks - very helpful. We were basically saying, we need to figure out exactly what the authors are talking about. Sounds like there's not a permutation-based anything for determining resistance in a circuit. – JoleT Jul 23 '16 at 17:48

The terms 'phase conductivity' and 'order conductivity' don't appear in standard EE for computing resistances. EE doesn't do permutations of components, or average conductivities of assemblies of components.

When a set of components is assembled into any network of any topology, and they can be any component, resistors, capacitors etc, there are techniques to solve what impedance the composite circuit presents to external terminals, and what it does when voltages and currents are applied. If you permute the order of components, then you have a different circuit, with different behaviour.

It might be an interesting intellectual puzzle 'if you shake out a box of components and solder them where they fall, what do you get on average?' You'd go about solving that question by writing a program to permute your components, then solve each circuit, and then aggregate the results. But it would be no more than an interesting pass-time.

• Again, thanks - very helpful. The authors' statement apparently makes no sense at all -- regarding determination of resistance in a circuit. While the authors' statement regarding resistance is unfounded, there is great utility in the technique regarding receipt of signals received within a network of nodes in the telecommunication field. We happen to be applying it to genetic data, and it quite helpful and results are in agreement with other findings based on numerous published quantitative genetic approaches. – JoleT Jul 23 '16 at 17:57
• The method is adopted from the telecommunications field, where for example, you have a data matrix X with rows representing days, and columns representing users' mobile phone numbers. Within a given day, whenever a user receives a call, a 1 is placed in the row element for that day under the number that received the call (you don’t need to know the number that called) and otherwise a 0 is placed in the elements if no calls were received that day. – JoleT Jul 23 '16 at 18:22
• (cont’d): Over an adequate period of time, say several hundred days, if there exists multiple days during which the same order of calls (in serial) are received among a group of users, then it is possible to determine who the users are and the order in which the calls are made. When done, there is a user-by-user non-symmetric matrix for the affinity between each caller. Row values in the matrix represent out-affinity to other callers, and columns represent in-affinity from other callers. Thus, you can empirically determine who is calling who. – JoleT Jul 23 '16 at 18:22