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Results for “Small-world networks”

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.

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9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quantum magnetism on small-world networks

While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. In this work, we investigate interacting quantum spins on small-world networks, building on mean-field theory and extensive quantum Monte Carlo simulations. Starting from one-dimensional (1D) rings, we consider two situations: All-to-all interacting and long-range interactions randomly added. The effective infinite dimension of the lattice leads to a magnetic ordering at finite temperature Tc with mean-field criticality. Nevertheless, in contrast to the classical case, we find two distinct power-law behaviors for Tc versus the average strength of the extra couplings. This is controlled by a competition between a characteristic length scale of the random graph and the thermal correlation length of the underlying 1D system, thus challenging mean-field theories. We also investigate the fate of a gapped 1D spin chain against the small-world effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Three-state majority-vote model on small-world networks

Abstract In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1- q , and a different opinion with chance q , where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p , we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise $$q_c$$ q c , as well as the standard critical exponents $$\beta /\nu$$ β / ν , $$\gamma /\nu$$ γ / ν , and $$1/\nu$$ 1 / ν for several values of the rewiring probability p . We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Small-world complex network generation on a digital quantum processor

Abstract Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

A Comparison of Geographic Information Systems, Complex Networks, and Other Models for Analyzing Transportation Network Topologies

This report reviews six classes of models that are used for studying transportation network topologies. The report is motivated by two main questions. First, what can the "new science" of complex networks (scale-free, small-world networks) contribute to our understanding of transport network structure, compared to more traditional methods? Second, how can geographic information systems (GIS) contribute to studying transport networks? The report defines terms that can be used to classify different kinds of models by their function, composition, mechanism, spatial and temporal dimensions, certainty, linearity, and resolution. Six broad classes of models for analyzing transport network topologies are then explored: GIS; static graph theory; complex networks; mathematical programming; simulation; and agent-based modeling. Each class of models is defined and classified according to the attributes introduced earlier. The paper identifies some typical types of research questions about network structure that have been addressed by each class of model in the literature.

Alexandrov, Natalia↗
DOE OSTI2026

NeuroCoreX: An Open-Source FPGA-Based Spiking Neural Network Emulator with On-Chip Learning

Spiking Neural Networks (SNNs) are computational models inspired by the event-driven communication and connectivity patterns of biological neural circuits. They enable high energy efficiency and natural support for diverse architectures ranging from layered networks to small-world and graphstructured topologies. In this work, we introduce NeuroCoreX, an open-source, FPGA-based spiking neural network emulator that provides real-time, on-chip learning and flexible network organization. NeuroCoreX supports both feedforward sensory inputs streamed directly from sensors or PCs via UART and recurrent on-chip connectivity, enabling simultaneous processing and learning from external stimuli and internal network dynamics-capabilities rarely available in existing FPGA SNN platforms. The system implements a Leaky Integrate-and-Fire (LIF) neuron model with current-based synapses and supports pair-based STDP learning on both feedforward and recurrent synapses. A lightweight Python interface enables interactive configuration, live monitoring, weight read-back, and experiment control. Importantly, NeuroCoreX is tightly integrated with the SuperNeuroMAT simulator, allowing SNN models to be transferred seamlessly from software to hardware for hardware-in-the-loop development. By combining real-time plasticity, flexible connectivity, and an open-source VHDL implementation, NeuroCoreX provides an extensible and accessible platform for neuromorphic research, algorithm-hardware co-design, and energy-efficient edge intelligence.

Gautam, Ashish [ORNL]↗
DOE OSTI2023

Trust based attachment

In social systems subject to indirect reciprocity, a positive reputation is key for increasing one’s likelihood of future positive interactions. The flow of gossip can amplify the impact of a person’s actions on their reputation depending on how widely it spreads across the social network, which leads to a percolation problem. To quantify this notion, we calculate the expected number of individuals, the “audience”, who find out about a particular interaction. For a potential donor, a larger audience constitutes higher reputational stakes, and thus a higher incentive, to perform “good” actions in line with current social norms. For a receiver, a larger audience therefore increases the trust that the partner will be cooperative. This idea can be used for an algorithm that generates social networks, which we call trust based attachment (TBA). TBA produces graphs that share crucial quantitative properties with real-world networks, such as high clustering, small-world behavior, and powerlaw degree distributions. We also show that TBA can be approximated by simple friend-of-friend routines based on triadic closure, which are known to be highly effective at generating realistic social network structures. Therefore, our work provides a new justification for triadic closure in social contexts based on notions of trust, gossip, and social information spread. These factors are thus identified as potential significant influences on how humans form social ties.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2004

Improving Search Algorithms by Using Intelligent Coordinates

We consider algorithms that maximize a global function G in a distributed manner, using a different adaptive computational agent to set each variable of the underlying space. Each agent eta is self-interested; it sets its variable to maximize its own function g (sub eta). Three factors govern such a distributed algorithm's performance, related to exploration/exploitation, game theory, and machine learning. We demonstrate how to exploit alI three factors by modifying a search algorithm's exploration stage: rather than random exploration, each coordinate of the search space is now controlled by a separate machine-learning-based player engaged in a noncooperative game. Experiments demonstrate that this modification improves simulated annealing (SA) by up to an order of magnitude for bin packing and for a model of an economic process run over an underlying network. These experiments also reveal interesting small-world phenomena.

Wolpert, David H.↗
NASA NTRS2003

Scale-free Graphs for General Aviation Flight Schedules

In the late 1990s a number of researchers noticed that networks in biology, sociology, and telecommunications exhibited similar characteristics unlike standard random networks. In particular, they found that the cummulative degree distributions of these graphs followed a power law rather than a binomial distribution and that their clustering coefficients tended to a nonzero constant as the number of nodes, n, became large rather than O(1/n). Moreover, these networks shared an important property with traditional random graphs as n becomes large the average shortest path length scales with log n. This latter property has been coined the small-world property. When taken together these three properties small-world, power law, and constant clustering coefficient describe what are now most commonly referred to as scale-free networks. Since 1997 at least six books and over 400 articles have been written about scale-free networks. In this manuscript an overview of the salient characteristics of scale-free networks. Computational experience will be provided for two mechanisms that grow (dynamic) scale-free graphs. Additional computational experience will be given for constructing (static) scale-free graphs via a tabu search optimization approach. Finally, a discussion of potential applications to general aviation networks is given.

Alexandov, Natalia M.↗
DOE OSTI2024

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

97 MATHEMATICS AND COMPUTING↗