Approximation of expectation values
Approximation of expectation values by perturbation theory
PERTURBATION THEORY↗
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Approximation of expectation values.
Approximation of expectation values for nonenergy properties via perturbation theory, obtaining values for molecular polarizability
POLARIZATION CHARACTERISTICS↗
Effects of expected-value information and display format on recognition of aircraft subsystem abnormalities
This study identifies improved methods to present system parameter information for detecting abnormal conditions and to identify system status. Two workstation experiments were conducted. The first experiment determined if including expected-value-range information in traditional parameter display formats affected subject performance. The second experiment determined if using a nontraditional parameter display format, which presented relative deviation from expected value, was better than traditional formats with expected-value ranges included. The inclusion of expected-value-range information onto traditional parameter formats was found to have essentially no effect. However, subjective results indicated support for including this information. The nontraditional column deviation parameter display format resulted in significantly fewer errors compared with traditional formats with expected-value-ranges included. In addition, error rates for the column deviation parameter display format remained stable as the scenario complexity increased, whereas error rates for the traditional parameter display formats with expected-value ranges increased. Subjective results also indicated that the subjects preferred this new format and thought that their performance was better with it. The column deviation parameter display format is recommended for display applications that require rapid recognition of out-of-tolerance conditions, especially for a large number of parameters.
Palmer, Michael T.↗
On Expected Value Strong Controllability
The Probabilistic Simple Temporal Network (PSTN) generalizes Simple Temporal Networks with Uncertainty (STNUs) by introducing probability distributions over the timing of uncontrollable timepoints. PSTNs are controllable if there is a strategy to execute the controllable timepoints while bounding the risk of violating any constraint to a small value. If this risk bound can't be satisfied, PSTNs are not considered controllable. We introduce the Expected Value Probabilistic SimpleTemporal Network (EPSTN), which extends PSTNs by including a benefit to the satisfaction of temporal constraints. We study the problem of Expected Value Strong Controllability (EvSC) of EPSTNs, which seeks a schedule maximizing the expected value of satisfied constraints. We solve the EvSC problem by extending a previously developed linear program, combined with search over constraints to violate at execution time. We describe conditions under which the solution to this linear program is the maximum expected value schedule. We then show how to search for constraints to discard, using the linear program at the core of the search. While the general problem is shown to be exponential, we conclude by providing several methods to bound the complexity of search.
Planning↗
Human versus automation in responding to failures: an expected-value analysis
A simple analytical criterion is provided for deciding whether a human or automation is best for a failure detection task. The method is based on expected-value decision theory in much the same way as is signal detection. It requires specification of the probabilities of misses (false negatives) and false alarms (false positives) for both human and automation being considered, as well as factors independent of the choice--namely, costs and benefits of incorrect and correct decisions as well as the prior probability of failure. The method can also serve as a basis for comparing different modes of automation. Some limiting cases of application are discussed, as are some decision criteria other than expected value. Actual or potential applications include the design and evaluation of any system in which either humans or automation are being considered.
NASA Discipline Space Human Factors↗
Improvement of uncoupled Hartree-Fock expectation values for physical properties.
Improving uncoupled Hartree-Fock expectation values for atomic and molecular properties
HARTREE-FOCK CALCULATION↗
Optimization of slowly-varying systems by minimization of the expected value of a quadratic performance index.
Algorithm for minimizing expected value of quadratic performance index in closed loop optimal control of linear time varying systems.
H D'Angelo↗
Improvement of uncoupled Hartree-Fock expectation values for physical properties, II
Improvement of uncoupled Hartree-Fock expectation values for physical properties
EXPECTANCY HYPOTHESIS↗
Eigenvalues and certain expectation values for all bound and quasibound levels of ground state /X /1 Sigma g plus// H2, HD and D2
Expectation values and kinetic energy for vibrational-rotational levels of ground states of H2, HD, and D2
Le Roy, R. J.↗
Provable bounds for noise-free expectation values computed from noisy samples
Quantum computing has emerged as a powerful computational paradigm capable of solving problems beyond the reach of classical computers. However, today’s quantum computers are noisy, posing challenges to obtaining accurate results. Here, we explore the impact of noise on quantum computing, focusing on the challenges in sampling bit strings from noisy quantum computers and the implications for optimization and machine learning. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the conditional value at risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on real quantum computers involving up to 127 qubits. The results show strong alignment with theoretical predictions.
97 MATHEMATICS AND COMPUTING↗
Coding for Parallel Links to Maximize the Expected Value of Decodable Messages
When multiple parallel communication links are available, it is useful to consider link-utilization strategies that provide tradeoffs between reliability and throughput. Interesting cases arise when there are three or more available links. Under the model considered, the links have known probabilities of being in working order, and each link has a known capacity. The sender has a number of messages to send to the receiver. Each message has a size and a value (i.e., a worth or priority). Messages may be divided into pieces arbitrarily, and the value of each piece is proportional to its size. The goal is to choose combinations of messages to send on the links so that the expected value of the messages decodable by the receiver is maximized. There are three parts to the innovation: (1) Applying coding to parallel links under the model; (2) Linear programming formulation for finding the optimal combinations of messages to send on the links; and (3) Algorithms for assisting in finding feasible combinations of messages, as support for the linear programming formulation. There are similarities between this innovation and methods developed in the field of network coding. However, network coding has generally been concerned with either maximizing throughput in a fixed network, or robust communication of a fixed volume of data. In contrast, under this model, the throughput is expected to vary depending on the state of the network. Examples of error-correcting codes that are useful under this model but which are not needed under previous models have been found. This model can represent either a one-shot communication attempt, or a stream of communications. Under the one-shot model, message sizes and link capacities are quantities of information (e.g., measured in bits), while under the communications stream model, message sizes and link capacities are information rates (e.g., measured in bits/second). This work has the potential to increase the value of data returned from spacecraft under certain conditions.
Klimesh, Matthew A.↗
Methods, systems, and apparatuses for calculating global fluence for neutron and photon monte carlo transport using expected value estimators
Global fluence estimators may be calculated on accelerators and processors for neutron and photon Monte Carlo transport. Monte Carlo random walk simulation may be performed on the processors and the calculation of a Volumetric-Ray-Casting (VRC) estimator may be offloaded to the accelerators. The VRC estimator may modify an expected-value estimator to extend a pseudo-particle ray along the direction of the emitted particle from source and collision event through not only the event volume, but also through all volumes that describe the problem geometry. Additionally, many pseudo-particle rays may be sampled per event, rather than just a single pseudo-particle ray per event, in order to provide more complete angular coverage.
Sweezy, Jeremy Ed↗
Time correlations from steady-state expectation values
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.
Górecki, Wojciech [INFN, Pavia]↗
Time correlations from steady-state expectation values
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.
Górecki, Wojciech [INFN, Pavia]↗
Time Correlations from Steady-State Expectation Values
Recovering properties of correlation functions is typically challenging. On the one hand, experimentally, it requires measurements with a temporal resolution finer than the system’s dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a system parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable, and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to the experimental characterization of ultrafast systems and to the theoretical analysis of many-body models whose dynamics are hard to compute.
Górecki, Wojciech [INFN, Pavia] (ORCID:00000001991↗
Computation of the expectation value of the spin operator S^ 2 for the spin-flip Bethe–Salpeter equation
Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator S^ 2 . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of S^ 2 may be found to differ from 2.00; this difference is called 'spin contamination'. The expectation values S^ 2 must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Here, our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for S^ 2 as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating S^ 2 , we present the derivation for the general equation for computing S^ 2 with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Beyond Expected Values Evolving Metrics for Resource Adequacy Assessment
Resource adequacy analysis quantifies the likelihood of capacity shortfall on a power system in a probabilistic manner. Using a combination of statistical techniques and power system fundamentals, the analysis typically evaluates hundreds or thousands of stochastic random samples (replications) of varying load, generator outages, variable renewable energy availability, and other aspects of power system uncertainty. In this range of uncertainty, there are - at times - periods where the power system's available resources are insufficient to meet system demand, referred to as a shortfall event. Today's power systems' rapidly evolving generation mix is changing the types of data needed by system planners and regulators, which can often render traditional resource adequacy metrics insufficient for ensuring resource adequacy for tomorrow's grid. In this paper we provide a critical assessment of traditional measures of shortfall risk in power systems, discussing their shortcomings and how they compare to metrics used in other domains. From this analysis we propose four steps forward for improving power system resource adequacy risk metrics in the future.
ENERGY PLANNING, POLICY, AND ECONOMY↗
BPS fivebrane stars. Part I. Expectation values of observables
We study ensembles of 1/2-BPS bound states of fundamental strings and NS-fivebranes (NS5-F1 states) in the AdS decoupling limit. We revisit a solution corresponding to an ensemble average of these bound states, and find that the appropriate duality frame for describing the near-source structure is the T-dual NS5-P frame, where the bound state is a collection of momentum waves on the fivebranes. We find that the fivebranes are generically well-separated; this property results in the applicability of perturbative string theory. The geometry sourced by the typical microstate is not close to that of an extremal non-rotating black hole; instead the fivebranes occupy a ball whose radius is parametrically much larger than the “stretched horizon” scale of the corresponding black hole. These microstates are thus better characterized as BPS fivebrane stars than as small black holes.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗