A Comparison of Methods for Representing and Aggregating Uncertainties involving Sparsely Sampled Random Variables - Final Results.
Abstract not provided.
Romero, Vicente Jose↗
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Direct Randomized Benchmarking for Multiqubit Devices
Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or “holistic” performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits—we present simulations on 10+ qubits—and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. Here, we show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
RanCompute: Computational Security in Embedded Devices via Random Input and Output Encodings
An embedded device in an insecure environment is subject to additional security risk through capture and reverse-engineering by a capable adversary. If this device contains a microchip performing sensitive computations, capture of the chip may leak functionality to an adversary. In this paper we propose a novel method in which we randomly encode the input operands and the outputs of a computation, thus not revealing the arithmetic operations being performed. The operations are sequenced in a graph representing the overall application. Once the initialization values are overwritten and lost, the results of these computations are indecipherable by the device performing the calculations as well as by any adversary. The result is transmitted back to a secure server which has stored the initialization values and so can decode the results which appear random to the adversary.
Embedded computing↗
Effect of dehydroepiandrosterone administration before in vitro fertilization on the live birth rate in poor ovarian responders according to the Bologna criteria: A randomised controlled trial
Abstract Objective To evaluate the effect of dehydroepiandrosterone (DHEA) pre‐treatment before in vitro fertilization and embryo transfer (IVF‐ET) on the live birth rate in infertile women with poor ovarian response (POR) defined according to the Bologna criteria. Design A randomized, double‐blind, placebo‐controlled trial. Setting Nine reproductive medical centers in China. Population A total of 821 participants with POR defined according to the Bologna criteria were enrolled in the study between April 2016 and December 2018. Methods Eligible participants were randomly assigned to receive either DHEA ( n = 410) or placebo ( n = 411) treatments for 4–12 weeks prior to IVF‐ET, in a 1:1 ratio. Main outcome measures Live birth rate after the first embryo transfer. Results Thirty‐six (8.8%) of 410 women in the DHEA group and 37 (9.0%) of 411 women in the placebo group had a live birth, with no significant difference observed between groups (relative risk, 0.98, 95% CI, 0.63–1.51; p = 0.911). There were no significant differences in the number of retrieved oocytes, and the rates of clinical pregnancy, pregnancy loss, and cumulative live births between the two groups. Conclusions DHEA administration prior to IVF‐ET had no beneficial effect on the live birth rate relative to placebo in women with POR defined according to the Bologna criteria. Tweetable Abstract No benefit was found in poor ovarian responders who received DHEA administration prior to IVF.
Wang, Ze↗
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↗
Linear-scaling implementation of the direct random-phase approximation
We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller–Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10 000 basis functions on a single processor.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The Half Monte Carlo Method: Combining Total Monte Carlo with Nuclear Data Sensitivity Profiles
Both Total Monte Carlo (TMC) and Generalized Linear Least Squares (GLLS) algorithms have been used extensively to perform nuclear uncertainty propagation. Both methods have strengths and weaknesses, for example, the time required to perform TMC limits its attractiveness, while GLLS cannot generate higher order moments of output distributions and also has trouble dealing with nonlinear distributions. This work uses a new method that overcomes many of the aforementioned limitations of TMC and GLLS, while at the same time reasonably reproduces the TMC result. The concept is a simple combination of the two methods i.e., generate the random nuclear data files using the TMC approach, and then propagate the effect on the integral parameters like k{sub eff} using sensitivity coefficients, as opposed to cumbersome neutron transport calculations. Agreement is demonstrated for the Jezebel sphere ICSBEP benchmark. Since the method is part TMC part GLLS, the term Half Monte Method (HMM) will be used.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Masking of a High-Reflectivity Sphere by a Layer with a Random Quasi-Zero Refractive Index
The method of masking of a large-radius sphere made of an arbitrary material by a masking coating with a random quasi-zero refractive index is substantiated theoretically and experimentally. In this method of masking, the sphere is first coated with a mirror layer (e.g., high-reflectivity silver) and then with a masking layer with a thickness much smaller than the radius of the sphere. The fraction of the external radiation intensity bending around the sphere at the points of observation near the surface of the sphere and the extinction cross section of the sphere with the masking coating for points of observation far away from the sphere are calculated. It is shown that extinction cross section Q of the sphere with a masking coating is much smaller than 2D, where D is the geometrical cross section of the sphere; this corresponds to the masking effect for the sphere in the wavelength range of at least 450–1200 nm in the transparency region of the masking coating.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses
Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.
97 MATHEMATICS AND COMPUTING↗
A review of setup error in supine breast radiotherapy using cone-beam computed tomography
Setup error in breast radiotherapy (RT) measured with 3-dimensional cone-beam computed tomography (CBCT) is becoming more common. The purpose of this study is to review the literature relating to the magnitude of setup error in breast RT measured with CBCT. The different methods of image registration between CBCT and planning computed tomography (CT) scan were also explored. A literature search, not limited by date, was conducted using Medline and Google Scholar with the following key words: breast cancer, RT, setup error, and CBCT. This review includes studies that reported on systematic and random errors, and the methods used when registering CBCT scans with planning CT scan. A total of 11 relevant studies were identified for inclusion in this review. The average magnitude of error is generally less than 5 mm across a number of studies reviewed. The common registration methods used when registering CBCT scans with planning CT scan are based on bony anatomy, soft tissue, and surgical clips. No clear relationships between the setup errors detected and methods of registration were observed from this review. Further studies are needed to assess the benefit of CBCT over electronic portal image, as CBCT remains unproven to be of wide benefit in breast RT.
61 RADIATION PROTECTION AND DOSIMETRY↗
Efficacy Endpoints of Radiation Therapy Group Protocol 0247: A Randomized, Phase 2 Study of Neoadjuvant Radiation Therapy Plus Concurrent Capecitabine and Irinotecan or Capecitabine and Oxaliplatin for Patients With Locally Advanced Rectal Cancer
Purpose: To report secondary efficacy endpoints of Radiation Therapy Oncology Group protocol 0247, primary endpoint analysis of which demonstrated that preoperative radiation therapy (RT) with capecitabine plus oxaliplatin achieved a pathologic complete remission prespecified threshold (21%) to merit further study, whereas RT with capecitabine plus irinotecan did not (10%). Methods and Materials: A randomized, phase 2 trial evaluated preoperative RT (50.4 Gy in 1.8-Gy fractions) with 2 concurrent chemotherapy regimens: (1) capecitabine (1200 mg/m{sup 2}/d Monday-Friday) plus irinotecan (50 mg/m{sup 2}/wk × 4); and (2) capecitabine (1650 mg/m{sup 2}/d Monday-Friday) plus oxaliplatin (50 mg/m{sup 2}/wk × 5) for clinical T3 or T4 rectal cancer. Surgery was performed 4 to 8 weeks after chemoradiation, then 4 to 6 weeks later, adjuvant chemotherapy (oxaliplatin 85 mg/m{sup 2}; leucovorin 400 mg/m{sup 2}; 5-fluorouracil 400 mg/m{sup 2}; 5-fluorouracil 2400 mg/m{sup 2}) every 2 weeks × 9. Disease-free survival (DFS) and overall survival (OS) were estimated univariately by the Kaplan-Meier method. Local–regional failure (LRF), distant failure (DF), and second primary failure (SP) were estimated by the cumulative incidence method. No statistical comparisons were made between arms because each was evaluated individually. Results: A total of 104 patients (median age, 57 years) were treated; characteristics were similar for both arms. Median follow-up for RT with capecitabine/irinotecan arm was 3.77 years and for RT with capecitabine/oxaliplatin arm was 3.97 years. Four-year DFS, OS, LRF, DF, and SP estimates for capecitabine/irinotecan arm were 68%, 85%, 16%, 24%, and 2%, respectively. The 4-year DFS, OS, LRF, DF, and SP failure estimates for capecitabine/oxaliplatin arm were 62%, 75%, 18%, 30%, and 6%, respectively. Conclusions: Efficacy results for both arms are similar to other reported studies but suggest that pathologic complete remission is an unsuitable surrogate for traditional survival metrics of clinical outcome. Although it remains uncertain whether the addition of a second cytotoxic agent enhances the effectiveness of fluorouracil plus RT, these results suggest that further study of irinotecan may be warranted.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
Comparing Methods for Assessing Reliability Uncertainty Based on Pass/Fail Data Collected Over Time
In this paper, we compare statistical methods for analyzing pass/fail data collected over time; some methods are traditional and one (the RADAR or Rationale for Assessing Degradation Arriving at Random) was recently developed. These methods are used to provide uncertainty bounds on reliability. We make observations about the methods' assumptions and properties. Finally, we illustrate the differences between two traditional methods, logistic regression and Weibull failure time analysis, and the RADAR method using a numerical example.
97 MATHEMATICS AND COMPUTING↗
Conservative Estimation of Tail Probabilities from Limited Sample Data
Several sparse-sample uncertainty quantification (UQ) methods are compared for conservative but not overly conservative estimation of small tail probabilities involving responses that lay beyond specified thresholds in the tails of probability distributions. Sixteen very differently shaped distributions (or probability density functions, PDFs) and tail probability magnitudes ranging from 10 -5 to 10 -1 are considered in order for the study to be relevant to a wide range of risk analysis and quantification of margins and uncertainty (QMU) problems. The emphasis of the study is on limited data regimes ranging from N = 2 to 20 samples, reflective of most experimental and some expensive computational situations. Relatively simple sparse-sample UQ methods tested for this regime involve statistical tolerance interval "Equivalent Normal and related "Ensemble of Normals" and "Superdistribution (SD) approaches. (The independently derived SD is effectively equivalent to the Bayesian posterior predictive distribution given the assumptions of the derivation.) The performance of the methods was generally improved for N ≥ 5 samples with a generalized Jackknife resampling technique, which determines a tail probability estimate by averaging estimates from smaller sub-samples. Several quantitative metrics for method conservatism and accuracy of tail probability estimation are used to assess and rank the methods' performance over many random trials for each test PDF and probability magnitude. A variant of Bootstrap resampling was also tried, but did not significantly improve tail probability estimates in most cases. Detailed results are presented from over 100-million tests over the above factors that provide useful granular information on which methods or combination of methods perform best in various areas of the factor space.
97 MATHEMATICS AND COMPUTING↗
Simple effective conservative treatment of uncertainty from sparse samples of random functions
This paper examines the variability of predicted responses when multiple stress-strain curves (reflecting variability from replicate material tests) are propagated through a finite element model of a ductile steel can being slowly crushed. Over 140 response quantities of interest (including displacements, stresses, strains, and calculated measures of material damage) are tracked in the simulations. Each response quantity’s behavior varies according to the particular stress-strain curves used for the materials in the model. We desire to estimate response variability when only a few stress-strain curve samples are available from material testing. Propagation of just a few samples will usually result in significantly underestimated response uncertainty relative to propagation of a much larger population that adequately samples the presiding random-function source. A simple classical statistical method, Tolerance Intervals, is tested for effectively treating sparse stress-strain curve data. The method is found to perform well on the highly nonlinear input-to-output response mappings and non-standard response distributions in the can-crush problem. The results and discussion in this paper support a proposition that the method will apply similarly well for other sparsely sampled random variable or function data, whether from experiments or models. Finally, the simple Tolerance Interval method is also demonstrated to be very economical.
36 MATERIALS SCIENCE↗
Upscaling of Regional Scale Transport Under Transient Conditions: Evaluation of the Multirate Mass Transfer Model
Abstract Regional scale transport models are needed to support the long‐term evaluation of groundwater quality and to develop management strategies aiming to prevent serious groundwater degradation. The purpose of this study is to evaluate the capacity of a previously developed upscaling approach to adequately describe the main solute transport processes, including the capture of late‐time tails under changing boundary conditions. Potential factors that impact the performance of upscaling methods, including temporal variations in mass transfer rates and mass distributions, were investigated. Advective‐dispersive contaminant transport in a 3‐D heterogeneous domain was simulated and used as a reference solution. The equivalent transport under homogeneous flow conditions was then evaluated by applying the multirate mass transfer (MRMT) model. The random walk particle tracking method was used to solve the solute transport for heterogeneous and homogeneous MRMT scenarios under steady state and transient conditions. The results indicate that the MRMT model can capture the tails satisfactorily for plumes transported with ambient steady state flow fields at all studied scales using the same parameters. However, when the boundary conditions change in either local, plume, or regional scale, the mass transfer model calibrated for transport under steady state conditions cannot accurately reproduce the tailings observed for the heterogeneous scenario. The deteriorating impacts of transient boundary conditions on the upscaled model are more significant for regions where the flow fields are dramatically affected, which highlights the poor applicability of the MRMT approach for complex field settings. This finding also has implications for the suitability of other potential upscaling approaches.
Guo, Zhilin↗
Designer Earthquakes: methods for creating test signatures
Overview: Creation of the Random Signal; Ensuring Signal Content; Filtering The Signal; Modeling; Method used; Creating a ground motion signal; Adjusting the signal; and, Generating the ASD.
42 ENGINEERING↗
Continued Discussion of Failure Mode Modeling and Overall Component Reliability: Is the Data Missing or Censored?
This paper is a continuation of a paper presented at the 13th Probabilistic Safety Assessment and Management Conference, in which a discussion of modeling failure modes of complex components was presented; see Paulos and Smith (2016). The paper demonstrated how the typical method of treating failure modes as being exponential in nature may yield optimistic predictions when estimating how improvements to components will perform in the real world. Instead of relying on textbook methods, it is more accurate to model the failure modes as a race in time; unfortunately, this does not give a closed-form solution. This work uses a simulation to solve for the model of the world, and is compared to the standard methodology of treating the failure modes as exponential random failures. The standard method is shown to have optimistic predictions, which will lead to prediction errors when failure modes were removed or “fixed.” The failure mode methodology presented in the first paper treated the data as being censored when the test stopped. In this paper, we will compare the results from treating the data as both censored and missing, and comparisons will be shown showing which method is more accurate and under what conditions.
97 MATHEMATICS AND COMPUTING↗
Propagation of partially spatially coherent laser beams in instantaneous Kerr media
The propagation of intense, partially spatially coherent laser beams in a medium with instantaneous third-order susceptibility is studied analytically and numerically. For sufficiently high power relative to that required for nonlinear self-focusing, the propagation initially proceeds in two stages. In the first stage, spatial coherence builds up, and in the second stage, the number of speckles reduces. Once the degree of coherence is sufficiently high, whole-beam self-focusing occurs. The beam power is mostly confined within the initial spot radius. Two analytical approaches for describing the evolution of the beam are presented. The method of moments leads to an analytical solution for the rms spot radius that is in excellent agreement with simulations. This method does not require any knowledge of the field statistics beyond the initial conditions and provides no information about the evolution of the individual speckles. The other approach employs a self-similar solution for the second-order coherence function of the field and assumes that the fourth-order coherence function is factorizable and obeys complex circular Gaussian random statistics. The latter method also leads to an analytical expression for the spot radius, but its predictions for the qualitative evolution of the speckles disagree with wave-optics simulations.
lasers↗