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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Speeding up software with VecCore

Portable and efficient vectorization is a significant challenge in large software projects such as GeantV, ROOT, and experiments’ frameworks. Nevertheless, fully exploiting SIMD parallelism will be a required step in order to bridge the widening gap between the needs and availability of computing resouces for data analysis and processing in particle physics. Although there are SIMD libraries that wrap compiler intrinsics into a convenient interface, they do not always support all available architectures, or they only perform well in some of them. The VecCore library was created to address some of these performance and portability issues by providing a unified abstraction layer on top of existing libraries, such as Vc or UME::SIMD. In this article, we discuss VecCore’s programming model for SIMD code and some use cases in HEP software packages such as VecGeom and GeantV.

Amadio, G.↗
DOE OSTI2026

Supporting multiple hardware architectures at CMS: the integration and validation of POWER9

Computing resources in the Worldwide LHC Computing Grid (WLCG) have been based entirely on the x86 architecture for more than two decades. In the near future, however, heterogeneous non-x86 resources, such as ARM, POWER and Risc-V, will become a substantial fraction of the resources that will be provided to the LHC experiments, due to their presence in existing and planned world-class HPC installations. The CMS experiment, one of the four large detectors at the LHC, has started to prepare for this situation, with the CMS software stack (CMSSW) already compiled for multiple architectures. In order to allow for a production use, the tools for workload management and job distribution need to be extended to be able to exploit heterogeneous architectures. Profiting from the opportunity to exploit the first sizable IBM Power9 allocation available on Marconi100 HPC system at CINECA, CMS developed all the needed modifications to the CMS workload management system. After a successful proof of concept, a full physics validation has been performed in order to bring the system in production. The experiences are of very high value, when it comes to commissioning of the similar (even larger) Summit HPC system at Oak Ridge, where CMS is also expecting a resource allocation. Moreover the compute power of those systems is being provided also via GPUs and this represents an extremely valuable opportunity to exploit the offloading capability already implemented in CMSSW. The status of the current integration including the exploitation of the GPUs, the results of the validation as well as the future plans will be shown and discussed.

Boccali, Tommaso [INFN, Pisa]↗
DOE OSTI2014

Improving robustness and computational efficiency using modern C++

For nearly two decades, the C++ programming language has been the dominant programming language for experimental HEP. The publication of ISO/IEC 14882:2011, the current version of the international standard for the C++ programming language, makes available a variety of language and library facilities for improving the robustness, expressiveness, and computational efficiency of C++ code. However, much of the C++ written by the experimental HEP community does not take advantage of the features of the language to obtain these benefits, either due to lack of familiarity with these features or concern that these features must somehow be computationally inefficient. In this paper, we address some of the features of modern C+-+, and show how they can be used to make programs that are both robust and computationally efficient. We compare and contrast simple yet realistic examples of some common implementation patterns in C, currently-typical C++, and modern C++, and show (when necessary, down to the level of generated assembly language code) the quality of the executable code produced by recent C++ compilers, with the aim of allowing the HEP community to make informed decisions on the costs and benefits of the use of modern C++.

Paterno, M.↗
DOE OSTI2015

Breaking the silos: The art documentation suite

The art event-processing framework is used by almost all new experiments at Fermilab, and by several outside of Fermilab. All use art as an external product in the same sense that the compiler, ROOT, Geant4, CLHEP and boost are external products. The art team has embarked on a campaign to document art and develop training materials for new users. Many new users of art have little or no knowledge of C++, software engineering, build systems or the many external packages used by art or their experiments, such as ROOT, CLHEP, HEPPDT, and boost. To effectively teach art requires that the training materials include appropriate introductions to these topics as they are encountered. Experience has shown that simply referring readers to the existing native documentation does not work, too often a simple idea that they need to understand is described in a context that presumes prerequisites that are unimportant for a beginning user of art. There is the additional complication that the training materials must be presented in a way that does not presume knowledge of any of the experiments using art. Finally, new users of art arrive at random times throughout the year and the training materials must allow them to start to learn art at any time. This presentation will explain the strategies adopted by the art team to develop a documentation suite that complies with these boundary conditions. It will also show the present status of the documentation suite, including feedback the art team has received from pilot users.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fast inference of deep neural networks in FPGAs for particle physics

Here, recent results at the Large Hadron Collider (LHC) have pointed to enhanced physics capabilities through the improvement of the real-time event processing techniques. Machine learning methods are ubiquitous and have proven to be very powerful in LHC physics, and particle physics as a whole. However, exploration of the use of such techniques in low-latency, low-power FPGA (Field Programmable Gate Array) hardware has only just begun. FPGA-based trigger and data acquisition systems have extremely low, sub-microsecond latency requirements that are unique to particle physics. We present a case study for neural network inference in FPGAs focusing on a classifier for jet substructure which would enable, among many other physics scenarios, searches for new dark sector particles and novel measurements of the Higgs boson. While we focus on a specific example, the lessons are far-reaching. A companion compiler package for this work is developed based on High-Level Synthesis (HLS) called hls4ml to build machine learning models in FPGAs. The use of HLS increases accessibility across a broad user community and allows for a drastic decrease in firmware development time. We map out FPGA resource usage and latency versus neural network hyperparameters to identify the problems in particle physics that would benefit from performing neural network inference with FPGAs. For our example jet substructure model, we fit well within the available resources of modern FPGAs with a latency on the scale of 100 ns.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Status and future plans for C 3 R&D

C 3 is an opportunity to realize an e + e - collider for the study of the Higgs boson at √s = 250 GeV, with a well defined upgrade path to 550 GeV while staying on the same short facility footprint. C 3 is based on a fundamentally new approach to normal conducting linear accelerators that achieves both high gradient and high efficiency at relatively low cost. Given the advanced state of linear collider designs, the key system that requires technical maturation for C 3 is the main linac. This paper presents the staged approach towards a facility to demonstrate C 3 technology with both Direct (source and main linac) and Parallel (beam delivery, damping ring, ancillary component) R&D. The primary goal of the C 3 Demonstration R&D Plan is to reduce technical and cost risk by building and operating the key components of C 3 at an adequate scale. This R&D plan starts with the engineering design, and demonstration of one cryomodule and will culminate in the construction of a 3 cryomodule linac with pre-production prototypes. This R&D program would also demonstrate the linac rf fundamentals including achievable gradient and gradient stability over a full electron bunch train and breakdown rates. It will also investigate beam dynamics including energy spread, wakefields, and emittance growth. This work will be critical to confirm the suitability of the C 3 beam parameters for the physics reach and detector performance in preparation for a Conceptual Design Report (CDR), as well as for follow-on technology development and industrialization. The C 3 Demonstration R&D Plan will open up significant new scientific and technical opportunities based on development of high-gradient and high-efficiency accelerator technology. It will push this technology to operate both at the GeV scale and mature the technology to be reliable and provide high-brightness electron beams. The timeline for progressing with C 3 technology development will be governed by practical limitations on both the technical progress and resource availability. It consists of four stages: Stage 0) Ongoing fundamental R&D on structure prototypes, damping and vibrations. Stage 1) Advancing the engineering maturity of the design and developing start-to-end simulations including space-charge and wakefield effects. This stage will include testing of strucutres operating at cryogenic temperatures. Beam tests would be performed with high beam current to test full beam loading. Stage 2) Production and testing of the first cryomodule at cryogenic temperatures. This would provide sufficient experimental data to compile a CDR and it is anticipated for Stage 2 to last 3 years and to culminate with the transport of photo-electrons through the first cryomodule. Stage 3) Updates to the engineering design of the cryomodules, production of the second and third cryomodule and their installation. Lower charge and lower emittance beams will be used to investigate emittance growth. The successful full demonstration of the 3 cryomodules to deliver up to a 3 GeV beam and achieve the C 3 five gradient will allow a comprehensive and robust evaluation of the technical design of C 3 as well as mitigate technical, schedule, and cost risks required to proceed with a Technical Design Report (TDR).

radiation hardened magnets↗
DOE OSTI2017

Mapping water availability, cost and projected consumptive use in the Eastern United States with comparisons to the West

The availability of freshwater supplies to meet future demand is a growing concern. Water availability metrics are needed to inform future water development decisions. Furthermore, with the help of water managers, water availability was mapped for over 1300 watersheds throughout the 31-contiguous states in the eastern U.S. complimenting a prior study of the west. The compiled set of water availability data is unique in that it considers multiple sources of water (fresh surface and groundwater, wastewater and brackish groundwater); accommodates institutional controls placed on water use; is accompanied by cost estimates to access, treat and convey each unique source of water, and; is compared to projected future growth in consumptive water use to 2030. Although few administrative limits have been set on water availability in the east, water managers have identified 315 fresh surface water and 398 fresh groundwater basins (with 151 overlapping basins) as Areas of Concern (AOCs) where water supply challenges exist due to drought related concerns, environmental flows, groundwater overdraft, or salt water intrusion. This highlights a difference in management where AOCs are identified in the east which simply require additional permitting, while in the west strict administrative limits are established. Although the east is generally considered "water rich" roughly a quarter of the basins were identified as AOCs; however, this is still in strong contrast to the west where 78% of the surface water basins are operating at or near their administrative limit. There was little effort noted on the part of eastern or western water managers to quantify non-fresh water resources.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2018

Missing pieces to modeling the Arctic-Boreal puzzle

NASA has launched the decade-long Arctic-Boreal Vulnerability Experiment (ABoVE). While the initial phases focus on field and airborne data collection, early integration with modeling activities is important to benefit future modeling syntheses. We compiled feedback from ecosystem modeling teams on key data needs, which encompass carbon biogeochemistry, vegetation, permafrost, hydrology, and disturbance dynamics. A suite of variables was identified as part of this activity with a critical requirement that they are collected concurrently and representatively over space and time. Furthermore, individual projects in ABoVE may not capture all these needs, and thus there is both demand and opportunity for the augmentation of field observations, and synthesis of the observations that are collected, to ensure that science questions and integrated modeling activities are successfully implemented.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Evapotranspiration simulations in ISIMIP2a—Evaluation of spatio-temporal characteristics with a comprehensive ensemble of independent datasets

Actual land evapotranspiration (ET) is a key component of the global hydrological cycle and an essential variable determining the evolution of hydrological extreme events under different climate change scenarios. However, recently available ET products show persistent uncertainties that are impeding a precise attribution of human-induced climate change. Here, we aim at comparing a range of independent global monthly land ET estimates with historical model simulations from the global water, agriculture, and biomes sectors participating in the second phase of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP2a). Among the independent estimates, we use the EartH2Observe Tier-1 dataset (E2O), two commonly used reanalyses, a pre-compiled ensemble product (LandFlux-EVAL), and an updated collection of recently published datasets that algorithmically derive ET from observations or observations-based estimates (diagnostic datasets). A cluster analysis is applied in order to identify spatiotemporal differences among all datasets and to thus identify factors that dominate overall uncertainties. The clustering is controlled by several factors including the model choice, the meteorological forcing used to drive the assessed models, the data category (models participating in the different sectors of ISIMIP2a, E2O models, diagnostic estimates, reanalysis-based estimates or composite products), the ET scheme, and the number of soil layers in the models. By using these factors to explain spatial and spatio-temporal variabilities in ET, we and that the model choice mostly dominates (24%{40% of variance explained), except for spatio-temporal patterns of total ET, where the forcing explains the largest fraction of the variance (29%). The most dominant clusters of datasets are further compared with individual diagnostic and reanalysis-based estimates to assess their representation of selected heat waves and droughts in the Great Plains, Central Europe and Western Russia. Although most of the ET estimates capture these extreme events, the generally large spread among the entire ensemble indicates substantial uncertainties.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

A decade of remotely sensed observations highlight complex processes linked to coastal permafrost bluff erosion in the Arctic

We report that eroding permafrost coasts are likely indicators and integrators of changes in the Arctic System as they are susceptible to the combined effects of declining sea ice extent, increases in open water duration, more frequent and impactful storms, sea-level rise, and warming permafrost. However, few observation sites in the Arctic have yet to link decadal-scale erosion rates with changing environmental conditions due to temporal data gaps. This study increases the temporal fidelity of coastal permafrost bluff observations using near-annual high spatial resolution (<1 m) satellite imagery acquired between 2008–2017 for a 9 km segment of coastline at Drew Point, Beaufort Sea coast, Alaska. Our results show that mean annual erosion for the 2007–2016 decade was 17.2 m yr -1 , which is 2.5 times faster than historic rates, indicating that bluff erosion at this site is likely responding to changes in the Arctic System. In spite of a sustained increase in decadal-scale mean annual erosion rates, mean open water season erosion varied from 6.7 m yr -1 in 2010 to more than 22.0 m yr -1 in 2007, 2012, and 2016. This variability provided a range of coastal responses through which we explored the different roles of potential environmental drivers. The lack of significant correlations between mean open water season erosion and the environmental variables compiled in this study indicates that we may not be adequately capturing the environmental forcing factors, that the system is conditioned by long-term transient effects or extreme weather events rather than annual variability, or that other not yet considered factors may be responsible for the increased erosion occurring at Drew Point. Finally, our results highlight an increase in erosion at Drew Point in the 21st century as well as the complexities associated with unraveling the factors responsible for changing coastal permafrost bluffs in the Arctic.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Fire reduces riverine DOC concentration draining a watershed and alters post-fire DOC recovery patterns

Abstract The loading of dissolved organic carbon (DOC) from soils to inland waters and ultimate transport to the ocean is a critical flux pathway in the terrestrial biosphere carbon cycle. Fires can significantly affect this flux through biogeochemical processes related to oxidation and mobilization of DOC in the soil. Therefore, in order to accurately estimate and model terrestrial carbon storage and export to the marine environment, we need to better understand the effects of fire on DOC flux. In this analysis, we compiled available observational data sets from seven watersheds across the conterminous United States generally spanning the years 1999–2019. We used these data sets to examine the effects of fire on riverine DOC concentration draining a watershed to study both the immediate impacts and the post-fire recovery patterns. Our results suggest that these fires result in an immediate decrease in riverine DOC concentration draining the watershed by 26 ± 15%, and the time required for DOC concentrations to recover to pre-fire levels was estimated to be, on average, approximately 9 months. During recovery, DOC concentration was 24 ± 11% lower than the long-term average for the watershed. In addition, the larger the proportion of the watershed that burned, the greater the concentration decrease and the longer the time period for post-fire recovery.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Urban NO x emissions around the world declined faster than anticipated between 2005 and 2019

Emission inventory development for air pollutants, by compiling records from individual emission sources, takes many years and involves extensive multi-national effort. A complementary method to estimate air pollution emissions is in the use of satellite remote sensing. In this study, NO 2 observations from the Ozone Monitoring Instrument are combined with re-analysis meteorology to estimate urban nitrogen oxide (NO X ) emissions for 80 global cities between 2005 and 2019. The global average downward trend in satellite-derived urban NO X emissions was 3.1%–4.0% yr -1 between 2009 and 2018 while inventories show a 0%–2.2% yr -1 drop over the same timeframe. This difference is primarily driven by discrepancies between satellite-derived urban NO X emissions and inventories in Africa, China, India, Latin America, and the Middle East. In North America, Europe, Korea, Japan, and Australasia, NO X emissions dropped similarly as reported in the inventories. In Europe, Korea, and Japan only, the temporal trends match the inventories well, but the satellite estimate is consistently larger over time. While many of the discrepancies between satellite-based and inventory emissions estimates represent real differences, some of the discrepancies might be related to the assumptions made to compare the satellite-based estimates with inventory estimates, such as the spatial disaggregation of emissions inventories. Overall, our work identifies that the three largest uncertainties in the satellite estimate are the tropospheric column measurements, wind speed and direction, and spatial definition of each city.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A new data-driven map predicts substantial undocumented peatland areas in Amazonia

Tropical peatlands are among the most carbon-dense terrestrial ecosystems yet recorded. Collectively, they comprise a large but highly uncertain reservoir of the global carbon cycle, with wide-ranging estimates of their global area (441 025–1700 000 km 2 ) and below-ground carbon storage (105–288 Pg C). Substantial gaps remain in our understanding of peatland distribution in some key regions, including most of tropical South America. Here we compile 2413 ground reference points in and around Amazonian peatlands and use them alongside a stack of remote sensing products in a random forest model to generate the first field-data-driven model of peatland distribution across the Amazon basin. Our model predicts a total Amazonian peatland extent of 251 015 km 2 (95th percentile confidence interval: 128 671–373 359), greater than that of the Congo basin, but around 30% smaller than a recent model-derived estimate of peatland area across Amazonia. The model performs relatively well against point observations but spatial gaps in the ground reference dataset mean that model uncertainty remains high, particularly in parts of Brazil and Bolivia. For example, we predict significant peatland areas in northern Peru with relatively high confidence, while peatland areas in the Rio Negro basin and adjacent south-western Orinoco basin which have previously been predicted to hold Campinarana or white sand forests, are predicted with greater uncertainty. Similarly, we predict large areas of peatlands in Bolivia, surprisingly given the strong climatic seasonality found over most of the country. Very little field data exists with which to quantitatively assess the accuracy of our map in these regions. Data gaps such as these should be a high priority for new field sampling. This new map can facilitate future research into the vulnerability of peatlands to climate change and anthropogenic impacts, which is likely to vary spatially across the Amazon basin.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Human–Earth system interactions under climate change

This special issue, titled ‘Focus on human–Earth system interactions under climate change,’ compiles cutting-edge research that deepens our understanding of the complex feedback mechanisms between anthropogenic activities and Earth system processes in the context of a changing climate (figure 1). The featured articles employ a diverse array of methodologies—including field studies, remote sensing, modeling, and socio-ecological analyses—to explore these interconnections. A unifying theme across these contributions is the imperative to bridge disciplinary divides, integrating physical Earth sciences with social sciences to fully capture the spectrum of human-Earth system interactions. Key topics addressed the impacts of human activities on natural systems, encompassing land-use change and water resource management on biogeochemistry, climate dynamics, and feedback on the climate system and socioeconomics from local to global scales under a changing climate.

Li, Huidong [Vanderbilt Univ., Nashville, TN (Unit↗
DOE OSTI2026

Advancing extreme pulsed lasers through measurements: summary of the pulsed laser metrology workshop

In this report we present consensus findings produced during the pulsed laser metrology (PLM) workshop (Boulder, CO, USA, August 2025). The workshop was a meeting of 35 scientists from private industry, academia, and U.S. government to compile a list of the metrology needs to support extreme pulsed laser development and implementation. We define ‘extreme pulsed lasers’ loosely as those with peak powers above 1 TW or multi-Joule pulse energies. Such lasers are being increasingly used and investigated for use in high energy particle acceleration, short wavelength radiation generation, laser-based fusion, etc. The rapid growth of these fields and the proliferation of extreme lasers for these applications, coupled with the extreme electric fields they generate and relative scarcity of such lasers, presents unique challenges to accuracy in their measurement. The PLM workshop was a two-day event designed to hear from users, developers, and researchers on the current state of optical metrology associated with these extreme pulsed lasers. The goal was to identify the most important measurement challenges limiting development and implementation of these lasers in practical applications. We report here the conclusions and recommendations of this workshop. The hope is that this document will become the first of many iterations which track the status of measurement needs supporting extreme pulsed lasers.

Lasers↗
DOE OSTI2010

A COMPARISON OF HARD X-RAY PHOTON INDICES AND IRON K{alpha} EMISSION LINES IN X-RAY LUMINOUS NARROW- AND BROAD-LINE SEYFERT 1 GALAXIES

We use publicly available XMM-Newton data to systematically compare the hard X-ray photon indices, {gamma}{sub 2-10keV}, and the iron K{alpha} emission lines of narrow- and broad-line Seyfert 1 (NLS1 and BLS1) galaxies. We compile a flux-limited (f {sub 2-10keV} {>=} 1 x 10{sup -12} erg s{sup -1} cm{sup -2}) sample including 114 radio-quiet objects, with the 2-10 keV luminosity ranging from 10{sup 41} to 10{sup 45} erg s{sup -1}. Our main results are: (1) NLS1s and BLS1s show similar luminosity distributions; (2) the weighted means of {gamma}{sub 2-10keV} of NLS1s, BLS1s, and the total sample are 2.04 {+-} 0.04, 1.74 {+-} 0.02, and 1.84 {+-} 0.02, respectively; a significant anti-correlation between {gamma}{sub 2-10keV} and FWHMH{beta} suggests that {gamma}{sub 2-10keV} > 2.0 may be taken to indicate the X-ray luminous NLS1 type; (3) the 6.4 keV narrow iron K{alpha} lines from NLS1s are generally weaker than that from BLS1s; this would indicate a smaller covering factor of the dusty tori in NLS1s if the line emission originates from the inner boundary region of the dusty torus in an active galactic nucleus; and (4) all the broadened iron K{alpha} lines with intrinsic width {sigma}>0.5 keV correspond to FWHMH{beta} {<=}4000 km s{sup -1}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

INDEPENDENT SIGNALS FROM THE INFLUENCE OF INTERNAL MAGNETIC LAYERS ON THE FREQUENCIES OF SOLAR p-MODES

The discovery that p-mode frequencies of low degree do not follow changes of solar surface activity during the recent solar minimum offers the possibility of a new diagnostic signature of the responsible pressure perturbation in the wave guiding medium, potentially rich of information regarding the structure of the Sun and the cause of the unusually long solar minimum. Magnetic fields, as well as temperature changes, introduce equilibrium pressure deviations that modify the resonant frequencies of p-mode oscillations. Assuming the perturbation to be caused by a horizontal layer of magnetic field located in a plane-stratified model of the Sun, we compile analytical frequency shifts and process them to allow direct comparison with observations. The effect of magnetism itself on the central p-mode frequencies can be neglected in comparison with the thermal effect of a perturbative layer buried in the solar interior. A parametric study shows that a layer as thin as 2100 km at subsurface depths is able to reproduce reported mean anomalous frequency shifts (not correlated with the surface activity), while a layer of size around 4200 km increasing by a small amount at depths near 0.08 R {sub sun} can explain individual low-degree shifts. It is also possible to obtain the mean shifts via the upward motion through depths near 0.03 R {sub sun} of a rising perturbative layer of thickness around 7000 km. Hence, the anomalous frequency shifts are best explained by thermal effects in the upper regions of the convection zone. The effects of latitudinal distribution are not treated here.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2010

TESTING THE DISTANCE-DUALITY RELATION WITH GALAXY CLUSTERS AND TYPE Ia SUPERNOVAE

In this Letter, we propose a new and model-independent cosmological test for the distance-duality (DD) relation, {eta} = D{sub L} (z)(1 + z){sup -2}/D{sub A} (z) = 1, where D{sub L} and D{sub A} are, respectively, the luminosity and angular diameter distances. For D{sub L} we consider two sub-samples of Type Ia supernovae (SNe Ia) taken from Constitution data whereas D{sub A} distances are provided by two samples of galaxy clusters compiled by De Filippis et al. and Bonamente et al. by combining Sunyaev-Zeldovich effect and X-ray surface brightness. The SNe Ia redshifts of each sub-sample were carefully chosen to coincide with the ones of the associated galaxy cluster sample ({Delta}z < 0.005), thereby allowing a direct test of the DD relation. Since for very low redshifts, D{sub A} (z) ape D{sub L} (z), we have tested the DD relation by assuming that {eta} is a function of the redshift parameterized by two different expressions: {eta}(z) = 1 + {eta}{sub 0} z and {eta}(z) = 1 + {eta}{sub 0} z/(1 + z), where {eta}{sub 0} is a constant parameter quantifying a possible departure from the strict validity of the reciprocity relation ({eta}{sub 0} = 0). In the best scenario (linear parameterization), we obtain {eta}{sub 0} = -0.28{sup +0.44} {sub -0.44} (2{sigma}, statistical + systematic errors) for the De Filippis et al. sample (elliptical geometry), a result only marginally compatible with the DD relation. However, for the Bonamente et al. sample (spherical geometry) the constraint is {eta}{sub 0} = -0.42{sup +0.34} {sub -0.34} (3{sigma}, statistical + systematic errors), which is clearly incompatible with the duality-distance relation.

79 ASTRONOMY AND ASTROPHYSICS↗