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The basic building block of a distributed-memory cluster or supercomputer is a node. Each node includes a host, which is a processor (xPU) + memory hierarchy. The host can communicate with other hosts via its NIC (network interface controller). A network connects the nodes. The nodes may be arranged in some topology, which determines the network’s carrying capacity and cost.
We simulate the motion of hydrogen and deuterium molecules in the magnetic system of a setup intended for obtaining nuclear-spin-polarized molecules. Spatial separation of molecules with different magnetic moment projections by the spin filtration method in a nonuniform magnetic field is performed using superconducting sextupole magnets. Calculations are carried out for a magnetic field induction of 3.7 T at the poles and a nozzle temperature of 7 K. Simulation show that the ratio of polarized flux of hydrogen molecules to the detector to the total flux from the source nozzle is 2.3 × 10{sup –6}, nuclear polarization being close to 100%. Calculations performed for deuterium reveal that this ratio is 7 times smaller due to the smallness of the magnetic moment relative to hydrogen molecules. Trajectories of molecules in the magnetic system and their spatial distribution are represented graphically. Mathematical aspects of the algorithm of the computer program developed for this purpose are considered.
Purpose: To determine the mean and range of volumetric glandular fraction (VGF) of the breast in a diagnostic population using a high-resolution flat-panel cone-beam dedicated breast CT system. This information is important for Monte Carlo-based estimation of normalized glandular dose coefficients and for investigating the dependence of VGF on breast dimensions, race, and pathology. Methods: Image data from a clinical trial investigating the role of dedicated breast CT that enrolled 150 women were retrospectively analyzed to determine the VGF. The study was conducted in adherence to a protocol approved by the institutional human subjects review boards and written informed consent was obtained from all study participants. All participants in the study were assigned BI-RADS{sup Registered-Sign} 4 or 5 as per the American College of Radiology assessment categories after standard diagnostic work-up and underwent dedicated breast CT exam prior to biopsy. A Gaussian-kernel based fuzzy c-means algorithm was used to partition the breast CT images into adipose and fibroglandular tissue after segmenting the skin. Upon determination of the accuracy of the algorithm with a phantom, it was applied to 137 breast CT volumes from 136 women. VGF was determined for each breast and the mean and range were determined. Pathology results with classification as benign, malignant, and hyperplasia were available for 132 women, and were used to investigate if the distributions of VGF varied with pathology. Results: The algorithm was accurate to within {+-}1.9% in determining the volume of an irregular shaped phantom. The study mean ({+-} inter-breast SD) for the VGF was 0.172 {+-} 0.142 (range: 0.012-0.719). VGF was found to be negatively correlated with age, breast dimensions (chest-wall to nipple length, pectoralis to nipple length, and effective diameter at chest-wall), and total breast volume, and positively correlated with fibroglandular volume. Based on pathology, pairwise statistical analysis (Mann-Whitney test) indicated that at the 0.05 significance level, there was no significant difference in distributions of VGF without adjustment for age between malignant and nonmalignant breasts (p= 0.41). Pairwise comparisons of the distributions of VGF in increasing order of mammographic breast density indicated all comparisons were statistically significant (p < 0.002). Conclusions: This study used a different clinical prototype breast CT system than that in previous studies to image subjects from a different geographical region, and used a different algorithm for analysis of image data. The mean VGF estimated from this study is within the range reported in previous studies, indicating that the choice of 50% glandular weight fraction to represent an average breast for Monte Carlo-based estimation of normalized glandular dose coefficients in mammography needs revising. In the study, the distributions of VGF did not differ significantly with pathology.
Abstract In the context of diffractive optics, phase retrieval is a heavily investigated process of recreating an entire complex electric field from partial amplitude-only information through iterative algorithms. However, existing methods can fall into local minima during reconstructions or struggle to recover unusual and novel electric field distributions. We present a numerical method based on a global-optimization genetic algorithm that reconstructs non-trivial electric field distributions from single diffracted intensity distributions. Diffraction and propagation of the optical fields over arbitrary distances is modeled through implementation of the angular spectrum technique. Additionally, a coherently-locked laser array system is used as an experimental case-study demonstrating 0.09 π phase reconstruction accuracy of initial laser parameters from single intensity images.
Penetration of the power grid by renewable energy sources, distributed storage, and distributed generators is becoming increasingly common. Increased utilization of these distributed energy resources (DERs) has given rise to additional protection coordination concerns, particularly where they are utilized in an unbalanced manner or where loading among phases is unbalanced. Digital relays such as the SEL-751 (produced by Schweitzer Engineering Laboratories, Pullman, WA, USA) series have the capability of being set on a per-phase basis. This capability is underutilized in common practice. Additionally, in optimization algorithms for determining relay settings, the time-overcurrent characteristics (TOCs) of relays are generally not treated as variables and are assigned before running the optimization algorithm. In this paper, TOC options themselves are treated as discrete variables to be considered in the optimization algorithm. A mixed integer nonlinear programming problem (MINLP) is set up where the goal is to minimize relay operating times. A genetic algorithm (GA) approach is implemented in MATLAB where two cases are considered. In the first case, the TOC and Time dial setting (TDS) of each relay is set on a three-phase basis. In the second case, per-phase settings are considered. Relay TDSs and TOCs are both considered as simultaneous discrete control variables. Despite the stochastic nature of using per-phase settings for unbalanced systems is found to generally allow for shorter operating times. However, for relatively balanced systems, it is best to use three-phase settings if computation time is of importance.
Multi-speckle X-ray photon correlation spectroscopy (XPCS) is a powerful technique for characterizing the dynamic nature of complex materials over a range of time scales. XPCS has been successfully applied to study a wide range of systems. Recent developments in higher-frame-rate detectors, while aiding in the study of faster dynamical processes, creates large amounts of data that require parallel computational techniques to process in near real-time. Here, an implementation of the multi-tau and two-time autocorrelation algorithms using the Hadoop MapReduce framework for distributed computing is presented. In conclusion, the system scales well with regard to the increase in the data size, and has been serving the users of beamline 8-ID-I at the Advanced Photon Source for near real-time autocorrelations for the past five years.
We present that the resilience of modern power systems has been constantly threatened by various natural disasters and manmade attacks. Under those threats, fast and automatic restoration actions are critical for restoring impacted systems to normal operating conditions and preventing from additional disastrous consequences. Smart grid technologies, such as distributed energy resources (DERs) and microgrids, provide both opportunities and challenges for distribution system restoration. In this paper, distributed load restoration (DLR), in unbalanced active distribution networks is developed using the alternating direction method of multipliers (ADMM) algorithm. The step-by-step restoration actions are provided to schedule the output of DERs and distribution system control devices, as well as the power consumption from transmission system restoration. The nonlinearities from three-phase unbalanced power flow and distribution components modeling are relaxed into a convex quadratic programming model. Then, the problem is decomposed into subproblems for each node by applying ADMM-DLR; and solves through each agent by exchanging limited information with neighboring nodes in an iterative procedure. The developed models and algorithms are validated and demonstrated through testing of the IEEE 13-node and 123-node test feeders. Lastly, simulation results demonstrate the effectiveness of restoring unbalanced distribution system with the hybrid bottom-up and top-down restoration strategies.
With the increased penetration of renewables and other distributed energy resources (DERs), the frequency response in power systems exhibits stochastic nature, where the standard deterministic swing equation should be either represented or transferred into an Ito stochastic differential equation whose solution should be the non-stationary transient behavior of the probability density function (PDF) of the frequency. This transfers the frequency quality control for power systems into a stochastic distribution control problem, where the shape of the frequency distribution, namely the frequency PDF, needs to be directly controlled. In this context, this requires the development of control strategies via controlling the power balance so that the PDF of the frequency is made as narrow as possible whilst centered at its required mean value simple because such a sharp distribution shape means less uncertainties or randomness for the frequency response. In this paper, the formulation of the stochastic swing equation will be made first taking into account of DERs. This will then be followed by the development of stochastic distribution control model that links the power sources with the PDF of the frequency using Fokker Planck Kolmogorov (FPK) equations. A generic constrained optimization problem will be formulated where the cost function is composed of a functional distance between the actual and the desired PDFs of the frequency. A feasible solution using B-spine Neural Networks based stochastic distribution control model will be described. Using the obtained stochastic distribution control model, a set of control algorithms will be described that uses available power sources to shape the PDF of the frequency or to minimize the randomness of the frequency via minimized entropy approach. Future directions will be discussed in the later part of the paper
We present an energy banding algorithm for Monte Carlo (MC) neutral particle transport simulations which depend on large cross section lookup tables. In MC codes, read-only cross section data tables are accessed frequently, exhibit poor locality, and are typically too much large to fit in fast memory. Thus, performance is often limited by long latencies to RAM, or by off-node communication latencies when the data footprint is very large and must be decomposed on a distributed memory machine. The proposed energy banding algorithm allows maximal temporal reuse of data in band sizes that can flexibly accommodate different architectural features. The energy banding algorithm is general and has a number of benefits compared to the traditional approach. In the present analysis we explore its potential to achieve improvements in time-to-solution on modern cache-based architectures.
Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. These include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.
We demonstrate robust, high-speed random number generation using interference of the steady-state emission of guaranteed random phases, obtained through gain-switching a semiconductor laser diode. Steady-state emission tolerates large temporal pulse misalignments and therefore significantly improves the interference quality. Using an 8-bit digitizer followed by a finite-impulse-response unbiasing algorithm, we achieve random number generation rates of 8 and 20 Gb/s, for laser repetition rates of 1 and 2.5 GHz, respectively, with a ±20% tolerance in the interferometer differential delay. We also report a generation rate of 80 Gb/s using partially phase-correlated short pulses. In relation to the field of quantum key distribution, our results confirm the gain-switched laser diode as a suitable light source, capable of providing phase-randomized coherent pulses at a clock rate of up to 2.5 GHz.
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm that runs in polynomial time to sample from the process once. The corresponding naive Markov Chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. Finally, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantum-inspired efficient classical algorithm.
The δf particle-in-cell algorithm has been a useful tool in studying the physics of plasmas, particularly turbulent magnetized plasmas in the context of gyrokinetics. The reduction in noise due to not having to resolve the full distribution function indicates an efficiency advantage over the standard (“full-f”) particle-in-cell. Despite its successes, the algorithm behaves strangely in some circumstances. In this work, we document a fully resolved numerical instability that occurs in the simplest of multiple-species test cases: the electrostatic Ω{sub H} mode. There is also a poorly understood numerical instability that occurs when one is under-resolved in particle number, which may require a prohibitively large number of particles to stabilize. Both of these are independent of the time-stepping scheme, and we conclude that they exist if the time advancement were exact. The exact analytic form of the algorithm is presented, and several schemes for mitigating these instabilities are also presented.
This paper presents an algorithm that increases vehicle regenerative braking energy recovery in autonomous driving by leveraging connected and automated vehicle (CAV) technology. Autonomous vehicles may select different maneuvers to increase kinetic energy recovery during deceleration. In the proposed algorithm, the cornering resistance that influences regenerative energy and energy consumption is defined in terms of steering angle during regenerative braking. In particular, a model predictive controller that distributes control inputs of the vehicle is adopted to reduce the cornering resistance for increasing regenerative braking torque. Utilizing the information from CAV technology, this algorithm enables the vehicle to safely conduct braking while increasing its regenerative energy recovery. CarSim-Simulink joint simulations demonstrate the effectiveness of the proposed method.
Purpose: Evaluate the excess relative risk (ERR) induced by photons and protons in each voxel of the lung, and display it as a three-dimensional map, known as the ERRM (i.e. excess relative risk map) along with the dose distribution map. In addition, we also study the effect of variations in the linear energy transfer (LET) distribution on ERRM for a given proton plan. Methods: The excess relative risk due to radiation is estimated using the initiation-inactivation-proliferation formalism. This framework accounts for three biological phenomenon: mutation induction, cell kill and proliferation. Cell kill and mutation induction are taken as a function of LET using experimental data. LET distributions are calculated using a Monte Carlo algorithm. ERR is then estimated for each voxel in the organ, and displayed as a three dimensional carcinogenic map. Results: The differences in the ERR’s between photons and protons is seen from the three-dimensional ERR map. In addition, we also varied the LET of a proton plan and observed the differences in the corresponding ERR maps demonstrating variations in the ERR maps depend on features of a proton plan. Additionally, our results suggest that any two proton plans that have the same integral dose does not necessarily imply identical ERR maps, and these changes are due to the variations in the LET distribution map. Conclusion: Clinically, it is important to have a three dimensional display of biological end points. This study is an effort to introduce 3D ERR maps into the treatment planning workflow for certain sites such as pediatric head and neck tumors.
PHISH is a lightweight framework which a set of independent processes can use to exchange data as they run on the same desktop machine, on processors of a parallel machine, or on different machines across a network. This enables them to work in a coordinated parallel fashion to perform computations on either streaming, archived, or self-generated data. The PHISH distribution includes a simple, portable library for performing data exchanges in useful patterns either via MPI message-passing or ZMQ sockets. PHISH input scripts are used to describe a data-processing algorithm, and additional tools provided in the PHISH distribution convert the script into a form that can be launched as a parallel job.
PHISH is a lightweight framework which a set of independent processes can use to exchange data as they run on the same desktop machine, on processors of a parallel machine, or on different machines across a network. This enables them to work in a coordinated parallel fashion to perform computations on either streaming, archived, or self-generated data. The PHISH distribution includes a simple, portable library for performing data exchanges in useful patterns either via MPI message-passing or ZMQ sockets. PHISH input scripts are used to describe a data-processing algorithm, and additional tools provided in the PHISH distribution convert the script into a form that can be launched as a parallel job.
Purpose: To efficiently find quality-guaranteed treatment plans with the minimum number of beams for stereotactic body radiation therapy using RayStation. Methods: For a pre-specified pool of candidate beams we use RayStation (a treatment planning software for clinical use) to identify the deliverable plan which uses all the beams with the minimum dose to organs at risk (OARs) and dose to the tumor and other structures in specified ranges. Then use the dose matrix information for the generated apertures from RayStation to solve a linear program to find the ideal plan with the same objective and constraints allowing use of all beams. Finally we solve a mixed integer programming formulation of the beam angle optimization problem (BAO) with the objective of minimizing the number of beams while remaining in a predetermined epsilon-optimality of the ideal plan with respect to the dose to OARs. Since the treatment plan optimization is a multicriteria optimization problem, the planner can exploit the multicriteria optimization capability of RayStation to navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus OARs sparing, and then use the proposed technique to reduce the number of beams while guaranteeing quality. For the numerical experiments two liver cases and one lung case with 33 non-coplanar beams are considered. Results: The ideal plan uses an impractically large number of beams. The proposed technique reduces the number of beams to the range of practical application (5 to 9 beams) while remaining in the epsilon-optimal range of 1% to 5% optimality gap. Conclusion: The proposed method can be integrated into a general algorithm for fast navigation of the ideal dose distribution Pareto surface and finding the treatment plan with the minimum number of beams, which corresponds to the delivery time, in epsilon-optimality range of the desired ideal plan. The project was supported by the Federal Share of program income earned by Massachusetts General Hospital on C06 CA059267, Proton Therapy Research and Treatment Center and partially by RaySearch Laboratories.