A Tensor-Based Formulation of Hetero-functional Graph Theory

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large flexible engineering systems. In that regard, it intellectually resembles a fusion of network science and model-based systems engineering. With respect to the former, it relies on multiple graphs as data structures so as to support matrix-based quantitative analysis. In the meantime, HFGT explicitly embodies the heterogeneity of conceptual and ontological constructs found in model-based systems engineering including system form, system function, and system concept. At their foundation, these disparate conceptual constructs suggest multi-dimensional rather than two-dimensional relationships. This paper provides the first tensor-based treatment of some of the most important parts of hetero-functional graph theory. In particular, it addresses the "system concept", the hetero-functional adjacency matrix, and the hetero-functional incidence tensor. The tensor-based formulation described in this work makes a stronger tie between HFGT and its ontological foundations in MBSE. Finally, the tensor-based formulation facilitates an understanding of the relationships between HFGT and multi-layer networks

Coding limits on the number of transcription factors

Transcription factor proteins bind specific DNA sequences to control the expression of genes. They contain DNA binding domains which belong to several super-families, each with a specific mechanism of DNA binding. The total number of transcription factors encoded in a genome increases with the number of genes in the genome. Here, we examined the number of transcription factors from each super-family in diverse organisms. We find that the number of transcription factors from most super-families appears to be bounded. For example, the number of winged helix factors does not generally exceed 300, even in very large genomes. The magnitude of the maximal number of transcription factors from each super-family seems to correlate with the number of DNA bases effectively recognized by the binding mechanism of that super-family. Coding theory predicts that such upper bounds on the number of transcription factors should exist, in order to minimize cross-binding errors between transcription factors. This theory further predicts that factors with similar binding sequences should tend to have similar biological effect, so that errors based on mis-recognition are minimal. We present evidence that transcription factors with similar binding sequences tend to regulate genes with similar biological functions, supporting this prediction. The present study suggests limits on the transcription factor repertoire of cells, and suggests coding constraints that might apply more generally to the mapping between binding sites and biological function.Comment: http://www.weizmann.ac.il/complex/tlusty/papers/BMCGenomics2006.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1590034/ http://www.biomedcentral.com/1471-2164/7/23

Generating functional analysis of complex formation and dissociation in large protein interaction networks

We analyze large systems of interacting proteins, using techniques from the non-equilibrium statistical mechanics of disordered many-particle systems. Apart from protein production and removal, the most relevant microscopic processes in the proteome are complex formation and dissociation, and the microscopic degrees of freedom are the evolving concentrations of unbound proteins (in multiple post-translational states) and of protein complexes. Here we only include dimer-complexes, for mathematical simplicity, and we draw the network that describes which proteins are reaction partners from an ensemble of random graphs with an arbitrary degree distribution. We show how generating functional analysis methods can be used successfully to derive closed equations for dynamical order parameters, representing an exact macroscopic description of the complex formation and dissociation dynamics in the infinite system limit. We end this paper with a discussion of the possible routes towards solving the nontrivial order parameter equations, either exactly (in specific limits) or approximately.Comment: 14 pages, to be published in Proc of IW-SMI-2009 in Kyoto (Journal of Phys Conference Series

Abrupt bifurcations in chaotic scattering : view from the anti-integrable limit

Bleher, Ott and Grebogi found numerically an interesting chaotic phenomenon in 1989 for the scattering of a particle in a plane from a potential field with several peaks of equal height. They claimed that when the energy E of the particle is slightly less than the peak height Ec there is a hyperbolic suspension of a topological Markov chain from which chaotic scattering occurs, whereas for E > Ec there are no bounded orbits. They called the bifurcation at E = Ec an abrupt bifurcation to chaotic scattering. The aim of this paper is to establish a rigorous mathematical explanation for how chaotic orbits occur via the bifurcation, from the viewpoint of the anti-integrable limit, and to do so for a general range of chaotic scattering problems

The Discrete-Event Modeling of Administrative Claims (DEMAC) System: Dynamically modeling the U.S. healthcare delivery system with Medicare claims data to improve end-of-life care

The shift of the U.S. healthcare delivery system from the treatment of acute conditions to chronic diseases requires a new method of healthcare system analysis to properly assess end- of-life (EOL) quality throughout the country. In this paper, we propose the Discrete-Event Modeling of Administrative Claims (DEMAC) system, which relies on a hetero-functional graph theory and discrete event-driven framework to dynamically model EOL care on multiple levels. The heat map visualizations produced by the DEMAC system enable the elucidation of not only patient-specific EOL care but also broader treatment patterns among providers and hospitals. As a whole, the DEMAC system provides visual insight into the “black box” of the U.S. healthcare delivery system that can help clinicians and hospital administrators learn where and how to improve EOL care within their institutions

The American Multi-modal Energy System: Model Development with Structural and Behavioral Analysis using Hetero-functional Graph Theory

In the 21st century, infrastructure is playing an ever greater role in our daily lives. Presidential Policy Directive 21 emphasizes that infrastructure is critical to public confidence, the nation\u27s safety, and its well-being. With global climate change demanding a host of changes across at least four critical energy infrastructures: the electric grid, the natural gas system, the oil system, and the coal system, it is imperative to study models of these infrastructures to guide future policies and infrastructure developments. Traditionally these energy systems have been studied independently, usually in their own fields of study. Therefore, infrastructure datasets often lack the structural and dynamic elements to describe the interdependencies with other infrastructures. This thesis refers to the integration of the aforementioned energy infrastructures into a singular system-of-systems within the context of the United States of America as the American Multi-modal Energy System (AMES). This work develops an open-source structural and behavioral model of the AMES using Hetero-functional Graph Theory (HFGT), a data-driven approach, and model-based systems engineering practices in the following steps. First, the HFGT toolbox code is made available on GitHub and advanced to produce HFGs of systems on the scale of the AMES using the languages Python and Julia. Second, the analytical insights that HFGs can provide relative to formal graphs are investigated through structural analysis of the American Electric Power System which demonstrates how HFGs are better equipped to describe changes in system behavior. Third, a reference architecture of the AMES is developed, providing a standardized foundation to develop future models of the AMES. Fourth, the AMES reference architecture is instantiated into a structural model from which structural properties are investigated. Finally, a physically informed Weighted Least Squares Error Hetero-functional Graph State Estimation analysis of the AMES\u27 socio-economic behavior is implemented to investigate the behavior of the AMES with asset level granularity. These steps provide a reproducible and reusable structural and behavioral model of the AMES for guiding future policies and infrastructural developments to critical energy infrastructures