Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “evolutionary algorithm”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Finding Your Niche: An Evolutionary Approach to HPC Topologies

Traditional interconnection network design approaches focus on building general network topologies by optimizing the bisection bandwidth or minimizing the network’s diameter to reduce the maximum distance between any two nodes, thus amortizing the overall execution time of the HPC workloads. While such network topologies may accommodate a wide variety of applications in general, this may result in sub-optimal performance for many frequently-executed or dynamic workloads. In this paper, instead of focusing on designing an all-encompassing, general-purpose network topology, we develop a methodology to design customized network interconnects, evolved by “finding” the optimal topologies for a particular target workload given by its communication and contention profiles. To this end, we implement a Genetic Algorithm (GA)-based approach for network topology design tailored to improve the overall execution time of a particular workload of interest. We conducted extensive experiments with well-known motifs in physics-based workloads (Sweep3D and FFT), as well as with a representative graph application (MiniVite), using the well-known Structural Simulation Toolkit (SST) Macroscale Element Library (SST/macro) simulator for network interconnect evaluation. We demonstrate that our genetic algorithm-based approach is robust enough to find the underlying optimal topology of a particular workload.

network interconnects, graph search, meta-heuristi↗

Intelligent Reservoir Generation for Liquid State Machines using Evolutionary Optimization

Neuromorphic Computing is a burgeoning field of research. Many groups are exploring hardware architectures and theoretical ideas about spiking recurrent neural networks. The overarching goal is to exploit the low power promise of these neuromorphic systems. However, it is difficult to train spiking recurrent neural networks (SRNNs) to perform tasks and make efficient use of neuromorphic hardware. Reservoir Computing is an attractive methodology because it requires no tuning of weights for the reservoir itself. Yet, to find optimal reservoirs, manual tuning of hyperparameters such as hidden neurons, synaptic density, and natural structure is still required. Because of this, researchers often have to generate and evaluate many networks, which can result in non-trivial amounts of computation. This paper employs the reservoir computing technique (specifically liquid state machines) and genetic algorithms in order to develop useful networks that can be deployed on neuromorphic hardware. We build on past work in reservoir computing and genetic algorithms to demonstrate the power of combining these two techniques and the advantage it can provide over manually tuning reservoirs for use on classification tasks. We discuss the complexities of determining whether or not to use the genetic algorithms approach for liquid state machine generation.

Reynolds, John↗

New Markov Model Approaches to Deciphering Microbial Genome Function and Evolution: Comparative Genomics of Laterally Transferred Genes

Algorithmic methods for gene prediction have been developed and successfully applied to many different prokaryotic genome sequences. As the set of genes in a particular genome is not homogeneous with respect to DNA sequence composition features, the GeneMark.hmm program utilizes two Markov models representing distinct classes of protein coding genes denoted "typical" and "atypical". Atypical genes are those whose DNA features deviate significantly from those classified as typical and they represent approximately 10% of any given genome. In addition to the inherent interest of more accurately predicting genes, the atypical status of these genes may also reflect their separate evolutionary ancestry from other genes in that genome. We hypothesize that atypical genes are largely comprised of those genes that have been relatively recently acquired through lateral gene transfer (LGT). If so, what fraction of atypical genes are such bona fide LGTs? We have made atypical gene predictions for all fully completed prokaryotic genomes; we have been able to compare these results to other "surrogate" methods of LGT prediction.

60 APPLIED LIFE SCIENCES↗

Development of a Modified Embedded Atom Force Field for Zirconium Nitride Using Multi-Objective Evolutionary Optimization

Zirconium nitride (ZrN) exhibits exceptional mechanical, chemical, and electrical properties, which make it attractive for a wide range of technological applications, including wear-resistant coatings, protection from corrosion, cutting/shaping tools, and nuclear breeder reactors. Despite its broad usability, an atomic scale understanding of the superior performance of ZrN, and its response to external stimuli, for example, temperature, applied strain, and so on, is not well understood. This is mainly due to the lack of interatomic potential models that accurately describe the interactions between Zr and N atoms. To address this challenge, we develop a modified embedded atom method (MEAM) interatomic potential for the Zr–N binary system by training against formation enthalpies, lattice parameters, elastic properties, and surface energies of ZrN (and, in some cases, also Zr3N4) obtained from density functional theory (DFT) calculations. The best set of MEAM parameters are determined by employing a multiobjective global optimization scheme driven by genetic algorithms. Our newly developed MEAM potential accurately reproduces structure, thermodynamics, energetic ordering of polymorphs, as well as elastic and surface properties of Zr–N compounds, in excellent agreement with DFT calculations and experiments. As a representative application, we employed molecular dynamics simulations based on this MEAM potential to investigate the atomic scale mechanisms underlying fracture of bulk and nanopillar ZrN under applied uniaxial strains, as well as the impact of strain rate on their mechanical behavior. These simulations indicate that bulk ZrN undergoes brittle fracture irrespective of the strain rate, while ZrN nanopillars show quasi-plasticity owing to amorphization at the crack front. The MEAM potential for Zr–N developed in this work is an invaluable tool to investigate atomic-scale mechanisms underlying the response of ZrN to external stimuli (e.g, temperature, pressure etc.), as well as other interesting phenomena such as precipitation.

36 MATERIALS SCIENCE↗

Benefits and Limits of Phasing Alleles for Network Inference of Allopolyploid Complexes

Abstract Accurately reconstructing the reticulate histories of polyploids remains a central challenge for understanding plant evolution. Although phylogenetic networks can provide insights into relationships among polyploid lineages, inferring networks may be hindered by the complexities of homology determination in polyploid taxa. We use simulations to show that phasing alleles from allopolyploid individuals can improve phylogenetic network inference under the multispecies coalescent by obtaining the true network with fewer loci compared with haplotype consensus sequences or sequences with heterozygous bases represented as ambiguity codes. Phased allelic data can also improve divergence time estimates for networks, which is helpful for evaluating allopolyploid speciation hypotheses and proposing mechanisms of speciation. To achieve these outcomes in empirical data, we present a novel pipeline that leverages a recently developed phasing algorithm to reliably phase alleles from polyploids. This pipeline is especially appropriate for target enrichment data, where the depth of coverage is typically high enough to phase entire loci. We provide an empirical example in the North American Dryopteris fern complex that demonstrates insights from phased data as well as the challenges of network inference. We establish that our pipeline (PATÉ: Phased Alleles from Target Enrichment data) is capable of recovering a high proportion of phased loci from both diploids and polyploids. These data may improve network estimates compared with using haplotype consensus assemblies by accurately inferring the direction of gene flow, but statistical nonidentifiability of phylogenetic networks poses a barrier to inferring the evolutionary history of reticulate complexes.

Evolutionary Biology↗

Refining the phylum Chlorobi by resolving the phylogeny and metabolic potential of the representative of a deeply branching, uncultivated lineage

Recent studies have expanded the phylum Chlorobi, demonstrating that the green sulfur bacteria (GSB), the original cultured representatives of the phylum, are a part of a larger lineage whose members have more diverse metabolic capabilities that overlap with members of the phylum Bacteroidetes. The 16S rRNA gene of an uncultivated clone, OPB56, distantly related to the phyla Chlorobi and Bacteroidetes, was recovered from Obsidian Pool in Yellowstone National Park; however, the detailed phylogeny and function of OPB56 and related clones have remained unknown. Culturing of thermophilic bacterial consortia from compost by adaptation to grow on ionic-liquid pretreated switchgrass provided a consortium in which one of the most abundant members, NICIL-2, clustered with OPB56-related clones. Phylogenetic analysis using the full-length 16S rRNA gene from NICIL-2 demonstrated that it was part of a monophyletic clade, referred to as OPB56, distinct from the Bacteroidetes and Chlorobi. A near complete draft genome ( > 95% complete) was recovered from metagenomic data from the culture adapted to grow on ionic-liquid pretreated switchgrass using an automated binning algorithm, and this genome was used for marker gene-based phylogenetic analysis and metabolic reconstruction. Six additional genomes related to NICIL-2 were reconstructed from metagenomic data sets obtained from thermal springs at Yellowstone National Park and Nevada Great Boiling Spring. In contrast to the 16S rRNA gene phylogenetic analysis, protein phylogenetic analysis was most consistent with the clustering of the Chlorobea, Ignavibacteria and OPB56 into a single phylum level clade. Metabolic reconstruction of NICIL-2 demonstrated a close linkage with the class Ignavibacteria and the family Rhodothermaceae, a deeply branching Bacteroidetes lineage. The combined phylogenetic and functional analysis of the NICIL-2 genome has refined the membership in the phylum Chlorobi and emphasized the close evolutionary and metabolic relationship between the phyla Chlorobi and the Bacteroidetes.

59 BASIC BIOLOGICAL SCIENCES↗

Structural characterization and computational analysis of PDZ domains in Monosiga brevicollis

Abstract Identification of the molecular networks that facilitated the evolution of multicellular animals from their unicellular ancestors is a fundamental problem in evolutionary cellular biology. Choanoflagellates are recognized as the closest extant nonmetazoan ancestors to animals. These unicellular eukaryotes can adopt a multicellular‐like “rosette” state. Therefore, they are compelling models for the study of early multicellularity. Comparative studies revealed that a number of putative human orthologs are present in choanoflagellate genomes, suggesting that a subset of these genes were necessary for the emergence of multicellularity. However, previous work is largely based on sequence alignments alone, which does not confirm structural nor functional similarity. Here, we focus on the PDZ domain, a peptide‐binding domain which plays critical roles in myriad cellular signaling networks and which underwent a gene family expansion in metazoan lineages. Using a customized sequence similarity search algorithm, we identified 178 PDZ domains in the Monosiga brevicollis proteome. This includes 11 previously unidentified sequences, which we analyzed using Rosetta and homology modeling. To assess conservation of protein structure, we solved high‐resolution crystal structures of representative M. brevicollis PDZ domains that are homologous to human Dlg1 PDZ2, Dlg1 PDZ3, GIPC, and SHANK1 PDZ domains. To assess functional conservation, we calculated binding affinities for mbGIPC, mbSHANK1, mbSNX27, and mbDLG‐3 PDZ domains from M. brevicollis . Overall, we find that peptide selectivity is generally conserved between these two disparate organisms, with one possible exception, mbDLG‐3. Overall, our results provide novel insight into signaling pathways in a choanoflagellate model of primitive multicellularity.

Gao, Melody↗

Phylogenetic relationships and phylogeography of relevant lineages within the complex Campanulaceae family in Macaronesia

Abstract Macaronesia has long been recognized as a natural model for studying evolutionary processes in plant diversification. Several studies have attempted to focus on single lineages, and few have covered the diversification of a family across all the archipelagos. We used a comprehensive sample to clarify the phylogenetic relationships and the biogeographic history of the Macaronesian Campanulaceae. Hypotheses related to the colonization of these archipelagos will be used to examine the diversification patterns of different lineages. We sequenced the ITS region and six cp DNA markers ( atpB , matK , petD , rbcL , trnL‐F , and psbA‐trnH ) from 10 Campanulaceae species, including seven endemic species in Macaronesia. The phylogeny of these taxa was reconstructed using maximum parsimony, maximum likelihood, and Bayesian inference. To study the relationships within each lineage, haplotype networks were calculated using NeighborNet and TCS algorithms. Moreover, data were combined with fossil information to construct time‐calibrated trees for the Macaronesian Campanulaceae species. The phylogenetic analyses are largely congruent with current taxon circumscriptions, and all the endemic genera formed monophyletic clades, namely Azorina in Azores; Musschia in Madeira; and Campanula in Cape Verde. The Azorina clade and the Cape Verde endemic Campanula may share a common ancestor in North Africa, and the divergence was dated ca. 12.3 million years ago (Mya). The divergence of the Musschia clade began in the Pliocene ca. 3.4 Mya. Moreover, several examples of intraspecific variation were revealed among the native species with a clear geographic structured patterns, suggesting that cryptic diversity might exist within the native Macaronesian Campanulaceae when compared to the close mainland taxa (e.g., Campanula erinus , Trachelium caeruleum ), but additional studies are needed to support the molecular data. This study highlights the power of combining data (e.g., phylogeny and divergence times, with species distribution data) for testing diversification hypotheses within the unique Macaronesian flora, providing useful information for future conservation efforts.

Menezes, Tiago↗

Functional protein mining with conformal guarantees

Molecular structure prediction and homology detection offer promising paths to discovering protein function and evolutionary relationships. However, current approaches lack statistical reliability assurances, limiting their practical utility for selecting proteins for further experimental and in-silico characterization. To address this challenge, we introduce a statistically principled approach to protein search leveraging principles from conformal prediction, offering a framework that ensures statistical guarantees with user-specified risk and provides calibrated probabilities (rather than raw ML scores) for any protein search model. Our method (1) lets users select many biologically-relevant loss metrics (i.e. false discovery rate) and assigns reliable functional probabilities for annotating genes of unknown function; (2) achieves state-of-the-art performance in enzyme classification without training new models; and (3) robustly and rapidly pre-filters proteins for computationally intensive structural alignment algorithms. Our framework enhances the reliability of protein homology detection and enables the discovery of uncharacterized proteins with likely desirable functional properties.

59 BASIC BIOLOGICAL SCIENCES↗

Scalable tuning of building models to hourly data

Energy models of existing buildings are unreliable unless calibrated so they correlate well with actual energy usage. Manual tuning requires a skilled professional, is prohibitively expensive for small projects, imperfect, non-repeatable, non-transferable, and not scalable to the dozens of sensor channels that smart meters, smart appliances, and cheap/ubiquitous sensors are beginning to make available today. A scalable, automated methodology is needed to quickly and intelligently calibrate building energy models to all available data, increase the usefulness of those models, and facilitate speed-and-scale penetration of simulation-based capabilities into the marketplace for actualized energy savings. The "Autotune'' project is a novel, model-agnostic methodology which leverages supercomputing, large simulation ensembles, and big data mining with multiple machine learning algorithms to allow automatic calibration of simulations that match measured experimental data in a way that is deployable on commodity hardware. This paper shares several methodologies employed to reduce the combinatorial complexity to a computationally tractable search problem for hundreds of input parameters. Furthermore, accuracy metrics are provided which quantify model error to measured data for either monthly or hourly electrical usage from a highly-instrumented, emulated-occupancy research home.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Parallel derivative-free optimization for simulation-based design of behind-the-meter energy systems

In this work, the integrated design and dispatch of behind-the-meter or distributed resources (e.g. stationary battery storage and solar PV generation) is considered. A simulation-based framework is employed, generating high-fidelity results with closed-loop predictive control at a fine resolution, at the expense of high computational cost (several minutes to a few hours per design point). To address this challenge, parallel derivative-free design methods are considered. Four methods are compared, including state-of-the-art surrogate-based methods (Radial-Basis Functions and Gaussian processes) and sampling strategies, an evolutionary-based method, and a simple sequential grid refinement method. As a case study, two types of design problem with increasing complexity are considered, namely, the design of behind-the-meter resources (three design variables) and the inclusion of grid capacity (four design variables). The second yields a constrained design problem for which violations can only be determined after solving the computationally expensive simulation. For the three-dimensional case, all methods present a good performance, achieving a solution within 1% of the optimum after the first iteration, with the sequential grid refinement exhibiting the fastest convergence and achieving the best final objective value. This indicates that the parallel evaluation of multiple sampling points may be more important than the choice of method for small decision spaces. For the four-dimensional constrained case, the Genetic Algorithm presents the best tradeoff between performance and computational effort, while the rough objective function terrain generated by constraint violation penalties reduces the performance of surrogate-based methods. Contour plots with flat regions indicate flexibility in the optimal design and highlight the importance of characterizing the solution space.

24 POWER TRANSMISSION AND DISTRIBUTION↗

SCOPe: improvements to the structural classification of proteins – extended database to facilitate variant interpretation and machine learning

Abstract The Structural Classification of Proteins—extended (SCOPe, https://scop.berkeley.edu) knowledgebase aims to provide an accurate, detailed, and comprehensive description of the structural and evolutionary relationships amongst the majority of proteins of known structure, along with resources for analyzing the protein structures and their sequences. Structures from the PDB are divided into domains and classified using a combination of manual curation and highly precise automated methods. In the current release of SCOPe, 2.08, we have developed search and display tools for analysis of genetic variants we mapped to structures classified in SCOPe. In order to improve the utility of SCOPe to automated methods such as deep learning classifiers that rely on multiple alignment of sequences of homologous proteins, we have introduced new machine-parseable annotations that indicate aberrant structures as well as domains that are distinguished by a smaller repeat unit. We also classified structures from 74 of the largest Pfam families not previously classified in SCOPe, and we improved our algorithm to remove N- and C-terminal cloning, expression and purification sequences from SCOPe domains. SCOPe 2.08-stable classifies 106 976 PDB entries (about 60% of PDB entries).

59 BASIC BIOLOGICAL SCIENCES↗

A Method to Constrain Genome-Scale Models with 13 C Labeling Data

Current limitations in quantitatively predicting biological behavior hinder our efforts to engineer biological systems to produce biofuels and other desired chemicals. Here, we present a new method for calculating metabolic fluxes, key targets in metabolic engineering, that incorporates data from 13C labeling experiments and genome-scale models. The data from 13 C labeling experiments provide strong flux constraints that eliminate the need to assume an evolutionary optimization principle such as the growth rate optimization assumption used in Flux Balance Analysis (FBA). This effective constraining is achieved by making the simple but biologically relevant assumption that flux flows from core to peripheral metabolism and does not flow back. The new method is significantly more robust than FBA with respect to errors in genome-scale model reconstruction. Furthermore, it can provide a comprehensive picture of metabolite balancing and predictions for unmeasured extracellular fluxes as constrained by 13 C labeling data. A comparison shows that the results of this new method are similar to those found through 13 C Metabolic Flux Analysis ( 13 C MFA) for central carbon metabolism but, additionally, it provides flux estimates for peripheral metabolism. The extra validation gained by matching 48 relative labeling measurements is used to identify where and why several existing COnstraint Based Reconstruction and Analysis (COBRA) flux prediction algorithms fail. We demonstrate how to use this knowledge to refine these methods and improve their predictive capabilities. This method provides a reliable base upon which to improve the design of biological systems.

59 BASIC BIOLOGICAL SCIENCES↗

Trigger Detection for Adaptive Scientific Workflows Using Percentile Sampling

The increasing complexity of both scientific simulations and high-performance computing system architectures are driving the need for adaptive workflows, in which the composition and execution of computational and data manipulation steps dynamically depend on the evolutionary state of the simulation itself. Consider, for example, the frequency of data storage. Critical phases of the simulation should be captured with high frequency and with high fidelity for postanalysis; however, we cannot afford to retain the same frequency for the full simulation due to the high cost of data movement. We can instead look for triggers, indicators that the simulation will be entering a critical phase, and adapt the workflow accordingly. In this paper, we present a methodology for detecting triggers and demonstrate its use in the context of direct numerical simulations of turbulent combustion using S3D. We show that chemical explosive mode analysis (CEMA) can be used to devise a noise-tolerant indicator for rapid increase in heat release. However, exhaustive computation of CEMA values dominates the total simulation, and thus is prohibitively expensive. To overcome this computational bottleneck, we propose a quantile sampling approach. Our sampling-based algorithm comes with provable error/confidence bounds, as a function of the number of samples. Most importantly, the number of samples is independent of the problem size, and thus our proposed sampling algorithm offers perfect scalability. Our experiments on homogeneous charge compression ignition and reactivity controlled compression ignition simulations show that the proposed method can detect rapid increases in heat release, and its computational overhead is negligible. Our results will be used to make dynamic workflow decisions regarding data storage and mesh resolution in future combustion simulations.

97 MATHEMATICS AND COMPUTING↗

Evolutionary Optimization of a Charge Transfer Ionic Potential Model for Ta/Ta-Oxide Heterointerfaces

Heterostructures of tantalum and its oxide are of tremendous technological interest for a myriad of technological applications, including electronics, thermal management, catalysis and biochemistry. In particular, local oxygen stoichiometry variation in TaO x memristors comprising of thermodynamically stable metallic (Ta) and insulating oxide (Ta 2 O 5 ) have been shown to result in fast switching on the subnanosecond timescale over a billion cycles. This rapid switching opens up the potential for advanced functional platforms such as stateful logic operations and neuromorphic computation. Despite its broad importance, an atomistic scale understanding of oxygen stoichiometry variation across Ta/TaO x heterointerfaces, such as during early stages of oxidation and oxide growth, is not well understood. This is mainly due to the lack of a unified interatomic potential model for tantalum oxides that can accurately describe metallic (Ta), ionic (TaO x ) as well as mixed (Ta/TaO x interfaces) bonding environments simultaneously. To address this challenge, we introduce a Charge Transfer Ionic Potential (CTIP) model for Ta/Ta-oxide system by training against lattice parameters, cohesive energies, equations of state (EOS), elastic properties, and surface energies of the various experimentally observed Ta 2 O 5 polymorphs (hexagonal, orthorhombic and monoclinic) obtained from density functional theory (DFT) calculations. The best CTIP parameters are determined by employing a global optimization scheme driven by genetic algorithms followed by local Simplex optimization. Our newly developed CTIP potential accurately predicts structure, thermodynamics, energetic ordering of polymorphs, as well as elastic and surface properties of both Ta and Ta 2 O 5 , in excellent agreement with DFT calculations and experiments. We employ our newly parameterized CTIP potential to investigate the early stages of oxidation and atomic scale mechanisms associated with oxide growth on Ta surface at various temperatures. Furthermore, the CTIP potential developed in this work is an invaluable tool to investigate atomic-scale mechanisms and transport phenomena underlying the response of Ta/TaO x interfaces to external stimuli (e.g, temperature, pressure, strain, electric field etc.), as well as other interesting dynamical phenomena including the physics of switching dynamics in TaO x based memristors and neuromorphic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhanced resonant ultrasound spectroscopy for measurement of the elastic properties of multi-material systems

Understanding the elastic properties of materials is critical for their safe incorporation and predictable performance. Current methods of bulk elastic characterization often have notable limitations for in situ structural applications, with usage restricted to simple geometries and material distributions. To address these existing issues, this study sought to expand the capabilities of resonant ultrasound spectroscopy (RUS), an established nondestructive evaluation method, to include the characterization of isotropic multi-material samples. In this work, finite-element-based RUS analysis consisted of numerical simulations and experimental testing of composite samples comprised of material pairs with varying elasticity and density contrasts. Utilizing genetic algorithm inversion and mode matching, our results demonstrate that elastic properties of multi-material samples can be reliably identified within several percent of known or nominal values using a minimum number of identified resonance modes, given sample mass is held consistent. The accurate recovery of material properties for composite samples of varying material similarity and geometry expands the pool of viable samples for RUS and advances the method towards in situ inspection and evaluation.

36 MATERIALS SCIENCE↗

Measuring photometric redshifts for high-redshift radio source surveys

With the advent of deep, all-sky radio surveys, the need for ancillary data to make the most of the new, high-quality radio data from surveys like the Evolutionary Map of the Universe (EMU), GaLactic and Extragalactic All-sky Murchison Widefield Array survey eXtended, Very Large Array Sky Survey, and LOFAR Two-metre Sky Survey is growing rapidly. Radio surveys produce significant numbers of Active Galactic Nuclei (AGNs) and have a significantly higher average redshift when compared with optical and infrared all-sky surveys. Thus, traditional methods of estimating redshift are challenged, with spectroscopic surveys not reaching the redshift depth of radio surveys, and AGNs making it difficult for template fitting methods to accurately model the source. Machine Learning (ML) methods have been used, but efforts have typically been directed towards optically selected samples, or samples at significantly lower redshift than expected from upcoming radio surveys. This work compiles and homogenises a radio-selected dataset from both the northern hemisphere (making use of Sloan Digital Sky Survey optical photometry) and southern hemisphere (making use of Dark Energy Survey optical photometry). We then test commonly used ML algorithms such as k-Nearest Neighbours (kNN), Random Forest, ANNz, and GPz on this monolithic radio-selected sample. We show that kNN has the lowest percentage of catastrophic outliers, providing the best match for the majority of science cases in the EMU survey. We note that the wider redshift range of the combined dataset used allows for estimation of sources up to z = 3 before random scatter begins to dominate. When binning the data into redshift bins and treating the problem as a classification problem, we are able to correctly identify ≈ 76% of the highest redshift sources—sources at redshift z > 2.51 —as being in either the highest bin (z > 2.51) or second highest (z = 2.25).

79 ASTRONOMY AND ASTROPHYSICS↗