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At least 847 records · Page 47

Verification of Numerical Algorithms

The following strategy is suggested for specification and proof: (1) Defer the construction of a formal program specification with respect to I/O assertions unit the correctness of the program with respect to an abstract mathematical model of program intent is demonstrated. (2) Prove that an abstract machine (using infinite precision arithmetic) would compute that object exactly. (3) Prove that the computational sequences of arithmetic operations that occur in the abstract machine must be precisely the same at every step as those occurring on an actual machine (with finite precision arithmetic), executing the same program. (4) Use a Verification Conditions VC-generator that knows about the semantics of arithmetic operations to annotate the program with assertions that bound (or in some circumstances estimate) the difference between the actual machine state variables and the corresponding ones of the abstract machine. Construct the formal program specification by combining the verification conditions into theorems about computational error that can be proved with mechanical assistance.

Source record↗

Use of the VLBI delay observable for orbit determination of Earth-orbiting VLBI satellites

Very long-baseline interferometry (VLBI) observations using a radio telescope in Earth orbit were performed first in the 1980s. Two spacecraft dedicated to VLBI are scheduled for launch in 1995; the primary scientific goals of these missions will be astrophysical in nature. This article addresses the use of space VLBI delay data for the additional purpose of improving the orbit determination of the Earth-orbiting spacecraft. In an idealized case of quasi-simultaneous observations of three radio sources in orthogonal directions, analytical expressions are found for the instantaneous spacecraft position and its error. The typical position error is at least as large as the distance corresponding to the delay measurement accuracy but can be much greater for some geometries. A number of practical considerations, such as system noise and imperfect calibrations, set bounds on the orbit-determination accuracy realistically achievable using space VLBI delay data. These effects limit the spacecraft position accuracy to at least 35 cm (and probably 3 m or more) for the first generation of dedicated space VLBI experiments. Even a 35-cm orbital accuracy would fail to provide global VLBI astrometry as accurate as ground-only VLBI. Recommended charges in future space VLBI missions are unlikely to make space VLBI competitive with ground-only VLBI in global astrometric measurements.

Ulvestad, J. S.↗

Calibration and postlaunch performance of the Meteor 3/TOMS instrument

Prelaunch and postlaunch calibration results for the Meteor 3/total ozone mapping spectrometer (TOMS) instrument are presented here. Ozone amounts are retrieved from measurements of Earth albedo in the 312- to 380-nm range. The accuracy of albedo measurements is primarily tied to knowledge of the reflective properties of diffusers used in the calibrations and to the instrument's wavelength selection. These and other important prelaunch calibrations are presented. Their estimated accuracies are within the bounds necessary to determine column ozone to better than 1%. However, postlaunch validation results indicate some prelaunch calibration uncertainties may be larger than originally estimated. Instrument calibrations have been maintained postlaunch to within a corresponding 1% error in retrieved ozone. Onboard calibrations, including wavelength monitoring and a three-diffuser solar measurement system, are described and specific results are presented. Other issues, such as the effects of orbital precession on calibration and recent chopper wheel malfunctions, are also discussed.

Jaross, G.↗

Precise and Scalable Static Program Analysis of NASA Flight Software

Recent NASA mission failures (e.g., Mars Polar Lander and Mars Orbiter) illustrate the importance of having an efficient verification and validation process for such systems. One software error, as simple as it may be, can cause the loss of an expensive mission, or lead to budget overruns and crunched schedules. Unfortunately, traditional verification methods cannot guarantee the absence of errors in software systems. Therefore, we have developed the CGS static program analysis tool, which can exhaustively analyze large C programs. CGS analyzes the source code and identifies statements in which arrays are accessed out of bounds, or, pointers are used outside the memory region they should address. This paper gives a high-level description of CGS and its theoretical foundations. It also reports on the use of CGS on real NASA software systems used in Mars missions (from Mars PathFinder to Mars Exploration Rover) and on the International Space Station.

Brat, G.↗

Mountain-Top-to-Mountain-Top Optical Link Demonstration

A mountain-top-to-mountain-top optical communications demonstration was conducted between the JPL Table Mountain Facility (TMF), Wrightwood, California, and Strawberry Peak (SP), Lake Arrowhead, California, during the months of August and September of 2000. The link was nearly horizontal at an altitude of 2 km and spanned a range of 46.8 km. A 780-nm multibeam beacon broadcast from TMF was received by the JPL Optical Communications Demonstrator (OCD) located at SP. The received beacon was utilized as a pointing reference to retransmit an 852-nm communications laser beam, modulated at 400 Mb/s by a PN7 pseudo-random bit stream (PRBS) sequence. The long atmospheric path resulted in atmospheric-turbulence-induced angle-of-arrival fluctuations of the beacon at the OCD aperture. A .ne-steering control loop was used to track the resulting beacon centroid motion and update the pointing of the communications laser beam transmitted from SP to TMF. Fried parameters, or r0, inferred from focal spot sizes received at SP were 4 to 5 cm whereas, using the spot sizes received at TMF, they were 2 to 3 cm. In both cases, theory predicts larger r0 values. The predicted angle-of-arrival fluctuations compare well with measured rms displacements exhibited by the focal spots at either end of the link. An uncompensated error of ~1.1 rad in the x-axis and ~2 rad in the y-axis was obtained using centroid data logged by the OCD. Average bit-error rates of 10-5 were recorded for extended periods of time. An atmospheric coherence length r0 of 3 to 5 cm was inferred using the focal-plane spot size measured on the CCD tracking sensor and compared to a predicted value of 5 to 7 cm using reasonable atmospheric models. The irradiance bounds required for the CCD tracking sensor to perform centroiding was found to range from 2000 to 3000 integrated pixel counts, although a more reliable range was 600 to 3000, indicating a dynamic range of 6 to 11 dB. The motion of the spot on the focal plane was also recorded and yielded rms angle-of-arrival-induced focal-plane displacement of 9 to 11 m, compared to a predicted value of 7.8 to 11 m. The irradiance measurements made with the OCD clearly indicate that best tracking performance is obtained when the mean received signal is 2000 to 2200 counts. The best tracking performance resulted in an rms uncompensated error of 1.1 rad. The uncompensated error appeared to increase with either an increase or decrease in mean beacon-signal level. The rms uncompensated error determined by deriving the beacon displacement power spectral density from the beacon centroid-versustime data and the rejection function of the control loop yielded a higher value of 3.4 rad.

Biswas, A.↗

Permutation codes for sources.

Source encoding techniques based on permutation codes are investigated. For a broad class of distortion measures it is shown that optimum encoding of a source permutation code is easy to instrument even for very long block lengths. Also, the nonparametric nature of permutation encoding is well suited to situations involving unknown source statistics. For the squared-error distortion measure a procedure for generating good permutation codes of a given rate and block length is described. The performance of such codes for a memoryless Gaussian source is compared both with the rate-distortion function bound and with the performance of various quantization schemes. The comparison reveals that permutation codes are asymptotically ideal for small rates and perform as well as the best entropy-coded quantizers presently known for intermediate rates. They can be made to compare favorably at high rates, too, provided the coding delay associated with extremely long block lengths is tolerable.

Berger, T.↗

Materials for Ultra‐Coherent, Mobile, Electron‐Spin Qubits

This research project has had the goal of gaining a better understanding of the physics of electrons bound to the surface of superfluid helium from both experimental and theoretical perspectives. It has particularly been aimed at two areas which had not been well studied: the relaxation and decoherence of the spin of the electrons on the helium surface and how the properties of underlying metallic layers affect the behavior of the electrons when the helium covering the metal is thin. This work is motivated in part by interest in using the spin of these electrons as a quantum bit, or qubit. Low levels of decoherence are advantageous for qubits, and moving the electrons, as one might do in a quantum processor, will be easiest if thin helium films can be employed. It had been suggested that spin decoherence should be very weak for electrons bound to superfluid He, but before this work there have been no quantitative studies of spin relaxation and decoherence. It is especially important to know how moving the electrons across the helium surface would affect their spin coherence. Calculations performed as part of this project show that the Rashba effective magnetic field, the mechanism which limits the spin coherence of mobile electrons in silicon-based devices (an actively pursued qubit technology), is exceptionally weak for electrons bound to helium. This project has identified other decoherence mechanisms which are stronger, but still weak compared to analogous silicon-based structures. Calculated spin coherence times for mobile electrons approach one day, as compared to microseconds in silicon. With coherence times of this magnitude, the spin qubit errors on helium will be completely dominated by errors in the quantum gates. In related work, the possibility of using an artificial spin-orbit interaction (a gradient magnetic field) for quantum operations on the electrons spins was considered. The calculations show that a moderate gradient field, small enough to be generated by a narrow superconducting wire, will enable high-fidelity quantum operations on electrons held in lithographically-defined quantum dots by driving them with a microwave electric field. The spin and motional coherence of the electrons is sufficient to allow high-fidelity 2-qubit quantum operations between electrons in neighboring quantum dots. As an outgrowth of experiments aiming to measure electron spin coherence it was discovered that very high densities of electrons can be stably supported on thin helium films coating ultra-smooth amorphous metallic layers. The measured densities are high enough that the electron system has almost certainly transitioned from an ordered array of electrons, known as a Wigner crystal (ordered by the electrons’ mutual repulsion), to a quantum fluid known as a Fermi liquid. This transition has been a subject of intense interest for over 40 years, since the electron Wigner crystal was first observed with electrons bound to superfluid helium, but it has never been unambiguously observed. Experiments are still underway in these new structures to definitively determine whether true quantum melting of the Wigner crystal has been demonstrated. This work has also catalyzed the development of a new approach for measuring the transport of electrons across very thin helium films, as will be needed for some of the quantum computing applications. The high electron density experiments as well as experiments with electrons bound in quantum dots have led to new techniques which may enable spin coherence measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

PUF Entropy

This note discusses aspects of fuzzy extraction: in particular, how the interplay between PUF entropy and the revelation of helper data affects the entropy of the underlying secret. We examine the theory behind a scheme by Dodis et alii to develop exact formulas for the entropy of the given seed, given that an adversary knows the helper data. We also give a simple lower bound on the security of the Dodis scheme that is achieved exactly in many instances. By way of several examples, we quantify the amount of entropy that can be lost due to interactions between imperfect PUF implementations and given error correction methods. We repeatedly show that understanding the details of the error correction scheme and the interaction with the PUF response is crucial to being able to estimate the entropy of the system.

97 MATHEMATICS AND COMPUTING↗

Low-Density Parity-Check Codes as Stable Phases of Quantum Matter

Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose ground-state degeneracy is robust against perturbations in the thermodynamic limit? We prove that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits “check soundness.” Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric-code phases are robust to spatially nonlocal few-body perturbations. Similarly, phases of matter defined by classical codes are stable against symmetric perturbations. In the classical setting, we present improved locality bounds on the quasiadiabatic evolution operator between two nearby states in the same code phase.

quantum error correction↗

Convex Q-Learning in Continuous Time with Application to Dispatch of Distributed Energy Resources

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure. This paper explores algorithm design in the continuous time domain, with a finite-horizon optimal control objective. The main contributions are (i) The new Q-ODE: a model-free characterization of the Hamilton-Jacobi-Bellman equation. (ii) A formulation of Convex Q-learning that avoids approximations appearing in prior work. The Bellman error used in the algorithm is defined by filtered measurements, which is necessary in the presence of measurement noise. (iii) Convex Q-learning with linear function approximation is a convex program. It is shown that the constraint region is bounded, subject to an exploration condition on the training input. (iv) The theory is illustrated in application to resource allocation for distributed energy resources, for which the theory is ideally suited.

Lu, Fan↗

Cumulative hardware distortion effects on coded and uncoded performance via a satellite repeater

An analytical investigation is presented of the cumulative impact of numerous hardware-induced distortions on BPSK bit-error-rate performance. Attention is given to 16 user and eight transponder constraints, as well as to the effect of filter bandlimiting. Uncoded and coded performance is evaluated with respect to both NRZ and Manchester signaling formats, and tight upper bounds to coded and uncoded SNR degradation are determined. Computed results based on TDRSS (Tracking and Data Relay Satellite System) specifications are presented as an example.

Benjamin, T.↗

Bit Error Rate of Coherent M-ary PSK

The bit error rate (BER) for the coherent detection of M-ary PSK signals with Gray code bit mapping is considered. A closed-form expression for the exact BER of M-ary PSK is presented. Tight upper and lower bounds on BER are also obtained for M-ary PSK with larger M.

Lee, P. J.↗

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated that there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implications of the existence of such infinite-gain operators is that: (1) sinusoidal reference inputs at specific frequencies and/or (2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.

Rohrs, C. E.↗

Characterization of the bending stiffness of large space structure joints

A technique for estimating the bending stiffness of large space structure joints is developed and demonstrated for an erectable joint concept. Experimental load-deflection data from a three-point bending test was used as input to solve a closed-form expression for the joint bending stiffness which was derived from linear beam theory. Potential error sources in both the experimental and analytical procedures are identified and discussed. The bending stiffness of a mechanically preloaded erectable joint is studied at three applied moments and seven joint orientations. Using this technique, the joint bending stiffness was bounded between 6 and 17 percent of the bending stiffness of the graphite/epoxy strut member.

Wu, K. Chauncey↗

Theoretical study of the bonding of Nb(2+) to CH2, C2H2, and C2H4

The bonding of Nb(2+) with CH2, C2H2, and C2H4 is studied by using electronic structure calculations that include high levels of electron correlation. The binding energy for NbCH2(2+) is in good agreement with the lower bound determined from the reaction with CH4 but is significantly smaller than the value determined from the binding energy and ionization potential of NbCH2(+). The calculations and a new interpretation of the experiment indicate that the larger value is in error primarily because the ionization potential of NbCH2(+) determined from bracketing charge-exchange reactions is too small. The computed binding energy of NbC2H2(2+) is in good agreement with experiment. The calculations show that the bonding is predominantly covalent in character for both NbCH2(2+) and NbC2H2(2+), whereas for NbC2H4(2+) the electronic states that are predominantly ionic and covalent are nearly degenerate. The trend in binding energies, CH2 greater than C2H2 greater than C2H4, is consistent with the energy required to prepare the ligands for bonding.

Bauschlicher, Charles W., Jr.↗

Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

This paper presents a verifiable model-reference adaptive control method based on an optimal control formulation for linear uncertain systems. A predictor model is formulated to enable a parameter estimation of the system parametric uncertainty. The adaptation is based on both the tracking error and predictor error. Using a singular perturbation argument, it can be shown that the closed-loop system tends to a linear time invariant model asymptotically under an assumption of fast adaptation. A stability margin analysis is given to estimate a lower bound of the time delay margin using a matrix measure method. Using this analytical method, the free design parameter n of the optimal control modification adaptive law can be determined to meet a specification of stability margin for verification purposes.

Nguyen, Nhan T.↗

Symmetrized Drude Oscillator Force Fields Improve Numerical Performance of Polarizable Molecular Dynamics

Drude oscillator potentials are a popular and computationally efficient class of polarizable models that represent each polarizable atom as a positively charged Drude core harmonically bound to a negatively charged Drude shell. Here we show that existing force fields that place all non-Coulomb forces on the Drude core and none on the shell inadvertently couple the dipole to non-Coulombic forces. This introduces errors where interactions with neutral particles can erroneously induce atomic polarization, leading to spurious polarizations in the absence of an electric field, exacerbating violations of equipartition in the employed Carr–Parinello scheme. A suitable symmetrization of the interaction potential that correctly splits the force between the Drude core and shell can correct this shortcoming, improving the stability and numerical performance of Drude oscillator-based simulations. The symmetrization procedure is straightforward and only requires the rescaling of a few force field parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗