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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Anion Photoelectron Spectroscopy and Ab Initio Studies of the UF – Anion

A synergistic anion photoelectron spectroscopic and ab initio computational study of photodetachment of UF – is reported. The measurement determined a vertical detachment energy of 0.63(03) eV, which is consistent with a spinor-based relativistic coupled-cluster CCSD(T) value of 0.61 eV. The complex spectral features due to excited electronic states and vibrational progressions of UF are analyzed and assigned with the help of spin–orbit-coupled multireference perturbation theory and spinor-based relativistic coupled-cluster calculations. UF and UF – are confirmed to be dominated by ionic bonding. Furthermore, the usefulness of the spinor CCSD(T) approach is demonstrated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A Cryogenic Muon Tagging System Integrated with a Superconducting Qubit Device for Radiation-Induced Error Mitigation

Superconducting qubits are highly sensitive to ionizing radiation, which can induce correlated errors and limit scalable fault-tolerant quantum computing. In particular, cosmic-ray muons can deposit energy in the substrate, generating phonon bursts that break Cooper pairs and produce quasiparticles, leading to correlated decoherence events across multiple qubits. We present the development of a cryogenic muon tagging system based on Kinetic Inductance Detectors (KIDs) and its integration with superconducting quantum hardware. Originally developed within the ACE-SuperQ project and validated as a standalone detector, the system demonstrated a muon tagging efficiency of approximately 90% and excellent agreement with Monte Carlo simulations. Building on this validation, the tagging system has been integrated with a multi-qubit superconducting chip operated in a dilution refrigerator. The detector configuration consists of a multi-layer KID stack arranged above and below the quantum device, enabling time-coincident identification of muon-induced events within the same cryogenic environment. The integrated setup has been successfully commissioned, enabling simultaneous operation of the qubit chip and the muon tagging system. A first measurement campaign has been carried out, and preliminary data show time-correlated events between the muon tagging detectors and the qubit readout. A quantitative analysis of radiation-induced effects on qubit performance is currently ongoing. This work represents a step toward the implementation of event-level radiation tagging as a tool for characterizing and potentially mitigating correlated errors in superconducting quantum processors, while establishing a modular platform for future studies at the interface between particle physics and quantum information science.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗
DOE OSTI2025

Upstreamness and downstreamness in input–output analysis from local and aggregate information

Abstract Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on the flows of money and goods between sectors and countries, which are encoded in input–output (I–O) tables. In this work, we show that an accurate estimation of the role played by sectors and countries in supply chain networks can be achieved without full knowledge of the I–O tables, but only relying on local and aggregate information, e.g., the total intermediate demand per sector. Our method, based on a rank-1 approximation to the I–O table, shows consistently good performance in reconstructing rankings (i.e., upstreamness and downstreamness measures for countries and sectors) when tested on empirical data from the world input–output database. Moreover, we connect the accuracy of our approximate framework with the spectral properties of the I–O tables, which ordinarily exhibit relatively large spectral gaps. Our approach provides a fast and analytically tractable framework to rank constituents of a complex economy without the need of matrix inversions and the knowledge of finer intersectorial details.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Preventing native oxide formation in niobium thin films through platinum encapsulation

Superconducting transmon qubits are a key technology in quantum computing, with niobium (Nb) widely used due to its favorable superconducting properties and compatibility with scalable fabrication. However, the performance of Nb-based qubits is hindered by two-level systems (TLS), which arise predominantly from native oxide layers at surfaces and interfaces. These oxides and suboxides form rapidly in air and contribute significantly to decoherence by introducing dielectric losses. While various mitigation strategies, including thermal-annealing, chemical-etching, and nitrogen plasma treatment, have been explored, many are challenging to integrate into large-scale manufacturing due to complexity and instability in ambient conditions. In this study, we investigate the structural, chemical, and superconducting properties of room-temperature sputtered Nb thin films grown on sapphire substrates. We focus on a surface protection strategy using noble metal encapsulation with platinum (Pt) to suppress oxides and reduce TLS-related losses. Structural and chemical characterization were performed using X-ray diffraction, X-ray photoelectron spectroscopy, and transmission electron microscopy. Superconducting properties were measured using a physical property measurement system. Results demonstrate that Pt encapsulation effectively suppresses surface oxidation and mitigates its detrimental impact on superconducting performance. In conclusion, this approach offers a promising path toward enhancing the coherence of Nb-based qubits while remaining compatible with scalable-fabrication processes.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Unconventional quantum oscillations and evidence of nonparabolic electronic states in quasi-two-dimensional electron system at complex oxide interfaces

The simultaneous occurrence of electric-field controlled superconductivity and spin-orbit interaction makes two-dimensional electron systems (2DES) constructed from perovskite transition metal oxides promising candidates for the next generation of spintronics and quantum computing. It is, however, essential to understand the electronic bands thoroughly and verify the predicted electronic states experimentally in these 2DES to advance technological applications. Here, we present insights into the electronic states of the 2DES at oxide interfaces through comprehensive investigations of Shubnikov–de Haas oscillations in three different systems: EuO/KTaO 3 , LaAlO 3 /SrTiO 3 , and amorphous-LaAlO 3 /KTaO 3 . To accurately resolve these oscillations, we conducted transport measurements in high magnetic fields up to 60 T and low temperatures down to 100 mK. For 2D confined electrons at these interfaces, we observed a progressive increase of oscillations frequency and cyclotron mass with the magnetic field. We interpret these universal and intriguing findings by considering the existence of nontrivial electronic bands, for which the 𝐸−𝑘 dispersion incorporates both linear and parabolic relations. In addition to providing experimental evidence for nonparabolic electronic states in KTaO 3 and SrTiO 3 2DES, the unconventional oscillations presented in this study establish a paradigm for quantum oscillations in 2DES based on perovskite transition metal oxides, where the oscillation frequencies in 1/𝐵 exhibit quadratic dependence on the magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Uncontrolled Learning: Codesign of Neuromorphic Hardware Topology for Neuromorphic Algorithms

Neuromorphic computing has the potential to revolutionize future technologies and our understanding of intelligence, yet it remains challenging to realize in practice. The learning-from-mistakes algorithm, inspired by the brain's simple learning rules of inhibition and pruning, is one of the few brain-like training methods. This algorithm is implemented in neuromorphic memristive hardware through a codesign process that evaluates essential hardware trade-offs. While the algorithm effectively trains small networks as binary classifiers and perceptrons, performance declines significantly with increasing network size unless the hardware is tailored to the algorithm. This work investigates the trade-offs between depth, controllability, and capacity—the number of learnable patterns—in neuromorphic hardware. This highlights the importance of topology and governing equations, providing theoretical tools to evaluate a device's computational capacity based on its measurements and circuit structure. The findings show that breaking neural network symmetry enhances both controllability and capacity. Additionally, by pruning the circuit, neuromorphic algorithms in all-memristive circuits can utilize stochastic resources to create local contrasts in network weights. Through combined experimental and simulation efforts, the parameters are identified that enable networks to exhibit emergent intelligence from simple rules, advancing the potential of neuromorphic computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Pushing the Boundaries of Coherence in Superconducting Quantum Systems at the SQMS Center for Computing, Sensing, and Metrology

This talk will highlight recent advances at the SQMS Center in understanding and mitigating decoherence in superconducting quantum systems, focusing on both transmon qubits and 3D superconducting cavities. I will present results from systematic studies of materials and devices, aimed at identifying key sources of loss: including two-level systems (TLS), quasiparticles, and other noise mechanisms. These studies span microwave loss characterization in materials such as niobium, tantalum, aluminum, and their native oxides, as well as substrate losses in silicon and sapphire. Using both qubits and cavities, we disentangle subsystem contributions to loss and develop a hierarchy of mitigation strategies. Through these efforts, we have achieved transmon coherence times exceeding one millisecond. I will also present investigations into quasiparticle dynamics, including bursts observed in qubits located above ground and in the Gran Sasso underground laboratory. Additional studies explore temperature dependence to distinguish between TLS and quasiparticle losses, and reveal that applying a magnetic field can reduce temporal T1 fluctuations in transmons. Building on these results, we demonstrate a record-coherence two-cell cavity-qudit system with coherence times exceeding 20 milliseconds. By leveraging sideband interactions and error-resilient protocols including measurement-based correction and post-selection, we achieve high-fidelity quantum state control. This includes preparation of Fock states up to N = 20 with fidelities over 95%, and two-mode entanglement with coherence-limited fidelities reaching 99.9% after post-selection. These achievements position the SQMS platform as a powerful foundation for scalable quantum information processing and high-dimensional qudit encodings. Finally, I will discuss how these ultra-coherent systems are being deployed in emerging quantum sensing applications, including dark matter searches and gravitational wave detection.

Roy, Tanay [Fermilab]↗
NASA NTRS1994

Computational modelling of Er(3+): Garnet laser materials

The Er(3+) ion has attracted a lot of interest for four reasons: (1) Its (4)I(sub 13/2) yields (4)I(sub 15/2) transition lases in the eyesafe region near 1.5 micron; (2) the (4)I(sub 13/2) transition lases near 2.8 micron, an important wavelength for surgical purposes; (3) it displays surprisingly efficient upconversion with lasing observed at 1.7, 1.2, 0.85, 0.56, 0.55, and 0.47 micron following 1.5 micron pumping; and (4) it has absorption bands at 0.96 and 0.81 micron and thus can be diode pumped. However, properties desirable for upconversion reduce the efficiency of 1.5 and 3 micron laser operation and vice versa. Since all of the processes are influenced by the host via the crystal field induced stark splittings in the Er levels, this project undertook modelling of the host influence on the Er lasinng behavior. While growth and measurement of all ten Er(3+) doped garnets is the surest way of identifying hosts which maximize upconversion (or conversly, 1.5 and 3 micron performance), it is also expensive - costing approximately $10,000/material or approximately $100,000 for the materials computationally investigated here. The calculations were performed using a quantum mechanical point charge model developed by Clyde Morrison at Harry Diamond Laboratories. The programs were used to fit the Er:YAG experimental energy levels so that the crystal field parameters, B(sub nm) could be extracted. From these radial factors, rho (sub n) were determined for Er(3+) in garnets. These, in combination with crystal field components, Anm, available from X-ray data, were used to predict energy levels for Er in the other nine garnet hosts. The levels in Er:YAG were fit with an rms error of 12.2/cm over a 22,000/cm range. Predicted levels for two other garnets for which literature values were available had rms errors of less than 17/cm , showing the calculations to be reliable. Based on resonances between pairs of calculated stark levels, the model predicts GSGG as the best host for 1.5 micron laser operation, GSGG or YSAG as the best host for a 2.8 micron operation, and LuGG as the best host for an upconversion material.

Spangler, Lee H.↗
DOE OSTI2026

Carbon-Based Quantum Information Science with Symmetry Protected Topological States (Final Report, DOE-BES award DE-SC0023105)

This research program established the scientific foundation for the rational, bottom-up design, synthesis, isolation, and investigation of symmetry-protected topological (SPT) electron spin qubits embedded in graphene nanoribbons (GNRs). The work focused on integrating atomically precise low-dimensional carbon nanostructures with emerging quantum logic architectures, providing a pathway toward scalable quantum materials for next-generation computing and sensing technologies. A central component of the program was the elucidation of fundamental relationships between real-space molecular architecture, local spin density distributions, electronic band dispersion, and energy level alignment in atomically precise GNR systems. These correlations define key operational parameters of SPT qubits and were systematically investigated to establish quantitative benchmarks against established molecular and solid-state spin qubit platforms. Attention was given to properties critical for quantum device performance, e.g. decoherence times, spectral sharpness of energy transitions, and tunable exchange interactions between spin states. The research demonstrated that these parameters can be engineered with atomic precision through scalable bottom-up synthetic strategies. Theory-guided design played a central role in identifying candidate structures hosting topologically protected spin states. Experimental validation was performed using both ensemble measurements and single-molecule characterization. In addition to advances in quantum materials synthesis, the program developed and applied spin-sensitive scanning probe microscopy techniques capable of directly probing quantum states and dynamic processes with atomic-scale spatial resolution. These capabilities enabled direct observation and characterization of quantum structures at the single-atom level. While the research activities were primarily hypothesis-driven fundamental investigations, the program adopted a comprehensive materials-by-design framework aimed at translating scientific discoveries into technological concepts compatible with scalable and intelligent manufacturing approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Entanglement engineering of optomechanical systems by reinforcement learning

Entanglement is fundamental to quantum information science and technology, yet controlling and manipulating entanglement—so-called entanglement engineering—for arbitrary quantum systems remains a formidable challenge. There are two difficulties: the fragility of quantum entanglement and its experimental characterization. We develop a model-free deep reinforcement-learning (RL) approach to entanglement engineering, in which feedback control together with weak continuous measurement and partial state observation is exploited to generate and maintain desired entanglement. We employ quantum optomechanical systems with linear or nonlinear photon–phonon interactions to demonstrate the workings of our machine-learning-based entanglement engineering protocol. In particular, the RL agent sequentially interacts with one or multiple parallel quantum optomechanical environments, collects trajectories, and updates the policy to maximize the accumulated reward to create and stabilize quantum entanglement over an arbitrary amount of time. The machine-learning-based model-free control principle is applicable to the entanglement engineering of experimental quantum systems in general.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

NASA Tech Briefs, January 2003

Topics covered include: Optoelectronic Tool Adds Scale Marks to Photographic Images; Compact Interconnection Networks Based on Quantum Dots; Laterally Coupled Quantum-Dot Distributed-Feedback Lasers; Bit-Serial Adder Based on Quantum Dots; Stabilized Fiber-Optic Distribution of Reference Frequency; Delay/Doppler-Mapping GPS-Reflection Remote-Sensing System; Ladar System Identifies Obstacles Partly Hidden by Grass; Survivable Failure Data Recorders for Spacecraft; Fiber-Optic Ammonia Sensors; Silicon Membrane Mirrors with Electrostatic Shape Actuators; Nanoscale Hot-Wire Probes for Boundary-Layer Flows; Theodolite with CCD Camera for Safe Measurement of Laser-Beam Pointing; Efficient Coupling of Lasers to Telescopes with Obscuration; Aligning Three Off-Axis Mirrors with Help of a DOE; Calibrating Laser Gas Measurements by Use of Natural CO2; Laser Ranging Simulation Program; Micro-Ball-Lens Optical Switch Driven by SMA Actuator; Evaluation of Charge Storage and Decay in Spacecraft Insulators; Alkaline Capacitors Based on Nitride Nanoparticles; Low-EC-Content Electrolytes for Low-Temperature Li-Ion Cells; Software for a GPS-Reflection Remote-Sensing System; Software for Building Models of 3D Objects via the Internet; "Virtual Cockpit Window" for a Windowless Aerospacecraft; CLARAty Functional-Layer Software; Java Library for Input and Output of Image Data and Metadata; Software for Estimating Costs of Testing Rocket Engines; Energy-Absorbing, Lightweight Wheels; Viscoelastic Vibration Dampers for Turbomachine Blades; Soft Landing of Spacecraft on Energy-Absorbing Self-Deployable Cushions; Pneumatically Actuated Miniature Peristaltic Vacuum Pumps; Miniature Gas-Turbine Power Generator; Pressure-Sensor Assembly Technique; Wafer-Level Membrane-Transfer Process for Fabricating MEMS; A Reactive-Ion Etch for Patterning Piezoelectric Thin Film; Wavelet-Based Real-Time Diagnosis of Complex Systems; Quantum Search in Hilbert Space; Analytic Method for Computing Instrument Pointing Jitter; and Semiselective Optoelectronic Sensors for Monitoring Microbes.

Source record↗
DOE OSTI2025

Partitioned Quantum Subspace Expansion

We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given Krylov subspace requires the same quantum resources in both the single step and sequential cases. We propose a variance-based criterion for determining a good iterative sequence and provide numerical evidence that these good sequences display improved numerical stability over a single step in the presence of finite sampling noise. Implementing the generalisation requires additional classical processing with a polynomial overhead in the subspace dimension. By exchanging quantum circuit depth for additional measurements the quantum subspace expansion algorithm appears to be an approach suited to near term or early error-corrected quantum hardware. Our work suggests that the numerical instability limiting the accuracy of this approach can be substantially alleviated in a parameter-free way.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Nonunitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation

Accurately describing strongly correlated systems with affordable quantum resources remains a central challenge for quantum chemistry applications on near and intermediate term quantum computers. The localized active space self-consistent field (LASSCF) approximates the complete active space self-consistent field (CASSCF) by generating active space-based wave functions within specific fragments while treating interfragment correlation with mean-field approach, hence is computationally less expensive. Hardware-efficient ansatzes (HEA) offer affordable and shallower circuits, yet they often fail to capture the necessary correlation. Previously, Jastrow-factor-inspired nonunitary qubit operators were proposed to use with HEA for variational quantum eigensolver (VQE) calculations (so-called nuVQE), as they do not increase circuit depths and recover correlation beyond the mean-field level for Hartree–Fock initial states. Here, in this study, we explore running nuVQE with LASSCF as the initial state. The method, named LAS-nuVQE, is shown to recover interfragment correlations, reach chemical accuracy with a small number of gates (<70) in both H 4 and square cyclobutadiene (C 4 H 4 ), and produces more accurate energetics than its HEA counterparts at all circuit depths. To further address the inherent symmetry-breaking in HEA, we implemented spin-constrained LAS-nuVQE to extend the capabilities of HEA further and show spin-pure results for square cyclobutadiene. We also mitigate the increased measurement overhead of nuVQE via Pauli grouping and shot-frugal sampling, reducing measurement costs by up to 2 orders of magnitude compared to ungrouped operator, and show that one can achieve better accuracy with a small number of shots (10 3–4 ) per one expectation value calculation compared to noiseless simulations with one or two orders of magnitude more shots. Finally, wall clock time estimates show that, with our measurement mitigation protocols, nuVQE becomes a cheaper and more accurate alternative than vanilla VQE with HEA. Taken together, these developments illustrate a practical pathway toward performing multireference chemical simulations with accuracy and affordable resources on today’s quantum hardware, achieving both accuracy and affordability in challenging correlated systems.

Wang, Qiaohong [Univ. of Chicago, IL (United State↗
DOE OSTI2025

A spline-based method to obtain spatially dependent viscosity in confined flows

Coupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. This paper will connect non-equilibrium molecular dynamics simulations to a continuum-based Navier-Stokes equation that has relaxed the assumption of spatial uniformity in viscosity. Using a form for viscosity based on spline interpolation, viscosity as a function of position is obtained from the least squares fit of the velocity profile measured from molecular simulations of flow in a nanochannel. Viscosity can vary widely, particularly near the channel boundaries, indicating that uniform viscosity is no longer appropriate. Variations of the viscosity near the channel surfaces imply that considering solution and surface chemistry could be necessary to rigorously understand molecular-scale flows in nanochannels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Chiral induction at the nanoscale and spin selectivity in electron transmission in chiral methylated BEDT-TTF derivatives

Great efforts have been made in the last few decades to realize electronic devices based on organic molecules. A possible approach in this field is to exploit the chirality of organic molecules for the development of spintronic devices, an applicative way to implement the chiral-induced spin selectivity (CISS) effect. In this work we exploit enantiopure tetrathiafulvalene (TTF) derivatives as chiral inducers at the nanoscale. The aim is to make use of TTF's well-known and unique semiconducting properties, to be expressed in the fields of enantio-selectivity and the chiral-induced spin selectivity (CISS) effect. Further, the experimental results shown in this paper further demonstrate how chirality and spin are deeply interrelated, as foreseen within the CISS effect theory, paving the way for the application of TTF derivatives in the field of spintronics. In this work, we demonstrate that tetramethyl-bis(ethylenedithio)-tetrathiafulvalene (TM-BEDT-TTF) (1) behaves as an efficient spin filter, as evidenced by magneto-atomic force microscopy (mc-AFM) measurements. Additionally, it is shown to be effective in transferring chirality to CdS/CdSe core–shell nanoparticles, as inferred from the analysis of circularly resolved photoluminescence spectra. This makes 1 a promising candidate for a variety of applications, ranging from plasmonics to quantum computing.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Tunable Few-Layer van der Waals Crystals and Heterostructures as Emerging Energy and Quantum Materials (Final Technical Report)

2D and layered (van der Waals) semiconductors offer extraordinary opportunities for manipulating optically excited charge carriers, many-body excitations, and non-charge based quantum numbers. To date, research has focused on a limited group of materials, mostly transition metal dichalcogenides in the monolayer limit. Other van der Waals semiconductors, and especially few-layer to multilayer crystals and their heterostructures, carry large potential for the discovery of phenomena of interest for future energy and information technologies. But they remain largely unexplored, often due to a lack of access to high-quality materials and approaches for measuring their properties at the relevant scales. The goal of this project was to develop an EPSCoR-State/National Laboratory Partnership that addresses the challenges of preparing high-quality van der Waals semiconductors and of probing their structure, composition, and especially their optoelectronic and photonic properties, near the atomic scale using electron microscopy techniques. A central component of the project was the development of advanced methods for electron microscopy and electron-excited spectroscopy, taking advantage of unique samples as well as leading capabilities and expertise at the partner institutions. Efforts to advance leading-edge techniques was supported by ancillary developments, such as precision sample preparation for electron microscopy/spectroscopy, coordinated chemical imaging, and analytical electron microscopy. Experiments in materials synthesis and technique development were closely linked to theory and computation. The results obtained under this project yielded multifaceted benefits to the involved partners and their institutions, DOE-BES, the wider scientific community, and society at large, particularly in the State of Nebraska through dividends from knowledge and human capital generated under the project.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping

We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $η$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(η^2\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $η ≲ \sqrt{N}$. To achieve such scaling, we require $O(\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford $+T$ gates and study the impact of noise on the prepared state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Distribution of centrality measures on undirected random networks via the cavity method

The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗