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At least 883 records · Page 49

A method to estimate the effect of deformable image registration uncertainties on daily dose mapping

Purpose: To develop a statistical sampling procedure for spatially-correlated uncertainties in deformable image registration and then use it to demonstrate their effect on daily dose mapping. Methods: Sequential daily CT studies are acquired to map anatomical variations prior to fractionated external beam radiotherapy. The CTs are deformably registered to the planning CT to obtain displacement vector fields (DVFs). The DVFs are used to accumulate the dose delivered each day onto the planning CT. Each DVF has spatially-correlated uncertainties associated with it. Principal components analysis (PCA) is applied to measured DVF error maps to produce decorrelated principal component modes of the errors. The modes are sampled independently and reconstructed to produce synthetic registration error maps. The synthetic error maps are convolved with dose mapped via deformable registration to model the resulting uncertainty in the dose mapping. The results are compared to the dose mapping uncertainty that would result from uncorrelated DVF errors that vary randomly from voxel to voxel. Results: The error sampling method is shown to produce synthetic DVF error maps that are statistically indistinguishable from the observed error maps. Spatially-correlated DVF uncertainties modeled by our procedure produce patterns of dose mapping error that are different from that due to randomly distributed uncertainties. Conclusions: Deformable image registration uncertainties have complex spatial distributions. The authors have developed and tested a method to decorrelate the spatial uncertainties and make statistical samples of highly correlated error maps. The sample error maps can be used to investigate the effect of DVF uncertainties on daily dose mapping via deformable image registration. An initial demonstration of this methodology shows that dose mapping uncertainties can be sensitive to spatial patterns in the DVF uncertainties.

61 RADIATION PROTECTION AND DOSIMETRY↗

PERIODOGRAMS FOR MULTIBAND ASTRONOMICAL TIME SERIES

This paper introduces the multiband periodogram, a general extension of the well-known Lomb–Scargle approach for detecting periodic signals in time-domain data. In addition to advantages of the Lomb–Scargle method such as treatment of non-uniform sampling and heteroscedastic errors, the multiband periodogram significantly improves period finding for randomly sampled multiband light curves (e.g., Pan-STARRS, DES, and LSST). The light curves in each band are modeled as arbitrary truncated Fourier series, with the period and phase shared across all bands. The key aspect is the use of Tikhonov regularization which drives most of the variability into the so-called base model common to all bands, while fits for individual bands describe residuals relative to the base model and typically require lower-order Fourier series. This decrease in the effective model complexity is the main reason for improved performance. After a pedagogical development of the formalism of least-squares spectral analysis, which motivates the essential features of the multiband model, we use simulated light curves and randomly subsampled SDSS Stripe 82 data to demonstrate the superiority of this method compared to other methods from the literature and find that this method will be able to efficiently determine the correct period in the majority of LSST’s bright RR Lyrae stars with as little as six months of LSST data, a vast improvement over the years of data reported to be required by previous studies. A Python implementation of this method, along with code to fully reproduce the results reported here, is available on GitHub.

79 ASTRONOMY AND ASTROPHYSICS↗

Prophylaxis of Radiation-Induced Nausea and Vomiting Using 5-Hydroxytryptamine-3 Serotonin Receptor Antagonists: A Systematic Review of Randomized Trials

Purpose: To systematically review the effectiveness and safety of 5-hydroxytryptamine-3 receptor antagonists (5-HT3 RAs) compared with other antiemetic medication or placebo for prophylaxis of radiation-induced nausea and vomiting. Methods and Materials: We searched the following electronic databases: MEDLINE, Embase, the Cochrane Central Register of Controlled Clinical Trials, and Web of Science. We also hand-searched reference lists of included studies. Randomized, controlled trials that compared a 5-HT3 RA with another antiemetic medication or placebo for preventing radiation-induced nausea and vomiting were included. We excluded studies recruiting patients receiving concomitant chemotherapy. When appropriate, meta-analysis was conducted using Review Manager (v5) software. Relative risks were calculated using inverse variance as the statistical method under a random-effects model. We assessed the quality of evidence by outcome using the Grading of Recommendations Assessment, Development, and Evaluation approach. Results: Eligibility screening of 47 articles resulted in 9 included in the review. The overall methodologic quality was moderate. Meta-analysis of 5-HT3 RAs vs. placebo showed significant benefit for 5-HT3 RAs (relative risk [RR] 0.70; 95% confidence interval [CI] 0.57-0.86 for emesis; RR 0.84, 95% CI 0.73-0.96 for nausea). Meta-analysis comparing 5-HT3 RAs vs. metoclopramide showed a significant benefit of the 5-HT3 RAs for emetic control (RR 0.27, 95% CI 0.15-0.47). Conclusion: 5-Hydroxytryptamine-3 RAs are superior to placebo and other antiemetics for prevention of emesis, but little benefit was identified for nausea prevention. 5-Hydroxytryptamine-3 RAs are suggested for prevention of emesis. Limited evidence was found regarding delayed emesis, adverse events, quality of life, or need for rescue medication. Future randomized, controlled trials should evaluate different 5-HT3 antiemetics and new agents with novel mechanisms of action such at the NK{sub 1} receptor antagonists to determine the most effective drug. Delayed nausea and vomiting should be a focus of future study, perhaps concentrating on the palliative cancer population.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Rapid Electrochemical Diagnosis of Battery Health and Safety from Cells to Modules

Rapid electrochemical diagnosis of battery health and failure is critical for ensuring reliable battery performance and battery safety. Traditional battery health diagnostics such as capacity measurements and DC pulse tests are reliable and well-understood, however, these measurements of battery capacity and resistance do not capture all aspects of battery degradation. Other aspects of degradation, such as electrolyte decomposition, lithium-plating, and particle cracking are difficult to detect electrochemically but are crucial to measure to get a full picture of battery safety and flag out potential failures. In this work, lab- and field-aged commercial lithium-ion batteries and modules of various chemistries and formats are tested using a variety of traditional electrochemical characterization methods as well as using 2-minute pseudo-random DC pulse sequences at rest and during charge/discharge. The electrochemical measurements are compared to physical cell measurements, cell efficiency, drive cycle performance, physical and thermal heterogeneity, and qualitative safety metrics using statistical and machine-learning methods to discover if a comprehensive "battery health map" can be accurately identified using only rapid DC measurements.

ADVANCED PROPULSION SYSTEMS,ENERGY STORAGE↗

Restricted Collision List method for faster Direct Simulation Monte-Carlo (DSMC) collisions

The ‘Restricted Collision List’ (RCL) method for speeding up the calculation of DSMC Variable Soft Sphere collisions, with Borgnakke–Larsen (BL) energy exchange, is presented. The method cuts down considerably on the number of random collision parameters which must be calculated (deflection and azimuthal angles, and the BL energy exchange factors). A relatively short list of these parameters is generated and the parameters required in any cell are selected from this list. The list is regenerated at intervals approximately equal to the smallest mean collision time in the flow, and the chance of any particle re-using the same collision parameters in two successive collisions is negligible. The results using this method are indistinguishable from those obtained with standard DSMC. The CPU time saving depends on how much of a DSMC calculation is devoted to collisions and how much is devoted to other tasks, such as moving particles and calculating particle interactions with flow boundaries. For 1-dimensional calculations of flow in a tube, the new method saves 20% of the CPU time per collision for VSS scattering with no energy exchange. With RCL applied to rotational energy exchange, the CPU saving can be greater; for small values of the rotational collision number, for which most collisions involve some rotational energy exchange, the CPU may be reduced by 50% or more.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Conservative tightly-coupled simulations of stochastic multiscale systems

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employing either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spatio-Temporal Surrogates for Interaction of a Jet with High Explosives: Part II - Clustering Extremely High-Dimensional Grid-Based Data

Building an accurate surrogate model for the spatio-temporal outputs of a computer simulation is a challenging task. A simple approach to improve the accuracy of the surrogate is to cluster the outputs based on similarity and build a separate surrogate model for each cluster. This clustering is relatively straightforward when the output at each time step is of moderate size. However, when the spatial domain is represented by a large number of grid points, numbering in the millions, the clustering of the data becomes more challenging. In this report, we consider output data from simulations of a jet interacting with high explosives. These data are available on spatial domains of different sizes, at grid points that vary in their spatial coordinates, and in a format that distributes the output across multiple files at each time step of the simulation. We first describe how we bring these data into a consistent format prior to clustering. Borrowing the idea of random projections from data mining, we reduce the dimension of our data by a factor of thousand, making it possible to use the iterative k-means method for clustering. We show how we can use the randomness of both the random projections, and the choice of initial centroids in k-means clustering, to determine the number of clusters in our data set. Our approach makes clustering of extremely high dimensional data tractable, generating meaningful cluster assignments for our problem, despite the approximation introduced in the random projections.

97 MATHEMATICS AND COMPUTING↗

The deterministic chaos and random noise in turbulent jet

A turbulent flow is usually treated as a superposition of coherent structure and incoherent turbulence. In this paper, the largest Lyapunov exponent and the random noise in the near field of round jet and plane jet are estimated with our previously proposed method of chaotic time series analysis [T. L. Yao, et al., Chaos 22, 033102 (2012)]. The results show that the largest Lyapunov exponents of the round jet and plane jet are in direct proportion to the reciprocal of the integral time scale of turbulence, which is in accordance with the results of the dimensional analysis, and the proportionality coefficients are equal. In addition, the random noise of the round jet and plane jet has the same linear relation with the Kolmogorov velocity scale of turbulence. As a result, the random noise may well be from the incoherent disturbance in turbulence, and the coherent structure in turbulence may well follow the rule of chaotic motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. Herein, we address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

97 MATHEMATICS AND COMPUTING↗

Late Breaking Results: COPPER: Computation Obfuscation by Producing Permutations for Encoding Randomly

Deployed embedded devices face security risks due to increased ease of physical access to the devices by unauthorized users. Capable adversaries can intercept a device to recover the data in memory, including results of performed sensitive computations. Device owners require data confidentiality on their physically insecure devices. To satisfy this goal we implement a novel method, COPPER (Computation Obfuscation by Producing Permutations for Encoding Randomly), to create data which never exists on the device digitally in plaintext format and which is subsequently used for computation. In this paper we utilize COPPER to calculate a moving average computation on encoded data.

embedded systems↗

Exploring Memory Hierarchy to Improve Scientific Data Read Performance, In: 2015 IEEE International Conference on Cluster Computing

Improving read performance is one of the major challenges with speeding up scientific data analytic applications. Utilizing the memory hierarchy is one major line of researches to address the read performance bottleneck. Related methods usually combine solide-state-drives(SSDs) with dynamic random-access memory(DRAM) and/or parallel file system(PFS) to mitigate the speed and space gap between DRAM and PFS. However, these methods are unable to handle key performance issues plaguing SSDs, namely read contention that may cause up to 50% performance reduction. In this paper, we propose a framework that exploits the memory hierarchy resource to address the read contention issues involved with SSDs. The framework employs a general purpose online read algorithm that able to detect and utilize memory hierarchy resource to relieve the problem. To maintain a near optimal operating environment for SSDs, the framework is able to orchastrate data chunks across different memory layers to facilitate the read algorithm. Compared to existing tools, our framework achieves up to 50% read performance improvement when tested on datasets from real-world scientific simulations.

Computer Science↗

Predictors of Adverse Cosmetic Outcome in the RAPID Trial: An Exploratory Analysis

Purpose: To evaluate factors associated with adverse cosmesis outcome in breast cancer patients randomized to accelerated partial breast irradiation (APBI) using 3-dimensional conformal radiation therapy or whole-breast irradiation in the RAPID (Randomized Trial of Accelerated Partial Breast Irradiation) trial. Methods and Materials: Subjects were trial participants with nurse-assessed global cosmetic scores at baseline and at 3 years. Adverse cosmesis was defined as a score of fair or poor. Cosmetic deterioration was defined as any adverse change in score from baseline to 3 years. The analysis is based on data from the previously reported interim analysis. Logistic regression models were used to assess the association of risk factors for these outcomes among all patients and those treated with APBI only. Results: Clinicopathologic characteristics were similar between subjects randomized to APBI (n=569) or whole-breast irradiation (n=539). For all subjects, factors associated with adverse cosmesis at 3 years were older age, central/inner tumor location, breast infection, smoking, seroma volume, breast volume, and use of APBI; factors associated with cosmetic deterioration were smoking, seroma volume, and use of APBI (P<.05). For APBI subjects, tumor location, smoking, age, and seroma volume were associated with adverse cosmesis (P<.05), and smoking was associated with cosmetic deterioration (P=.02). An independent association between the V95/whole-breast volume ratio and adverse cosmesis (P=.28) or cosmetic deterioration (P=.07) was not detected. On further exploration a V95/whole-breast volume ratio <0.15 was associated with a lower risk of cosmetic deterioration (p=.04), but this accounted for only 11% of patients. Conclusion: In the RAPID trial, a number of patient tumor and treatment-related factors, including the use of APBI, were associated with adverse cosmesis and cosmetic deterioration. For patients treated with APBI alone, the high-dose treatment volume was not independently associated with an adverse cosmetic outcome, and a useful clinical threshold could not be identified.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Decline in Tested and Self-Reported Cognitive Functioning After Prophylactic Cranial Irradiation for Lung Cancer: Pooled Secondary Analysis of Radiation Therapy Oncology Group Randomized Trials 0212 and 0214

Purpose: To assess the impact of prophylactic cranial irradiation (PCI) on self-reported cognitive functioning (SRCF), a functional scale on the European Organization for Research and Treatment of Cancer Core Quality of Life Questionnaire (EORTC QLQ-C30). Methods and Materials: Radiation Therapy Oncology Group (RTOG) protocol 0214 randomized patients with locally advanced non-small cell lung cancer to PCI or observation; RTOG 0212 randomized patients with limited-disease small cell lung cancer to high- or standard-dose PCI. In both trials, Hopkins Verbal Learning Test (HVLT)-Recall and -Delayed Recall and SRCF were assessed at baseline (after locoregional therapy but before PCI or observation) and at 6 and 12 months. Patients developing brain relapse before follow-up evaluation were excluded. Decline was defined using the reliable change index method and correlated with receipt of PCI versus observation using logistic regression modeling. Fisher's exact test correlated decline in SRCF with HVLT decline. Results: Of the eligible patients pooled from RTOG 0212 and RTOG 0214, 410 (93%) receiving PCI and 173 (96%) undergoing observation completed baseline HVLT or EORTC QLQ-C30 testing and were included in this analysis. Prophylactic cranial irradiation was associated with a higher risk of decline in SRCF at 6 months (odds ratio 3.60, 95% confidence interval 2.34-6.37, P<.0001) and 12 months (odds ratio 3.44, 95% confidence interval 1.84-6.44, P<.0001). Decline on HVLT-Recall at 6 and 12 months was also associated with PCI (P=.002 and P=.002, respectively) but was not closely correlated with decline in SRCF at the same time points (P=.05 and P=.86, respectively). Conclusions: In lung cancer patients who do not develop brain relapse, PCI is associated with decline in HVLT-tested and self-reported cognitive functioning. Decline in HVLT and decline in SRCF are not closely correlated, suggesting that they may represent distinct elements of the cognitive spectrum.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Phase 2 Randomized Controlled Trial of Radiation Therapy Plus Concurrent Interferon-Alpha and Retinoic Acid Versus Cisplatin for Stage III Cervical Carcinoma

Purpose: Because a combination of retinoic acid, interferon-alpha, and radiation therapy demonstrated synergistic action and effectiveness to treat advanced cervical cancers in earlier studies, we designed this randomized phase 2 open-label trial to assess efficacy and safety of interferon alpha-2b (IFN) and 13-cis-retinoic acid (RA) administered concomitantly with radiation therapy (IFN-RA-radiation) to treat stage III cervical cancer. Methods and Materials: Stage III cervical cancer patients were randomized to study and control groups in a 1:1 ratio. All patients were treated with radiation therapy; study arm patients received IFN (3 × 10{sup 6} IU subcutaneously) 3 times a week for 4 weeks and daily RA (40 mg orally) for 30 days starting on day 1 of radiation, whereas control arm patients received weekly cisplatinum (40 mg/m{sup 2}) for 5 weeks during radiation. Patients were followed for 3 years. The primary endpoint was overall survival at 3 years. Results: Patients in the study (n=104) and control (n=105) groups were comparable for clinicopathological characteristics, radiation therapy–related variables and treatment response. Proportions of disease-free patients in the study and control groups were 38.5% and 44.8%, respectively, after median follow-up of 29.2 months. Hazard ratios were 0.67 (95% confidence interval [CI]: 0.44-1.01) and 0.69 (95% CI: 0.44-1.06) for overall and disease-fee survival, respectively, comparing the study group to control, and demonstrated an inferior outcome with RA-IFN-radiation, although differences were statistically nonsignificant. Kaplan-Meier curves of disease-free and overall survival probabilities also showed inferior survival in the study group compared to those in the control. Acute toxicities of chemoradiation were significantly higher with 2 acute toxicity-related deaths. Conclusions: Treatment with RA-IFN-radiation did not demonstrate survival advantage over chemoradiation despite being less toxic. The trends predicted an inferior outcome with the RA-IFN combination.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-C-207A-07: Cumulative 18F-FDG Uptake Histogram Relative to Radiation Dose Volume Histogram of Lung After IMRT Or PSPT and Their Association with Radiation Pneumonitis

Purpose: To determine whether the difference in cumulative 18F-FDG uptake histogram of lung treated with either IMRT or PSPT is associated with radiation pneumonitis (RP) in patients with inoperable stage II and III NSCLC. Methods: We analyzed 24 patients from a prospective randomized trial to compare IMRT (n=12) with vs. PSPT (n=12) for inoperable NSCLC. All patients underwent PET-CT imaging between 35 and 88 days post-therapy. Post-treatment PET-CT was aligned with planning 4D CT to establish a voxel-to-voxel correspondence between post-treatment PET and planning dose images. 18F-FDG uptake as a function of radiation dose to normal lung was obtained for each patient. Distribution of the standard uptake value (SUV) was analyzed using a volume histogram method. The image quantitative characteristics and DVH measures were correlated with clinical symptoms of pneumonitis. Results: Patients with RP were present in both groups: 5 in the IMRT and 6 in the PSPT. The analysis of cumulative SUV histograms showed significantly higher relative volumes of the normal lung having higher SUV uptake in the PSPT patients for both symptomatic and asymptomatic cases (VSUV=2: 10% for IMRT vs 16% for proton RT and VSUV=1: 10% for IMRT vs 23% for proton RT). In addition, the SUV histograms for symptomatic cases in PSPT patients exhibited a significantly longer tail at the highest SUV. The absolute volume of the lung receiving the dose >70 Gy was larger in the PSPT patients. Conclusion: 18F-FDG uptake – radiation dose response correlates with RP in both groups of patients by means of the linear regression slope. SUV is higher for the PSPT patients for both symptomatic and asymptomatic cases. Higher uptake after PSPT patients is explained by larger volumes of the lung receiving high radiation dose.

60 APPLIED LIFE SCIENCES↗

Magnetic cluster expansion model for random and ordered magnetic face-centered cubic Fe-Ni-Cr alloys

A Magnetic Cluster Expansion model for ternary face-centered cubic Fe-Ni-Cr alloys has been developed, using DFT data spanning binary and ternary alloy configurations. Using this Magnetic Cluster Expansion model Hamiltonian, we perform Monte Carlo simulations and explore magnetic structures of alloys over the entire range of compositions, considering both random and ordered alloy structures. In random alloys, the removal of magnetic collinearity constraint reduces the total magnetic moment but does not affect the predicted range of compositions where the alloys adopt low-temperature ferromagnetic configurations. During alloying of ordered fcc Fe-Ni compounds with Cr, chromium atoms tend to replace nickel rather than iron atoms. Replacement of Ni by Cr in ordered alloys with high iron content increases the Curie temperature of the alloys. This can be explained by strong antiferromagnetic Fe-Cr coupling, similar to that found in bcc Fe-Cr solutions, where the Curie temperature increase, predicted by simulations as a function of Cr concentration, is confirmed by experimental observations. In random alloys, both magnetization and the Curie temperature decrease abruptly with increasing chromium content, in agreement with experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗

Robust and non-fragile finite time H{sub ∞} synchronization control for complex networks with uncertain inner coupling

This paper addresses robust finite time H{sub ∞} synchronization problem for non-fragile complex networks with uncertain inner coupling. In order to achieve synchronization, a non-fragile controller subjected to randomly occurring perturbations will be considered. By constructing a suitable Lyapunov–Krasovskii functional and utilizing reciprocally convex approach, the criteria for the networks are established in terms of linear matrix inequalities (LMIs). Theoretical analysis and numerical simulations about robust finite time H{sub ∞} synchronization for uncertain inner coupling complex networks are presented.

97 MATHEMATICS AND COMPUTING↗