Results for “Evolving networks”

NASA NTRS2020

Dynamic Stability And Adaptive Control of Networked Evolving Formations with Weak Nonlinearities

The dynamic stability of formation geometry is vital to the design of large scale multiagent systems. In this paper, we probe into the structure of the formation system matrix using the Laplacian of a digraph to develop several fundamental theoretical results on the stability of formation geometry. Our key-results include the integration of the graph Laplacian into linear and weak-nonlinear relative dynamics, the development of several new coordinate transformations that expose the influence of the graph Laplacian matrix on the control laws of the agents, and the use of direct adaptive control as stability restoring devices. We also develop two fundamental results that provide upper bounds for stable formation evolution under nonlinear perturbations of agent dynamics. Finally, we use an illustrative example to demonstrate our theoretical findings.

Gehlot, Vinod P.↗

NASA NTRSDate not supplied

Assessing Commercialization Strategies for Evolving Network Demand (ASCEND) in the NASA Space Communications and Navigation (SCaN) Program

Explore the source record for details and available documents.

Near Earth Network↗

NASA NTRS2025

Assessing Commercialization Strategies for Evolving Network Demand (ASCEND) in the NASA Space Communications and Navigation (SCaN) Program

What will NASA’s future communications demand and expenditure look like, in a paradigm where space policy encourages maximum private sector involvement? In this paper we consider this question, as NASA moves towards commercial procurement for Direct-To-Earth and Space Relay communication services. We develop a new quantitative Techno-Economic Assessment (TEA) model capable of evaluating the incremental cost over time to NASA of utilizing commercial communication services, for different mission and market scenarios. We find that current and future NASA demand could be viably procured from commercial services, with the potential to reduce cost using non-exclusive networks and the sharing of fixed costs. However, there is a key trade-off identified between maximizing economies of scale benefits and ensuring sufficient competition between communication providers to avoid collusion and excessive pricing. For example, procuring from 1-2 providers would maximize scale economies, whereas procuring from 5-6 providers would maximize competition. Given this context, it would be prudent to seek to award service contracts for 3-4 providers to optimize economies of scale benefits, while mitigating possible market collusion. These recommendations enable NASA to successfully achieve its scientific mission over the next decade, while managing limited financial and networking resources.

NSN↗

NASA NTRS1989

Queuing theory models for computer networks

A set of simple queuing theory models which can model the average response of a network of computers to a given traffic load has been implemented using a spreadsheet. The impact of variations in traffic patterns and intensities, channel capacities, and message protocols can be assessed using them because of the lack of fine detail in the network traffic rates, traffic patterns, and the hardware used to implement the networks. A sample use of the models applied to a realistic problem is included in appendix A. Appendix B provides a glossary of terms used in this paper. This Ames Research Center computer communication network is an evolving network of local area networks (LANs) connected via gateways and high-speed backbone communication channels. Intelligent planning of expansion and improvement requires understanding the behavior of the individual LANs as well as the collection of networks as a whole.

Galant, David C.↗

NASA NTRSDate not supplied

NASA Delay Tolerant Networks: Operational, Evolving, an Ready for Expansion

The future of humanity’s presence beyond Earth depends on the successful commercialization of space. For commercialization to succeed, companies need cost-efficient architectures to support their business models and minimize risks for human capital, design, development, and operations. An ongoing challenge to any space enterprise is the reality that terrestrial network technologies are insufficient to provide reliable communications between assets in space. Whether you need to ensure your valuable data is safely transmitted to the ground or reliably delivered between platforms in orbit, ensuring data integrity over intermittent communication links is a necessity. Current solutions to space communications rely heavily on manual recording, storing, and retrieval of data from spacecraft. The current standard in space communication protocols, Consultative Committee for Space Data Systems (CCSDS) Space Packet standard, is reliant on inflexible network architectures based around mission-critical infrastructure to ensure data delivery. However, by automating the recording, storing, retrieval, and verification of data with Delay Tolerant Networks (DTN), the operator is freed from the dependence on manual data management and expensive mission critical infrastructure. NASA has been developing delay tolerant systems since the late 1990’s. Multiple DTN implementations have been established during that time, each suited to different use cases. Most notably, the DTN deployment for the International Space Station (ISS) includes demonstration of two DTN technologies: Interplanetary Overlay Network (ION) and Delay Tolerant Network Marshall Enterprise (DTNME). Beyond ISS, there are even more NASA DTN deployments being considered. Now that DTN implementations are maturing, it is appropriate to reflect upon these decades of work, review the integration and performance of the existing ISS deployment, and explore the future possibilities for DTN deployment industry-wide. The ISS DTN deployment is a complex architecture consisting of different DTN implementations for the onboard and ground network environments. The ION DTN implementation is being used in the on-board network. The Huntsville Operations Support Center (HOSC) DTN implementation, DTNME, is used by the ground network supporting ISS and will soon be a second onboard gateway too. The two implementations work cooperatively to provide high fidelity data services to flight operations users and payload developers across the globe. Though the two implementations yield a quality service, limitations are evident. Data rate, data storage, and device management are constrained by the services themselves and the complex nature of the deployment. Evolution of operations concepts will improve system capabilities and stability, but significant improvement will require additional development to the implementations themselves and to the overall deployment architecture. Taking advantage of the ongoing development and operation of the ISS DTN service will be central to the success of the future evolutions of NASA DTN deployments while demonstrating the benefits of DTN’s low-cost reliable data communication protocols for the growing commercial space industry. A broad effort on DTN integration and support is necessary to promote expansion beyond existing applications. NASA is developing several useful DTN implementations across a number of different systems: ION, DTNME, High-Rate DTN (HDTN), Bundle Protocol Library (BPLib), and others. To prevent fragmentation, DTN implementation teams need to communicate, collaborate, and integrate with one another to build a solid operational foundation for new DTN deployments. The establishment of a group that can assist new DTN users with understanding the purpose of each DTN implementation, provide best practices, and serve as a general knowledge base is paramount. Potential use of DTN on Gateway and other future NASA missions further drives the need for streamlined communication between DTN implementation teams. A well-integrated and highly engaged NASA DTN working group should help provide system architects the best DTN solutions for future commercial space efforts. This paper will first review the history of DTN implementations, explore the shortcoming of current space networking solutions given available limits in technology, and therefore establish the need for Delay Tolerant Networking in space communications. Secondly, the authors will explore NASA’s array of DTN implementations and highlight their usefulness to space applications. Thirdly, this paper will establish general DTN implementation distinguishing factors. Fourthly, the authors will discuss attempts to create a generic DTN comparison matrix, and the authors will review potential future topics in DTN innovation and collaboration, highlighting several key future efforts. Finally, this paper will describe how the institution of a NASA DTN Working Group will benefit DTN adoption across the governmental and commercial space sector. The goal of this paper is to encourage enthusiasm for DTN, share strategies for improving DTN on both current and future applications, promote the collaboration of DTN implementation groups within the international space operations community, and open the conversations about DTN, priorities, complexities, and innovation to the wider spaceflight industry.

DTN↗

NASA NTRSDate not supplied

NASA Delay Tolerant Networks: Operational, Evolving, an Ready for Expansion

The future of humanity’s presence beyond Earth depends on the successful commercialization of space. For commercialization to succeed, companies need cost-efficient architectures to support their business models and minimize risks for human capital, design, development, and operations. An ongoing challenge to any space enterprise is the reality that terrestrial network technologies are insufficient to provide reliable communications between assets in space. Whether you need to ensure your valuable data is safely transmitted to the ground or reliably delivered between platforms in orbit, ensuring data integrity over intermittent communication links is a necessity. Current solutions to space communications rely heavily on manual recording, storing, and retrieval of data from spacecraft. The current standard in space communication protocols, Consultative Committee for Space Data Systems (CCSDS) Space Packet standard, is reliant on inflexible network architectures based around mission-critical infrastructure to ensure data delivery. However, by automating the recording, storing, retrieval, and verification of data with Delay Tolerant Networks (DTN), the operator is freed from the dependence on manual data management and expensive mission critical infrastructure. NASA has been developing delay tolerant systems since the late 1990’s. Multiple DTN implementations have been established during that time, each suited to different use cases. Most notably, the DTN deployment for the International Space Station (ISS) includes demonstration of two DTN technologies: Interplanetary Overlay Network (ION) and Delay Tolerant Network Marshall Enterprise (DTNME). Beyond ISS, there are even more NASA DTN deployments being considered. Now that DTN implementations are maturing, it is appropriate to reflect upon these decades of work, review the integration and performance of the existing ISS deployment, and explore the future possibilities for DTN deployment industry-wide. The ISS DTN deployment is a complex architecture consisting of different DTN implementations for the onboard and ground network environments. The ION DTN implementation is being used in the on-board network. The Huntsville Operations Support Center (HOSC) DTN implementation, DTNME, is used by the ground network supporting ISS and will soon be a second onboard gateway too. The two implementations work cooperatively to provide high fidelity data services to flight operations users and payload developers across the globe. Though the two implementations yield a quality service, limitations are evident. Data rate, data storage, and device management are constrained by the services themselves and the complex nature of the deployment. Evolution of operations concepts will improve system capabilities and stability, but significant improvement will require additional development to the implementations themselves and to the overall deployment architecture. Taking advantage of the ongoing development and operation of the ISS DTN service will be central to the success of the future evolutions of NASA DTN deployments while demonstrating the benefits of DTN’s low-cost reliable data communication protocols for the growing commercial space industry. A broad effort on DTN integration and support is necessary to promote expansion beyond existing applications. NASA is developing several useful DTN implementations across a number of different systems: ION, DTNME, High-Rate DTN (HDTN), Bundle Protocol Library (BPLib), and others. To prevent fragmentation, DTN implementation teams need to communicate, collaborate, and integrate with one another to build a solid operational foundation for new DTN deployments. The establishment of a group that can assist new DTN users with understanding the purpose of each DTN implementation, provide best practices, and serve as a general knowledge base is paramount. Potential use of DTN on Gateway and other future NASA missions further drives the need for streamlined communication between DTN implementation teams. A well-integrated and highly engaged NASA DTN working group should help provide system architects the best DTN solutions for future commercial space efforts. This paper will first review the history of DTN implementations, explore the shortcoming of current space networking solutions given available limits in technology, and therefore establish the need for Delay Tolerant Networking in space communications. Secondly, the authors will explore NASA’s array of DTN implementations and highlight their usefulness to space applications. Thirdly, this paper will establish general DTN implementation distinguishing factors. Fourthly, the authors will discuss attempts to create a generic DTN comparison matrix, and the authors will review potential future topics in DTN innovation and collaboration, highlighting several key future efforts. Finally, this paper will describe how the institution of a NASA DTN Working Group will benefit DTN adoption across the governmental and commercial space sector. The goal of this paper is to encourage enthusiasm for DTN, share strategies for improving DTN on both current and future applications, promote the collaboration of DTN implementation groups within the international space operations community, and open the conversations about DTN, priorities, complexities, and innovation to the wider spaceflight industry.

DTN↗

DOE OSTI2026

Growth in heterogeneous, evolving macromolecular networks: toward functional, biomimetic material

This report summarizes research carried out by the Balazs and Matyjaszewski Labs at Pitt and CMU, respectively, during 2025-26, supported by the DOE grant. It has produced the following 3 research articles and 2 review publications that acknowledged grant ER45998: 1. Computational Modeling of Hyperbranched Polymers 2. Synthesis of Structurally Tailored Networks 3. Sustainable and Oxygen-Tolerant Catalysis 4. A review paper on Current Status and Outlook for ATRP 5. A review paper on Future Directions for Atom Transfer Radical Polymerization

Balazs, Anna (ORCID:0000000255552692)↗

NASA NTRS1988

Patterns of the cosmic microwave background from evolving string networks

A network of cosmic strings generated in the early universe may still exist today. As the strings move across the sky, they produce, by gravitational lensing, a characteristic pattern of anisotropies in the temperature of the cosmic microwave background. The observed absence of such anisotropies places constraints on theories in which galaxy formation is seeded by strings, but it is anticipated that the next generation of experiments will detect them.

Bouchet, Francois R.↗

NASA NTRS2012

Relay Support for the Mars Science Laboratory and the Coming Decade of Mars Relay Network Evolution

In the past decade, an evolving network of Mars relay orbiters has provided telecommunication relay services to the Mars Exploration Rovers, Spirit and Opportunity, and to the Mars Phoenix Lander, enabling high-bandwidth, energy-efficient data transfer and greatly increasing the volume of science data that can be returned from the Martian surface, compared to conventional direct-to-Earth links. The current relay network, consisting of NASA's Odyssey and Mars Reconnaissance Orbiter and augmented by ESA's Mars Express Orbiter, stands ready to support the Mars Science Laboratory, scheduled to arrive at Mars on Aug 6, 2012, with new capabilities enabled by the Electra and Electra-Lite transceivers carried by MRO and MSL, respectively. The MAVEN orbiter, planned for launch in 2013, and the ExoMars/Trace Gas Orbiter, planned for launch in 2016, will replenish the on-orbit relay network as the current orbiter approach their end of life. Currently planned support scenarios for this future relay network include an ESA EDL Demonstrator Module deployed by the 2016 ExoMars/TGO orbiter, and the 2018 NASA/ESA Joint Rover, representing the first step in a multimission Mars Sample Return campaign.

MAVEN↗

NASA NTRS2022

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↗

DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗

NASA NTRS2005

A model to assess the Mars Telecommunications Network relay robustness

The relatively long mission durations and compatible radio protocols of current and projected Mars orbiters have enabled the gradual development of a heterogeneous constellation providing proximity communication services for surface assets. The current and forecasted capability of this evolving network has reached the point that designers of future surface missions consider complete dependence on it. Such designers, along with those architecting network requirements, have a need to understand the robustness of projected communication service. A model has been created to identify the robustness of the Mars Network as a function of surface location and time. Due to the decade-plus time horizon considered, the network will evolve, with emerging productive nodes and nodes that cease or fail to contribute. The model is a flexible framework to holistically process node information into measures of capability robustness that can be visualized for maximum understanding. Outputs from JPL's Telecom Orbit Analysis Simulation Tool (TOAST) provide global telecom performance parameters for current and projected orbiters. Probabilistic estimates of orbiter fuel life are derived from orbit keeping burn rates, forecasted maneuver tasking, and anomaly resolution budgets. Orbiter reliability is estimated probabilistically. A flexible scheduling framework accommodates the projected mission queue as well as potential alterations.

Mars Telecommunications Orbiter (MTO)↗

DOE OSTI2022

Netostat: analyzing dynamic flow patterns in high-speed networks

Understanding flow traffic patterns in networks, such as the Internet or service provider networks, is crucial to improving their design and building them robustly. However, as networks grow and become more complex, it is increasingly cumbersome and challenging to study how the many flow patterns, sizes and the continually changing source-destination pairs in the network evolve with time. Here, we present Netostat, a visualization-based network analysis tool that uses visual representation and a mathematics framework to study and capture flow patterns, using graph theoretical methods such as clustering, similarity and difference measures. Netostat generates an interactive graph of all traffic patterns in the network, to isolate key elements that can provide insights for traffic engineering. We present results for U.S. and European research networks, ESnet and GEANT, demonstrating network state changes, to identify major flow trends, potential points of failure, and bottlenecks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Degree-preserving graph dynamics: a versatile process to construct random networks

Real-world networks evolve over time via the addition or removal of vertices and edges. In current network evolution models, vertex degree varies or grows arbitrarily. A recently introduced degree-preserving network growth (DPG) family of models preserves vertex degree, resulting in structures significantly different from and more diverse than previous models. Despite its degree preserving property, the DPG model is able to replicate the output of several well-known real-world network growth models. Simulations showed that many real-world networks can also be constructed from small seed graphs via the DPG process. Here, we start the development of a rigorous mathematical theory underlying the DPG family of network growth models. We prove that the degree sequence of the output of some of the well-known, real-world network growth models can be reconstructed via the DPG process, using proper parametrization. We also show that the general problem of deciding whether a simple graph can be obtained via the DPG process from a small seed (DPG feasibility) is, however, NP-complete. In conclusion, it is an intriguing open problem to uncover whether there is a structural reason behind the DPG-constructability of real-world networks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

SENTRA: A Modular Computational Graph Framework for Critical Mineral and Materials Supply Chains: Part I: Network Construction Latent-Quantity Estimation, and Temporal Graph Forecasting

Global supply chains for critical minerals and materials are complex, evolving networks of countries, products, production stages, and trade relationships. Existing analytical approaches are limited by fragmented data and static network representations that do not capture the dynamic production dependencies linking raw materials, intermediate products, and final goods across multiple countries. Trade and production statistics provide only a partial view of domestic production, inventories, and material flows, making it difficult to identify indirect sourcing pathways, hidden dependencies, and embedded foreign exposures. This paper introduces the Supply Chain Exposure Network Tracking and Risk Assessment (SENTRA) framework, a modular graph-based computational framework for constructing, analyzing, and forecasting dynamic supply chain networks. As the first paper in a three-part methodological series, it establishes the computational foundation of SENTRA by constructing a temporal attributed multi-relational graph whose nodes represent product–country pairs and whose edges encode observed trade and within-country value-chain relationships. Statistical estimation and constrained optimization recover latent production, final demand, and product input dependency coefficients while enforcing economic accounting constraints. Graph-derived exposure measures quantify direct, transshipment, value-chain, and multi-hop supply chain dependencies independently of the forecasting model. A temporal graph forecasting architecture based on a relational graph neural network then forecasts the evolution of the graph under mass-balance constraints with distribution-free conformal uncertainty quantification. Validation on the global aluminum supply chain shows that the learned graph representations recover economically meaningful supply chain structure, accurately forecast out-of-sample trade relationships, and produce well-calibrated prediction intervals. Subsequent papers apply this computational foundation to exposure assessment, disruption analysis, and scenario-based policy analysis, and extend the framework to multimaterial supply chain modeling and decision support.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A quantitative comparison of the fingerprint of twinned microstructures through surface and three-dimensional techniques

Assessing the fingerprint of a material’s microstructure is key for supporting materials design. With the emergence of a wide range of 3D characterization techniques, it is critical to understand the main differences in fingerprints reconstructed from 2D and 3D datasets. To this end, we introduce a graph-based microstructure reconstruction framework that enables structural comparisons of twin domain networks in high purity Ti using 3D and 2D electron backscatter diffraction. Insights into the structure of the twin networks are facilitated by combining statistical analysis of twin crystallography with visual and graphical analysis of the novel graph abstractions of the twins. We demonstrate that compared to 3D reconstructions, conventional 2D views of twinning miss key aspects of the microstructure including the high interconnectivity of domains into networks that span the full reconstruction volume. The reduced cross-grain and in-grain twin connectivity typically observed in 2D has notable implications on our understanding of how twinning mediates the plastic response of microstructures and how twin networks evolve. It is thus clear that 3D characterization is critical for accurately inferring both twin network morphologies as well as the key unit processes facilitating network formation.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Advances in Modeling Solar System Internet Structures and their Data Flows

With an ever-increasing presence in space, there is also an increasing burden on existing communications infrastructure. We are heading towards an inflection point where the traditional approach of scheduled, single-path communications for space will no longer be viable. One answer is Delay Tolerant Networking (DTN), which takes the once disparate system of point-to-point links and unifies them in a networked architecture, thereby making communications more scalable. However, much work remains for discovering and harnessing the underlying theory of DTN. For example, in the terrestrial setting the interplay between routing domains is well-understood, however this is not the case in DTNs. In this paper, we build up the fundamental foundations of DTN, with an emphasis on modeling time varying networks and data flows across them, with examples of cross-domain routing in a DTN. A lofty goal of DTN is to enable the so-called Solar System Internet (SSI), which implies a standardized and robust suite of protocols. These protocols include routing across disconnected networks using store, carry, and forward mechanisms, which is necessary due to the disconnections, delays, and mobility intrinsic to space networks. Due to these factors, each of which generalize traditional networking, there is a deep and rich theory of DTNs. Here we build off of past successes to broaden this theory while striving to keep actionable results a goal for future implementations and operations. The approach includes modeling the unicast, broadcast, and multicast communications using the language of hypergraphs, which capture the geometric properties of such networked communications algebraically. Also inherent to these networks is their time-varying nature, particularly given mobility, and hence we also cultivate modeling techniques that respect this time dependence. This leads us to develop models using tools from category theory and algebraic geometry, which provide a language well-suited to describing synchronization and optimization over such networks. We also introduce and study a novel generalization of curvature applicable to time-evolving networks, which provides quantitative controls on diffusion processes on the network. Because an interplanetary network would feature links with propagation delays the preclude discovery (feedback) mechanisms, they will always feature a scheduled component. However, it is beneficial to support discovery where possible. While DTNs do not yet have strong definitions for their analogues of autonomous systems or network areas, we show how to join dynamic and schedule-based routing domains, using the language of sheaves, which marks progress towards such definitions. We conclude with a discussion of the progress made, as well as suggestions for future work.

Delay Tolerant Networking↗

NASA NTRSDate not supplied

Multi-Domain Routing in Delay Tolerant Networks

The goal of Delay Tolerant Networking (DTN) is to provide the missing ingredient for the ever-growing collection of communicating nodes in our solar system to become a Solar System Internet (SSI). Great strides have been made in modeling particular types of DTNs, such as schedule- or discovery-based. Now, analogously to the Internet, these smaller DTNs can be considered routing domains which must be stitched together to form the overall SSI. In this paper, we propose a framework for cross-domain routing in DTNs as well as methodologies for detecting these sub-domains. Example time-varying networks are given to demonstrate the techniques proposed. A basic component is the mathematical theory of sheaves, which unifies the underlying model of DTN routing algorithms, by giving rise to routing sheaves – these can be defined for the dynamic and scheduled networks as noted above, and can also be used to define the interfaces between these domains in order to route across them. An immediate application would be routing across discovery-based networks connected by scheduled networks. These DTN subdomains remain elusive, however, and need to become well-defined and properly sized for tractable computability. In particular, a balance must be determined between areas that are too large (i.e. large matrix computations) versus areas that are too small (i.e. “many” single-noded domains). Moreover, the connections between the domains should, at least locally, be chosen to optimize data flow and connectivity: we address this in three ways. First, tools from persistent homology are given to understand underlying structures, reminiscent of hierarchies in the Internet Protocol (IP) addressing. Second, we construct a notion of temporal graph curvature based on network geometry to analyze flows induced by dynamical processes on these networks. Finally, Schrodinger Bridges, a tool arising from statistical physics, are proposed as a method of constructing flows on time-evolving networks with desirable properties such as speed, robustness, and load sensitivity. We construct an approach to temporal hypergraphs to simultaneously model unicast, multicast, and broadcast, using the language of scheme theory, and then consider DTN network coding as a way to achieve network-level computation and organization. The paper concludes with a discussion and ideas for future work.

Alan Hylton↗