Application of modern network theory to analysis of complex systems
Modern network theory applications to analysis of complex systems
Faken, J. C.↗
SEARCH · Engineering Papers
Results for “Network theory”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Application of modern network theory to analysis of manned systems
Application of modern network theory to analysis of manned systems
Fakan, J. C.↗
Quantifying Spatial Drought Propagation Potential in North America Using Complex Network Theory
Droughts have a dominant three-dimensional (3-D) spatiotemporal structure typically spanning hundreds of kilometers and often lasting for months to years. Here, we introduced a novel framework to explore the 3-D structure of the evolution of droughts based on network theory concepts. The proposed framework is applied to identify critical source regions responsible for large-scale drought onsets during 1901–2014 for the North American continent using the Standardized Precipitation Evaporation Index (SPEI). We built a spatial network connecting the drought onset timings for the North American continent. Using a spatially weighted network partitioning algorithm, the whole continent is then classified into regional spatial drought networks (RSN), where droughts are more likely to propagate within these regional systems. Finally, a customized network metric was applied to identify locations (source regions) where the drought onsets further propagate to other areas within the regional spatial network. Our results indicated that the West coast, Texas coastal region, and Southeastern Arkansas as major source regions through which atmospheric drought propagates to Western, South Central, and Eastern North America. The formation of drought source regions are due to presence of high pressure ridges and anomalous wind patterns. Furthermore, our results indicate that the drought propagation from these source regions may be due to inadequate moisture transport. The proposed framework can help to develop an early warning detection system for droughts and other spatially extensive extreme events such as heatwaves and floods.
Goutam Konapala↗
Predicting the viscoplastic response of a crystallizing fluoropolymer using transient network theory
We employ a molecular theory of dynamic polymer networks to describe the viscoplastic response of rubbery FK-800, a thermoplastic copolymer of chlorotrifluoroethylene and vinylidene fluoride, over a broad range of thermal histories. The kinetics of crystallization at different annealing temperatures was modeled using a modified Avrami equation, whose parameters were found to evolve through simple relationships over the full temperature range of the rubbery state. By fitting experimental compression data, we discovered predictable trends for the physical parameters in our mechanical model over its full range of crystallinities (up to ≈20%) and provided insights based on molecular-level physics to justify them. Using this, an end-to-end model was developed to predict the yielding and post-yield behavior of rubbery FK-800 for arbitrary thermal histories. The model successfully predicted the highly nonlinear evolution of characteristic mechanical signatures (stiffness, yield point, post-yield drop) throughout the crystallization process. A statistical analysis of variance test was employed to determine that the measured variations in the mechanical behavior of rubbery FK-800 are primarily dictated by its fractional crystallinity, regardless of its exact thermal history.
36 MATERIALS SCIENCE↗
Network Theory: A Primer and Questions for Air Transportation Systems Applications
A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.
Holmes, Bruce J.↗
Controlled gate networks: theory and application to eigenvalue estimation
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates. We present the general theory of controlled gate networks and show that, under quite general conditions, it can significantly reduce the number of two-qubit gates needed to produce linear combinations of unitary operators. The first example we consider is a variational subspace calculation for a two-qubit system. The second example is estimating the eigenvalues of a two-qubit Hamiltonian via the rodeo algorithm (Choi et al. in Phys Rev Lett 127(4):040505, 2021. https://doi.org/10.1103/PhysRevLett.127.040505) using operators that we call controlled reversal gates. We use the Quantinuum H1-2 and IBM Perth devices to realize the quantum circuits. The third example is the application of controlled gate networks to the controlled time evolution of a free nucleon on a three-dimensional lattice. For all of the examples, we show very substantial reductions in the number of two-qubit gates required. Our work demonstrates that controlled gate networks are a useful tool for reducing gate complexity in quantum algorithms for quantum many-body problems such as those relevant to nuclear physics.
Bee-Lindgren, Max [Georgia Institute of Technology↗
Adapting an AMTRAN terminal to graphical network theory and to develop software for adapting AMTRAN to the IBM 1620 Computer
Interface between IBM 1620 computer and NASA AMTRAN, hardware, graphic techniques, and rectangular diagrams for network analysis
Erdey, M. R. A.↗
Assessing and Promoting Functional Resilience in Flight Crews During Exploration Missions
NASA plans to send humans to Mars in about 20 years. The NASA Human Research Program supports research to mitigate the major risks to human health and performance on extended missions. However, there will undoubtedly be unforeseen events on any mission of this nature - thus mitigation of known risks alone is not sufficient to ensure optimal crew health and performance. Research should be directed not only to mitigating known risks, but also to providing crews with the tools to assess and enhance resilience, as a group and individually. We can draw on ideas from complexity theory and network theory to assess crew and individual resilience. The entire crew or the individual crewmember can be viewed as a complex system that is composed of subsystems (individual crewmembers or physiological subsystems), and the interactions between subsystems are of crucial importance for overall health and performance. An understanding of the structure of the interactions can provide important information even in the absence of complete information on the component subsystems. This is critical in human spaceflight, since insufficient flight opportunities exist to elucidate the details of each subsystem. Enabled by recent advances in noninvasive measurement of physiological and behavioral parameters, subsystem monitoring can be implemented within a mission and also during preflight training to establish baseline values and ranges. Coupled with appropriate mathematical modeling, this can provide real-time assessment of health and function, and detect early indications of imminent breakdown. Since the interconnected web of physiological systems (and crewmembers) can be interpreted as a network in mathematical terms, we can draw on recent work that relates the structure of such networks to their resilience (ability to self-organize in the face of perturbation). There are many parameters and interactions to choose from. Normal variability is an established characteristic of a healthy physiological response. Healthy coupling has been investigated less extensively, but there are cases in which too tight or too loose coupling can be problematic. This might be in inter-individual behaviors, such as sleep cycles, coordination of work and meal times, and coupled motions during communication. Less apparent are couplings of physiological systems, nevertheless examples abound of coupled systems which might be monitored: cardio-respiratory rhythms; circadian rhythms, body temperature, and sleep; stress markers and cognition, sleep, and performance; profiles of biochemical markers related to immune function and nutritional status; sensorimotor aspects such as motion sickness, ataxia, reaction time, and manual control. Tools for resilience are then the means to measure and analyze these parameters, incorporate them into appropriate models of normal variability and interconnectedness, and recognize when parameters or their couplings are outside of normal limits. What to do when a problem is identified depends on its nature. Changes can be made to crew procedures, work pacing, interpersonal interactions, sleep cycles, meal timing and content, as guided by the model. Use and continued development of these methods could not only provide tools for resilience, but also meaningful autonomous work for the crew on an extended flight.
Shelhamer, Mark↗
Theory of pulsed molecular-flow networks.
Molecular flow network theory applicable to volumes interconnected by small orifices or porous membranes for transient pressure measurements
Kendall, B. R. F.↗
Quantum graph learning and algorithms applied in quantum computer sciences and image classification
Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A Lagrangian Formulation of Neural Networks I: Theory and Analog Dynamics
We expand the mathematicla apparatus for relaxation networks, which conventionally consists of an objective function E and a dynamics given by a system of differenctial equations along whose trajectories E is diminished.
Neural Networks Analog↗
A Survey of Mathematical Structures for Lunar Networks
To sustain the current and increasing accessibility of space, a scalable communications infrastructure (i.e. the Solar System Internet, SSI) is necessary. The goal of this paper is to begin the discovery of the fundamental underlying mathematical structure of space networks to help the research community harness these structures for algorithm development and optimization. To ensure the applicability of the research, the approaches are considered through the lens of simulated scenarios inspired by the Artemis Back-to-the-Moon mission set for 2024. We note that any approach to an SSI must fit under the umbrella of Delay Tolerant Networking (DTN), due to celestial mobility, high link latencies, high variance in link latencies, disconnections, lack of end-to-end paths, and so on. These difficulties are exacerbated by the fact that the underlying structure of a space network is a time-evolving network and may experience multiple discontinuities in its topology. In this paper we propose several novel approaches to a mathematical foundation for Delay Tolerant Networking Theory that fall outside the traditional scope of temporal network theory. These techniques include methods from Topological Data Analysis, Dynamic Graph Analysis, Applied Algebraic Geometry, Probability Theory, and Game Theory. Some of these methods include tools adapted to the study of dynamic metric spaces, such as zigzag persistent homology and their higher parameter analogs. We find that several of these methods target desired engineering outcomes such as discovery and automatic sub-netting. While each approach is theoretical, they are also algorithmic in nature and offer immediate practical applications. The paper concludes with comparisons of the various methods along with suggestions for future work.
Delay tolerant networking↗
On the Current State of Sheaf Theoretic Networking
Advancing the Delay Tolerant Networking (DTN) effort has proven to be a unique and difficult challenge. In the journey to implementing space networking, NASA has considered several strategies. From direct translations of Internet Protocol (IP) to satellite networks to pre-planned routing structures in Contact Graph Routing (CGR), each potential solution for DTN has come with its fair share of setbacks and challenges. Frequently, these challenges can be traced back to specific assumptions made in the development of each protocol that do not carry over from ground networks to space networks. To address these fundamental assumptions, a more general and foundational networking theory is required. In this paper, we survey a novel mathematical foundation for networking using the theory of cellular sheaves. Sheaves form a mathematical tool for modeling local phenomenon that leads to global effects. Sheaves have been introduced a number of times, and our goal here is to summarize the applications and point towards important future work that must be done to build a stronger, cohesive theory for networking.
Sheaves↗
A hereditary integral, transient network approach to modeling permanent set and viscoelastic response in polymers
An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with different natural equilibrium states. Chains continually detach from previously formed networks and reattach to new networks in a state of zero stress. The free energy of these networks is given in terms of the deformation gradient relative to the configuration at which the network was born . A decomposition of the kernel for various free energies allows for a recurrence relationship to be established, bypassing the need to integrate over all time history. The technique is established for both highly compressible and nearly incompressible materials through the use of neo-Hookean, Blatz–Ko, Yeoh, and Ogden-Hill material models. Multiple examples are presented showing the ability to handle rate-dependent response and residual strains under complex loading histories.
Finite element method↗
Combining Flux Balance and Energy Balance Analysis for Large-Scale Metabolic Network: Biochemical Circuit Theory for Analysis of Large-Scale Metabolic Networks
Predicting behavior of large-scale biochemical metabolic networks represents one of the greatest challenges of bioinformatics and computational biology. Approaches, such as flux balance analysis (FBA), that account for the known stoichiometry of the reaction network while avoiding implementation of detailed reaction kinetics are perhaps the most promising tools for the analysis of large complex networks. As a step towards building a complete theory of biochemical circuit analysis, we introduce energy balance analysis (EBA), which compliments the FBA approach by introducing fundamental constraints based on the first and second laws of thermodynamics. Fluxes obtained with EBA are thermodynamically feasible and provide valuable insight into the activation and suppression of biochemical pathways.
Beard, Daniel A.↗
Transformations in Air Transportation Systems For the 21st Century
Globally, our transportation systems face increasingly discomforting realities: certain of the legacy air and ground infrastructures of the 20th century will not satisfy our 21st century mobility needs. The consequence of inaction is diminished quality of life and economic opportunity for those nations unable to transform from the 20th to 21st century systems. Clearly, new thinking is required regarding business models that cater to consumers value of time, airspace architectures that enable those new business models, and technology strategies for innovating at the system-of-networks level. This lecture proposes a structured way of thinking about transformation from the legacy systems of the 20th century toward new systems for the 21st century. The comparison and contrast between the legacy systems of the 20th century and the transformed systems of the 21st century provides insights into the structure of transformation of air transportation. Where the legacy systems tend to be analog (versus digital), centralized (versus distributed), and scheduled (versus on-demand) for example, transformed 21st century systems become capable of scalability through technological, business, and policy innovations. Where air mobility in our legacy systems of the 20th century brought economic opportunity and quality of life to large service markets, transformed air mobility of the 21st century becomes more equitable available to ever-thinner and widely distributed populations. Several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems create new foundations for 21st thinking about air transportation. One of the technological developments of importance arises from complexity science and modern network theory. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of robustness, resilience, and other metrics. The lecture offers an air transportation system topology and a scale-free network linkage graphic as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system topologies, and airspace architectures and procedural concepts. These new paradigms could support scalable alternatives for the expansion of future air mobility to more consumers in more parts of the world.
Holmes, Bruce J.↗
Irreducible realizations and the degree of a rational matrix.
Equivalence of irreducible realization in control theory and degree of rational matrix in network theory
COMPLEX VARIABLE↗
Self-organization in neural networks - Applications in structural optimization
The present paper discusses the applicability of ART (Adaptive Resonance Theory) networks, and the Hopfield and Elastic networks, in problems of structural analysis and design. A characteristic of these network architectures is the ability to classify patterns presented as inputs into specific categories. The categories may themselves represent distinct procedural solution strategies. The paper shows how this property can be adapted in the structural analysis and design problem. A second application is the use of Hopfield and Elastic networks in optimization problems. Of particular interest are problems characterized by the presence of discrete and integer design variables. The parallel computing architecture that is typical of neural networks is shown to be effective in such problems. Results of preliminary implementations in structural design problems are also included in the paper.
Hajela, Prabhat↗