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At least 127 records · Page 7

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Modular-Invariant Random Matrix Theory and AdS 3 Wormholes

We develop a nonperturbative definition of RMT 2 : a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its 𝑛-point spectral correlations admit a prescribed modular-invariant lift to RMT 2 , which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL⁡(2,ℤ) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT 2 lift of two-point correlations of the GUE Airy model. We propose that in AdS 3 pure gravity, semiclassical amplitudes for off-shell 𝑛-boundary torus wormholes with topology Σ 0,𝑛 × 𝑆 1 are given by the RMT 2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT 2 result.

conformal field theory↗

DOE OSTI2024

Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses

Here, this work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on largescale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson-Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Machine Learning Inference of Random Medium Properties

Earth materials are heterogeneous across a range of spatial scales, but the resolvability of small structures is limited by sparse data coverage, noise, bandlimitedness, and other difficulties. In practice, heterogeneities below a certain size cannot be recovered from seismic data except through statistical medium descriptions, which even then can be difficult to uniquely determine. To improve the characterization of such heterogeneities, we develop a novel supervised machine learning (ML) model that provides insight about the recoverability of statistical medium properties from elastic waveform data and succeeds despite cycle-skipping and other challenges well known from elastic waveform inversion. We demonstrate the approach using random media generated by superimposing self-affine random variations on homogeneous and layered background structures. After training on sparsely-recorded, high-frequency waveforms from hundreds of different random medium realizations, we show the ability of our ML model to recover correlation lengths and other statistical properties of interest to near-surface and crustal seismology, among other fields. For frequency passbands and spatial offsets encountered in seismology, Gaussian correlation lengths and the amplitude of the random variations relative to the background model are recovered even in challenging scenarios involving unknown medium parameters, complex crustal structures, and low signal-to-noise ratio. In comparison, von Kármán correlation lengths, which are related to larger-wavelength variations of the medium than Gaussian correlation lengths, are not as well recovered. These results provide one of the first and most systematic investigations of the recoverability of statistical properties of heterogeneities below the resolution limit of deterministic seismic tomography, and suggest practical ML strategies for high-frequency waveform seismology.

58 GEOSCIENCES↗

DOE OSTI2023

Development of a High Min-Entropy Quantum Random Number Generator Based on Amplified Spontaneous Emission

We present the theory, architecture, and performance characteristics of a quantum random number generator (QRNG) which operates in a PCI express form factor-compatible plug-and-play design. The QRNG relies on a thermal light source (in this case, amplified spontaneous emission), which exhibits photon bunching according to the Bose–Einstein (BE) statistics. We demonstrate that 98.7% of the unprocessed random bit stream min-entropy is traceable to the BE (quantum) signal. The classical component is then removed using a non-reuse shift-XOR protocol, and the final random numbers are generated at a 200 Mbps rate and shown to pass the statistical randomness test suites FIPS 140-2, Alphabit, SmallCrush, DIEHARD, and Rabbit of the TestU01 library.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1997

Image discrimination models predict detection in fixed but not random noise

By means of a two-interval forced-choice procedure, contrast detection thresholds for an aircraft positioned on a simulated airport runway scene were measured with fixed and random white-noise masks. The term fixed noise refers to a constant, or unchanging, noise pattern for each stimulus presentation. The random noise was either the same or different in the two intervals. Contrary to simple image discrimination model predictions, the same random noise condition produced greater masking than the fixed noise. This suggests that observers seem unable to hold a new noisy image for comparison. Also, performance appeared limited by internal process variability rather than by external noise variability, since similar masking was obtained for both random noise types.

NASA Center ARC↗

NASA NTRS2018

Randomizer for High Data Rates

NASA as well as a number of other space agencies now recognize that the current recommended CCSDS randomizer used for telemetry (TM) is too short. When multiple applications of the PN8 Maximal Length Sequence (MLS) are required in order to fully cover a channel access data unit (CADU), spectral problems in the form of elevated spurious discretes (spurs) appear. Originally the randomizer was called a bit transition generator (BTG) precisely because it was thought that its primary value was to insure sufficient bit transitions to allow the bit/symbol synchronizer to lock and remain locked. We, NASA, have shown that the old BTG concept is a limited view of the real value of the randomizer sequence and that the randomizer also aids in signal acquisition as well as minimizing the potential for false decoder lock. Under the guidelines we considered here there are multiple maximal length sequences under GF(2) which appear attractive in this application. Although there may be mitigating reasons why another MLS sequence could be selected, one sequence in particular possesses a combination of desired properties which offsets it from the others.

randomizer↗

NASA NTRS2018

Randomizer for High Data Rates

primitive polynomials↗

NASA NTRS2023

Multilevel Logistic Regression with Random Slope for Community Annoyance Survey Data

This paper documents recent dose-response modeling work at NASA in anticipation of follow-on work by a contactor. Specifically, this paper compares the results of a Bayesian MLR model with a fixed slope to one with a random slope using WSPR and QSF18 data. Previously reported dose-response modeling efforts of WSPR and QSF18 data have used a MLR model with a fixed slope term. A random slope may more accurately depict the dose-response relationship of individuals in the efforts to produce a population summary dose-response curve. Results of a fixed versus random slope model with WSPR and QSF18 data indicate minimal difference between the modeling methods. The simpler fixed slope model is preferable for these data, but these results do not preclude consideration of a random slope term in modeling efforts of future X-59 community test data.

dose-response↗

DOE OSTI2021

Detector Calibration to Quantify Random Summing in HPGe Spectroscopy

While calibrating a High Purity Germanium (HPGe) Radiation Detector for Xenon-133 (133Xe) the process of random summing occurs which leads to excess counts in the 160.6keV peak from random summing of the 81keV photons at the 162keV energy. Multiple samples of 133Xe with varying levels of radioactivity were assayed to determine a relationship between the occurrence of random summing and the net area of the 160.6keV peak. When the calculated efficiencies in the 160.6keV peak were compared to the theoretical efficiency obtained from a multi-energy calibration at 160.6keV, the amount of random summing could be estimated as excess observed efficiency and correlated to the sample activity. While a trend is apparent in the data, the mechanisms that contribute to the trend are still being studied so the data can be accurately correlated.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗

DOE OSTI2020

Hormonal contraception alters vaginal microbiota and cytokines in South African adolescents in a randomized trial

Young women in sub-Saharan Africa are disproportionally affected by HIV infection and unintended pregnancies. However, hormonal contraceptive (HC) use may influence HIV risk through changes in genital tract microbiota and inflammatory cytokines. To investigate this, 130 HIV negative adolescent females aged 15–19 years were enrolled into a substudy of UChoose, an open-label randomized crossover study (NCT02404038), comparing acceptability and contraceptive product preference as a proxy for HIV prevention delivery methods. Participants were randomized to injectable norethisterone enanthate (Net-En), combined oral contraceptives (COC) or etonorgesterol/ethinyl estradiol combined contraceptive vaginal ring (CCVR) for 16 weeks, then crossed over to another HC for 16 weeks. Cervicovaginal samples were collected at baseline, crossover and exit for characterization of the microbiota and measurement of cytokine levels; primary endpoints were cervical T cell activation, vaginal microbial diversity and cytokine concentrations. Adolescents randomized to COCs had lower vaginal microbial diversity and relative abundance of HIV risk-associated taxa compared to Net-En or CCVR. Cervicovaginal inflammatory cytokine concentrations were significantly higher in adolescents randomized to CCVR compared to COC and Net-En. This suggests that COC use may induce an optimal vaginal ecosystem by decreasing bacterial diversity and inflammatory taxa, while CCVR use is associated with genital inflammation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Integration of multiple coinflip devices for high-quality random sampling

Artificial intelligence, scientific computing, and probabilistic computing use random sampling to approximate solutions to various problems, with larger models requiring a substantial quantity of random numbers. To generate the required vast quantity of random numbers at high rates, we explore so-called “coinflip” devices, which are stochastic microelectronic devices ideally capable of independently generating random bits with a tunable weight at a high rate. However, coinflip devices are inherently analog and demonstrate nonidealities, like temperature dependence and drift, that can introduce determinism into the outputs. We present important considerations for building systems of multiple coinflip devices to produce high-quality bitstreams with low error and little dependency on previous bits. Using tunnel diodes as coinflip devices, we implement a control loop to adapt to temperature dependence and generate fair bitstreams with each device. While this can lead to dependencies between bits in a single bitstream, we demonstrate that combining results generated in parallel with individual tunnel diodes can produce fair and unpredictable bitstreams. The suitability of these bitstreams for use in probabilistic computing is then demonstrated through a Monte Carlo approximation of π.

Taylor, Brady Garland [Sandia National Laboratorie↗

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↗

DOE OSTI2020

Effective pair potential for random fcc CoCrFeMnNi alloys

The single-phase equiatomic CoCrFeMnNi alloy is a random solid solution of five elements on the face-centered cubic lattice, whose pure constituents crystallize in very different structures and exhibit diverse magnetic properties. Due to the randomness of the alloy, 80% of nearest neighbor bonds are between unlike elements and thus the details of bonding in pure structures are less important. The elastic moduli of this alloy give rise to small Cauchy pressure C 12 - C 44 , which suggests that the dominant part of bonding may be described by a simple pair potential. We test this hypothesis by developing a long-range Lennard-Jones potential in which the equilibrium crystal structures of pure constituents are taken as reference. The standard mixing rules for regular solutions are then adopted to obtain parameters for bonds between unlike elements in the quinary system. The transferability of this potential to quaternary CoCrFeNi, ternary CoCrNi, and binary FeNi alloys is investigated and the predictions compared with experiments and density functional theory calculations. By sampling over a large number of random configurations, we investigate the effect of compositional randomness on misfit volumes, energies of point defects and stacking faults, and the dislocation friction stresses experienced by moving edge and screw dislocations.

Materials Science↗

DOE OSTI2026

Spectral Properties and Coding Transitions of Haar-Random Quantum Codes

A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical information is encoded in a random subspace of the physical Hilbert space. We focus on the spectrum of the encoded system density matrix as a function of the rate of uncorrelated, single-qudit errors. For low error rates, this spectrum consists of well-separated bands, representing errors of different weights. As the error rate increases, the bands for high-weight errors merge. The evolution of these bands with increasing error rate is well described by a simple analytic ansatz. Using this ansatz, as well as an explicit calculation, we show that the threshold for Haar-random quantum codes saturates the hashing bound, and thus coincides with that for random stabilizer codes. For error rates that exceed the hashing bound, typical errors are uncorrectable, but postselected error correction remains possible until a much higher detection threshold. Postselection can in principle be implemented by projecting onto subspaces corresponding to low-weight errors, which remain correctable past the hashing bound.

decoherence↗

DOE OSTI2026

Faster Randomized Dynamical Decoupling

We present a randomized dynamical decoupling (DD) protocol that can substantially improve the performance of any given deterministic DD scheme for suppressing coherent noise by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system’s Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. Here, we also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.

Quantum algorithms & computation↗

DOE OSTI2021

Topological and symmetry-enriched random quantum critical points

In this work, we study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogs of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of such symmetry-enriched random quantum spin chains. We uncover a new class of symmetry-enriched infinite randomness fixed points: while local bulk properties are indistinguishable from conventional random singlet phases, nonlocal observables, and boundary critical behavior are controlled by a different renormalization group fixed point. We also illustrate how such new quantum critical points emerge naturally in Floquet systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Random insights into the complexity of two-dimensional tensor network calculations

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (“not too entangled”) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work, we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at a large bond dimension. Through this statistical-mechanics lens, we argue that (i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, and (ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. Furthermore, these results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗