Publications
In addition to my dissertation (see the link on the ESB Problem page), here is a list of current publications with a brief description, citation, and a representative figure.
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).
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
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)
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.
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)
Stochastic and Mixed Flower Graphs
A re-introduction of stochasticity to a well studied deterministic hierarchical graph with power law degree distribution and small world properties when u=1. A fully deterministic mixing is also provided to allow tuning of properties while retaining all the exact analytical results from the original net.
C. T. Diggans, E. M. Bollt, and D. ben-Avraham, “Stochastic and Mixed Flower Graphs” PRE 101, 052315 (2020)
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
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://ejde.math.txstate.edu/conf-proc/21/d3/diggans.pdf