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At least 1,441 records · Page 80

A Novel Local Learning based Approach With Application to Breast Cancer Diagnosis

The purpose of this study is to develop and evaluate a novel local learning-based approach for computer-assisted diagnosis of breast cancer. Our new local learning based algorithm using the linear logistic regression method as its base learner is described. Overall, our algorithm will perform its stochastic searching process until the total allowed computing time is used up by our random walk process in identifying the most suitable population subdivision scheme and their corresponding individual base learners. The proposed local learning-based approach was applied for the prediction of breast cancer given 11 mammographic and clinical findings reported by physicians using the BI-RADS lexicon. Our database consisted of 850 patients with biopsy confirmed diagnosis (290 malignant and 560 benign). We also compared the performance of our method with a collection of publicly available state-of-the-art machine learning methods. Predictive performance for all classifiers was evaluated using 10-fold cross validation and Receiver Operating Characteristics (ROC) analysis. Figure 1 reports the performance of 54 machine learning methods implemented in the machine learning toolkit Weka (version 3.0). We introduced a novel local learning-based classifier and compared it with an extensive list of other classifiers for the problem of breast cancer diagnosis. Our experiments show that the algorithm superior prediction performance outperforming a wide range of other well established machine learning techniques. Our conclusion complements the existing understanding in the machine learning field that local learning may capture complicated, non-linear relationships exhibited by real-world datasets.

59 BASIC BIOLOGICAL SCIENCES↗

Comparative Evaluation of Spectral Methods for Robust Reactor Noise Estimation

Reactor noise analysis provides a noninvasive means to determine neutron kinetic parameters from stochastic fluctuations in detector signals. However, standard cross-power spectral density (CPSD) analyses can be sensitive to numerical processing choices, which may introduce processing-dependent systematic shifts in estimates of the prompt neutron decay constant (α) and limit reproducibility. This study uses a hybrid multitaper–Welch spectral estimator to analyze subcritical noise measurements from a fast-spectrum critical assembly. The decay constant α was extracted using three frequency-domain methods: the CPSD, the magnitude-squared coherence (MSC), and the generalized magnitude-squared coherence (GMSC). These coherence-based estimators normalize detector auto-spectral structure and are expected to reduce the sensitivity of fitted α values to processing parameters. A Sobol global sensitivity analysis identified which numerical inputs most strongly influence the fitted values of α. All estimators produced a linear dependence of α on inverse count rate, with delayed-critical extrapolations near 1.7 × 10 4 s −1 , in agreement within 8% of MCNP6.3 KOPTS benchmark calculations. Sensitivity results show that while the CPSD depends on both time-bin width and taper selection, the MSC and GMSC are dominated by time-bin width alone, indicating reduced parameter coupling and greater robustness to processing variability. These findings demonstrate the feasibility and practical value of coherence-based spectral estimators for extracting α from reactor noise and support their broader application to multi-detector and irregular datasets in subcritical system characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model

We consider a moving shutter and non-deterministic generalization of the diffraction in time model introduced by Moshinsky several decades ago to study a class of quantum transients. We first develop a moving-mesh finite element method (FEM) to simulate the determisitic version of the model. We then apply the FEM and multilevel Monte Carlo (MLMC) algorithm to the stochastic moving-domain model for simulation of approximate statistical moments of the density profile of the stochastic transients.

97 MATHEMATICS AND COMPUTING↗

High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons

We recently proposed a novel approach to converging electronic energies equivalent to high-level coupled-cluster (CC) computations by combining the deterministic CC(P;Q) formalism with the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)], which focused on recovering the energies obtained with the CC method with singles, doubles, and triples (CCSDT) using the information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches truncated at triples and quadruples. It also reports our first semi-stochastic CC(P;Q) calculations aimed at converging the energies that correspond to the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The ability of the semi-stochastic CC(P;Q) formalism to recover the CCSDT and CCSDTQ energies, even when electronic quasi-degeneracies and triply and quadruply excited clusters become substantial, is illustrated by a few numerical examples, including the F–F bond breaking in F 2 , the automerization of cyclobutadiene, and the double dissociation of the water molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗

An Atomic Mix Closure for Stochastic Media Transport Problems

The accurate modeling of stochastic media in radiation transport calculations remains on ongoing research challenge. The Levermore-Pomraning (LP) closure for the statistical transport equation is simple and inexpensive, but it is often inaccurate. More accurate closures have been proposed, but they can be prohibitively expensive. In this work we present a relatively inexpensive closure that we have observed to be more accurate than LP in almost all cases studied. Obtaining solutions to stochastic transport problems can be quite difficult. Transport calculations on an ensemble of explicit realizations generated by Monte Carlo sampling can be prohibitively expensive. Atomic mix or LP calculations are relatively inexpensive, but they can be inaccurate. The present work illustrates an approach that is less expensive than Monte Carlo sampling yet more accurate than atomic mix or LP approximations. We still need to analyze the reasons why the atomic mix closures derived for thicker problems lead to source iteration instabilities. It is not clear if the closure itself induces an ill-posed problem or if it is merely the iterative process that is problematic. We hope to examine alternative source terms to drive the subsidiary calculations. We also want to extend the work to multigroup and multidimensional problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Delensing CMB polarization with external datasets

One of the primary scientific targets of current and future CMB polarization experiments is the search for a stochastic background of gravity waves in the early universe. As instrumental sensitivity improves, the limiting factor will eventually be B-mode power generated by gravitational lensing, which can be removed through use of so-called ''delensing'' algorithms. We forecast prospects for delensing using lensing maps which are obtained externally to CMB polarization: either from large-scale structure observations, or from high-resolution maps of CMB temperature. We conclude that the forecasts in either case are not encouraging, and that significantly delensing large-scale CMB polarization requires high-resolution polarization maps with sufficient sensitivity to measure the lensing B-mode. We also present a simple formalism for including delensing in CMB forecasts which is computationally fast and agrees well with Monte Carlos.

79 ASTRONOMY AND ASTROPHYSICS↗

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.

58 GEOSCIENCES↗

Coupling of kinetic Monte Carlo simulations of surface reactions to transport in a fluid for heterogeneous catalytic reactor modeling

We have developed a method to couple kinetic Monte Carlo simulations of surface reactions at a molecular scale to transport equations at a macroscopic scale. This method is applicable to steady state reactors. We use a finite difference upwinding scheme and a gap-tooth scheme to efficiently use a limited amount of kinetic Monte Carlo simulations. In general the stochastic kinetic Monte Carlo results do not obey mass conservation so that unphysical accumulation of mass could occur in the reactor. We have developed a method to perform mass balance corrections that is based on a stoichiometry matrix and a least-squares problem that is reduced to a non-singular set of linear equations that is applicable to any surface catalyzed reaction. The implementation of these methods is validated by comparing numerical results of a reactor simulation with a unimolecular reaction to an analytical solution. Furthermore, the method is applied to two reaction mechanisms. The first is the ZGB model for CO oxidation in which inevitable poisoning of the catalyst limits the performance of the reactor. The second is a model for the oxidation of NO on a Pt(111) surface, which becomes active due to lateral interaction at high coverages of oxygen. This reaction model is based on ab initio density functional theory calculations from literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Integrated Model, Batch and Domain Parallelism in Training Neural Networks

We propose a new integrated method of exploiting model, batch and domain parallelism for the training of deep neural networks (DNNs) on large distributed-memory computers using minibatch stochastic gradient descent (SGD). Our goal is to find an efficient parallelization strategy for a fixed batch size using $P$ processes. Our method is inspired by the communication-avoiding algorithms in numerical linear algebra. We see $P$ processes as logically divided into a $P_r \times P_c$ grid where the $P_r$ dimension is implicitly responsible for model/domain parallelism and the $P_c$ dimension is implicitly responsible for batch parallelism. In practice, the integrated matrix-based parallel algorithm encapsulates these types of parallelism automatically. We analyze the communication complexity and analytically demonstrate that the lowest communication costs are often achieved neither with pure model nor with pure data parallelism. We also show how the domain parallel approach can help in extending the theoretical scaling limit of the typical batch parallel method.

97 MATHEMATICS AND COMPUTING↗

Almost periodic oscillations for delay impulsive stochastic Nicholson’s blowflies timescale model

In this paper, we employ the new concepts of piecewise almost periodic stochastic process on a new periodic time scale and study a type of delay impulsive stochastic Nicholson’s blowflies timescale model under shifts operators. Some sufficient conditions for the existence and exponential stability of piecewise mean-square almost periodic solutions to the model are established. In addition, we provide numerical examples and computer simulations to demonstrate the feasibility of the obtained results. The methods and definitions introduced in the paper can be applied to study other types of stochastic dynamic models involving q-difference models and more.

97 MATHEMATICS AND COMPUTING↗

Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises

In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, cadlag, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L{sup 2} and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the paper.

97 MATHEMATICS AND COMPUTING↗

First principles prediction of amorphous phases using evolutionary algorithms

We discuss the efficacy of evolutionary method for the purpose of structural analysis of amorphous solids. At present, ab initio molecular dynamics (MD) based melt-quench technique is used and this deterministic approach has proven to be successful to study amorphous materials. We show that a stochastic approach motivated by Darwinian evolution can also be used to simulate amorphous structures. Applying this method, in conjunction with density functional theory based electronic, ionic and cell relaxation, we re-investigate two well known amorphous semiconductors, namely silicon and indium gallium zinc oxide. We find that characteristic structural parameters like average bond length and bond angle are within ∼2% of those reported by ab initio MD calculations and experimental studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stochastic multiscale flux basis for Stokes-Darcy flows

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional domain decomposition implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed for each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is used over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost compared to the other two algorithms.

97 MATHEMATICS AND COMPUTING↗

EFFECTS OF NON-ISOTROPIC SCATTERING, MAGNETIC HELICITY, AND ADIABATIC FOCUSING ON DIFFUSIVE TRANSPORT OF SOLAR ENERGETIC PARTICLES

Transport of solar energetic particles in interplanetary space is analyzed. A new systematic derivation of the diffusion approximation is given, which incorporates the effects of non-isotropic scattering, magnetic helicity, and adiabatic focusing in a non-uniform large-scale magnetic field. The derivation is based on a system of stochastic differential equations, equivalent to the Fokker-Planck equation, and the new method is a generalization of the Smoluchowski approximation in the theory of the Brownian motion. Simple, physically transparent expressions for the transport coefficients are derived. Different results of earlier treatments of the problem are related to the assumptions regarding the evolving particle distribution.

79 ASTRONOMY AND ASTROPHYSICS↗

A stochastic flow-capturing model to optimize the location of fast-charging stations with uncertain electric vehicle flows

Here, we develop a model to optimize the location of public fast charging stations for electric vehicles (EVs). A difficulty in planning the placement of charging stations is uncertainty in where EV charging demands appear. For this reason, we use a stochastic flow-capturing location model (SFCLM). A sample-average approximation method and an averaged two-replication procedure are used to solve the problem and estimate the solution quality. We demonstrate the use of the SFCLM using a Central-Ohio based case study. We find that most of the stations built are concentrated around the urban core of the region. As the number of stations built increases, some appear on the outskirts of the region to provide an extended charging network. We find that the sets of optimal charging station locations as a function of the number of stations built are approximately nested. We demonstrate the benefits of the charging-station network in terms of how many EVs are able to complete their daily trips by charging midday—six public charging stations allow at least 60% of EVs that would otherwise not be able to complete their daily tours without the stations to do so. We finally compare the SFCLM to a deterministic model, in which EV flows are set equal to their expected values. We show that if a limited number of charging stations are to be built, the SFCLM outperforms the deterministic model. As the number of stations to be built increases, the SFCLM and deterministic model select very similar station locations.

33 ADVANCED PROPULSION SYSTEMS↗

Controlling the high frequency response of H{sub 2} by ultra-short tailored laser pulses: A time-dependent configuration interaction study

We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H{sub 2} treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a “non-harmonic” response of H{sub 2} to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Adaptive Stress Testing of Airborne Collision Avoidance Systems

This paper presents a scalable method to efficiently search for the most likely state trajectory leading to an event given only a simulator of a system. Our approach uses a reinforcement learning formulation and solves it using Monte Carlo Tree Search (MCTS). The approach places very few requirements on the underlying system, requiring only that the simulator provide some basic controls, the ability to evaluate certain conditions, and a mechanism to control the stochasticity in the system. Access to the system state is not required, allowing the method to support systems with hidden state. The method is applied to stress test a prototype aircraft collision avoidance system to identify trajectories that are likely to lead to near mid-air collisions. We present results for both single and multi-threat encounters and discuss their relevance. Compared with direct Monte Carlo search, this MCTS method performs significantly better both in finding events and in maximizing their likelihood.

Verification and Validation↗