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At least 829 records · Page 46

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

A study of two-pion scattering for the isospin channels, 𝐼 = 0 and 𝐼 = 2, using lattice QCD is presented. Möbius domain-wall fermions, on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions, are used for the lattice computations, which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD Collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of 𝐿 = 4.63 and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states—two pions with a nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the 𝐼 = 0 and 𝐼 = 2 channels are consistent with the Roy equation and chiral perturbation theory, though at this preliminary stage our errors for 𝐼 = 0 are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying 𝐾 → 𝜋⁢𝜋 decay, on physical-mass ensembles using the GEVP.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A cosmological redshift-distance square law

This paper directly examines the claims of Segal (1976) that the (m,z) Hubble diagram is fitted best by a square law z = Kr-squared rather than by the traditional Hubble law z = Hr in the low-redshift range, z no more than about 0.01, corresponding to galaxies brighter than 14th mag. Segal attempts to fit a distance relation to the (m,z) scatter diagram in which each individual galaxy is plotted. The exact relation between the mean redshift for all galaxies in a small magnitude interval and the apparent magnitude is calculated. This relation is independent of luminosity function and peculiar velocity distribution about the general expansion, and is not affected by sample incompleteness as a function of apparent magnitude or the clustering of galaxies in the sample. Segal's method is affected by all of these and requires a highly sophisticated statistical analysis to deal with the non-Gaussian pointwise scatter. The present analysis favors the Hubble law and conclusively rules out the square law for the small redshift region.

Soneira, R. M.↗

Functional Techniques for Data Analysis

This dissertation develops a new general method of solving Prony's problem. Two special cases of this new method have been developed previously. They are the Matrix Pencil and the Osculatory Interpolation. The dissertation shows that they are instances of a more general solution type which allows a wide ranging class of linear functional to be used in the solution of the problem. This class provides a continuum of functionals which provide new methods that can be used to solve Prony's problem.

Tomlinson, John R.↗

Engineering Second Sphere Interactions in a Host–Guest Multicomponent Catalyst System for the Hydrogenation of Carbon Dioxide to Methanol

Many enzymes utilize interactions extending beyond the primary coordination sphere to enhance catalyst activity and/or selectivity. Such interactions could improve the efficacy of synthetic catalyst systems, but the supramolecular assemblies employed by biology to incorporate second sphere interactions are challenging to replicate in synthetic catalysts. Herein, a strategy is reported for efficiently manipulating outer sphere influence on catalyst reactivity by modulating host–guest interactions between a noncovalently encapsulated transitionmetal-based catalyst guest and a metal–organic framework (MOF) host. This composite consists of a ruthenium PNP pincer complex encapsulated in the MOF UiO-66 that is used in tandem with the zirconium oxide nodes of UiO-66 and a ruthenium PNN pincer complex to hydrogenate carbon dioxide to methanol. Due to the method used to incorporate the complexes in UiO-66, structure–activity relationships could be efficiently determined using a variety of functionalized UiO-66-X hosts. These investigations uncovered the beneficial effects of the ammonium functional group (i.e., UiO-66-NH 3 + ). Mechanistic experiments revealed that the ammonium functionality improved efficiency in the hydrogenation of carbon dioxide to formic acid, the first step in the cascade. Isotope effects and structure–activity relationships suggested that the primary role of the ammonium functionality is to serve as a general Brønsted acid. Importantly, the cooperative influence from the host was effective only with the functional group in close proximity to the encapsulated catalyst. Here, reactions carried out in the presence of molecular sieves to remove water highlighted the beneficial effects of the ammonium functional group in UiO-66-NH 3 + and resulted in a 4-fold increase in activity. As a result of the modular nature of the catalyst system, the highest reported turnover number (TON) (19 000) and turnover frequency (TOF) (9100 h –1 ) for the hydrogenation of carbon dioxide to methanol are obtained. Moreover, the reaction was readily recyclable, leading to a cumulative TON of 100 000 after 10 reaction cycles.

08 HYDROGEN↗

Strategy for Risk Quantification of Spaceflight Crew Health and Performance Using Dynamic Probabilistic Risk Assessment

At NASA, the Crew Health and Performance (CHP) system represents the span of countermeasures, capabilities, interventions, and tested processes and procedures that in combination work to mitigate the human component of spaceflight mission risk. Across the varying NASA mental models of the CHP system, the different functionalities needed to meet human flight systems standards can be broken down into specific categories (i.e. medical capability, environmental health, behavioral health). These categories can be further broken down into specific subgroups generally associated with the CHP functionalities meant to mitigate or buy down individual human system risks. Taking a similar development approach we seek to leverage dynamic probabilistic risk assessment as a means to quantify and relatively assess the human risk state within the crew health and performance domain. By utilizing existing tools as integrators, we propose a rapid development strategy for incorporating research and operational data that represent the influence of the CHP system functionalities, in order to provide order of magnitudes estimates of the influence on most human system risks outcomes. The model system utilizes a modest cumulative risk approach and that limits the scope to primary paths of influence between the CHP functionalities and human system risks, thus enabling quick prototypes of the integrative effects of CHP functional combinations to solicit valuable feedback from stakeholders and customers on the data, relationship, and structure of the integration.

Drayton Munster↗

Mapping the functional landscape of the receptor binding domain of T7 bacteriophage by deep mutational scanning

The interaction between a bacteriophage and its host is mediated by the phage's receptor binding protein (RBP). Despite its fundamental role in governing phage activity and host range, molecular rules of RBP function remain a mystery. Here, we systematically dissect the functional role of every residue in the tip domain of T7 phage RBP (1660 variants) by developing a high-throughput, locus-specific, phage engineering method. This rich dataset allowed us to cross compare functional profiles across hosts to precisely identify regions of functional importance, many of which were previously unknown. Substitution patterns showed host-specific differences in position and physicochemical properties of mutations, revealing molecular adaptation to individual hosts. We discovered gain-of-function variants against resistant hosts and host-constricting variants that eliminated certain hosts. To demonstrate therapeutic utility, we engineered highly active T7 variants against a urinary tract pathogen. Our approach presents a generalized framework for characterizing sequence–function relationships in many phage–bacterial systems.

59 BASIC BIOLOGICAL SCIENCES↗

Diffraction image formation in optical systems with polarization aberrations. I - Formulation and example

This paper is the first in a series that will examine image formation in optical systems with polarization aberrations. The present paper derives the point-spread function (PSF) and the optical transfer function for optical systems with polarization aberration and explores how image formation depends on the coherence and polarization state of the source. It is shown that the scalar PSF of Fourier optics can be generalized in the presence of polarization aberration to a 4 x 4 point-spread matrix (PSM) in Mueller matrix notation. A similar 4 x 4 optical transfer matrix (OTM) is shown to be an appropriate generalization of the optical transfer function. The PSM and the OTM are associated with the optical system and are independent of the incident polarization state but dependent on the coherence of the illumination. Since an optical system with polarization aberrations will have a different PSF and optical transfer function for different incident polarization states, the PSM and the OTM act as filters with regard to the incident polarization state. Example calculations are performed for a circularly retarding lens.

Mcguire, James P., Jr.↗

Optimal Reward Functions in Distributed Reinforcement Learning

We consider the design of multi-agent systems so as to optimize an overall world utility function when (1) those systems lack centralized communication and control, and (2) each agents runs a distinct Reinforcement Learning (RL) algorithm. A crucial issue in such design problems is to initialize/update each agent's private utility function, so as to induce best possible world utility. Traditional 'team game' solutions to this problem sidestep this issue and simply assign to each agent the world utility as its private utility function. In previous work we used the 'Collective Intelligence' framework to derive a better choice of private utility functions, one that results in world utility performance up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we extend these results. We derive the general class of private utility functions that both are easy for the individual agents to learn and that, if learned well, result in high world utility. We demonstrate experimentally that using these new utility functions can result in significantly improved performance over that of our previously proposed utility, over and above that previous utility's superiority to the conventional team game utility.

Wolpert, David H.↗

Rapid State Space Modeling Tool for Rectangular Wing Aeroservoelastic Studies

This paper introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this paper is on tool presentation, verification, and validation. These processes are carried out in stages throughout the paper. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.

Modeling and Simulation↗

Rapid State Space Modeling Tool for Rectangular Wing Aeroservoelastic Studies

This report introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this report is on tool presentation, verification, and validation. These processes are carried out in stages throughout the report. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.

Verification and Validation↗

A generalized forward fit for neutron detectors with energy-dependent response functions

To date, most analysis of neutron time-of-flight data from inertial confinement fusion experiments has focused on the relatively small range of energies corresponding to the primary neutrons from DD and DT fusion, and have therefore employed instrument response functions (IRF’s) corresponding to monoenergetic 2.45-MeV or 14.03-MeV neutrons. For analysis of time-of-flight signals corresponding to broader ranges of neutron energies, accurate treatment of the data requires the use of an energy-dependent IRF. Here, this work describes interpolation of the IRF for neutrons of arbitrary energy, construction of an energy-dependent IRF, and application of this IRF in a forward fit via matrix multiplication. As an example of the application of this method, an analysis of synthetic data relevant to TT fusion experiments at the Omega Laser Facility is discussed. This example is used to illustrate the differences between a forward fit that uses an energy-dependent IRF and a forward fit that uses a monoenergetic IRF. Use of the energy-dependent IRF is shown to result in accurate inference of the fit parameters of interest.

47 OTHER INSTRUMENTATION↗

Scalable Linked Dynamic Equilibrium (SLiDE)

SLiDE (Scalable Linked Dynamic Equilibrium) replicates the blueNOTE (National Open source Tools for general Equilibrium analysis) datastream from the Wisconsin National Data Consortium. From there, it produces a recursive dynamic computable general equilibrium model of the US states and eventually the global/national economies. The datastream operations have been set up to allow for scalability of both regions and sectors represented. The model has the capability to flexibly define functional forms similar to other general equilibrium model construction software.

Hughes, Caroline↗

A generalized algorithm to design finite field normal basis multipliers

Finite field arithmetic logic is central in the implementation of some error-correcting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the Massey-Omura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.

Wang, C. C.↗

Intrinsic bulk viscosity of the one-component plasma

The intrinsic bulk viscosity of the one-component plasma (OCP) is computed and analyzed using equilibrium molecular dynamics simulations and the Green-Kubo formalism. It is found that bulk viscosity exhibits a maximum at Γ ≈ 1, corresponding to the condition that the average kinetic energy of particles equals the potential energy at the average interparticle spacing. The weakly coupled and strongly coupled limits are analyzed and used to construct a model that captures the full range of coupling strengths simulated: Γ ≈ 10 –2 –10 2 . Simulations are also run of the Yukawa one-component plasma (YOCP) in order to understand the impact of electron screening. It is found that electron screening leads to a smaller bulk viscosity due to a reduction in the excess heat capacity of the system. Bulk viscosity is shown to be at least an order of magnitude smaller than shear viscosity in both the OCP and YOCP. The generalized frequency-dependent bulk viscosity coefficient is also analyzed. This is found to exhibit a peak near twice the plasma frequency in strongly coupled conditions, which is associated with the oscillatory decay observed in the bulk viscosity autocorrelation function. As a result, the generalized shear and bulk viscosity coefficients are found to have a similar magnitude for ω ≳ 2⁢ω p at strongly coupled conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Learning local and semi-local density functionals from exact exchange-correlation potentials and energies

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, attaining general purpose chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functional by using the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN)–based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies and densities. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA on various thermochemistry datasets. These results underscore the promise of using the XC potential in modeling XC functionals and can pave the way for systematic learning of increasingly accurate XC functionals.

Science & Technology - Other Topics↗

Dynamic analysis of the GEOS satellite

The assumed modes method is used to investigate the stability of the GEOS satellite. The system is discretized by representing the continuous displacement by finite series of space-dependent admissible functions multiplied by time-dependent generalized coordinates. The spatial dependence is eliminated by integration over the elastic domains, so that the testing functional reduces to a testing function. The sign properties of the testing function are then tested and the equilibrium defined as nontrivial. In considering the stability of small motions about nontrivial equilibrium, it is shown that if the analysis performed by ignoring the motion of the mass center indicates stability, then the system remains stable if the motion of the mass center is included.

Meirovitch, L.↗

A bivariate gamma probability distribution with application to gust modeling

A five-parameter gamma distribution (BGD) having two shape parameters, two location parameters, and a correlation parameter is investigated. This general BGD is expressed as a double series and as a single series of the modified Bessel function. It reduces to the known special case for equal shape parameters. Practical functions for computer evaluations for the general BGD and for special cases are presented. Applications to wind gust modeling for the ascent flight of the space shuttle are illustrated.

Smith, O. E.↗