https://www.tylerdiggans.com/pubs daily 0.75 2025-09-16 https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/57a73d96-ddd9-4839-8930-46b5610fe33f/ST.png Publications - Spanning Trees of Recursive SF graphs Revisiting the topic of spanning trees for recursive finitely articulated graphs such as the DGM net, we provide explicit rules for building all spanning trees of such graphs and provide guidance on how one can select for solutions to many optimization problems C. T. Diggans, E. M. Bollt, and D. ben-Avraham, “Spanning Trees of Recursive Scale-Free Graphs.” PRE 105, 024312 (2022) https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/94b50b17-1aea-4c62-b46f-fad8d097838c/Clustering.png Publications - Contextual Clustering for Automated State Estimation by Sensor Networks Through the lens of a space tracking application, a framework for defining a similarity measure that incorporates the data set as context for clustering partial information observations is explored C. T. Diggans, "Contextual Clustering for Automated State Estimation by Sensor Networks," 2020 IEEE Aerospace Conference, 2020, pp. 1-9 https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/351c58e9-5962-454f-aba9-fe5040fa4c1e/BSIEHighlight.png Publications - Boltzmann-Shannon Interaction Entropy The BSIE is a normalized entropy measure that utilizes both frequency histograms and geometric partition entropy to provide an unbiased measure within the context of the measurement domain, particularly useful as a subsample quality metric. Diggans, C. Tyler, and Abd AlRahman R. AlMomani. "Boltzmann–Shannon interaction entropy: A normalized measure for continuous variables with an application as a subsample quality metric." Chaos: An Interdisciplinary Journal of Nonlinear Science 33.12 (2023). https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/1580655428839-0FI4T0CF3E2EMM2V7MWV/digraph92.png Publications - Symmetry Breaking Bifurcation Surfaces and a Cusp Catastrophe A bifurcation surface was created for a two parameter family of coupled Hamiltonian-type PDE. A modified Gradient Newton Galerkin Algorithm (GNGA) was created to explore the parameter space of the system, using symmetry breaking bifurcation analysis to explain the types of solutions present; specifically the existence of a cusp catastrophe on the diagonal where the parameters were equal. C. T. Diggans, J. W. Swift, and J. M. Neuberger, “Symmetry and numerical solutions to semilinear elliptic systems of partial differential equations.” Proc. Variational and Topological Methods https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/0034dc8c-f969-4dc6-8441-604eef7fd6f6/ESB.png Publications - Essential Synchronization Backbone Problem A new optimization problem in the field of synchronization that helps identify the role of conductance in the synchronization of oscillator systems C. T. Diggans, J. Fish, A. Al-Momani, and E. M. Bollt, “The essential synchronization backbone problem.” Chaos 31, 113142 (2021) https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/a504be8f-1b97-486c-9b72-5505b1b096d7/Chaos_GGPE4MI_Thumbnail.png Publications - GGPE4MI A comprehensive summary of over three years of work with my collaborator Dr. Abd AlRahman R. AlMomani at Embry-Riddle Aeronautical University developing the seed of the idea from the GPE paper below into a new data-driven approach to non-parametric entropy analysis of samples from higher-dimensional continuous state spaces. Diggans, C. Tyler, and Abd AlRahman R. AlMomani. “Generalizing Geometric Partition Entropy for the Estimation of Mutual Information in the Presence of Informative Outliers.” Chaos: An interdisciplinary Journal of Nonlinear Science 35, 033141 (2025) https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/894a8e90-6455-4df8-94ee-c759fbacea9a/MCP_Diagram.png Publications - Modeling Resource Consumption via Minimum Cost Percolation An agent-based percolation framework for assessing how well a supply-and-demand network infrastructure functions. Initially applied to Flight Connection Networks, we are now exploring adaptations to power grid models and supply chain multi-layer networked systems Kim, M., Diggans, C.T. & Radicchi, F. Modeling resource consumption in the US air transportation system via minimum-cost percolation. Nat Commun 16, 8105 (2025). https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/b165b427-83d4-4ba4-888f-5c7b6351e642/GPE_alpha.png Publications - Geometric Partition Entropy Using a proportionality distribution of distances associated with a set of quantiles leads to improved estimates of entropy for samples taken from a continuous state space, especially in the context of sparse data. Information metrics are under development that utilize this basic concept. C. T. Diggans and A. A. R. AlMomani, “Geometric Partition Entropy: Course-graining a Continuous State Space“ Entropy 2022, 24(10), 1432 https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/173e08cc-7526-4f68-b9be-6129fb8d89b0/HierarchyDistros_alpha.png Publications - Emergent Hierarchy from Imposed Degree Constraints Inspired by the concept of Dunbar’s number, imposing simple node degree limits in growing random networks results in increased measures of hierarchy, hinting at one source of hierarchical organization being the limitations on flow through any single node. C. T. Diggans, J. Fish, and E. Bollt, “Emergent Hierarchy through Conductance-based Degree Constraints.” Northeast Journal of Complex Systems (NEJCS): Vol. 3 : No. 1 , Article 4. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/a9138d4f-8e52-4622-ba57-ea29dd1210de/SMF.png Publications - Stochastic and Mixed Flower Graphs The first three generations of a stochastic flower graph growth process https://www.tylerdiggans.com/home daily 1.0 2025-09-15 https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/1550951655253-YTBM4XPQ4SLGD8DPKMSX/IMG_1137.JPG Home https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/0e50b6eb-808f-4386-946a-410b47c9f331/RDLogo_black.png Home - A Complex Systems Science Company Exploring the interface between real-world complex systems and our discrete models of them https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/9c544115-b2f8-473b-9689-7c28abc4f42a/treesinsnow.jpg Home https://www.tylerdiggans.com/research-interests daily 0.75 2025-07-08 https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/d4dcfaad-1eb0-49e1-94ca-1a6706b3cc7b/DSCN0066.jpg Research Interests - Hierarchical Networks My main interest centers on understanding the source of hierarchy in real-world networks and modeling growing systems. I believe that hierarchy emerges as the result of all network models being a coarse-graining of a more complex network of systems of systems, e.g., in a social network, nodes are people, but really each person could be modeled (whether correctly or not) as a complex network of neurons. The conductance or limit on information flow of these sub-networks should lead to restrictions on the flow through each node in the coarse-grained model. Hierarchy then naturally emerges to allow for efficient dissemination of information (or control) across the network. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/6e02869d-090c-49f9-aebe-9b95fe769900/unsplash-image-eR4ira0Jgvw.jpg Research Interests - Information Theory / Entropy I am interested in quantification and characterization of high dimensional data using geometric partition entropy and kernel-based spectral clustering for the purposes of quantifying data quality for various purposes. In addition, I am interested in the flow of information between coupled dynamical systems far from equilibrium and synchronization as a process of information transfer and exchange. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/1976afa1-ee4e-462d-8052-63d0e7459112/SnowCrystals.jpg Research Interests - Aggregated Growth In the cold upstate NY air, crystals form out of the air and melt within hours. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/baa6df6e-138d-4792-81dc-5ae4ae6ee360/RosslerConverge.jpg Research Interests - Synchronization of Chaos Information flows and the process of synchronization of dynamical systems. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/79f163b9-9eba-4ccb-a983-3d21f51bf7af/local_substation_man.jpg Research Interests - Power Grid & Supply-and-Demand Network Systems Modeling Modeling and simulation for resilient SDN systems combines my love of hierarchical flow structures and a fundamental interest in quantifying information flows in continuous dynamics. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/ccc485b1-cb16-4ebe-a2e7-f2c6051b4230/GoldenLion.jpg Research Interests - Wildlife Conservation Beginning with a school project in 6th grade at the Atlanta Zoo, I have had a desire to use my skills to help develop better tools for wildlife conservation. Currently, I am interested in the network theory aspects of fractured habitats of endangered species Picture from: https://nationalzoo.si.edu/animals/ https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/685227e6-0979-48a1-87a7-17d852ef79a4/100_0612.jpg Research Interests - Ecological Dynamics Perhaps the embodiment of Bonini’s Paradox, no model of complex interacting species can be made complete, but viewing ecological webs as multi-layer networks of flowing resources provides an endless number of interesting modeling questions. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/1580653942365-UW29H6OGA8ARPSBSDTOA/String4.jpg Research Interests - Symmetry and Numerical Analysis of PDE Using modifications of the Gradient Newton Galerkin Algorithm (GNGA), numerical symmetry breaking bifurcation analysis was done to find solutions of all symmetry types for a two-parameter family of coupled PDE. A cusp catastrophe was found along the main diagonal in the parameter space due to symmetry in the equations. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/ebe9ec67-78dd-4734-b8be-f9d66168032d/Lorenz_Osc.png Research Interests - Chaos-based Encryption As traditional encryption protocols become increasingly threatened by both increased computational power and quantum algorithms, I believe there is more to explore in leveraging chaos for real-time E2EE. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/4e5a1a6b-ba0e-445c-b0b9-53b2f774338f/WormCycleofLife1.jpg Research Interests - Social Organization Although sad to happen upon this scene, I chose to be amazed at the efficiency and organization of the ants rather than be disgusted by the destruction. https://www.tylerdiggans.com/whoami daily 0.75 2025-07-08 https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/b08c6bdb-8de6-4625-b82c-bbfff3ebc1c1/Munda.jpg C. Tyler Diggans - Munda (2003-2021) Although Munda did not impact my work life aside from attacking me at the desk when he was younger, he was the most loving cat I have ever known. Rest in Peace Good Boy! https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/1727306652243-IK0ZF7Y12C4WA5F5H4LU/unsplash-image-dtKOByR6KQ8.jpg C. Tyler Diggans - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/9e392a68-f1e8-426c-8284-450ea0a5337b/UsinSnow.jpg C. Tyler Diggans - My Family I have been married to Elizabeth since 2009. She has been a guiding force in my life and has taught me how to work with life, rather than against it; supporting me through the many ups and downs of a rather non-traditional path through decades of education and experience building. The year 2021 was a tough one as both of our long time pets, Munda and Sidka (see below), passed away, but we now have a new cohort of animals in the house with Newt and Maya (also below). Living out west resulted in a love for the outdoors, and although more domesticated these days due to work, we love to be out in Nature. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/6ab442e0-6a20-4a00-96e3-756aab462270/maya.jpg C. Tyler Diggans - Maya We welcomed Maya back in 2023, and she keeps me out walking in Nature and is one of the sweetest animals alive. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/addd7dd5-7af9-4642-93fa-08e0694d7ca9/IMG_20220120_113504416.jpg C. Tyler Diggans - Newt! We rescued Newt back in 2021, and he likes to play fetch and roll around on his back. https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/1548819857165-J6HM86BEKHEMUQMEE7X5/Sitka+in+form.jpg C. Tyler Diggans - Sidka (2009-2021) Another force of Nature in my life was our dog, Sidka, who dragged me out to the woods for about an hour each day for over a decade. Much of my creative thinking occurred while on these walks and if not for her, I would still be studying quantum mechanics inside instead of complex systems science. https://www.tylerdiggans.com/esb daily 0.75 2025-07-08 https://images.squarespace-cdn.com/content/v1/5b523c2dda02bc590ead7a28/c328e500-d84e-4be0-a287-a5c3cc620fb0/BackboneGIFER50_3.gif The ESB problem - Make it stand out Above is a GIF showing the greedy algorithm process for approximating a Greedy-ESB for 50 Rossler attractors linearly coupled through their x-components on an ER graph with p=0.3. The resulting network is best described as an entangled network (Donetti et. al. 2005)