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DOE OSTI2020

A novel active optimization approach for rapid and efficient design space exploration using ensemble machine learning

In this work, a novel design optimization technique based on active learning, which involves dynamic exploration and exploitation of the design space of interest using an ensemble of machine learning algorithms, is presented. In this approach, a hybrid methodology incorporating an explorative weak learner (regularized basis function model) which fits high-level information about the response surface, and an exploitative strong learner (based on committee machine) that fits finer details around promising regions identified by the weak learner, is employed. For each design iteration, an aristocratic approach is used to select a set of nominees, where points that meet a threshold merit value as predicted by the weak learner are selected to be evaluated using expensive function evaluation. In addition to these points, the global optimum as predicted by the strong learner is also evaluated to enable rapid convergence to the actual global optimum once the most promising region has been identified by the optimizer. This methodology is first tested by applying it to the optimization of a two-dimensional multi-modal surface. The performance of the new active learning approach is compared with traditional global optimization methods, namely micro-genetic algorithm (pGA) and particle swarm optimization (PSO). It is demonstrated that the new optimizer is able to reach the global optimum much faster with a significantly fewer number of function evaluations. Subsequently, the new optimizer is also applied to a complex internal combustion (IC) engine combustion optimization case with nine control parameters related to fuel injection, initial thermodynamic conditions, and in-cylinder flow. It is again found that the new approach significantly lowers the number of function evaluations that are needed to reach the optimum design configuration (by up to 80%) when compared to particle swarm and genetic algorithm-based optimization techniques.

Machine learning, active learning, design optimiza↗

DOE OSTI2011

Covariance Spectroscopy Applied to Nuclear Radiation Detection

Covariance spectroscopy is a method of processing second order moments of data to obtain information that is usually absent from average spectra. In nuclear radiation detection it represents a generalization of nuclear coincidence techniques. Correlations and fluctuations in data encode valuable information about radiation sources, transport media, and detection systems. Gaining access to the extra information can help to untangle complicated spectra, uncover overlapping peaks, accelerate source identification, and even sense directionality. Correlations existing at the source level are particularly valuable since many radioactive isotopes emit correlated gammas and neutrons. Correlations also arise from interactions within detector systems, and from scattering in the environment. In particular, correlations from Compton scattering and pair production within a detector array can be usefully exploited in scenarios where direct measurement of source correlations would be unfeasible. We present a covariance analysis of a few experimental data sets to illustrate the utility of the concept.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

SU-E-T-229: Craniospinal Radiotherapy Planning with VMAT, Two First Years Experience

Purpose: To describe how we moved to VMAT in the craniospinal radiotherapy planning process, the actual procedure details, and the results for the patients treated. Methods: Twelve patients underwent craniospinal irradiation with the new procedure, based on the paper by Lee et al. (IJROBP 82, 2012), with some additional modifications. Patients were treated in supine position in Varian Clinac iX linacs with 6 MV RapidArc; prescription doses ranged from 23.4 to 40 Gy (13 to 20 fractions); depending on the PTV length, 2 or 3 isocenters were used, all coordinates being equal except the longitudinal one, setting a few centimeter-long overlapping region; 2 arcs (RA) sharing isocentre for the cranial region, RA1 encompassing cranium and superior spinal region, and RA2 intended to improve conformity, only for cranium; for spine, 1 or 2 isocenters were employed; optimization was performed with Eclipse (V 13.0) using AAA algorithm, establishing sets of optimization parameters to give high conformity while sparing OAR. In pediatric patients, homogeneous irradiation of the vertebrae was also required.Conformity (CI) and heterogeneity (HI) indices (same as Lee et al.), and mean and maximum doses for OAR were calculated. Several pre-treatment verification methods were used: Octavius4D (PTW) for each isocentre, point dose at the junction region, Portal Dosimetry (when possible), and independent MU verification software (Diamond, PTW). Results: CI median value was 1.02 (0.99–1.07) and HI, 1.07 (1.06–1.09); a great reduction was observed for CI and OAR mean doses with respect to Lee et al. data; median maximum eye lens dose was 7.3 Gy (4.0–12.0); mean LungV20Gy was 1.9%; in children, vertebrae were homogeneously irradiated (D95%=20.8 Gy, Dmean= 23.2 Gy).All pre-treatment verifications were found within our action levels except for Portal Dosimetry. Conclusion: A RapidArc planning process for craniospinal axis irradiation has been implemented with significant advantages on conformity, homogeneity, feasibility and efficiency. and increase brain tissue sparing. Variations in volume decrease may be related to shape or location of the tumor.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Yearly report for the period Jan. 2018 – Feb. 2019 IC Project: w17_faultprediction “Critical Stress in Earth”

The consequence of earthquake is usually catastrophic. Currently, we cannot determine when a fault is approaching failure due to either anthropogenic activities or tectonic movement. In an anthropogenically perturbed setting, the rate of physical changes on faults far exceeds most natural processes with currently unpredictable and unmeasurable results. In a tectonic setting we generally do not know where a fault is in the earthquake cycle beyond noting how long has passed since the last rupture, which is itself sometimes unknown. The Laboratory has therefore funded a multi million multi-year LDRD-DR program that comprises experiments, numerical modeling, and machine learning in order to develop and test a highly novel approach to probe the earthquake cycle and in particular, to detect and locate stressed faults that are approaching failure. For this program, modeling of a series of sheared granular layers undergoing stick-slip behavior using the EES-17’s Combined Finite-Discrete Element Method (FDEM) based code HOSS (Hybrid Optimization Software Suite) plays a pivotal role since numerical simulations of granular fault gouge allow for analysis of the mechanical behavior of the system at a level of spatial and temporal resolution not accessible experimentally, and also offer the possibility of identifying the most important parameters governing earthquake dynamics. The simulated data also provide very detailed stress, strain and motion information for machine learning purpose to predict earthquake. The code – HOSS – has been developed in Geophysics Group in LANL during the past ten years and is used to simulate the stick-slip behavior of granular fault gouge. One of the key feature of HOSS is that it is superior to pure finite element method and discrete element method and can provide very detailed evolvement information of granular fault gouge. Additionally, its parallel computing capability makes large scale earthquake gouge simulation possible. Taking these facts into account, and also because few other fully parallel FDEM code exists, this IC project allows LANL to stay at the forefront of earthquake gouge and granular material simulation in the world.

42 ENGINEERING↗

DOE OSTI2017

Construction of a Cyber Attack Model for Nuclear Power Plants

The consideration of how one compromised digital equipment can impact neighboring equipment is critical to understanding the progression of cyber attacks. The degree of influence that one component may have on another depends on a variety of factors, including the sharing of resources such as network bandwidth or processing power, the level of trust between components, and the inclusion of segmentation devices such as firewalls. The interactions among components via mechanisms that are unique to the digital world are not usually considered in traditional PRA. This means potential sequences of events that may occur during an attack may be missed if one were to only look at conventional accident sequences. This paper presents a method where, starting from the initial attack vector, the progression of a cyber attack can be modeled. The propagation of the attack is modeled by considering certain attributes of the digital components in the system. These attributes determine the potential vulnerability of a component to a class of attack and the capability gained by the attackers once they are in control of the equipment. The use of attributes allows similar components (components with the same set of attributes) to be modeled in the same way, thereby reducing the computing resources required for analysis of large systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Video Summarization Using Deep Action Recognition Features and Robust Principal Components Analysis

In an instance where desired pre-defined actions, behaviors, or other categories are known a priori, various video classification and recognition models can be trained to discover those classifications and their location within the video. Absent that information, one might still be tasked with identifying interesting portions within a video, a process which—if done manually—is onerous and time-consuming as it requires manual inspection of the video itself. Recognizing high-level interesting segments within a whole video has been a general area of interest due to the ubiquity of video data. However the size of the data makes storage, retrieval, and inspection of large collections of videos cumbersome. This problem motivates the task of generating shortened clips highlighting the primary content of a video, relieving the burden of having to watch the entire video. This paper presents an unsupervised method of creating shortened clips of videos, enabling the rapid review of the most interesting content within a video. Our method uses features extracted from pre-trained action recognition models as input to online moving window robust principal component analysis to generate summaries. The procedure is tested on a publicly available video summarization dataset and demonstrates comparable performance to state-of-the-art in an un-augmented setting while requiring no training.

Claborne, Daniel M.↗

DOE OSTI2015

MO-F-CAMPUS-I-01: A System for Automatically Calculating Organ and Effective Dose for Fluoroscopically-Guided Procedures

Purpose: A system was developed that automatically calculates the organ and effective dose for individual fluoroscopically-guided procedures using a log of the clinical exposure parameters. Methods: We have previously developed a dose tracking system (DTS) to provide a real-time color-coded 3D- mapping of skin dose. This software produces a log file of all geometry and exposure parameters for every x-ray pulse during a procedure. The data in the log files is input into PCXMC, a Monte Carlo program that calculates organ and effective dose for projections and exposure parameters set by the user. We developed a MATLAB program to read data from the log files produced by the DTS and to automatically generate the definition files in the format used by PCXMC. The processing is done at the end of a procedure after all exposures are completed. Since there are thousands of exposure pulses with various parameters for fluoroscopy, DA and DSA and at various projections, the data for exposures with similar parameters is grouped prior to entry into PCXMC to reduce the number of Monte Carlo calculations that need to be performed. Results: The software developed automatically transfers data from the DTS log file to PCXMC and runs the program for each grouping of exposure pulses. When the dose from all exposure events are calculated, the doses for each organ and all effective doses are summed to obtain procedure totals. For a complicated interventional procedure, the calculations can be completed on a PC without manual intervention in less than 30 minutes depending on the level of data grouping. Conclusion: This system allows organ dose to be calculated for individual procedures for every patient without tedious calculations or data entry so that estimates of stochastic risk can be obtained in addition to the deterministic risk estimate provided by the DTS. Partial support from NIH grant R01EB002873 and Toshiba Medical Systems Corp.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2013

DFT investigation on the electronic structure of Faujasite

We report here first-principle pseudopotential DFT calculations to investigate relevant aspects of the electronic structure of zeolites based FAU. Fundamental molecular issues of the band-gap and electronic population analysis were reviewed under GGA/RPBE level of theory, corroborated with a DZP basis set and Troullier-Martins norm conserving pseudo-potentials. The atom-projected density of states and the analysis of HOMO-LUMO frontier orbitals at Gamma point were performed. Their electronic transfers are discussed through the alignment and relative positions of orbitals in order to determine the way that the molecule interacts with adsorbed molecules and other practical applications. Mulliken population analysis was employed for describing atomic charge distribution in the chosen systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Embedded-cluster calculations in a numeric atomic orbital density-functional theory framework

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level density functional theory calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO{sub 2}(110)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Full Modeling and parameter compression methods in configuration space for DESI 2024 and beyond

In the contemporary era of high-precision spectroscopic surveys, led by projects like DESI, there is an increasing demand for optimizing the extraction of cosmological information from clustering data. This work conducts a thorough comparison of various methodologies for modeling the full shape of the two-point statistics in configuration space. We investigate the performance of both direct fits (Full Modeling) and the parameter compression approaches (ShapeFit and Standard). We utilize the ABACUS-SUMMIT simulations, tailored to exceed DESI's precision requirements. Particularly, we fit the two-point statistics of three distinct tracers (LRG, ELG, and QSO), by employing a Gaussian Streaming Model in tandem with Convolution Lagrangian Perturbation Theory and Effective Field Theory. We explore methodological setup variations, including the range of scales, the set of galaxy bias parameters, the inclusion of the hexadecapole, as well as model extensions encompassing varying ns and allowing for w 0 w a CDM dark energy model. Throughout these varied explorations, while precision levels fluctuate and certain configurations exhibit tighter parameter constraints, our pipeline consistently recovers the parameter values of the mocks within 1σ in all cases for a 1-year DESI volume. Additionally, we compare the performance of configuration space analysis with its Fourier space counterpart using three models: PyBird, FOLPS and velocileptors, presented in companion papers. We find good agreement with the results from all these models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Diagnostics of Data-Driven Models: Uncertainty Quantification of PM7 Semi-Empirical Quantum Chemical Method

Abstract We report an evaluation of a semi-empirical quantum chemical method PM7 from the perspective of uncertainty quantification. Specifically, we apply Bound-to-Bound Data Collaboration, an uncertainty quantification framework, to characterize (a) variability of PM7 model parameter values consistent with the uncertainty in the training data and (b) uncertainty propagation from the training data to the model predictions. Experimental heats of formation of a homologous series of linear alkanes are used as the property of interest. The training data are chemically accurate , i.e., they have very low uncertainty by the standards of computational chemistry. The analysis does not find evidence of PM7 consistency with the entire data set considered as no single set of parameter values is found that captures the experimental uncertainties of all training data. A set of parameter values for PM7 was able to capture the training data within ±1 kcal/mol, but not to the smaller level of uncertainty in the reported data. Nevertheless, PM7 was found to be consistent for subsets of the training data. In such cases, uncertainty propagation from the chemically accurate training data to the predicted values preserves error within bounds of chemical accuracy if predictions are made for the molecules of comparable size. Otherwise, the error grows linearly with the relative size of the molecules.

42 ENGINEERING↗

DOE OSTI2011

Automatic Energy Calibration of Gamma-Ray Spectrometers

The software provides automatic method for calibrating the energy scale of high-purity germanium (HPGe) and scintillation gamma-ray spectrometers, using natural background radiation as the source of calibration gamma rays. In field gamma-ray spectroscopy, radioactive check sources may not be available; temperature changes can shift detector electronic gain and scintillator light output; and a user's experience and training may not include gamma-ray energy calibration. Hence, an automated method of calibrating the spectrometer using natural background would simplify its operation, especially by technician-level users, and by enhancing spectroscopic data quality, it would reduce false detections. Following a typically one-minute count of background gamma-rays, the measured spectrum is searched for gamma-ray peaks, producing a list of peak centroids, in channels1. Next, the ratio algorithm attempts to match the peak centroids found in the search to a user-supplied list of calibration gamma-ray energies. Finally, if three or more calibration energies have been matched to peaks, the energy equation parameters are determined by a least-squares fit2, and the spectrum has been energy-calibrated. The ratio algorithm rests on the repeatable but irregular spacing of the background gamma-ray energies together they form a unique set of ratios, when normalized to the highest energy calibration gamma ray; so too, the corresponding peak centroids in the spectrum. The algorithm matches energy ratios to peak centroid ratios, to determine which peak matches a given calibration energy.

Caffrey, Gus↗

DOE OSTI2012

Strategic Analysis of Complex Security Scenarios

Many advanced technical tools are available to prevent attacks on national infrastructure. Nevertheless, while traditional analyses of security problems have succeeded in producing good technical solutions, they have often ignored the human factor integral to these problems. Human attackers (who may be individuals or state-level attackers) expend substantial effort to breach security because they have the incentive for doing so. People involved in implementing security follow individual incentives, which need not align with global security concerns; consequently, desired security solutions are often implemented poorly, or not at all. This complex interplay between individual incentives and global (organizational and/or national) goals can be modeled and analyzed using game theoretic techniques. By analyzing not only what is possible, but also what is motivated, a holistic approach to security problems can be developed, informing policy and providing tools to policy makers. We study game theoretic models that unify several current incentive-based approaches to security, and develop simulation-based and mathematical optimization methods for analyzing such models that exploit the high-performance computing capabilities at Sandia. Our first model studies security in interdependent settings, offering a scalable local search heuristic to approximate optimal security decisions in general, and a linear programming approach, coupled with simulations of consequences, to optimally compute security in an important special case. Our second class of models addresses security patrolling problems when an adversary gets to observe the patrol location. We present a general framework, based on stochastic games, for computing optimal security policies in such settings, and present more scalable tools that apply in the important special cases. Our third contribution is a model of security that involves many defenders, but only models non-adaptive attackers (or natural disasters, inadvertent errors, etc). In this model, we demonstrate that the security decisions of many players result in global security configuration that is not very far from optimal, and is much more resilient to environment changes that an optimal solution. This positive effect dissipates, however, when the number of decision makers becomes too large.

Vorobeychik, Yevgeniy↗

DOE OSTI2013

Topology for Statistical Modeling of Petascale Data

Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, the approach of the entire team involving all three institutions is based on the complementary techniques of combinatorial topology and statistical modelling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modelling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. The overall technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modelling, and (3) new integrated topological and statistical methods. Roughly speaking, the division of labor between our 3 groups (Sandia Labs in Livermore, Texas A&M in College Station, and U Utah in Salt Lake City) is as follows: the Sandia group focuses on statistical methods and their formulation in algebraic terms, and finds the application problems (and data sets) most relevant to this project, the Texas A&M Group develops new algebraic geometry algorithms, in particular with fewnomial theory, and the Utah group develops new algorithms in computational topology via Discrete Morse Theory. However, we hasten to point out that our three groups stay in tight contact via videconference every 2 weeks, so there is much synergy of ideas between the groups. The following of this document is focused on the contributions that had grater direct involvement from the team at the University of Utah in Salt Lake City.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Initial CEED API (CEED-MS10)

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone, we initiated the development and implementation of a common CEED API consisting of two main components: low-level and high-level APIs. We accomplished the goal of having the low-level component ready for the release of CEED v1.0 in the next quarter, see CEED-MS13. In this report we also provide a highlight from CEED’s integration with the MARBL app and the corresponding Laghos miniapp. A main theme in this work has been the systematic transition of advanced algorithms, developed and tested in Laghos, to the large-scale multi-physics settings of the MARBL code. The low-level CEED API provides a set of FE kernels and components for writing new low-level kernels. Examples include: vector and sparse linear algebra, element matrix assembly over a batch of elements, partial assembly and action for efficient high-order operators like mass, diffusion, advection, etc. The main goal of the low-level API is to establish the basis for the high-level API. Also, identifying such low-level kernels and providing a reference implementation for them serves as the basis for collaboration with vendors and STs. Another goal for the low-level API is to make it easy for applications with their own discretization infrastructure, who do not want to switch directly to using the high-level CEED API, to still evaluate and use the core operations provided by the low-level API. One of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order linear operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for a matvec. Thus, another important question we tried to address while developing the low-level API is: is it possible to abstract out in a natural and efficient way the different implementations and data structures that arise when dealing with various computational device types: CPUs, GPUs, etc. Fully answering this question is beyond the scope of this particular milestone, since that requires longer time as we develop and expand the devices we support. The future high-level API will be the frontend provided by CEED consisting of high-level abstractions such as meshes, finite element spaces and solutions, bilinear forms, solvers, etc. At this high-level, an important aspect of the API will be to provide a uniform abstraction layer for writing code in a portable manner. To achieve that, we plan to utilize the MPI programming model combined with a device abstraction layer (DAL) for finite element computations that we will develop. The DAL will serve as the bridge between the low- and the high-level APIs, allowing a variety of programming models to be used for the low-level kernel implementations. The software artifacts delivered as part of this milestone include an initial CEED API software implementation (libCEED) provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q1 of FY18, including: the Nek5000 v17.0 MFEM v3.3.2 and PETSc v3.8 releases, collaborations with ECP/ST and SciDAC projects, the inaugural Nek5000 hackathon and various outreach activities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Progress Report on Computing Excited-State Hadron Masses in Lattice QCD

Our progress in computing the spectrum of excited baryons and mesons in lattice QCD is described. Sets of spatially-extended hadron operators with a variety of different momenta are used. A new method of stochastically estimating the low-lying effects of quark propagation is utilized which allows reliable determinations of temporal correlations of both single-hadron and multi-hadron operators. The method is tested on the isoscalar mesons in the scalar, pseudoscalar, and vector channels, and on the two-pion system of total isospin I = 0,1,2.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Galaxy Cluster Mass Reconstruction Project – III. The impact of dynamical substructure on cluster mass estimates

With the advent of wide-field cosmological surveys, we are approaching samples of hundreds of thousands of galaxy clusters. While such large numbers will help reduce statistical uncertainties, the control of systematics in cluster masses is crucial. Here we examine the effects of an important source of systematic uncertainty in galaxy-based cluster mass estimation techniques: the presence of significant dynamical substructure. Dynamical substructure manifests as dynamically distinct subgroups in phase-space, indicating an ‘unrelaxed’ state. This issue affects around a quarter of clusters in a generally selected sample. We employ a set of mock clusters whose masses have been measured homogeneously with commonly used galaxy-based mass estimation techniques (kinematic, richness, caustic, radial methods). We use these to study how the relation between observationally estimated and true cluster mass depends on the presence of substructure, as identified by various popular diagnostics. We find that the scatter for an ensemble of clusters does not increase dramatically for clusters with dynamical substructure. However, we find a systematic bias for all methods, such that clusters with significant substructure have higher measured masses than their relaxed counterparts. This bias depends on cluster mass: the most massive clusters are largely unaffected by the presence of significant substructure, but masses are significantly overestimated for lower mass clusters, by ~ 10 percent at 10 14 and ≳ 20 percent for ≲ 10 13.5 . Finally, the use of cluster samples with different levels of substructure can therefore bias certain cosmological parameters up to a level comparable to the typical uncertainties in current cosmological studies.

79 ASTRONOMY AND ASTROPHYSICS↗