Biological systems are commonly represented using networks consisting of interactions between various elements in the system. Reverse engineering, a method of mathematical modeling, is used to recover how the elements in the biological network are connected. These connections are encoded using wiring diagrams, which are directed graphs that describe how elements in a network affect one another. A signed wiring diagram provides additional information about the interactions between elements relating to activation and inhibition. Due to cost concerns, it is optimal to gain insight into biological networks with as few experiments and data as possible. Minimal wiring diagrams identify the minimal sets of variables for which a model that fits the data exists. Previously established algorithms to compute possible minimal wiring diagrams rely on the primary decomposition of ideals in polynomial rings. Stanley-Reisner theory provides a one-to-one correspondence between squarefree monomial ideals and abstract simplicial complexes. In this work, we use this correspondence to determine conditions under which a given set of inputs is guaranteed to have a unique signed minimal wiring diagram, regardless of the output assignment.

Projektet har gjorts på uppdrag av Ölandsfärjan AB för att tillverka elscheman för huvudinstrumenttavlan ombord på deras fartyg M/S Solsund. Anledningen till detta var att det inte fanns någon dokumentation om huvudinstrumenttavlan och detta försvårade arbetet med felsökning och underhåll. Därför önskades elscheman som kunde användas för att se skåpets funktioner och uppbyggnad.Uppdraget var att skapa ett layoutschema som beskriver indikeringslampor och knappars fysiska positioner för huvudinstrumenttavlans framsida. Det skulle även skapa ett kretsschema över förbrukardelen och ett kretsschema för kraftförsörjningsdelen som beskriver funktioner och utgående matningar. Kraftförsörjningen består av två generatorer och möjlighet till landanslutning. Det gjordes även separata kretsschema över generatorernas övervakningsskåp som innehöll effektbrytarnas utlösningsskydd. För samtliga scheman gjordes en gemensam apparatlista. För att skapa elscheman så påbörjades uppdraget med detektering av huvudinstrumenttavlan. Arbetsmetoden för detekteringen utfördes genom att visuellt följa eller resistansmäta kablarna. Avslutningsvis ritades den slutliga produkten i datorprogrammet Easy EL. / This project was commissioned by Ölandsfärjan AB to manufacture wiring diagrams for the main switchboard on board their ship M/S Solsund. The reason for this was that there was no documentation found on the main switchboard and this complicated the process of troubleshooting and maintenance. Therefore, Ölandsfärjan AB required wiring diagrams, which could be used to see cabinet functions and the contexture of the wiring.  The task was to create a layout diagram that would be able to provide a description for the physical positions of indicator lights and buttons on the front of the main switchboard. The task was also to create a circuit diagram of the consuming section and a circuit diagram of power supply section of the main switchboard, the purpose for this was to reveal the functions and output feeds. The power supply consists of two generators and also the opportunity for shore connection. Separate circuit diagrams of the generators' control boxes were also constructed for the circuit breaker tripping protection devices. For all diagrams a common device list was made. The project began to create wiring diagrams of the main switchboard. The work methods for the detection were performed by visually monitoring the cables or measuring the cables' resistance. Finally, the diagrams were made in the computer program Easy EL. / Main Switchboard Drawing