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At least 199 records · Page 11

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. Here, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green’s kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal ϵ -2 asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

97 MATHEMATICS AND COMPUTING↗

A bi-fidelity method for the multiscale Boltzmann equation with random parameters

In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [52], [70], [71]. By choosing the compressible Euler system as the low-fidelity model, we adapt the bi-fidelity SC method to combine computational efficiency of the low-fidelity model with high accuracy of the high-fidelity (Boltzmann) model. With only a small number of high-fidelity asymptotic-preserving solver runs for the Boltzmann equation, the bi-fidelity approximation can capture well the macroscopic quantities of the solution to the Boltzmann equation in the random space. Additionally, a priori estimate on the accuracy between the high- and bi-fidelity solutions together with a convergence analysis is established. Finally, we present extensive numerical experiments to verify the efficiency and accuracy of our proposed method.

97 MATHEMATICS AND COMPUTING↗

A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential

In this paper, we consider the numerical solution of the one-dimensional Schrödinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness results from complicated phenomena that are not exactly known. Here we generalize the Bloch decomposition-based time-splitting pseudospectral method to the stochastic setting using the generalized polynomial chaos with a Galerkin procedure so that the main effects of dispersion and periodic potential are still computed together. We prove that our method is unconditionally stable and numerical examples show that it has other nice properties and is more efficient than the traditional method. Finally, we give some numerical evidence for the well-known phenomenon of Anderson localization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A novel approach to assess the treatment response using Gaussian random field in PET

Purpose: The assessment of early therapeutic response to anticancer therapy is vital for treatment planning and patient management in clinic. With the development of personal treatment plan, the early treatment response, especially before any anatomically apparent changes after treatment, becomes urgent need in clinic. Positron emission tomography (PET) imaging serves an important role in clinical oncology for tumor detection, staging, and therapy response assessment. Many studies on therapy response involve interpretation of differences between two PET images, usually in terms of standardized uptake values (SUVs). However, the quantitative accuracy of this measurement is limited. This work proposes a statistically robust approach for therapy response assessment based on Gaussian random field (GRF) to provide a statistically more meaningful scale to evaluate therapy effects. Methods: The authors propose a new criterion for therapeutic assessment by incorporating image noise into traditional SUV method. An analytical method based on the approximate expressions of the Fisher information matrix was applied to model the variance of individual pixels in reconstructed images. A zero mean unit variance GRF under the null hypothesis (no response to therapy) was obtained by normalizing each pixel of the post-therapy image with the mean and standard deviation of the pretherapy image. The performance of the proposed method was evaluated by Monte Carlo simulation, where XCAT phantoms (128{sup 2} pixels) with lesions of various diameters (2–6 mm), multiple tumor-to-background contrasts (3–10), and different changes in intensity (6.25%–30%) were used. The receiver operating characteristic curves and the corresponding areas under the curve were computed for both the proposed method and the traditional methods whose figure of merit is the percentage change of SUVs. The formula for the false positive rate (FPR) estimation was developed for the proposed therapy response assessment utilizing local average method based on random field. The accuracy of the estimation was validated in terms of Euler distance and correlation coefficient. Results: It is shown that the performance of therapy response assessment is significantly improved by the introduction of variance with a higher area under the curve (97.3%) than SUVmean (91.4%) and SUVmax (82.0%). In addition, the FPR estimation serves as a good prediction for the specificity of the proposed method, consistent with simulation outcome with ∼1 correlation coefficient. Conclusions: In this work, the authors developed a method to evaluate therapy response from PET images, which were modeled as Gaussian random field. The digital phantom simulations demonstrated that the proposed method achieved a large reduction in statistical variability through incorporating knowledge of the variance of the original Gaussian random field. The proposed method has the potential to enable prediction of early treatment response and shows promise for application to clinical practice. In future work, the authors will report on the robustness of the estimation theory for application to clinical practice of therapy response evaluation, which pertains to binary discrimination tasks at a fixed location in the image such as detection of small and weak lesion.

61 RADIATION PROTECTION AND DOSIMETRY↗

Treating random sequential addition via the replica method

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Markov stochasticity coordinates

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Conjunctival Autograft Alone or Combined With Adjuvant Beta-Radiation? A Randomized Clinical Trial

Purpose: To evaluate the effectiveness and safety of postoperative low single-dose of beta-irradiation ({beta}-RT) in pterygium comparing conjunctival autograft (CAG) surgery with CAG plus adjuvant {beta}-RT in a randomized clinical trial. Methods: This trial was designed as a prospective, randomized, single-center study. Surgery was performed in all cases according to the CAG technique. One hundred and eight pterygia were postoperatively randomized to CAG + {beta}-RT or CAG alone. In the case of {beta}-RT, a (90) Sr eye applicator was used to deliver 10 Gy to the sclera surface at a dose rate of between 200 and 250 cGy/min. After treatment, both an ophthalmologist and a radiation oncologist performed the follow-up examinations. The accumulated data were analyzed using a group sequential test. Results: Between February 2008 and September 2008, 116 eyes with primary pterygium were operated on according to the trial protocol. Adjuvant treatment was performed within 24 h postoperatively. Eight patients were lost to follow-up, resulting in 108 patients who could be analyzed. At a mean follow-up of 18 months (range, 8-33), in the 54 eyes randomized to receive CAG + {beta}-RT, 5 relapses occurred compared with 12 recurrences in the 54 eyes in CAG, for a crude control rate of 90.8 % vs. 78%; p = 0.032, respectively. The treatment complications as hyperemia, total dehiscence of the autograft and dellen were significantly more frequent in the CAG (p < 0.05). The arm of {beta}-RT resulted in better cosmetic results and improves of symptoms than CAG. Conclusions: A low single-dose of {beta}-RT of 10 Gy after CAG surgery was a simple, effective, and safe treatment that reduced the risk of primary pterygium recurrence, improved symptoms after surgery, resulting in a better cosmetic effect than only CAG.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Comparing thermal wave function methods for multi-configuration time-dependent Hartree simulations

We compare two methods for creating stochastic temperature wave functions that can be used for Multi-Configuration Time-Dependent Hartree (MCTDH) simulations. In the first method, the MCTDH coefficients are chosen randomly, while the other method uses a single Hartree product of random single-particle functions (SPFs). We find that using random SPFs dramatically improves convergence for a model system for surface sticking.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SPICE: discovery of phenotype-determining component interplays

Background: A latent behavior of a biological cell is complex. Deriving the underlying simplicity, or the fundamental rules governing this behavior has been the Holy Grail of systems biology. Data-driven prediction of the system components and their component interplays that are responsible for the target system’s phenotype is a key and challenging step in this endeavor. Results: The proposed approach, which we call System Phenotype-related Interplaying Components Enumerator (SPICE), iteratively enumerates statistically significant system components that are hypothesized (1) to play an important role in defining the specificity of the target system’s phenotype(s); (2) to exhibit a functionally coherent behavior, namely, act in a coordinated manner to perform the phenotype-specific function; and (3) to improve the predictive skill of the system’s phenotype(s) when used collectively in the ensemble of predictive models. SPICE can be applied to both instance-based data and network-based data. When validated, SPICE effectively identified system components related to three target phenotypes: biohydrogen production, motility, and cancer. Manual results curation agreed with the known phenotype-related system components reported in literature. Additionally, using the identified system components as discriminatory features improved the prediction accuracy by 10% on the phenotype-classification task when compared to a number of state-of-the-art methods applied to eight benchmark microarray data sets. Conclusion: We formulate a problem—enumeration of phenotype-determining system component interplays—and propose an effective methodology (SPICE) to address this problem. SPICE improved identification of cancer-related groups of genes from various microarray data sets and detected groups of genes associated with microbial biohydrogen production and motility, many of which were reported in literature. SPICE also improved the predictive skill of the system’s phenotype determination compared to individual classifiers and/or other ensemble methods, such as bagging, boosting, random forest, nearest shrunken centroid, and random forest variable selection method.

59 BASIC BIOLOGICAL SCIENCES↗

Speckle spectroscopy of fluorescent randomly inhomogeneous media

We propose a coherence optical method for probing fluorescent randomly inhomogeneous media based on the statistical analysis of spatial fluctuations of spectrally selected fluorescence radiation. We develop a phenomenological model that interrelates the flicker index of the spatial distribution of the fluorescence intensity at a fixed wavelength and the mean path difference of partial components of the fluorescence radiation field in the probed medium. The results of experimental approbation of the developed method using the layers of densely packed silicon dioxide particles saturated with the aqueous rhodamine 6G solution with a high concentration of the dye are presented. The experimentally observed significant decrease in the flicker index under the wavelength tuning from the edges of the fluorescence spectrum towards it central part is presumably a manifestation of spectrally dependent negative absorption in the medium. (speckle spectroscopy)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Sentinel Lymph Node Biopsy Using Indocyanine Green Fluorescence Plus Radioisotope Method Compared With the Radioisotope-Only Method for Breast Cancer Patients After Neoadjuvant Chemotherapy: A Prospective, Randomized, Open-Label, Single-Center Phase 2 Trial

Background: This study aimed to compare the sentinel lymph node (SLN) identification rates for breast cancer patients after neoadjuvant chemotherapy (NAC) between the dual method (DM) of indocyanine green fluorescence (ICG-F) plus a radioisotope (RI) and RI alone. Methods: This randomized study enrolled 130 patients who received NAC for breast cancer and 122 patients who received SLN biopsy (SLNB) using either DM (n = 58) or RI only (n = 64). The study compared the identification rate, number of SLNs, and detection time of SLNB. Results: Among the 122 patients, 113 (92.6%) were clinically node-positive before NAC. The SLN identification rate was 98.3% in the DM group and 93.8% in the RI group (p = 0.14). The DM group and the RI group were similar in the average number of SLNs (2.2 ± 1.13 vs. 1.9 ± 1.33; p = 0.26) and the time to detection of the first SLN (8.7 ± 4.98 vs. 8.3 ± 4.31 min; p = 0.30). In the DM group, transcutaneous lymphatic drainage was visualized by fluorescence imaging for 65.5% (38 of 58) of the patients. The SLN identification rate was 94.7% using ICG-F and 93% using RI (p = 0.79). During and after the operation, no complications, including allergic reactions or skin necrosis, occurred. Conclusions: This study is the first randomized trial to use ICG-F for SLNB in breast cancer patients after NAC. The DM including ICG-F could be a feasible and safe method for SLNB in initially node-positive breast cancer patients with NAC.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Fast Fault Injection and Sensitivity Analysis for Collective Communications, In: 2015 IEEE International Conference on Cluster Computing

The collective communication operations, which are widely used in parallel applications for global communication and synchronization are critical for application's performance and scalability. However, how faulty collective communications impact the application and how errors propagate between the application processes is largely unexplored. One of the critical reasons for this situation is the lack of fast evaluation method to investigate the impacts of faulty collective operations. The traditional random fault injection methods relying on a large amount of fault injection tests to ensure statistical significance require a significant amount of resources and time. These methods result in prohibitive evaluation cost when applied to the collectives. In this paper, we introduce a novel tool named Fast Fault Injection and Sensitivity Analysis Tool (FastFIT) to conduct fast fault injection and characterize the application sensitivity to faulty collectives. The tool achieves fast exploration by reducing the exploration space and predicting the application sensitivity using Machine Learning (ML) techniques. A basis for these techniques are implicit correlations between MPI semantics, application context, critical application features, and application responses to faulty collective communications. The experimental results show that our approach reduces the fault injection points and tests by 97% for representative benchmarks (NAS Parallel Benchmarks (NPB)) and a realistic application (Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)) on a production supercomputer. Further, we statistically generalize the application sensitivity to faulty collective communications for these workloads, and present correlation between application features and the sensitivity.

Computer Science↗

Using porous random fields to predict the elastic modulus of unoxidized and oxidized superfine graphite

Nuclear graphite is a candidate material for Generation IV nuclear power plants. Porous materials such as graphite can contain complex networks of pores that influence the material's mechanical and irradiation response. A methodology known as the random finite element method (RFEM) was adapted to create synthetic microstructures and predict the influence of porosity on the elastic properties of graphite during oxidation. RFEM combines random field theory and the finite element method in a Monte Carlo framework to estimate the mechanical response of a given grade of graphite. In this research, the random fields were verified through experimental characterization to predict the elastic response of three nuclear graphite grades, ETU-10, IG-110, and 2114. Finite element models (FEM) were generated using segmentations of x-ray computed tomography (XCT) data known as image-based models (IBMs) to validate and compare with the RFEM results and better understand the effects of uniform oxidation in these graphite grades. The RFEM predictions appear to correlate well with the experimental values of the measured Young’s modulus of the three graphite grades and display the same trends as IBMs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

ASSESSING THE SIGNIFICANCE OF APPARENT CORRELATIONS BETWEEN RADIO AND GAMMA-RAY BLAZAR FLUXES

Whether or not a correlation exists between the radio and gamma-ray flux densities of blazars is a long-standing question, and one that is difficult to answer confidently because of various observational biases, which may either dilute or apparently enhance any intrinsic correlation between radio and gamma-ray luminosities. We introduce a novel method of data randomization to evaluate quantitatively the effect of these biases and to assess the intrinsic significance of an apparent correlation between radio and gamma-ray flux densities of blazars. The novelty of the method lies in a combination of data randomization in luminosity space (to ensure that the randomized data are intrinsically, and not just apparently, uncorrelated) and significance assessment in flux space (to explicitly avoid Malmquist bias and automatically account for the limited dynamical range in both frequencies). The method is applicable even to small samples that are not selected with strict statistical criteria. For larger samples we describe a variation of the method in which the sample is split in redshift bins, and the randomization is applied in each bin individually; this variation is designed to yield the equivalent to luminosity-function sampling of the underlying population in the limit of very large, statistically complete samples. We show that for a smaller number of redshift bins, the method yields a worse significance, and in this way it is conservative: although it may fail to confirm an existing intrinsic correlation in a small sample that cannot be split into many redshift bins, it will not assign a stronger, artificially enhanced significance. We demonstrate how our test performs as a function of number of sources, strength of correlation, and number of redshift bins used, and we show that while our test is robust against common-distance biases and associated false positives for uncorrelated data, it retains the power of other methods in rejecting the null hypothesis of no correlation for correlated data.

79 ASTRONOMY AND ASTROPHYSICS↗

A randomized multiplex CRISPRi-Seq approach for the identification of critical combinations of genes

Identifying virulence-critical genes from pathogens is often limited by functional redundancy. To rapidly interrogate the contributions of combinations of genes to a biological outcome, we have developed a multiplex, randomized CRISPR interference sequencing (MuRCiS) approach. At its center is a new method for the randomized self-assembly of CRISPR arrays from synthetic oligonucleotide pairs. When paired with PacBio long-read sequencing, MuRCiS allowed for near-comprehensive interrogation of all pairwise combinations of a group of 44 Legionella pneumophila virulence genes encoding highly conserved transmembrane proteins for their role in pathogenesis. Both amoeba and human macrophages were challenged with L. pneumophila bearing the pooled CRISPR array libraries, leading to the identification of several new virulence-critical combinations of genes. lpg2888 and lpg3000 were particularly fascinating for their apparent redundant functions during L. pneumophila human macrophage infection, while lpg3000 alone was essential for L. pneumophila virulence in the amoeban host Acanthamoeba castellanii. Thus, MuRCiS provides a method for rapid genetic examination of even large groups of redundant genes, setting the stage for application of this technology to a variety of biological contexts and organisms.

79 ASTRONOMY AND ASTROPHYSICS↗

Entropy-driven Optimal Sub-sampling of Fluid Dynamics for Developing Machine-learned Surrogates

Optimal sub-sampling of large datasets from fluid dynamics simulations is essential for training reduced-order machine learned models. A method using Shannon entropy was developed to weight flow features according to their level of information content, such that the most informative features can be extracted and used for training a surrogate model. The method is demonstrated in the canonical flow over a cylinder problem simulated with OpenFOAM. Both time-independent predictions and temporal forecasting were investigated as well as two types of prediction targets: local per-grid-point predictions and global per-time-step predictions. When tested on training a surrogate model, results indicate that our entropy-based sampling method typically outperforms random sampling and yields more reproducible results in less iterations. Finally, the method was used to train a surrogate model for modeling turbulence in magnetohydrodynamic flows, which revealed various challenges and opportunities for future research.

Brewer, Wes↗