Galaxy Correlation Functions Provide a More Robust Cosmological Standard Ruler
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The scalability of quantum networking will benefit from quantum and classical communications coexisting in shared fibers, the main challenge being spontaneous Raman scattering noise. We investigate the coexistence of multi-channel O-band quantum and C-band classical communications. We characterize multiple narrowband entangled photon pair channels across 1282 nm-1318 nm co-propagating over 48 km of installed standard fiber with record C-band power (>18 dBm) and demonstrate that some quantum-classical wavelength combinations significantly outperform others. We analyze the Raman noise spectrum, optimal wavelength engineering, multi-photon pair emission in entangled photon-classical coexistence, and evaluate the implications for future quantum applications.
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Purpose: Robust optimization leads to intensity-modulated proton therapy (IMPT) plans that are less sensitive to uncertainties and superior in terms of organs-at-risk (OARs) sparing, target dose coverage, and homogeneity compared to planning target volume (PTV)-based optimized plans. Robust optimization incorporates setup and range uncertainties, which implicitly adds margins to both targets and OARs and is also able to compensate for perturbations in dose distributions within targets and OARs caused by uncertainties. In contrast, the traditional PTV-based optimization considers only setup uncertainties and adds a margin only to targets but no margins to the OARs. It also ignores range uncertainty. The purpose of this work is to determine if robustly optimized plans are superior to PTV-based plans simply because the latter do not assign margins to OARs during optimization. Methods: The authors retrospectively selected from their institutional database five patients with head and neck (H and N) cancer and one with prostate cancer for this analysis. Using their original images and prescriptions, the authors created new IMPT plans using three methods: PTV-based optimization, optimization based on the PTV and planning risk volumes (PRVs) (i.e., 'PTV+PRV-based optimization'), and robust optimization using the 'worst-case' dose distribution. The PRVs were generated by uniformly expanding OARs by 3 mm for the H and N cases and 5 mm for the prostate case. The dose-volume histograms (DVHs) from the worst-case dose distributions were used to assess and compare plan quality. Families of DVHs for each uncertainty for all structures of interest were plotted along with the nominal DVHs. The width of the 'bands' of DVHs was used to quantify the plan sensitivity to uncertainty. Results: Compared with conventional PTV-based and PTV+PRV-based planning, robust optimization led to a smaller bandwidth for the targets in the face of uncertainties {l_brace}clinical target volume [CTV] bandwidth: 0.59 [robust], 3.53 [PTV+PRV], and 3.53 [PTV] Gy (RBE){r_brace}. It also resulted in higher doses to 95% of the CTV {l_brace}D{sub 95%}: 60.8 [robust] vs 59.3 [PTV+PRV] vs 59.6 [PTV] Gy (RBE){r_brace}, smaller D{sub 5%} (doses to 5% of the CTV) minus D{sub 95%} {l_brace}D{sub 5%}- D{sub 95%}: 13.2 [robust] vs 17.5 [PTV+PRV] vs 17.2 [PTV] Gy (RBE){r_brace}. At the same time, the robust optimization method irradiated OARs less {l_brace}maximum dose to 1 cm{sup 3} of the brainstem: 48.3 [robust] vs 48.8 [PTV+PRV] vs 51.2 [PTV] Gy (RBE); mean dose to the oral cavity: 22.3 [robust] vs 22.9 [PTV+PRV] vs 26.1 [PTV] Gy (RBE); maximum dose to 1% of the normal brain: 66.0 [robust] vs 68.0 [PTV+PRV] vs 69.3 [PTV] Gy (RBE){r_brace}. Conclusions: For H and N cases studied, OAR sparing in PTV+PRV-based optimization was inferior compared to robust optimization but was superior compared to PTV-based optimization; however, target dose robustness and homogeneity were comparable in the PTV+PRV-based and PTV-based optimizations. The same pattern held for the prostate case. The authors' data suggest that the superiority of robust optimization is not due simply to its inclusion of margins for OARs, but that this is due mainly to the ability of robust optimization to compensate for perturbations in dose distributions within target volumes and normal tissues caused by uncertainties.
Purpose: To develop a new robust optimization strategy for intensity-modulated proton therapy as an important step in translating robust proton treatment planning from research to clinical applications. Methods: In selective robust optimization, a worst-case-based robust optimization algorithm is extended, and terms of the objective function are selectively computed from either the worst-case dose or the nominal dose. Two lung cancer cases and one head and neck cancer case were used to demonstrate the practical significance of the proposed robust planning strategy. The lung cancer cases had minimal tumor motion less than 5 mm, and, for the demonstration of the methodology, are assumed to be static. Results: Selective robust optimization achieved robust clinical target volume (CTV) coverage and at the same time increased nominal planning target volume coverage to 95.8%, compared to the 84.6% coverage achieved with CTV-based robust optimization in one of the lung cases. In the other lung case, the maximum dose in selective robust optimization was lowered from a dose of 131.3% in the CTV-based robust optimization to 113.6%. Selective robust optimization provided robust CTV coverage in the head and neck case, and at the same time improved controls over isodose distribution so that clinical requirements may be readily met. Conclusions: Selective robust optimization may provide the flexibility and capability necessary for meeting various clinical requirements in addition to achieving the required plan robustness in practical proton treatment planning settings.
Abstract Critical point tracking is a core topic in scientific visualization for understanding the dynamic behaviour of time‐varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural stability of critical points, that is, the robustness of a critical point is the minimum amount of perturbation to the vector field necessary to cancel it. A theoretical basis has been established previously that relates critical point tracking with the notion of robustness, in particular, critical points could be tracked based on their closeness in stability, measured by robustness, instead of just distance proximity within the domain. However, in practice, the computation of classic robustness may produce artifacts when a critical point is close to the boundary of the domain; thus, we do not have a complete picture of the vector field behaviour within its local neighbourhood. To alleviate these issues, we introduce a multilevel robustness framework for the study of 2D time‐varying vector fields. We compute the robustness of critical points across varying neighbourhoods to capture the multiscale nature of the data and to mitigate the boundary effect suffered by the classic robustness computation. We demonstrate via experiments that such a new notion of robustness can be combined seamlessly with existing feature tracking algorithms to improve the visual interpretability of vector fields in terms of feature tracking, selection and comparison for large‐scale scientific simulations. We observe, for the first time, that the minimum multilevel robustness is highly correlated with physical quantities used by domain scientists in studying a real‐world tropical cyclone dataset. Such an observation helps to increase the physical interpretability of robustness.
Purpose: In left-sided tangential breast intensity modulated radiation therapy (IMRT), the heart may enter the radiation field and receive excessive radiation while the patient is breathing. The patient’s breathing pattern is often irregular and unpredictable. We verify the clinical applicability of a heart-sparing robust optimization approach for breast IMRT. We compare robust optimized plans with clinical plans at free-breathing and clinical plans at deep inspiration breath-hold (DIBH) using active breathing control (ABC). Methods: Eight patients were included in the study with each patient simulated using 4D-CT. The 4D-CT image acquisition generated ten breathing phase datasets. An average scan was constructed using all the phase datasets. Two of the eight patients were also imaged at breath-hold using ABC. The 4D-CT datasets were used to calculate the accumulated dose for robust optimized and clinical plans based on deformable registration. We generated a set of simulated breathing probability mass functions, which represent the fraction of time patients spend in different breathing phases. The robust optimization method was applied to each patient using a set of dose-influence matrices extracted from the 4D-CT data and a model of the breathing motion uncertainty. The goal of the optimization models was to minimize the dose to the heart while ensuring dose constraints on the target were achieved under breathing motion uncertainty. Results: Robust optimized plans were improved or equivalent to the clinical plans in terms of heart sparing for all patients studied. The robust method reduced the accumulated heart dose (D10cc) by up to 801 cGy compared to the clinical method while also improving the coverage of the accumulated whole breast target volume. On average, the robust method reduced the heart dose (D10cc) by 364 cGy and improved the optBreast dose (D99%) by 477 cGy. In addition, the robust method had smaller deviations from the planned dose to the accumulated dose. The deviation of the accumulated dose from the planned dose for the optBreast (D99%) was 12 cGy for robust versus 445 cGy for clinical. The deviation for the heart (D10cc) was 41 cGy for robust and 320 cGy for clinical. Conclusions: The robust optimization approach can reduce heart dose compared to the clinical method at free-breathing and can potentially reduce the need for breath-hold techniques.
Purpose: To develop a 4DCT robust optimization method to reduce the dosimetric impact from respiratory motion in intensity modulated proton therapy (IMPT) for esophageal cancer. Methods: Four esophageal cancer patients were selected for this study. The different phases of CT from a set of 4DCT were incorporated into the worst-case dose distribution robust optimization algorithm. 4DCT robust treatment plans were designed and compared with the conventional non-robust plans. Result doses were calculated on the average and maximum inhale/exhale phases of 4DCT. Dose volume histogram (DVH) band graphic and ΔD95%, ΔD98%, ΔD5%, ΔD2% of CTV between different phases were used to evaluate the robustness of the plans. Results: Compare to the IMPT plans optimized using conventional methods, the 4DCT robust IMPT plans can achieve the same quality in nominal cases, while yield a better robustness to breathing motion. The mean ΔD95%, ΔD98%, ΔD5% and ΔD2% of CTV are 6%, 3.2%, 0.9% and 1% for the robustly optimized plans vs. 16.2%, 11.8%, 1.6% and 3.3% from the conventional non-robust plans. Conclusion: A 4DCT robust optimization method was proposed for esophageal cancer using IMPT. We demonstrate that the 4DCT robust optimization can mitigate the dose deviation caused by the diaphragm motion.
It is the purpose of this study to develop an economical Robust design methodology for microscale secondary flow control in compact inlet diffusers. To illustrate the potential of economical Robust Design methodology, two different mission strategies were considered for the subject inlet, namely Maximum Performance and Maximum HCF Life Expectancy. The Maximum Performance mission maximized total pressure recovery while the Maximum HCF Life Expectancy mission minimized the mean of the first five Fourier harmonic amplitudes, i.e., 'collectively' reduced all the harmonic 1/2 amplitudes of engine face distortion. Each of the mission strategies was subject to a low engine face distortion constraint, i.e., DC60<0.10, which is a level acceptable for commercial engines. For each of these missions strategies, an 'Optimal Robust' (open loop control) and an 'Optimal Adaptive' (closed loop control) installation was designed over a twenty degree angle-of-incidence range. The Optimal Robust installation used economical Robust Design methodology to arrive at a single design which operated over the entire angle-of-incident range (open loop control). The Optimal Adaptive installation optimized all the design parameters at each angle-of-incidence. Thus, the Optimal Adaptive installation would require a closed loop control system to sense a proper signal for each effector and modify that effector device, whether mechanical or fluidic, for optimal inlet performance. In general, the performance differences between the Optimal Adaptive and Optimal Robust installation designs were found to be marginal. This suggests, however, that Optimal Robust open loop installation designs can be very competitive with Optimal Adaptive close loop designs. Secondary flow control in inlets is inherently robust, provided it is optimally designed. Therefore, the new methodology presented in this paper, combined array 'Lower Order' approach to Robust DOE, offers the aerodynamicist a very viable and economical way of exploring the concept of Robust inlet design, where the mission variables are brought directly into the inlet design process and insensitivity or robustness to the mission variables becomes a design objective.
Purpose: The purpose of this study was to compare the impact of uncertainties and interplay on 3-dimensional (3D) and 4D robustly optimized intensity modulated proton therapy (IMPT) plans for lung cancer in an exploratory methodology study. Methods and Materials: IMPT plans were created for 11 nonrandomly selected non-small cell lung cancer (NSCLC) cases: 3D robustly optimized plans on average CTs with internal gross tumor volume density overridden to irradiate internal target volume, and 4D robustly optimized plans on 4D computed tomography (CT) to irradiate clinical target volume (CTV). Regular fractionation (66 Gy [relative biological effectiveness; RBE] in 33 fractions) was considered. In 4D optimization, the CTV of individual phases received nonuniform doses to achieve a uniform cumulative dose. The root-mean-square dose-volume histograms (RVH) measured the sensitivity of the dose to uncertainties, and the areas under the RVH curve (AUCs) were used to evaluate plan robustness. Dose evaluation software modeled time-dependent spot delivery to incorporate interplay effect with randomized starting phases of each field per fraction. Dose-volume histogram (DVH) indices comparing CTV coverage, homogeneity, and normal tissue sparing were evaluated using Wilcoxon signed rank test. Results: 4D robust optimization plans led to smaller AUC for CTV (14.26 vs 18.61, respectively; P=.001), better CTV coverage (Gy [RBE]) (D{sub 95%} CTV: 60.6 vs 55.2, respectively; P=.001), and better CTV homogeneity (D{sub 5%}-D{sub 95%} CTV: 10.3 vs 17.7, resspectively; P=.002) in the face of uncertainties. With interplay effect considered, 4D robust optimization produced plans with better target coverage (D{sub 95%} CTV: 64.5 vs 63.8, respectively; P=.0068), comparable target homogeneity, and comparable normal tissue protection. The benefits from 4D robust optimization were most obvious for the 2 typical stage III lung cancer patients. Conclusions: Our exploratory methodology study showed that, compared to 3D robust optimization, 4D robust optimization produced significantly more robust and interplay-effect-resistant plans for targets with comparable dose distributions for normal tissues. A further study with a larger and more realistic patient population is warranted to generalize the conclusions.
Purpose: We compared conventionally optimized intensity-modulated proton therapy (IMPT) treatment plans against the worst-case robustly optimized treatment plans for lung cancer. The comparison of the two IMPT optimization strategies focused on the resulting plans' ability to retain dose objectives under the influence of patient set-up, inherent proton range uncertainty, and dose perturbation caused by respiratory motion. Methods: For each of the 9 lung cancer cases two treatment plans were created accounting for treatment uncertainties in two different ways: the first used the conventional Method: delivery of prescribed dose to the planning target volume (PTV) that is geometrically expanded from the internal target volume (ITV). The second employed the worst-case robust optimization scheme that addressed set-up and range uncertainties through beamlet optimization. The plan optimality and plan robustness were calculated and compared. Furthermore, the effects on dose distributions of the changes in patient anatomy due to respiratory motion was investigated for both strategies by comparing the corresponding plan evaluation metrics at the end-inspiration and end-expiration phase and absolute differences between these phases. The mean plan evaluation metrics of the two groups were compared using two-sided paired t-tests. Results: Without respiratory motion considered, we affirmed that worst-case robust optimization is superior to PTV-based conventional optimization in terms of plan robustness and optimality. With respiratory motion considered, robust optimization still leads to more robust dose distributions to respiratory motion for targets and comparable or even better plan optimality [D95% ITV: 96.6% versus 96.1% (p=0.26), D5% - D95% ITV: 10.0% versus 12.3% (p=0.082), D1% spinal cord: 31.8% versus 36.5% (p =0.035)]. Conclusion: Worst-case robust optimization led to superior solutions for lung IMPT. Despite of the fact that robust optimization did not explicitly account for respiratory motion it produced motion-resistant treatment plans. However, further research is needed to incorporate respiratory motion into IMPT robust optimization.
Purpose: Lack of plan robustness may contribute to local failure in volumetric-modulated arc therapy (VMAT) to treat head and neck (H&N) cancer. Thus we compared plan robustness of VMAT with intensity-modulated radiation therapy (IMRT). Methods: VMAT and IMRT plans were created for 9 H&N cancer patients. For each plan, six new perturbed dose distributions were computed — one each for ± 3mm setup deviations along the S-I, A-P and L-R directions. We used three robustness quantification tools: (1) worst-case analysis (WCA); (2) dose-volume histograms (DVHs) band (DVHB); and (3) root-mean-square-dose deviation (RMSD) volume histogram (DDVH). DDVH represents the relative volume (y) on the vertical axis and the RMSD (x) on the horizontal axis. Similar to DVH, this means that y% of the volume of the indicated structure has the RMSD at least x Gy[RBE].The width from the first two methods at different target DVH indices (such as D95 and D5) and the area under the DDVH curves (AUC) for the target were used to indicate plan robustness. In these robustness quantification tools, the smaller the value, the more robust the plan is. Plan robustness evaluation metrics were compared using Wilcoxon test. Results: DVHB showed the width at D95 from IMRT to be larger than from VMAT (unit Gy) [1.59 vs 1.18 (p=0.49)], while the width at D5 from IMRT was found to be slightly larger than from VMAT [0.59 vs 0.54 (p=0.84)]. WCA showed similar results [D95: 3.28 vs 3.00 (p=0.56); D5: 1.68 vs 1.95 (p=0.23)]. DDVH showed the AUC from IMRT to be slightly smaller than from VMAT [1.13 vs 1.15 (p=0.43)]. Conclusion: VMAT plan robustness is comparable to IMRT plan robustness. The plan robustness conclusions from WCA and DVHB are DVH parameter dependent. On the other hand DDVH captures the overall effect of uncertainties on the dose to a volume of interest. NIH/NCI K25CA168984; Eagles Cancer Research Career Development; The Lawrence W. and Marilyn W. Matteson Fund for Cancer Research Mayo ASU Seed Grant; The Kemper Marley Foundation.
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Stochastic robustness, a simple technique used to estimate the robustness of linear, time-invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters is discussed. The application of stochastic performance robustness and the relationship between performance objectives and design parameters are demonstrated by means of the example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
The dramatic increase of renewable energy resources in recent years, together with the long-existing load forecast errors and increasingly involved price sensitive demands, has introduced significant uncertainties into power systems operation. In order to guarantee the operational security of power systems with such uncertainties, robust optimization has been extensively studied in security-constrained unit commitment (SCUC) problems, for immunizing the system against worst uncertainty realizations. However, traditional robust SCUC models with single-band uncertainty sets may yield over-conservative solutions in most cases. This paper proposes a multi-band robust model to accurately formulate various uncertainties with higher resolution. By properly tuning band intervals and weight coefficients of individual bands, the proposed multi-band robust model can rigorously and realistically reflect spatial/temporal relationships and asymmetric characteristics of various uncertainties, and in turn could effectively leverage the tradeoff between robustness and economics of robust SCUC solutions. The proposed multi-band robust SCUC model is solved by Benders decomposition (BD) and outer approximation (OA), while taking the advantage of integral property of the proposed multi-band uncertainty set. In addition, several accelerating techniques are developed for enhancing the computational performance and the convergence speed. Numerical studies on a 6-bus system and the modified IEEE 118-bus system verify the effectiveness of the proposed robust SCUC approach for enhancing uncertainty modeling capabilities and mitigating conservativeness of the robust SCUC solution.