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.
","abstract_html":"<p>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.</p> <p>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.</p>","abstract_has_math":false,"creators":["Newsome-Slade, Vanessa"],"institution":null,"degree_name":"MS in Mathematics","degree_level":null,"degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Elena Dimitrova","Mathematics","College of Science and Mathematics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-06-01T07:00:00Z","date_published":"2022-06-01T07:00:00Z","updated_at":"2026-07-24T01:32:55Z","subjects":["Minimal Wiring Diagrams","Stanley-Reisner Theory","Primary Decomposition Of Ideals","Algebra","Other Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.15368/theses.2022.73"],"render_values":[{"text":"10.15368/theses.2022.73","href":"https://doi.org/10.15368/theses.2022.73","code":true}]}]},"links":{"outbound_url":"https://digitalcommons.calpoly.edu/theses/2489","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Elena Dimitrova","Mathematics","College of Science and Mathematics"]},{"key":"dc:creator","label":"Author","values":["Newsome-Slade, Vanessa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2022-06-10T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Minimal Wiring Diagrams","Stanley-Reisner Theory","Primary Decomposition Of Ideals","Algebra","Other Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.calpoly.edu/theses/2489","10.15368/theses.2022.73"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Unique Signed Minimal Wiring Diagrams and the Stanley-Reisner Correspondence"]}]}],"canonical_facts":{"dc:contributor":["Elena Dimitrova","Mathematics","College of Science and Mathematics"],"dc:creator":["Newsome-Slade, Vanessa"],"dc:date.available":["2022-06-10T07:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://digitalcommons.calpoly.edu/theses/2489","10.15368/theses.2022.73"],"dc:subject":["Minimal Wiring Diagrams","Stanley-Reisner Theory","Primary Decomposition Of Ideals","Algebra","Other Applied Mathematics"],"dc:title":["Unique Signed Minimal Wiring Diagrams and the Stanley-Reisner Correspondence"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_name":["MS in Mathematics"]},"updated_at":"2026-07-24T01:32:55Z"}